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Modelling, Volume 5, Issue 4 (December 2024) – 38 articles

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24 pages, 6009 KiB  
Article
Investigation into the Hyperparameters of Error-Based Adaptive Sampling Approach for Surrogate Modeling
by Leonid Legashev, Sergey Tolmachev, Irina Bolodurina, Alexander Shukhman and Lyubov Grishina
Modelling 2024, 5(4), 2051-2074; https://doi.org/10.3390/modelling5040106 - 16 Dec 2024
Viewed by 747
Abstract
Surrogate modeling technology is used to create lightweight analogs of resource- and calculation-intensive software, provided that the problem can be reduced to the regression problem. In this article, we construct a surrogate model for predicting annual energy consumption using the open-source EnergyPlus software [...] Read more.
Surrogate modeling technology is used to create lightweight analogs of resource- and calculation-intensive software, provided that the problem can be reduced to the regression problem. In this article, we construct a surrogate model for predicting annual energy consumption using the open-source EnergyPlus software and various sampling techniques. A general algorithm for an error-based adaptive sampling technique to build the surrogate model is presented. The best results were shown by the composite Mixed Sampling method with a data refining window the size of 70% and a LightGBM regression model. The best attained metrics values are as follows: MSE = 7.76, RMSE = 1.47, MAE = 0.98 and R2 = 0.99. For a small number of iterations, an error-based adaptive sampling technique with hyperparameter tuning is preferable to the static sampling approach. For a large number of iterations, both techniques show approximately good predictive results of the built surrogate model. After hyperparameter tuning was performed, the average value of the MSE metric decreased from 43.43 to 7.76. A gas thickness feature greater than 0.015 had no positive effect on energy-saving optimization. For temperatures on a summer day of 30 degrees and above, there was a sharp increase in energy consumption. The maximum dry bulb temperature on a winter and summer day and the wind speed on a winter day were the most important features of the built surrogate model with 492, 483 and 443 gain values of the feature importance method, respectively. Full article
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<p>Algorithm block diagram of an error-based adaptive surrogate modeling design.</p>
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<p>Schematic render of building proposed in “5ZoneAirCooled.idf” demo example.</p>
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<p>MSE error values on test and validation datasets for adaptive sampling technique.</p>
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<p>MSE error values on test and validation datasets for static sampling technique.</p>
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<p>A two-dimensional scatterplot of initial and final distribution of input values (<b>a</b>) for the error-based adaptive sampling technique and (<b>b</b>) for static sampling technique.</p>
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<p>MSE error values on the test and validation datasets for ten variations in the data refining window size.</p>
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<p>MSE error values on the test and validation datasets for three variations in the data refining window size.</p>
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<p>MSE error values on the test and validation datasets for three variations in the data refining Mixed Sampling method.</p>
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<p>(<b>a</b>) Residuals vs. predicted values, (<b>b</b>) Leverage vs. predicted values, (<b>c</b>) DFITS vs. predicted values, (<b>d</b>) Cook’s Distance vs. predicted values.</p>
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<p>(<b>a</b>) Feature importance for LightGBM regression model, (<b>b</b>) SHAP model of each feature contribution to the model outcome, (<b>c</b>) SHAP model force plot.</p>
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<p>(<b>a</b>) Validation of the built surrogate model on four most important features; (<b>b</b>) SHAP model dependence plots on four most important features.</p>
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11 pages, 2707 KiB  
Article
Path Planning Method for Wire-Based Additive Manufacturing Processes
by Alexey Shcherbakov, Alexander Gudenko, Andrey Sliva, Daria Gaponova, Artem Marchenkov and Alexey Goncharov
Modelling 2024, 5(4), 2040-2050; https://doi.org/10.3390/modelling5040105 - 14 Dec 2024
Viewed by 574
Abstract
The relevance of creating specialized computer programs that convert a virtual 3D model of an object into machine code (G-code) for controlling the process of 3D printing products from wire raw materials is substantiated. It is shown that for wire-based additive technologies, a [...] Read more.
The relevance of creating specialized computer programs that convert a virtual 3D model of an object into machine code (G-code) for controlling the process of 3D printing products from wire raw materials is substantiated. It is shown that for wire-based additive technologies, a fundamentally important requirement is to ensure the continuity of the surfacing trajectory within one section. A method for determining a continuous surfacing trajectory is proposed, the implementation of which requires two stages: performing a numerical analysis of a two-dimensional region with boundary conditions describing this section; and running a heuristic algorithm for the movement of the surfacing head, in which the direction of movement is selected based on the results of the analysis. The procedure for setting boundary conditions and an algorithm for numerically solving the boundary value problem of determining the field of the “height” function for each section are described. The principles of operation of the heuristic algorithm for selecting the direction of head movement based on the calculated height field and continuous determination of the proximity of adjacent layers and section boundaries are disclosed. An analysis of the algorithm operation is carried out using a section with holes as an example, and the potential of using numerical methods to calculate the change in the temperature field during the surfacing process is shown. Full article
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<p>Deviation of layer height at the initial and final sections of formation: (<b>a</b>) photographs of typical multilayer thin walls; (<b>b</b>) schematic representation in section.</p>
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<p>Path strategies for generating continuous trajectories: (<b>a</b>) zigzag [<a href="#B13-modelling-05-00105" class="html-bibr">13</a>]; (<b>b</b>) spiral [<a href="#B14-modelling-05-00105" class="html-bibr">14</a>]; (<b>c</b>) contour parallel [<a href="#B14-modelling-05-00105" class="html-bibr">14</a>]; (<b>d</b>) hybrid [<a href="#B16-modelling-05-00105" class="html-bibr">16</a>]; (<b>e</b>) pixel [<a href="#B12-modelling-05-00105" class="html-bibr">12</a>,<a href="#B14-modelling-05-00105" class="html-bibr">14</a>]; (<b>f</b>) convex polygon decomposition [<a href="#B16-modelling-05-00105" class="html-bibr">16</a>]; (<b>g</b>) medial axis transformation [<a href="#B17-modelling-05-00105" class="html-bibr">17</a>]; (<b>h</b>) level set [<a href="#B18-modelling-05-00105" class="html-bibr">18</a>].</p>
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<p>Graphical view of the solution of the boundary value problem for <span class="html-italic">h</span>(<span class="html-italic">x</span>,<span class="html-italic">y</span>).</p>
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<p>Illustration of defining a destination point with coordinates <span class="html-italic">x<sub>n</sub></span>, <span class="html-italic">y<sub>n</sub></span>: (<b>a</b>) formation of a bead with constant <span class="html-italic">h</span> value; (<b>b</b>) transition to the next layer of the contour (the direction is chosen so that there is no overlap with the deposited bead, and the change in <span class="html-italic">h</span> value is minimal).</p>
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<p>The results of planning the welding path with the calculation of the temperature (°C) distribution for different moments of time: (<b>a</b>) 0.5 s; (<b>b</b>) 62 s; (<b>c</b>) 124 s; (<b>d</b>) 186 s; (<b>e</b>) 248 s; (<b>f</b>) 310 s; electron beam surfacing process photo (<b>g</b>); and the section deposited on the ELA-15I electron-beam installation (<b>h</b>).</p>
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<p>Computational results of trajectory planning for sections with no geometric similarity between the inner and outer boundaries: (<b>a</b>) section from <a href="#modelling-05-00105-f004" class="html-fig">Figure 4</a> with a rectangular hole; (<b>b</b>) section considered in [<a href="#B16-modelling-05-00105" class="html-bibr">16</a>]; (<b>c</b>,<b>d</b>) experimental trajectories of the electron beam movement on the surface of AISI 316L steel plate, treated without feeding filler wire.</p>
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39 pages, 6902 KiB  
Article
Supply Chains Problem During Crises: A Data-Driven Approach
by Farima Salamian, Amirmohammad Paksaz, Behrooz Khalil Loo, Mobina Mousapour Mamoudan, Mohammad Aghsami and Amir Aghsami
Modelling 2024, 5(4), 2001-2039; https://doi.org/10.3390/modelling5040104 - 12 Dec 2024
Viewed by 612
Abstract
Efficient management of hospital evacuations and pharmaceutical supply chains is a critical challenge in modern healthcare, particularly during emergencies. This study addresses these challenges by proposing a novel bi-objective optimization framework. The model integrates a Mixed-Integer Linear Programming (MILP) approach with advanced machine [...] Read more.
Efficient management of hospital evacuations and pharmaceutical supply chains is a critical challenge in modern healthcare, particularly during emergencies. This study addresses these challenges by proposing a novel bi-objective optimization framework. The model integrates a Mixed-Integer Linear Programming (MILP) approach with advanced machine learning techniques to simultaneously minimize total costs and maximize patient satisfaction. A key contribution is the incorporation of a Gated Recurrent Unit (GRU) neural network for accurate drug demand forecasting, enabling dynamic resource allocation in crisis scenarios. The model also accounts for two distinct patient destinations—receiving hospitals and temporary care centers (TCCs)—and includes a specialized pharmaceutical supply chain to prevent medicine shortages. To enhance system robustness, probabilistic demand patterns and disruption risks are considered, ensuring supply chain reliability. The solution methodology combines the Grasshopper Optimization Algorithm (GOA) and the ɛ-constraint method, efficiently addressing the multi-objective nature of the problem. Results demonstrate significant improvements in cost reduction, resource allocation, and service levels, highlighting the model’s practical applicability in real-world scenarios. This research provides valuable insights for optimizing healthcare logistics during critical events, contributing to both operational efficiency and patient welfare. Full article
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<p>Steps of this article.</p>
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<p>GRU structure.</p>
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<p>Supply chain configuration.</p>
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<p>TCC parallel configuration.</p>
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<p>Average number of patients per medicine.</p>
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<p>Distribution of average number of patients by crisis type.</p>
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<p>Reginal distribution of the average number of patients by crisis type.</p>
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<p>Average number of patients by crisis severity.</p>
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<p>Comparison of model performances.</p>
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<p>Effect of <span class="html-italic">re<sub>k</sub></span> on objective function.</p>
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<p>Effect of FC on OF1.</p>
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<p>Relationship between OF1 and OF2.</p>
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<p>Relationship between <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>σ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> and OF2.</p>
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<p>Relationship between <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>c</mi> <mi>t</mi> </mrow> <mrow> <mi>k</mi> </mrow> </msub> </mrow> </semantics></math>, OF1 and OF2.</p>
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<p>Relationship between CV, OF1, and OF2.</p>
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<p>Comparison of objective functions across scenarios.</p>
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<p>A comparison of run times.</p>
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<p>Algorithm performance comparison (objective function values and time).</p>
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<p>Sensitivity analysis of GOA parameters.</p>
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21 pages, 21050 KiB  
Article
Development of a Methodology for Obtaining Solid Models of Products That Are Objects of Reverse Engineering Using the Example of the Capstone Micro-GTU C 65
by Sergey Osipov, Ivan Komarov, Olga Zlyvko, Andrey Vegera and George Gertsovsky
Modelling 2024, 5(4), 1980-2000; https://doi.org/10.3390/modelling5040103 - 6 Dec 2024
Viewed by 535
Abstract
Currently, about a thousand micro gas turbine units of small and medium capacity are in operation in the Russian Federation, which are used as an autonomous power source at critical infrastructure facilities. During long-term operation, the component parts of the micro GTU may [...] Read more.
Currently, about a thousand micro gas turbine units of small and medium capacity are in operation in the Russian Federation, which are used as an autonomous power source at critical infrastructure facilities. During long-term operation, the component parts of the micro GTU may fail and require replacement or repair. The lack of spare parts and design documentation for their production makes it impossible to operate. As a way to solve the problem, the reverse engineering process can be used to produce components. One of the stages of reverse engineering is to determine the geometric parameters of the object. The fastest and most accurate way to obtain geometric characteristics in the reverse engineering process is 3D scanning. Three-dimensional scanning technology is used to obtain a solid 3D model of the prototype surface, based on which design documentation is subsequently developed. This article presents the results of a study of the influence of the parameters of the distance between polygonal grid points and the scanner exposure on the detailing of the outer surface and the geometric parameters of the resulting polygonal model. As a result of this study, the dependence of the final file size and the time spent on scanning and processing on the distance between the points of the polygonal grid and the model was established. Based on the dependence of the parameters, recommendations were obtained for choosing the distance between the points of the polygonal grid of laser 3D scanning. Also, after performing the stages of reverse engineering, the methodology for creating solid models and design documentation of parts of power equipment units using 3D scanning technology was improved. Full article
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Figure 1
<p>Components of the combustion chamber housing of the Capstone micro-GTU C 65: (<b>a</b>) main view, (<b>b</b>) view of the combustion chamber body from below, (<b>c</b>) view of the combustion chamber body from below. 1—shell (body), 2—outer flange, 3—adapter plate, 4—shell lower, 5—adapter plate, 6—external flange, 7—bottom, 8—lower funnel, 9—lower branch pipe, 10—funnel.</p>
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<p>Deformations of combustion chamber parts of the Capstone micro-GTU C 65 of the housing part near the injector holes.</p>
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<p>Flowchart of an improved methodology for creating preliminary design documentation for the Capstone C 65 gas turbine plant (stage 1—obtaining a polygonal model).</p>
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<p>Flowchart of an improved methodology for creating preliminary design documentation for the Capstone C 65 gas turbine unit (stage 2—processing of the polygonal and solid-state models).</p>
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<p>The combustion chamber body of the Capstone micro-GTU prepared for the 3D laser scanning process C 65 with reflective markings applied.</p>
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<p>Operating principle of a 3D laser scanner.</p>
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<p>Modes for displaying the radiation source during 3D laser scanning: (<b>a</b>) light source—grid, (<b>b</b>) light source—seven parallel lines, (<b>c</b>) light source—single line.</p>
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<p>Selecting the brightness setting when scanning markers on the surface of the combustion chamber of the Capstone C 65 micro-GTU.</p>
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<p>Surface defects of scanned polygonal models of the combustion chamber housing of the Capstone micro-GTU C 65: (<b>a</b>) surface defects of the first polygonal model; (<b>b</b>) surface defects of the second polygonal model; (<b>c</b>) surface defects of the third polygonal model.</p>
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<p>The resulting polygonal model of the combustion chamber housing of the Capstone micro-GTU 65 after the fourth scan.</p>
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<p>Dependence of the distance between points of the polygonal mesh on the final size of the polygonal model file and the total time spent on scanning and processing the polygonal model.</p>
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<p>Creating a sketch to obtain a solid-state model of the lower shell using the built-in mesh sketch function.</p>
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<p>Receipt and inspection of solid parts of the combustion chamber housing of the Capstone micro-GTU C 65 in the Geomagic program Design X: (<b>a</b>) creating solid geometry from a polygonal mesh; (<b>b</b>) checking deviations of the solid part from the polygonal model using the Body Deviation function.</p>
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<p>The deviations obtained during the development of the initial solid-state model of the combustion chamber housing micro-GTU Capstone C 65 (Areas of greatest deviations highlighted in red): (<b>a</b>) the value of the smallest deviation on the body part; (<b>b</b>) the value of the largest deviations on the funnel part.</p>
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<p>Solid 3D model of the combustion chamber housing of the Capstone micro-GTU C 65 (Areas of greatest deviations highlighted in red): (<b>a</b>) shell (body) detail on the combustion chamber body; (<b>b</b>) the largest deviation of the shell (body) part from the polygonal model.</p>
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<p>Solid 3D model of the combustion chamber housing of the Capstone micro-GTU C 65: (<b>a</b>) dimensional deviation of the solid model shell (body) at the defect site; (<b>b</b>) the surface of the polygonal model at the site of the defect.</p>
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<p>Detail of the rotor of the gas turbine of the Capstone C 65 micro-GTU installation.</p>
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<p>Obtaining the geometric dimensions of the diameters of the cooling and mixing holes using a caliper: (<b>a</b>) measurement of mixing holes; (<b>b</b>) measuring the cooling holes.</p>
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<p>The dimensions for the holes obtained as a result of the development of a solid-state model of the combustion chamber housing: (<b>a</b>) mixing hole size; (<b>b</b>) the size of the cooling hole.</p>
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<p>Diagram of the distribution of time spent on training employees in the reverse engineering process.</p>
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19 pages, 7073 KiB  
Article
Simulation and Modeling of Data Transmission Process in Boreholes Using Intelligent Drill Pipe for a Laboratory Experiment
by Mohammed A. Namuq, Ezideen A. Hasso, Mohammed A. Jamal, Koran A. Namuq and Yibing Yu
Modelling 2024, 5(4), 1961-1979; https://doi.org/10.3390/modelling5040102 - 6 Dec 2024
Viewed by 633
Abstract
Currently, most oil and gas wells are drilled by continuously transmitting downhole measured information (directional and geological information) in real-time to the surface to monitor and steer the well along a pre-defined path. The intelligent drill pipe method can transmit data over longer [...] Read more.
Currently, most oil and gas wells are drilled by continuously transmitting downhole measured information (directional and geological information) in real-time to the surface to monitor and steer the well along a pre-defined path. The intelligent drill pipe method can transmit data over longer distances and at a higher rate than other methods, such as mud pulse telemetry, acoustic telemetry, and electromagnetic telemetry. Nevertheless, it is expensive and requires boosters along the drill string. In the available literature, academic research rarely addresses the data transmission process in boreholes using intelligent drill pipes. Furthermore, there is a need for an effective and validated model to study various controllable parameters to enhance the efficiency of the intelligent drill pipe telemetry without the need to develop several physical lab or field prototypes. This paper presents the development of a model based on MATLAB Simulink to simulate the process of data transmission in boreholes utilizing intelligent drill pipes. Laboratory experimental prototype measurements have been used to test the model’s effectiveness. A good correlation is found between the measured lab data and the model’s predictions for the signals transmitted contactless through intelligent drill pipes with a correlation coefficient (R2) above 0.9. This model can enhance data transmission efficiency via intelligent drill pipes, study different concepts, and eliminate the need to develop several unnecessarily expensive and time-consuming physical lab prototypes. Full article
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<p>Section view of double-shouldered pine tool joint, inductive coil, and armored coaxial cable used in intelligent drill pipe telemetry network [<a href="#B22-modelling-05-00102" class="html-bibr">22</a>].</p>
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<p>One drill pipe at rest with data conduit [<a href="#B23-modelling-05-00102" class="html-bibr">23</a>].</p>
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<p>Wired drill pipe telemetry network schematic, modified [<a href="#B4-modelling-05-00102" class="html-bibr">4</a>].</p>
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<p>Laboratory test setup for conducting data transmission tests using intelligent drill pipe telemetry.</p>
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<p>Data transmission concept by using intelligent drill pipe telemetry.</p>
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<p>Schematic diagram of the experimental setup for the test.</p>
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<p>Measured experimental test values for the input voltage value of 41 Volt RMS and the output value of 2 Volt RMS.</p>
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<p>Measured experimental test values for the input voltage value of 90 Volt RMS and the output value of 6.4 Volt RMS.</p>
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<p>Developed model using MATLAB—Simulink for data transmission using intelligent drill pipes for the laboratory experiment with the case of the input voltage value of 90 Volt RMS.</p>
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<p>Flowchart for the developed model using MATLAB Simulink (Note: Vpp = peak-to-peak voltage).</p>
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<p>Estimated voltage curve by the model at the input and output for the 90 Volt RMS input value case.</p>
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<p>Comparison of output voltages measured in the lab and estimated by the model.</p>
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<p>The predicted output voltage by the model versus actual lab test data.</p>
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<p>The model estimation for input voltage value equals 70 Volt RMS (<b>left</b>) and 41 Volt RMS (<b>right</b>).</p>
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<p>Measured experimental test values for the input voltage value of 14.3 Volt RMS and the output value of 0.5 Volt RMS.</p>
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<p>The measured test data (<b>top</b>) and the model estimation (<b>bottom</b>) for the input voltage value of 14.3 Volt RMS.</p>
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25 pages, 2917 KiB  
Article
Modeling and Simulation of Electric–Hydrogen Coupled Integrated Energy System Considering the Integration of Wind–PV–Diesel–Storage
by Shuguang Zhao, Yurong Han, Qicheng Xu, Ziping Wang and Yinghao Shan
Modelling 2024, 5(4), 1936-1960; https://doi.org/10.3390/modelling5040101 - 5 Dec 2024
Viewed by 715
Abstract
Hydrogen energy plays an increasingly vital role in global energy transformation. However, existing electric–hydrogen coupled integrated energy systems (IESs) face two main challenges: achieving stable operation when integrated with large-scale networks and integrating optimal dispatching code with physical systems. This paper conducted comprehensive [...] Read more.
Hydrogen energy plays an increasingly vital role in global energy transformation. However, existing electric–hydrogen coupled integrated energy systems (IESs) face two main challenges: achieving stable operation when integrated with large-scale networks and integrating optimal dispatching code with physical systems. This paper conducted comprehensive modeling, optimization and joint simulation verification of the above IES. Firstly, a low-carbon economic dispatching model of an electric–hydrogen coupled IES considering carbon capture power plants is established at the optimization layer. Secondly, by organizing and selecting representative data in the optimal dispatch model, an electric–hydrogen coupled IES planning model considering the integration of wind, photovoltaic (PV), diesel and storage is constructed at the physical layer. The proposed electric–hydrogen coupling model mainly consists of the following components: an alkaline electrolyzer, a high-pressure hydrogen storage tank with a compressor and a proton exchange membrane fuel cell. The IES model proposed in this paper achieved the integration of optimal dispatching mode with physical systems. The system can maintain stable control and operation despite unpredictable changes in renewable energy sources, showing strong resilience and reliability. This electric–hydrogen coupling model also can integrate with large-scale IES for stable joint operation, enhancing renewable energy utilization and absorption of PV and wind power. Co-simulation verification showed that the optimized model has achieved a 29.42% reduction in total system cost and an 83.66% decrease in carbon emissions. Meanwhile, the simulation model proved that the system’s total harmonic distortion rate is controlled below 3% in both grid-connected and islanded modes, indicating good power quality. Full article
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<p>The basic structure of IES.</p>
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<p>Power forecast curves.</p>
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<p>Power balance diagram simulation results: (<b>a</b>) system electrical power balance diagram; (<b>b</b>) system heat power balance diagram; (<b>c</b>) system gas power balance diagram; (<b>d</b>) system hydrogen power balance diagram.</p>
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<p>Simulink model snapshot of IES system.</p>
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<p>Output power of each system of wind–PV–diesel–storage–hydrogen.</p>
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<p>(<b>a</b>) Wind power; (<b>b</b>) PV power; (<b>c</b>) load power.</p>
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<p>(<b>a</b>) Wind power; (<b>b</b>) PV power; (<b>c</b>) load power.</p>
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<p>(<b>a</b>) Grid voltage; (<b>b</b>) grid frequency; (<b>c</b>) THD rate of grid-connected grid voltage; (<b>d</b>) THD rate of islanded voltage.</p>
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<p>(<b>a</b>) Grid voltage; (<b>b</b>) grid frequency; (<b>c</b>) THD rate of grid-connected grid voltage; (<b>d</b>) THD rate of islanded voltage.</p>
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12 pages, 1121 KiB  
Article
Modeling the Bending of a Bi-Layer Cantilever with Shape Memory Controlled by Magnetic Field and Temperature
by Olga S. Stolbova and Oleg V. Stolbov
Modelling 2024, 5(4), 1924-1935; https://doi.org/10.3390/modelling5040100 - 5 Dec 2024
Viewed by 599
Abstract
This paper presents a model of the bending behavior of a bi-layer cantilever composed of titanium nickelide and a magnetoactive elastomer embedded with magnetically hard particles. The cantilever is initially subjected to an external magnetic field in its high-temperature state, followed by cooling [...] Read more.
This paper presents a model of the bending behavior of a bi-layer cantilever composed of titanium nickelide and a magnetoactive elastomer embedded with magnetically hard particles. The cantilever is initially subjected to an external magnetic field in its high-temperature state, followed by cooling to a low-temperature state before the magnetic field is removed. This sequence results in residual bending deformation. Basic relations describing the material behavior of titanium nickelide and the magnetoactive elastomer are presented. A variational formulation for the problem under consideration is written down. The problem is solved numerically using the finite element method. The influence of the applied magnetic field magnitude and the thickness of the titanium nickelide layer on the cantilever deflection magnitude is studied. The dependence of the residual cantilever deflection on the applied magnetic field is obtained. The possibility of this structure as a controllable gripping element for applications in robotics and micro-manipulation is demonstrated. Full article
(This article belongs to the Special Issue Finite Element Simulation and Analysis)
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<p>Cross-section of the bi-layer plate made of titanium nickelide (red area) and MAE (blue area).</p>
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<p>Fragments of the finite element mesh (<b>left</b> and <b>right</b> ends) with thickening in the titanium nickelide region.</p>
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<p>Loading diagram: dependence of magnetic field and temperature on step number <span class="html-italic">k</span>.</p>
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<p>Configurations of the bi-layer plate: 1—initial configuration, 2—after application of the magnetic field, 3—after cooling under a constant magnetic field, and 4—after removal of the magnetic field.</p>
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<p>Stress intensity distribution (<b>a</b>) and phase strain distribution (<b>b</b>) in the left part of the sample.</p>
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<p>Dependence of the displacement of the right end of the cantilever on step number <span class="html-italic">k</span> for different values of the thickness of the titanium nickelide layer.</p>
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<p>Dependence of the plate deflection magnitude on the thickness of the titanium nickelide layer.</p>
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<p>Dependence of the plate deflection magnitude on the applied magnetic field.</p>
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<p>Dependence of the displacement vector norm on the number of mesh nodes.</p>
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<p>Working scheme of the gripper: element position in the absence of a magnetic field (<b>a</b>) and element position in a magnetic field (<b>b</b>).</p>
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19 pages, 2011 KiB  
Article
A Fast and Accurate Method for dq Impedance Modeling of Power Electronics Systems Based on Finite Differences
by Julio Hernández-Ramírez, Juan Segundo-Ramírez, Nancy Visairo-Cruz and C. Alberto Núñez Guitiérrez
Modelling 2024, 5(4), 1905-1923; https://doi.org/10.3390/modelling5040099 - 5 Dec 2024
Viewed by 601
Abstract
This paper presents a finite-difference-based method for numerically deriving the DQ impedance model of power electronics-based power systems, specifically tailored for stability analysis. The proposed method offers a computationally efficient alternative to traditional approaches by directly applying finite-difference approximations to the large-signal [...] Read more.
This paper presents a finite-difference-based method for numerically deriving the DQ impedance model of power electronics-based power systems, specifically tailored for stability analysis. The proposed method offers a computationally efficient alternative to traditional approaches by directly applying finite-difference approximations to the large-signal dynamic system, without relying on repetitive time-domain simulations or small-signal analytical models. This method eliminates the need for additional models or complex procedures to compute the steady-state solution, streamlining the impedance modeling process. The accuracy, efficiency, and precision of the proposed method are evaluated through comparative studies with analytical and time-domain perturbation methods. Results demonstrate that the proposed approach provides accuracy comparable to analytical models while significantly reducing computational effort, outperforming perturbation methods in both speed and precision. These findings highlight the practical value of the proposed method for real-time and large-scale system analysis, making it a robust tool for power systems stability assessment. Full article
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Figure 1

Figure 1
<p>Separation of the subsystems in <span class="html-italic">DQ</span>.</p>
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<p>Small-signal Thévenin equivalents of source and load subsystems.</p>
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<p>Flowchart of the three approaches.</p>
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<p>Test case 1: an inverter connected to the grid.</p>
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<p>Impedance models computed using the analytical (<span style="color: #8E8E8E"><b>−</b></span>), finite-difference-impedance, (<span class="html-fig-inline" id="modelling-05-00099-i001"><img alt="Modelling 05 00099 i001" src="/modelling/modelling-05-00099/article_deploy/html/images/modelling-05-00099-i001.png"/></span>) and perturbation (∘) methods.</p>
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<p>Magnitude of <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">Z</mi> <mrow> <mi>e</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> </semantics></math> in the source subsystem for: FDIM-forward (<span style="color: #0000FF"><b>−</b></span>), FDIM-backward (<span style="color: #f316d5 "><b>−</b></span>), FDIM-central (<span style="color: #040003"><b>−</b></span>), perturbation method (<span style="color: #FF0000"><b>−</b></span>).</p>
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<p>Test case 1 operating in a stable steady state.</p>
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<p>Test case 1 operating in an unstable steady state.</p>
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<p>Test case 2: an HVDC-VSC transmission system.</p>
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<p>Impedance model of the source subsystem: FDIM (<span style="color: #000000"><b>−</b></span>) and perturbation method (<span style="color: #FF0000">*</span>).</p>
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16 pages, 9340 KiB  
Article
Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations
by Angelo M. Tusset, Jonierson A. Cruz, Jose M. Balthazar, Maria E. K. Fuziki and Giane G. Lenzi
Modelling 2024, 5(4), 1889-1904; https://doi.org/10.3390/modelling5040098 - 5 Dec 2024
Viewed by 2379
Abstract
This work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurcation diagrams, [...] Read more.
This work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurcation diagrams, and the Lyapunov exponent. Considering that cutting tool vibration in the machining process is one of the main problems of productivity and machining accuracy, the introduction of a magnetorheological damper was considered in the proposed model to reduce the vibration amplitudes of the cutting tool and suppress the chaotic behavior. Hysteresis was considered in the magnetorheological damper model and its application in the system as both a passive and active absorber. The active control strategy considered the application of two non-linear control signals: feedforward to maintain the vibration with a desired behavior and state feedback to drive the system to the desired behavior. The numerical results demonstrated that the proposed controls efficiently reduced the vibration amplitude by introducing the MR damper. Active control has proven effective in controlling the force of the MR damper by varying the electrical voltage applied to the damper coil. Full article
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Figure 1
<p>Physical model of turning process with mass eccentricity: (<b>a</b>) orthogonal turning considering mass eccentricity in a non-ideal source; (<b>b</b>) schematic diagram of orthogonal turning considering mass eccentricity in a non-ideal source.</p>
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<p>Variation in parameters <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open="[" close="]" separators="|"> <mrow> <mn>0.01</mn> <mo>:</mo> <mn>0.3</mn> </mrow> </mfenced> </mrow> </semantics></math>: (<b>a</b>) bifurcation diagrams; (<b>b</b>) largest Lyapunov exponent.</p>
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<p>Variation in parameters <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfenced open="[" close="]" separators="|"> <mrow> <mn>0.01</mn> <mo>:</mo> <mn>0.5</mn> </mrow> </mfenced> </mrow> </semantics></math>: (<b>a</b>) bifurcation diagrams; (<b>b</b>) largest Lyapunov exponent.</p>
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<p>The case of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>: (<b>a</b>) historical in time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Physical model of turning process with mass eccentricity and MR damper: (<b>a</b>) orthogonal turning considering mass eccentricity in a non-ideal system with MR damper; (<b>b</b>) schematic diagram of orthogonal turning considering mass eccentricity in a non-ideal system with MR damper.</p>
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<p>Case <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>: (<b>a</b>) bifurcation diagrams; (<b>b</b>) largest Lyapunov exponent.</p>
Full article ">Figure 6 Cont.
<p>Case <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>: (<b>a</b>) bifurcation diagrams; (<b>b</b>) largest Lyapunov exponent.</p>
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<p>Case <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>: (<b>a</b>) bifurcation diagrams; (<b>b</b>) largest Lyapunov exponent.</p>
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<p>History in time and phase diagram for <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>: (<b>a</b>) history in time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>b</b>) history in time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>; (<b>c</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> para <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>d</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> para <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 8 Cont.
<p>History in time and phase diagram for <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>: (<b>a</b>) history in time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>b</b>) history in time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>; (<b>c</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> para <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>d</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> para <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>.</p>
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<p>Comparison of the system without MR damper and with MR damper: (<b>a</b>) passive damping force only and MR damping only; (<b>b</b>) bifurcation diagram for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> displacement of MR damping only; (<b>c</b>) time history for the system with only passive damping and only MR; (<b>d</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> for the system with only passive damping and only MR.</p>
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<p>Comparison of the system without MR damper and with MR damper for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>,<math display="inline"><semantics> <mrow> <mtext> </mtext> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0.008</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>: (<b>a</b>) history in time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) phase diagram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> versus <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>FFT: (<b>a</b>) system with only passive damping without MR; (<b>b</b>) system with only MR damping; (<b>c</b>) system with passive damper and MR.</p>
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<p>Phase diagram for maximum voltage variations: (<b>a</b>) phase diagram for maximum voltage variations <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>7.5</mn> </mrow> </semantics></math>; (<b>b</b>) phase diagram for variations <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>10.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>15.0</mn> </mrow> </semantics></math>.</p>
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<p>Variation of electrical voltage: (<b>a</b>) variation of electrical voltage <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>7.5</mn> </mrow> </semantics></math>; (<b>b</b>) variation of electrical voltage <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>10.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>15.0</mn> </mrow> </semantics></math>.</p>
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<p>Variation of the force of the MR damper: (<b>a</b>) variation of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>m</mi> <mi>r</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>5.0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>7.5</mn> </mrow> </semantics></math>; (<b>b</b>) variation of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>m</mi> <mi>r</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>10.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>15.0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 15
<p>Phase diagram force versus velocity: (<b>a</b>) phase diagram for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>5.0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>7.5</mn> </mrow> </semantics></math>; (<b>b</b>) phase diagram for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>10.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ν</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>15.0</mn> </mrow> </semantics></math>.</p>
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24 pages, 5443 KiB  
Article
Efficient Numerical Modeling of Oil-Immersed Transformers: Simplified Approaches to Conjugate Heat Transfer Simulation
by Ivan Smolyanov and Evgeniy Shmakov
Modelling 2024, 5(4), 1865-1888; https://doi.org/10.3390/modelling5040097 - 2 Dec 2024
Viewed by 588
Abstract
The development of digital twins for power transformers has become increasingly important to predict possible operating modes and reduce the likelihood of faults. The accuracy of these predictions relies heavily on the numerical models used, which must be both simple and computationally efficient. [...] Read more.
The development of digital twins for power transformers has become increasingly important to predict possible operating modes and reduce the likelihood of faults. The accuracy of these predictions relies heavily on the numerical models used, which must be both simple and computationally efficient. This work focuses on creating a simplified numerical model for a template oil-immersed power transformer (100 MVA, 230/69 KV). The study investigates how the number of elements and the strategies used to set up the mesh in the domain of interest influence the results, aiming to identify the key parameters that affect the outcomes. Furthermore, a significant effect of resolving thermal boundary layers on the accurate identification of hot spots is demonstrated. Two approaches to resolving thermal boundary layers are explored in this work. This study presents a comprehensive analysis of three numerical models for conjugate heat transfer simulations, each with distinct features and computational domain compositions. The results show that the addition of extra calculation domains leads to the emergence of new vortex structures, affecting the velocity profile at the channel inlet and altering the location of hot spots. This study provides valuable insights into the configuration and composition of calculated domains in numerical models of oil-immersed power transformers, essential for the accurate prediction of hot spot temperatures and ensuring reliable operation. Full article
(This article belongs to the Special Issue Finite Element Simulation and Analysis)
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Figure 1

Figure 1
<p>Schematic representation of an idealized 100 MVA, 230/69 kV power transformer.</p>
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<p>Sliced sketch of numerical model’s geometry.</p>
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<p>Temperature dependence of oil density.</p>
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<p>Mesh illustrating the discretization of the problem domain into sub-domains for numerical analysis. Figure (<b>a</b>) shows a general view of the mesh, highlighting the main mesh parameters. Figures (<b>b</b>,<b>c</b>) present a zoomed-in view of a section of the left channel, demonstrating the resolution of thermal boundary layers using the implicit and explicit approaches, respectively.</p>
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<p>Time-dependent maximum velocity at (<b>a</b>) the inlet of the left duct, (<b>b</b>) the middle duct and (<b>c</b>) the right duct under heat load coefficient <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>heat</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. The black, orange and green colors mean the radial discretizations in 10, 20 and 30 elements, correspondingly. The solid, dotted and dashed line styles represent the azimutal discretizations in 100, 200 and 300 elements, correspondingly, for each color’s corresponding radial discretizations.</p>
Full article ">Figure 6
<p>The maximum temperature on the low- (<b>a</b>) and high-voltage (<b>b</b>) windings is dependent on time under the heat load coefficient <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. The black, orange and green colors mean the radial discretizations in the 10, 20 and 30 elements, correspondingly. The solid, dotted and dashed line styles represent the azimutal discretizations in 100, 200 and 300 elements, correspondingly, for each color’s corresponding radial discretizations.</p>
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<p>Time-dependent maximum velocity at (<b>a</b>) the inlet of the left duct, (<b>b</b>) the middle duct and (<b>c</b>) the right duct under heat load coefficient <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>heat</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. The black, orange and green colors mean the radial discretizations in 10, 20 and 30 elements, correspondingly. The solid, dotted and dashed line styles represent the azimutal discretizations in 100, 200 and 300 elements, correspondingly, for each color’s corresponding radial discretizations.</p>
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<p>The maximum temperature on the low- (<b>a</b>) and high-voltage (<b>b</b>) windings, dependent on time under the heat load coefficient <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. The black, orange and green colors mean the radial discretizations in 10, 20 and 30 elements, correspondingly. The solid, dotted and dashed line styles represent the azimutal discretizations in 100, 200 and 300 elements, correspondingly, for each color’s corresponding radial discretizations.</p>
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<p>Relative differences in percent of calculated temperature and velocity. The sensitivity of temperature and velocity are measured dependent on the number of elements in the radial direction for the thermal boundary layer (<b>a</b>), flow core (<b>b</b>) and solid parts (<b>c</b>), and in the azimuthal direction (<b>d</b>). The simulation is conducted for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. The graphs are drawn with two different colors of axes for matching scales of temperature and velocity. The blue color corresponds to the velocity curve and the red to the temperature one.</p>
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<p>Velocity (<b>a</b>) and temperature (<b>b</b>) profiles at the inlet of the right channel for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, with different mesh resolutions in the thermal boundary layer: 4, 10 and 40 elements.</p>
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<p>The velocity profile at the inlet of the right channel. The simulation is conducted for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and the number of mesh elements in azimuthal direction; 20, 100, 200 and 400.</p>
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<p>The average velocity at the outlets of the left (<b>a</b>), middle (<b>b</b>) and right (<b>c</b>) channels over time for heat load coefficient <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> </mrow> </semantics></math>. The velocity curves are calculated by 3 different numerical models. A detailed description of these models is provided in <a href="#sec2dot2-modelling-05-00097" class="html-sec">Section 2.2</a>.</p>
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<p>The maximum temperature in low- (<b>a</b>) and high-voltage (<b>b</b>) windings over time for heat load coefficient <math display="inline"><semantics> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> </semantics></math> = 1, 5, 10. The velocity curves are calculated by 3 different numerical models. A detailed description of these models is provided in <a href="#sec2dot2-modelling-05-00097" class="html-sec">Section 2.2</a>.</p>
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<p>Velocity distribution in the oil and temperature distribution in the solid components of the transformer, calculated using three different models. Results for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> are shown in subfigures (<b>a</b>–<b>c</b>), and results for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> are shown in subfigures (<b>d</b>–<b>f</b>).</p>
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<p>Velocity distribution in the oil and temperature distribution in the solid components of the transformer, calculated using three different models. Results for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> are shown in subfigures (<b>a</b>–<b>c</b>), and results for <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> are shown in subfigures (<b>d</b>–<b>f</b>).</p>
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<p>Velocity distribution in the oil and temperature distribution in the solid components of the transformer, calculated by models #2 and #3 for different heat load coefficients: <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. The distributions are calculated by (<b>a</b>) model #2 <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>b</b>) model #2 <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, (<b>c</b>) model #3 <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and (<b>d</b>) model #3 <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
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<p>The magnitude of the velocity profile on the left (<b>a</b>), middle (<b>b</b>) and right (<b>c</b>) inlets and the left (<b>d</b>), middle (<b>e</b>) and right (<b>f</b>) outlets of the channel calculated by the three models for a heat load coefficient <math display="inline"><semantics> <msub> <mi>k</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> </semantics></math> from 1 to 10. The colors of the lines indicate the value of heat load coefficient and line styles depict the corresponding numerical model.</p>
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<p>The relative velocity deviation between the finest mesh and the one built by optimal parameters in this study.</p>
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12 pages, 7202 KiB  
Article
Analysis of Short-Range Ordering Effect on Tensile Deformation Behavior of Equiatomic High-Entropy Alloys TiNbZrV, TiNbZrTa and TiNbZrHf Based on Atomistic Simulations
by Rita I. Babicheva, Aleksander S. Semenov, Artem A. Izosimov and Elena A. Korznikova
Modelling 2024, 5(4), 1853-1864; https://doi.org/10.3390/modelling5040096 - 1 Dec 2024
Viewed by 665
Abstract
In the study, the combined molecular dynamics and Monte Carlo (MD/MC) simulation was used to investigate the short-range ordering effect on tensile deformation of bicrystals with grain boundaries (GBs) Σ3(11¯2)[110]. Three different equiatomic high-entropy alloys, namely, ZrTiNbV, ZrTiNbTa and ZrTiNbHf, [...] Read more.
In the study, the combined molecular dynamics and Monte Carlo (MD/MC) simulation was used to investigate the short-range ordering effect on tensile deformation of bicrystals with grain boundaries (GBs) Σ3(11¯2)[110]. Three different equiatomic high-entropy alloys, namely, ZrTiNbV, ZrTiNbTa and ZrTiNbHf, were considered. The tensile loading at 300K was applied in the direction perpendicular to the GBs’ planes. The stress–strain response as well as the structure evolution of the alloys with initial random distribution of atoms were compared with results obtained for the corresponding materials relaxed during the MD/MC procedure. It was revealed that the distribution of atoms in the alloys significantly affects the deformation process. Ordered clusters of Nb atoms are able to suppress the dislocation sliding and twin formation increasing the yield strength of ZrTiNbV. On the contrary, in ZrTiNbTa, the twinning mechanism is dominant in the case of the ordered structure due to the absence of Nb clusters and the presence of areas enriched with Zr atoms, which ease nucleation of dislocations and twins. Since Hf decreases the stability of the body-centered cubic lattice, the main deformation mechanism of ZrTiNbHf is the stress-induced phase transition; however, Nb clusters inside grains of the relaxed alloy slightly delay this process. Full article
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<p>Initial configuration of the bicrystal with GBs Σ3(1<math display="inline"><semantics> <mrow> <mover accent="false"> <mrow> <mn>1</mn> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>2)[110].</p>
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<p>Dependence of the average total energy per atom on number of MC/MD simulation cycles.</p>
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<p><span class="html-italic">WCP</span>s for different atomic pairs of the HEAs M1o (<b>a</b>), M2o (<b>b</b>) and M3o (<b>c</b>) obtained after 50 MC/MD relaxation cycles.</p>
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<p>Atomic structures of the HEAs after the MD/MC relaxation.</p>
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<p>Tensile deformation stress–strain curves.</p>
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<p>Structure evolution during tensile deformation of M1r and M1o. In the bottom left corner, atoms of the fcc structure are extracted for M1o (ε = 0.10) with the content of each atom type indicated.</p>
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<p>Structure evolution during tensile deformation of M2r and M2o.</p>
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<p>(<b>a</b>) Dislocation structure of M2r at ε =0.15. The lines of the &lt;100&gt; sessile edge dislocations and 1/2&lt;111&gt; perfect screw dislocations are shown in pink and green colors, respectively; (<b>b</b>) distribution of atoms in amorphous and crystal regions in the deformed M2o.</p>
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<p>Structure evolution during tensile deformation of M3r and M3o.</p>
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29 pages, 3720 KiB  
Article
Modeling, Simulation, and Control of a Rotary Inverted Pendulum: A Reinforcement Learning-Based Control Approach
by Ruben Hernandez, Ramon Garcia-Hernandez and Francisco Jurado
Modelling 2024, 5(4), 1824-1852; https://doi.org/10.3390/modelling5040095 - 27 Nov 2024
Viewed by 1200
Abstract
In this paper, we address the modeling, simulation, and control of a rotary inverted pendulum (RIP). The RIP model assembled via the MATLAB (Matlab 2021a)®/Simulink (Simulink 10.3) Simscape (Simscape 7.3)™ environment demonstrates a high degree of fidelity in its capacity to [...] Read more.
In this paper, we address the modeling, simulation, and control of a rotary inverted pendulum (RIP). The RIP model assembled via the MATLAB (Matlab 2021a)®/Simulink (Simulink 10.3) Simscape (Simscape 7.3)™ environment demonstrates a high degree of fidelity in its capacity to capture the dynamic characteristics of an actual system, including nonlinear friction. The mathematical model of the RIP is obtained via the Euler–Lagrange approach, and a parameter identification procedure is carried out over the Simscape model for the purpose of validating the mathematical model. The usefulness of the proposed Simscape model is demonstrated by the implementation of a variety of control strategies, including linear controllers as the linear quadratic regulator (LQR), proportional–integral–derivative (PID) and model predictive control (MPC), nonlinear controllers such as feedback linearization (FL) and sliding mode control (SMC), and artificial intelligence (AI)-based controllers such as FL with adaptive neural network compensation (FL-ANC) and reinforcement learning (RL). A design methodology that integrates RL with other control techniques is proposed. Following the proposed methodology, a FL-RL and a proportional–derivative control with RL (PD-RL) are implemented as strategies to achieve stabilization of the RIP. The swing-up control is incorporated into all controllers. The visual environment provided by Simscape facilitates a better comprehension and understanding of the RIP behavior. A comprehensive analysis of the performance of each control strategy is conducted, revealing that AI-based controllers demonstrate superior performance compared to linear and nonlinear controllers. In addition, the FL-RL and PD-RL controllers exhibit improved performance with respect to the FL-ANC and RL controllers when subjected to external disturbance. Full article
(This article belongs to the Topic Agents and Multi-Agent Systems)
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<p>Simscape model of the RIP. The control input is denoted by <span class="html-italic">u</span>; the angular displacement of the horizontal arm is denoted by <math display="inline"><semantics> <msub> <mi>q</mi> <mn>1</mn> </msub> </semantics></math>, and the angular position of the pendulum is denoted by <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>Simulink blocks of the RIP system: (<b>a</b>) main subsystem, (<b>b</b>) elements of the main subsystem: <span class="html-italic">Configuration block</span> components (box-dashed lines), <span class="html-italic">Support_base</span>, <span class="html-italic">Actuated_arm</span> and <span class="html-italic">Pendulum</span> subsystems.</p>
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<p>(<b>a</b>) Simulink block of the support base and (<b>b</b>) components of the support base.</p>
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<p>(<b>a</b>) Simulink block of the <span class="html-italic">Actuated_arm</span> subsystem and (<b>b</b>) elements of the subsystem.</p>
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<p>Elements of the <span class="html-italic">Actuator</span> subsystem Simulink block.</p>
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<p>Elements of the <span class="html-italic">Pendulum</span> subsystem Simulink block.</p>
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<p>(<b>a</b>) Rotational friction torque and (<b>b</b>) components of the friction subsystem.</p>
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<p>Evolution of the estimated parameters <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>p</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Time evolution of angular positions of the Simscape and mathematical model for (<b>a</b>) arm position and (<b>b</b>) pendulum position.</p>
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<p>Block diagram of the elements of an RL framework.</p>
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<p>Flowchart of the proposed methodology.</p>
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<p>Block diagram of the DDPG algorithm.</p>
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<p>Simulink diagram of the RL controller.</p>
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<p>Curve of the RL agent learning process.</p>
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<p>Block diagram of implemented controllers.</p>
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<p>Simulink diagram of the FL controller: (<b>a</b>) control scheme implementation, (<b>b</b>) control law implementation.</p>
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<p>Simulink diagram of the FL-ANC controller: (<b>a</b>) control scheme implementation, (<b>b</b>) adaptive neural network controller subsystem block.</p>
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<p>Simulink block diagram of swing-up controller.</p>
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<p>Time evolution of controller signals. Left-hand side upper plot: arm position <math display="inline"><semantics> <msub> <mi>q</mi> <mn>1</mn> </msub> </semantics></math>. Left-hand side bottom plot: control signal <span class="html-italic">u</span>. Right-hand side plot: pendulum position <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>Time evolution of controller signals under an external force. Left-hand side upper plot: arm position <math display="inline"><semantics> <msub> <mi>q</mi> <mn>1</mn> </msub> </semantics></math>. Left-hand side bottom plot: control signal <span class="html-italic">u</span>. Right-hand side plot: pendulum position <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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16 pages, 2134 KiB  
Review
Recent Trends in Proxy Model Development for Well Placement Optimization Employing Machine Learning Techniques
by Sameer Salasakar, Sabyasachi Prakash and Ganesh Thakur
Modelling 2024, 5(4), 1808-1823; https://doi.org/10.3390/modelling5040094 - 25 Nov 2024
Viewed by 710
Abstract
Well placement optimization refers to the identification of optimal locations for wells (producers and injectors) to maximize net present value (NPV) and oil recovery. It is a complex challenge in all phases of production (primary, secondary and tertiary) of a reservoir. Reservoir simulation [...] Read more.
Well placement optimization refers to the identification of optimal locations for wells (producers and injectors) to maximize net present value (NPV) and oil recovery. It is a complex challenge in all phases of production (primary, secondary and tertiary) of a reservoir. Reservoir simulation is primarily used to solve this intricate task by analyzing numerous scenarios with varied well locations to determine the optimum location that maximizes the targeted objective functions (e.g., NPV and oil recovery). Proxy models are a computationally less expensive alternative to traditional reservoir simulation techniques since they approximate complex simulations with simpler models. Previous review papers have focused on analyzing various optimization algorithms and techniques for well placement. This article explores various types of proxy models that are the most suitable for well placement optimization due their discrete and nonlinear natures and focuses on recent advances in the area. Proxy models in this article are sub-divided into two primary classes, namely data-driven models and reduced order models (ROMs). The data-driven models include statistical- and machine learning (ML)-based approximations of nonlinear problems. The second class, i.e., a ROM, uses proper orthogonal decomposition (POD) methods to reduce the dimensionality of the problem. This paper introduces various subcategories within these two proxy model classes and presents the successful applications from the well placement optimization literature. Finally, the potential of integrating a data-driven approach with ROM techniques to develop more computationally efficient proxy models for well placement optimization is also discussed. This article is intended to serve as a comprehensive review of the latest proxy model techniques for the well placement optimization problem. In conclusion, while proxy models have their own challenges, their ability to significantly reduce the complexity of the well placement optimization process for huge reservoir simulation areas makes them extremely appealing. With active research and development occurring in this area, proxy models are poised to play an increasingly central role in oil and gas well placement optimization. Full article
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<p>Cumulative oil production map for single well placement.</p>
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<p>Flowchart of well placement optimization.</p>
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<p>Proxy model classification [<a href="#B2-modelling-05-00094" class="html-bibr">2</a>].</p>
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<p>Examples of different machine learning algorithms [<a href="#B27-modelling-05-00094" class="html-bibr">27</a>].</p>
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<p>Typical ANN structure for WPO showing individual connections between inputs, hidden layer and outputs by colored lines (based on [<a href="#B38-modelling-05-00094" class="html-bibr">38</a>]).</p>
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<p>Input (time of flight maps for injector and producers on 60 × 60 grid system) and output data (NPV) in a CNN [<a href="#B4-modelling-05-00094" class="html-bibr">4</a>]. The colors on TOF map highlight the scale for time of flight with blue as highest value.</p>
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<p>Example of an autoencoder with six inputs and four features [<a href="#B45-modelling-05-00094" class="html-bibr">45</a>].</p>
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<p>Flowchart of reduced order waterflooding optimization [<a href="#B51-modelling-05-00094" class="html-bibr">51</a>].</p>
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19 pages, 268 KiB  
Article
Analytical Study of Magnetohydrodynamic Casson Fluid Flow over an Inclined Non-Linear Stretching Surface with Chemical Reaction in a Forchheimer Porous Medium
by José Luis Díaz Palencia
Modelling 2024, 5(4), 1789-1807; https://doi.org/10.3390/modelling5040093 - 25 Nov 2024
Viewed by 398
Abstract
This study investigates the steady, two-dimensional boundary layer flow of a Casson fluid over an inclined nonlinear stretching surface embedded within a Forchheimer porous medium. The governing partial differential equations are transformed into a set of ordinary differential equations through similarity transformations. The [...] Read more.
This study investigates the steady, two-dimensional boundary layer flow of a Casson fluid over an inclined nonlinear stretching surface embedded within a Forchheimer porous medium. The governing partial differential equations are transformed into a set of ordinary differential equations through similarity transformations. The analysis incorporates the effects of an external uniform magnetic field, gravitational forces, thermal radiation modeled by the Rosseland approximation, and first-order homogeneous chemical reactions. We consider several dimensionless parameters, including the Casson fluid parameter, magnetic parameter, Darcy and Forchheimer numbers, Prandtl and Schmidt numbers, and the Eckert number to characterize the flow, heat, and mass transfer phenomena. Analytical solutions for the velocity, temperature, and concentration profiles are derived under simplifying assumptions, and expressions for critical physical quantities such as the skin friction coefficient, Nusselt number, and Sherwood number are obtained. Full article
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<p>Schematic diagram of the physical model showing the inclined nonlinear stretching surface with the coordinate system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </semantics></math> aligned along and normal to the surface, respectively. The inclination angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> is measured with respect to the horizontal axis.</p>
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16 pages, 4570 KiB  
Article
Study of the Possibility to Combine Deep Learning Neural Networks for Recognition of Unmanned Aerial Vehicles in Optoelectronic Surveillance Channels
by Vladislav Semenyuk, Ildar Kurmashev, Dmitriy Alyoshin, Liliya Kurmasheva, Vasiliy Serbin and Alessandro Cantelli-Forti
Modelling 2024, 5(4), 1773-1788; https://doi.org/10.3390/modelling5040092 - 21 Nov 2024
Viewed by 694
Abstract
This article explores the challenges of integrating two deep learning neural networks, YOLOv5 and RT-DETR, to enhance the recognition of unmanned aerial vehicles (UAVs) within the optical-electronic channels of Sensor Fusion systems. The authors conducted an experimental study to test YOLOv5 and Faster [...] Read more.
This article explores the challenges of integrating two deep learning neural networks, YOLOv5 and RT-DETR, to enhance the recognition of unmanned aerial vehicles (UAVs) within the optical-electronic channels of Sensor Fusion systems. The authors conducted an experimental study to test YOLOv5 and Faster RT-DETR in order to identify the average accuracy of UAV recognition. A dataset in the form of images of two classes of objects, UAVs, and birds, was prepared in advance. The total number of images, including augmentation, amounted to 6337. The authors implemented training, verification, and testing of the neural networks exploiting PyCharm 2024 IDE. Inference testing was conducted using six videos with UAV flights. On all test videos, RT-DETR-R50 was more accurate by an average of 18.7% in terms of average classification accuracy (Pc). In terms of operating speed, YOLOv5 was 3.4 ms more efficient. It has been established that the use of RT-DETR as the only module for UAV classification in optical-electronic detection channels is not effective due to the large volumes of calculations, which is due to the relatively large number of parameters. Based on the obtained results, an algorithm for combining two neural networks is proposed, which allows for increasing the accuracy of UAV and bird classification without significant losses in speed. Full article
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<p>Data set preparation in Roboflow.com service: (<b>a</b>) Annotation of UAVs and birds; (<b>b</b>) Data set partitioning interface for training, validation, and testing of neural networks.</p>
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<p>Metrics of the results of training the YOLOv5 neural network for 100 epochs (O<span class="html-italic">x</span>-axis): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Metrics of the results of training the YOLOv5 neural network for 100 epochs (O<span class="html-italic">x</span>-axis): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Metrics of the results of training the RT-DETR neural network for 100 epochs (axis Ox): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Metrics of the results of training the RT-DETR neural network for 100 epochs (axis Ox): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Example of data obtained as a result of validation of the YOLOv5 experimental model.</p>
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<p>Example of data obtained from the validation of the RT-DETR experimental model.</p>
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<p>Frames from inference tests of trained neural network models: (<b>a</b>,<b>c</b>) RT-DETR-R50; (<b>b</b>,<b>d</b>) YOLOv5s.</p>
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<p>Frames from inference tests of trained neural network models: (<b>a</b>,<b>c</b>) RT-DETR-R50; (<b>b</b>,<b>d</b>) YOLOv5s.</p>
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<p>Comparative diagram of the values of the average class probability in UAV recognition by trained neural network models.</p>
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<p>Algorithm for combining trained neural network models YOLOv5s and RT-DETR-R50.</p>
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28 pages, 2533 KiB  
Article
Multiphysics Modeling of Power Transmission Line Failures Across Four US States
by Prakash KC, Maryam Naghibolhosseini and Mohsen Zayernouri
Modelling 2024, 5(4), 1745-1772; https://doi.org/10.3390/modelling5040091 - 20 Nov 2024
Viewed by 653
Abstract
The failure of overhead transmission lines in the United States can lead to significant economic losses and widespread blackouts, affecting the lives of millions. This study focuses on analyzing the failure of transmission lines, specifically considering the effects of wind, ambient temperature, and [...] Read more.
The failure of overhead transmission lines in the United States can lead to significant economic losses and widespread blackouts, affecting the lives of millions. This study focuses on analyzing the failure of transmission lines, specifically considering the effects of wind, ambient temperature, and current demands, incorporating minimal and significant pre-existing damage. We propose a multiphysics framework to analyze the transmission line failures across sensitive and affected states of the United States, integrating historical data on wind and ambient temperature. By combining numerical simulation with historical data analysis, our research assesses the impact of varying environmental conditions on the reliability of transmission lines. Our methodology begins with a deterministic approach to model temperature and damage evolution, using phase-field modeling for fatigue and damage coupled with electrical and thermal models. Later, we adopt the probability collocation method to investigate the stochastic behavior of the system, enhancing our understanding of uncertainties in model parameters, conducting sensitivity analysis to identify the most significant model parameters, and estimating the probability of failures over time. This approach allows for a comprehensive analysis of factors affecting transmission line reliability, contributing valuable insights into improving power line’s resilience against environmental conditions. Full article
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<p>Schematic representation of transmission lines.</p>
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<p>One-dimensional representation of transmission line.</p>
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<p>Values of <math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math> for different <math display="inline"><semantics> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>D</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Wind and temperature data for Texas. (<b>a</b>) Original wind data. (<b>b</b>) Transformed wind data. (<b>c</b>) Original temperature data. (<b>d</b>) Transformed temperature data.</p>
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<p>Wind and temperature data for California. (<b>a</b>) Original wind data. (<b>b</b>) Transformed wind data. (<b>c</b>) Original temperature data. (<b>d</b>) Transformed temperature data.</p>
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<p>Wind and temperature data for Michigan. (<b>a</b>) Original wind data. (<b>b</b>) Transformed wind data. (<b>c</b>) Original temperature data. (<b>d</b>) Transformed temperature data.</p>
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<p>Wind and temperature data for Florida. (<b>a</b>) Original wind data. (<b>b</b>) Transformed wind data. (<b>c</b>) Original temperature data. (<b>d</b>) Transformed temperature data.</p>
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<p>Schematic diagram illustrating the interconnection between four different aspects of the multiphysics framework.</p>
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<p>Variable cross-section areas for different values of <math display="inline"><semantics> <msub> <mi>A</mi> <mi>σ</mi> </msub> </semantics></math>.</p>
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<p>Evolution of field variables. (<b>a</b>) Damage evolution along the line. (<b>b</b>) Fatigue evolution along the line. (<b>c</b>) Temperature evolution along the line. (<b>d</b>) Voltage drops along the line.</p>
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<p>Effect of initial damage on maximum field values over time. (<b>a</b>) Maximum damage. (<b>b</b>) Maximum fatigue. (<b>c</b>) Maximum Temperature. (<b>d</b>) Maximum voltage drop.</p>
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<p>The failure of transmission lines for different values of initial damage. (<b>a</b>) Texas. (<b>b</b>) California. (<b>c</b>) Michigan. (<b>d</b>) Florida.</p>
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<p>Expected temperature and standard deviation of temperature under the material parametric space <math display="inline"><semantics> <mrow> <msub> <mi>ξ</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in the Texas scenario. (<b>a</b>) Expected temperature. (<b>b</b>) Temperature standard deviation.</p>
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<p>Expected maximum temperature and standard deviation of maximum temperature under material parametric space <math display="inline"><semantics> <mrow> <msub> <mi>ξ</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in the Texas scenario. (<b>a</b>) Maximum expected temperature. (<b>b</b>) Standard deviation of maximum temperature.</p>
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<p>Expected maximum temperature and standard deviation of maximum temperature under the parametric space <math display="inline"><semantics> <mrow> <msub> <mi>ξ</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in the Texas scenario. (<b>a</b>) Maximum expected temperature. (<b>b</b>) Standard deviation of maximum temperature.</p>
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<p>Sensitivity index <math display="inline"><semantics> <msub> <mi>S</mi> <mi>i</mi> </msub> </semantics></math> for the Texas scenario for material parameters, <math display="inline"><semantics> <mrow> <msub> <mi>ξ</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and loading parameters, <math display="inline"><semantics> <mrow> <msub> <mi>ξ</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>a</b>) Material parameters. (<b>b</b>) External loading.</p>
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<p>Expected maximum temperature, standard deviation of maximum temperature, and sensitivity index over time under parametric space <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> in the Texas scenario. (<b>a</b>) Maximum expected temperature. (<b>b</b>) Standard deviation of maximum temperature. (<b>c</b>) Sensitivity index.</p>
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<p>Expected maximum temperature, standard deviation of maximum temperature, and sensitivity index over time under parametric space <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> in the California scenario. (<b>a</b>) Maximum expected temperature. (<b>b</b>) Standard deviation of maximum temperature. (<b>c</b>) Sensitivity index.</p>
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<p>Expected maximum temperature, standard deviation of maximum temperature, and sensitivity index over time under parametric space <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> in the Michigan scenario. (<b>a</b>) Maximum expected temperature. (<b>b</b>) Standard deviation of maximum temperature. (<b>c</b>) Sensitivity index.</p>
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<p>Expected maximum temperature, standard deviation of maximum temperature, and sensitivity index over time under parametric space <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> in the Florida scenario. (<b>a</b>) Maximum expected temperature. (<b>b</b>) Standard deviation of maximum temperature. (<b>c</b>) Sensitivity index.</p>
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<p>Probability of failure for Texas, California, Michigan, and Florida.</p>
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<p>The probability of failure of transmission lines for different values of initial damage (shown in legends). (<b>a</b>) Texas. (<b>b</b>) California. (<b>c</b>) Michigan. (<b>d</b>) Florida.</p>
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<p>The probability of failure of transmission lines for different values of initial damage (shown in legends). (<b>a</b>) Texas. (<b>b</b>) California. (<b>c</b>) Michigan. (<b>d</b>) Florida.</p>
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<p>Error estimation using PCM and MC method plots (<b>a</b>) PCM; (<b>b</b>) MC.</p>
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17 pages, 2007 KiB  
Article
Modeling of the Nanofiltration Process Based on Convective Diffusion Theory
by Sergei Lazarev, Dmitrii Protasov, Dmitrii Konovalov, Irina Khorokhorina and Oleg Abonosimov
Modelling 2024, 5(4), 1729-1744; https://doi.org/10.3390/modelling5040090 - 18 Nov 2024
Viewed by 585
Abstract
The article formulates the state of the problem of improving the theoretical calculation of the nanofiltration kinetic characteristics in the time cycle of separation of industrial solutions containing copper(II), iron(III), trisodium phosphate and OP-10 (a wetting agent used in electroplating, a product of [...] Read more.
The article formulates the state of the problem of improving the theoretical calculation of the nanofiltration kinetic characteristics in the time cycle of separation of industrial solutions containing copper(II), iron(III), trisodium phosphate and OP-10 (a wetting agent used in electroplating, a product of treating a mixture of mono- and dialkylphenols with ethylene oxide) using the equations of convective diffusion, hydrodynamics and mass transfer. To calculate the kinetic characteristics of the nanofiltration process, the mathematical model was improved by numerically solving the equations of convective diffusion, the Navier–Stokes equation and the flow continuity equation in a polar coordinate system with initial and boundary conditions. The theoretical results obtained in the process of an analytical solution of the system of equations allow calculating changes in concentrations in the permeate and retentate tracts and the permeate volume during nanofiltration separation. The acceptability of the developed nanofiltration method for separating solutions is assessed by comparing the calculated data according to the mathematical model with the experimental data obtained on the nanofiltration unit during separation of solutions containing copper(II), iron(III), trisodium phosphate and OP-10. Full article
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<p>Block diagram of the application of modeling to calculate the concentration along the length of the intermembrane channel.</p>
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<p>Scheme of the main flows in a tubular nanofiltration apparatus.</p>
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<p>Flow chart of wastewater treatment by nanofiltration: 1—averaging tank; 2—alkali dispenser: 3—acid dispenser; 4—flocculant dispenser; 5—press filter; 6—preliminary filter; 7—intermediate tank; 8—first-stage nanofiltration unit; 9—second-stage nanofiltration unit; 10—storage tank for permeate of first and second stages of nanofiltration.</p>
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<p>(<b>a</b>) Change in the concentration of copper ions in the retentate depending on the length of the separation chamber channel (at P = 4 MPa) during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation. (<b>b</b>) Change in the concentration of iron ions in the retentate depending on the length of the separation chamber channel (at P = 4 Mpa) during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation. (<b>c</b>) Change in the concentration of trisodium phosphate in the retentate depending on the length of the separation chamber channel (at P = 4 Mpa) during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation. (<b>d</b>) Change in the concentration of OP-10 in the retentate depending on the length of the separation chamber channel (at P = 4 Mpa) during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation.</p>
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<p>(<b>a</b>) Change in the concentration of copper ions in the retentate depending on the value of the transmembrane pressure P during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation. (<b>b</b>) Change in the concentration of iron ions in the retentate depending on the value of the transmembrane pressure P during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation. (<b>c</b>) Change in the concentration of trisodium phosphate ions in the retentate depending on the value of the transmembrane pressure P during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation. (<b>d</b>) Change in the concentration of OP-10 ions in the retentate depending on the value of the transmembrane pressure P during nanofiltration separation on the OPMN-P membrane: solid line—experiment, dotted line—calculation.</p>
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20 pages, 2952 KiB  
Article
Deep Q-Network-Enhanced Self-Tuning Control of Particle Swarm Optimization
by Oussama Aoun
Modelling 2024, 5(4), 1709-1728; https://doi.org/10.3390/modelling5040089 - 15 Nov 2024
Viewed by 693
Abstract
Particle Swarm Optimization (PSO) is a widespread evolutionary technique that has successfully solved diverse optimization problems across various application fields. However, when dealing with more complex optimization problems, PSO can suffer from premature convergence and may become stuck in local optima. The primary [...] Read more.
Particle Swarm Optimization (PSO) is a widespread evolutionary technique that has successfully solved diverse optimization problems across various application fields. However, when dealing with more complex optimization problems, PSO can suffer from premature convergence and may become stuck in local optima. The primary goal is accelerating convergence and preventing solutions from falling into these local optima. This paper introduces a new approach to address these shortcomings and improve overall performance: utilizing a reinforcement deep learning method to carry out online adjustments of parameters in a homogeneous Particle Swarm Optimization, where all particles exhibit identical search behaviors inspired by models of social influence among uniform individuals. The present method utilizes an online parameter control to analyze and adjust each primary PSO parameter, particularly the acceleration factors and the inertia weight. Initially, a partially observed Markov decision process model at the PSO level is used to model the online parameter adaptation. Subsequently, a Hidden Markov Model classification, combined with a Deep Q-Network, is implemented to create a novel Particle Swarm Optimization named DPQ-PSO, and its parameters are adjusted according to deep reinforcement learning. Experiments on different benchmark unimodal and multimodal functions demonstrate superior results over most state-of-the-art methods regarding solution accuracy and convergence speed. Full article
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<p>Improvement methods to enhance PSO.</p>
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<p>Diagram of PSO iterations.</p>
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<p>Markov chain on PSO states.</p>
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<p>Comparison of execution time in seconds across different PSO variants. Grey dots represent individual execution times, blue boxes show the interquartile range, and red lines indicate mean execution times.</p>
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<p>Comparison of convergence speed on benchmark functions for (<b>a</b>) Elliptic; (<b>b</b>) Step; (<b>c</b>) Sphere; (<b>d</b>) Tablet; (<b>e</b>) Quadric; (<b>f</b>) Rastrigrin; (<b>g</b>) Ackley; (<b>h</b>) Griewang; (<b>i</b>) Schewefel; and (<b>j</b>) Drop wave.</p>
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<p>Comparison of convergence speed on benchmark functions for (<b>a</b>) Elliptic; (<b>b</b>) Step; (<b>c</b>) Sphere; (<b>d</b>) Tablet; (<b>e</b>) Quadric; (<b>f</b>) Rastrigrin; (<b>g</b>) Ackley; (<b>h</b>) Griewang; (<b>i</b>) Schewefel; and (<b>j</b>) Drop wave.</p>
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<p>Comparison of convergence speed on benchmark functions for (<b>a</b>) Elliptic; (<b>b</b>) Step; (<b>c</b>) Sphere; (<b>d</b>) Tablet; (<b>e</b>) Quadric; (<b>f</b>) Rastrigrin; (<b>g</b>) Ackley; (<b>h</b>) Griewang; (<b>i</b>) Schewefel; and (<b>j</b>) Drop wave.</p>
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22 pages, 3794 KiB  
Article
Selection of Support System to Provide Vibration Frequency and Stability of Beam Structure
by Alexander P. Lyapin, Ilya V. Kudryavtsev, Sergey G. Dokshanin, Andrey V. Kolotov and Alexander E. Mityaev
Modelling 2024, 5(4), 1687-1708; https://doi.org/10.3390/modelling5040088 - 14 Nov 2024
Viewed by 623
Abstract
The current engineering theories on bending vibrations and the stability of beam structures are based on solving eigenvalue problems through similarly formulated differential equations. Solving the eigenvalue problem for engineering calculations is particularly laborious, especially for non-classical supports, where factors like the stiffness [...] Read more.
The current engineering theories on bending vibrations and the stability of beam structures are based on solving eigenvalue problems through similarly formulated differential equations. Solving the eigenvalue problem for engineering calculations is particularly laborious, especially for non-classical supports, where factors like the stiffness of supports, axial forces, or temperature must be considered. In this case, the solution can be obtained only by numerical methods using specially created programs, which makes it difficult to select supports for a given planar beam structure in engineering practice. This work utilizes established solutions from eigenvalue problems in the theory of vibrations and stability of beams, incorporating factors such as axial forces, temperature, and support stiffness. This combined solution is applicable to beam structures of any type and cross-section, as it is determined solely by the selected support conditions (stiffness) and loading (axial force, temperature). Approximation of eigenvalue problem solutions through continuous functions allows the readers to use them for the analytical solution of the design problem of choosing a support system to ensure the frequency of vibrations and stability of the planar beam structure. At the same time, the known solutions given in the reference books on bending vibrations and stability become their particular solutions. This approach is applicable to solving problems of vibrations and loss of stability of various types (torsional, longitudinal, etc.), and is also applicable in other disciplines where solving problems for eigenvalues is required. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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<p>Bending vibrations of a straight element. (<b>a</b>) Scheme; (<b>b</b>) frequency plot against axial force.</p>
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<p>Straight element stability.</p>
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<p>Graphical representation of support factor functions. (<b>a</b>) Graph <span class="html-italic">α</span><sub>1</sub>(<span class="html-italic">C</span><sub>1</sub>, <span class="html-italic">C</span><sub>2</sub>); (<b>b</b>) graph <span class="html-italic">µ</span><sub>1</sub>(<span class="html-italic">C</span><sub>1</sub>, <span class="html-italic">C</span><sub>2</sub>).</p>
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<p>Bending vibrations of curvilinear element from arc plane. (<b>a</b>) Hinge supports; (<b>b</b>) hinge–fixed supports; (<b>c</b>) fixed–fixed supports.</p>
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<p>Multi-support schemes. (<b>a</b>) Hinge–hinge; (<b>b</b>) fixed–fixed; (<b>c</b>) fixed–hinge.</p>
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<p>Influence of support stiffness on new values of support factors.</p>
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<p>Graphical interpretation of the solution of the resolving equation.</p>
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<p>Vibrations of a straight beam element. (<b>a</b>) Δ<span class="html-italic">T</span> = 90 °C, <span class="html-italic">k</span>* = 0 и N = 6; (<b>b</b>) Δ<span class="html-italic">T</span> = 90 °C, <span class="html-italic">k</span>* = 300 and N = 5.</p>
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<p>Curved beam structure. (<b>a</b>) Initial supports; (<b>b</b>) with intermediate supports.</p>
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<p>Curved beam vibrations. (<b>a</b>) Δ<span class="html-italic">T</span> = 90 °C и C = 1444, N = 7; (<b>b</b>) Δ<span class="html-italic">T</span> = 90 °C, C = 63,518, N = 7.</p>
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<p>Support factor approximation error.</p>
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13 pages, 5482 KiB  
Article
Simulation Analysis of the Annular Liquid Disturbance Induced by Gas Leakage from String Seals During Annular Pressure Relief
by Qiang Du, Ruikang Ke, Xiangwei Bai, Cheng Du, Zhaoqian Luo, Yao Huang, Lang Du, Senqi Pei and Dezhi Zeng
Modelling 2024, 5(4), 1674-1686; https://doi.org/10.3390/modelling5040087 - 8 Nov 2024
Viewed by 558
Abstract
Due to the failure of string seals, gas can leak and result in the abnormal annulus pressure in gas wells, so it is necessary to relieve the pressure in gas wells. In the process of pressure relief, the leaked gas enters the annulus, [...] Read more.
Due to the failure of string seals, gas can leak and result in the abnormal annulus pressure in gas wells, so it is necessary to relieve the pressure in gas wells. In the process of pressure relief, the leaked gas enters the annulus, causes a the great disturbance to the annulus flow field, and thus reduces the protection performance of the annular protection fluid in the string. In order to investigate the influence of gas leakage on the annular flow field, a VOF finite element model of the gas-liquid two-phase flow disturbed by gas leakage in a casing was established to simulate the transient flow field in the annular flow disturbed by gas leakage, and the influences of leakage pressure differences, leakage direction, and leakage time on annular flow field disturbance and wall shear force were analyzed. The analysis results showed that the larger leakage pressure difference corresponded to the faster diffusion rate of the leaked gas in the annulus, the faster the flushing rate of the leaked gas against the casing wall, and a larger shear force on the tubing wall was detrimental to the formation of the corrosion inhibitor film on the tubing wall and casing wall. Under the same conditions, the shear action on the outer wall of tubing in the leakage direction of 90° was stronger than that in the leakage directions of 135° and 45° and the diffusion range was also larger. With the increase in leakage time, leaked gas further moved upward in the annulus and the shear effect on the outer wall of tubing was gradually strengthened. The leaked acid gas flushed the outer wall of casing, thus increasing the peeling-off risk of the corrosion inhibitor film. The study results show that the disturbance law of gas leakage to annular protection fluid is clear, and it was suggested to reduce unnecessary pressure relief time in the annulus to ensure the safety and integrity of gas wells. Full article
(This article belongs to the Topic Oil and Gas Pipeline Network for Industrial Applications)
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<p>Gas leakage model of wellbore tubing. (<b>a</b>) Gas leakage model and (<b>b</b>) model mesh.</p>
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<p>Three leakage models in different directions. (<b>a</b>) Leakage direction at 90°, (<b>b</b>) leakage direction at 45°, and (<b>c</b>) leakage direction at 135°.</p>
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<p>Wall shear force.</p>
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<p>Cloud map of the pressure distribution under the leakage pressure difference of 5 MPa.</p>
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<p>Cloud maps of the velocity and phase distributions under different pressure differences. (<b>a</b>) Velocity field and (<b>b</b>) phase distribution.</p>
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<p>Comparison of the gas extension displacements under different pressure differences. (<b>a</b>) Lateral displacement and (<b>b</b>) longitudinal displacement.</p>
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<p>Shear force on the outer wall of tubing under different leakage pressure differences.</p>
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<p>Variations in the velocity field and phase distribution in the leakage direction of 45°. (<b>a</b>) Velocity field and (<b>b</b>) phase distribution.</p>
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<p>Variations of the velocity field and phase distribution in the leakage direction of 135°. (<b>a</b>) Velocity field and (<b>b</b>) phase distribution.</p>
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<p>Comparison diagram of extension displacements in different leakage directions. (<b>a</b>) Lateral displacement and (<b>b</b>) longitudinal displacement.</p>
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<p>Comparison of wall shear forces in different leakage directions.</p>
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<p>Variations in shear force and gas phase on the outer wall of tubing.</p>
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32 pages, 1410 KiB  
Article
Modeling the Production of Nanoparticles via Detonation—Application to Alumina Production from ANFO Aluminized Emulsions
by Pedro M. S. Santos, Belmiro P. M. Duarte, Nuno M. C. Oliveira, Ricardo A. L. Mendes, José L. S. A. Campos and João M. C. Silva
Modelling 2024, 5(4), 1642-1673; https://doi.org/10.3390/modelling5040086 - 7 Nov 2024
Viewed by 718
Abstract
This paper investigates the production of nanoparticles via detonation. To extract valuable knowledge regarding this route, a phenomenological model of the process is developed and simulated. This framework integrates the mathematical description of the detonation with a model representing the particulate phenomena. The [...] Read more.
This paper investigates the production of nanoparticles via detonation. To extract valuable knowledge regarding this route, a phenomenological model of the process is developed and simulated. This framework integrates the mathematical description of the detonation with a model representing the particulate phenomena. The detonation process is simulated using a combination of a thermochemical code to determine the Chapman–Jouguet (C-J) conditions, coupled with an approximate spatially homogeneous model that describes the radial expansion of the detonation matrix. The conditions at the C-J point serve as initial conditions for the detonation dynamic model. The Mie–Grüneisen Equation of State (EoS) is used, with the “cold curve” represented by the Jones–Wilkins–Lee Equation of State. The particulate phenomena, representing the formation of metallic oxide nanoparticles from liquid droplets, are described by a Population Balance Equation (PBE) that accounts for the coalescence and coagulation mechanisms. The variables associated with detonation dynamics interact with the kernels of both phenomena. The numerical approach employed to handle the PBE relies on spatial discretization based on a fixed-pivot scheme. The dynamic solution of the models representing both processes is evolved with time using a Differential-Algebraic Equation (DAE) implicit solver. The strategy is applied to simulate the production of alumina nanoparticles from Ammonium Nitrate Fuel Oil aluminized emulsions. The results show good agreement with the literature and experience-based knowledge, demonstrating the tool’s potential in advancing understanding of the detonation route. Full article
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<p>Schematic representation of transformations in the <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>−</mo> <mover accent="true"> <mi>v</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math> plane.</p>
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<p>Conceptual model of the system, consisting of a set of infinitely thin, mutually independent cylinders.</p>
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<p>Normalized coalescence kernel for particle collisions with volumes of 500 nm<sup>3</sup>, 1000 nm<sup>3</sup>, and 1500 nm<sup>3</sup>.</p>
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<p>Dynamics of key properties during the expansion of the detonation matrix: (<b>a</b>) isentropic vs. system pressure; (<b>b</b>) system temperature vs. solidification temperature of liquid alumina particles; (<b>c</b>) isentropic vs. system internal energy; (<b>d</b>) radial expansion velocity.</p>
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<p>Initial numerical concentration distributions of liquid alumina particles: (<b>a</b>) mass-based PSD; (<b>b</b>) number concentration-based PSD.</p>
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<p>Evolution of the particle size distribution: (<b>a</b>) mass-based PSD; (<b>b</b>) number concentration-based PSD.</p>
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<p>Dynamics of (<b>a</b>) coalescence kernel for two isolated particles, each with a fixed volume of <math display="inline"><semantics> <mrow> <mrow> <mn>2.7488</mn> </mrow> <mrow> <mo> </mo> <msup> <mi>nm</mi> <mn>3</mn> </msup> </mrow> </mrow> </semantics></math>, and (<b>b</b>) total number of liquid alumina particles.</p>
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<p>Evolution of particle size characteristics: (<b>a</b>) Aaverage particle diameter distribution under coalescence-only and coalescence+coagulation conditions; (<b>b</b>) standard deviation of the particle diameter distribution; (<b>c</b>) relationship between the standard deviation and the average particle diameter.</p>
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<p>Evolution of the Knudsen number throughout the simulation.</p>
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24 pages, 1143 KiB  
Article
Machine Learning-Based Optimization Models for Defining Storage Rules in Maritime Container Yards
by Daniela Ambrosino and Haoqi Xie
Modelling 2024, 5(4), 1618-1641; https://doi.org/10.3390/modelling5040085 - 5 Nov 2024
Viewed by 629
Abstract
This paper proposes an integrated approach to define the best consignment strategy for storing containers in an export yard of a maritime terminal. The storage strategy identifies the rules for grouping homogeneous containers, which are defined simultaneously with the assignment of each group [...] Read more.
This paper proposes an integrated approach to define the best consignment strategy for storing containers in an export yard of a maritime terminal. The storage strategy identifies the rules for grouping homogeneous containers, which are defined simultaneously with the assignment of each group of containers to the available blocks (bay-locations) in the yard. Unlike recent literature, this study focuses specifically on weight classes and their respective limits when establishing the consignment strategy. Another novel aspect of this work is the integration of a data-driven algorithm and operations research. The integrated approach is based on unsupervised learning and optimization models and allows us to solve large instances within a few seconds. Results obtained by spectral clustering are treated as input datasets for the optimization models. Two different formulations are described and compared: the main difference lies in how containers are assigned to bay-locations, shifting from a time-consuming individual container assignment to the assignment of groups of containers, which offers significant advantages in computational efficiency. Experimental tests are organized into three campaigns to evaluate the following: (i) The computational time and solution quality (i.e., space utilization) of the proposed models; (ii) The performance of these models against a benchmark model; (iii) The practical effectiveness of the proposed solution approach. Full article
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<p>Two blocks with different capacities.</p>
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<p>The structure of the proposed approach.</p>
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<p>Input data reorganized by PCA method.</p>
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<p>CPU times for 1000 and 2000 Ctrs: Model 1 vs. Model 2.</p>
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<p>CPU time comparison for instances of 4000, 6000, and 8000 Ctrs.</p>
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<p>Number of bay-locations used and empty slots created: Model 1 and 2 vs. Model-DA.</p>
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<p>Number of bay-locations used and empty slots obtained: Opt-DA rule vs. SC-based rule.</p>
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17 pages, 12404 KiB  
Article
Predicting Cyclist Speed in Urban Contexts: A Neural Network Approach
by Ricardo Montoya-Zamora, Luisa Ramírez-Granados, Teresa López-Lara, Juan Bosco Hernández-Zaragoza and Rosario Guzmán-Cruz
Modelling 2024, 5(4), 1601-1617; https://doi.org/10.3390/modelling5040084 - 5 Nov 2024
Viewed by 765
Abstract
Bicycle use has become more important today, but more information and planning models are needed to implement bike lanes that encourage cycling. This study aimed to develop a methodology to predict the speed a cyclist can reach in an urban environment and to [...] Read more.
Bicycle use has become more important today, but more information and planning models are needed to implement bike lanes that encourage cycling. This study aimed to develop a methodology to predict the speed a cyclist can reach in an urban environment and to provide information for planning cycling infrastructure. The methodology consisted of obtaining GPS data on longitude, latitude, elevation, and time from a smartphone of two groups of cyclists to calculate the speeds and slopes through a model based on a recurrent short-term memory (LSTM) type neural network. The model was trained on 70% of the dataset, with the remaining 30% used for validation and varying training epochs (100, 200, 300, and 600). The effectiveness of recurrent neural networks in predicting the speed of a cyclist in an urban environment is shown with determination coefficients from 0.77 to 0.96. Average cyclist speeds ranged from 6.1 to 20.62 km/h. This provides a new methodology that offers valuable information for various applications in urban transportation and bicycle line planning. A limitation can be the variability in GPS device accuracy, which could affect speed measurements and the generalizability of the findings. Full article
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<p>Comparison between the current cycling infrastructure and the travel preferences of cyclists in the urban area of Querétaro. (<b>a</b>) shows the current classification and connectivity of the infrastructure. (<b>b</b>) represents the GPS routes the cyclists choose for trips between the different origins and proposed destinations.</p>
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<p>Repetitive module of the LSTM-type neural network with four layers. (<b>a</b>) Information flow, (<b>b</b>) forget gate, (<b>c</b>) information added, (<b>d</b>) update information, and (<b>e</b>) output data [<a href="#B42-modelling-05-00084" class="html-bibr">42</a>].</p>
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<p>Variation of speed along the route for four selected cyclists on four routes.</p>
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<p>Autocorrelation graph of three selected cyclists on three different routes. (<b>a</b>) Cyclist 1, (<b>b</b>) Cyclist 2, and (<b>c</b>) Cyclist 3.</p>
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<p>Recurrent neural network that learns the cyclist’s behavior and predicts their speed with a coefficient of determination of 0.7. (<b>a</b>) 2–3 km, (<b>b</b>) 4–5 km, (<b>c</b>) 6–7 km, and (<b>d</b>) 8–9 km.</p>
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<p>The matrix of determination coefficients between ten models was estimated using data from 10 cycling routes and applied to data from other cyclist routes using speed as previous data.</p>
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<p>Prediction of cyclist’s speed with a coefficient of determination of 0.96. (<b>a</b>) 2–3 km, (<b>b</b>) 4–5 km, (<b>c</b>) 6–7 km, and (<b>d</b>) 8–9 km.</p>
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<p>The matrix of determination coefficients between ten models was estimated using data from 10 cycling routes and applied to data from other cyclist routes using speed and slope as previous data.</p>
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<p>Cyclist speed prediction with one variable versus two variables. (<b>a</b>) 2–3 km, (<b>b</b>) 4–5 km, (<b>c</b>) 6–7 km, and (<b>d</b>) 8–9 km.</p>
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<p>Using quantile classification, estimated speeds on different avenues in Querétaro are based on slope and the trained recurrent neural network.</p>
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19 pages, 7375 KiB  
Article
Squirrel Cage Induction Motors Accurate Modelling for Digital Twin Applications
by Adamou Amadou Adamou, Chakib Alaoui, Mouhamadou Moustapha Diop and Adam Skorek
Modelling 2024, 5(4), 1582-1600; https://doi.org/10.3390/modelling5040083 - 22 Oct 2024
Viewed by 890
Abstract
The ongoing industrial revolution emphasizes the importance of precise machinery monitoring. Among these machines, induction motors (IMs) stand out due to their large numbers, which imply a significant part of industrial energy consumption. To achieve accurate in-service IM monitoring, robust modelling is required, [...] Read more.
The ongoing industrial revolution emphasizes the importance of precise machinery monitoring. Among these machines, induction motors (IMs) stand out due to their large numbers, which imply a significant part of industrial energy consumption. To achieve accurate in-service IM monitoring, robust modelling is required, with a particular emphasis on in situ constraints. In this study, we create a precise digital model for squirrel cage induction motors (SCIMs) that can be used in Industry 4.0 digital twin applications. To achieve this, we survey the existing literature, describe the main modelling techniques, identify the best models in terms of ease of implementation, and ensure the accuracy of our digital representation. We develop four methods, namely finite element analysis (FEA), thermal modelling, circuit-based models, and quantum-based fuzzy logic control, as a crucial first step in implementing digital twin (DT) technology for IMs. The quantum fuzzy logic is based on the transition from classical equations to the quantum equation determining the speed of the motor in the quantum world by passing through the Schrödinger equation. We propose the DT level of integration architecture for IMs based on the industry 4.0 reference architecture model. Finally, the main tools used to successfully implement DT for IMs are revealed. Full article
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<p>Steady-state star equivalent circuit for the single-cage (<b>a</b>) and double-cage (<b>b</b>,<b>c</b>).</p>
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<p>Comparison of single-cage (<a href="#modelling-05-00083-f001" class="html-fig">Figure 1</a>a) and double-cage model without iron loss resistance (<a href="#modelling-05-00083-f001" class="html-fig">Figure 1</a>b,c).</p>
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<p>Proposed double-cage model with core loss resistance.</p>
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<p>3D FEA of motor housing using SOLIDWORKS thermal simulation toolbox: (<b>a</b>) mesh visualization, (<b>b</b>) thermal distribution.</p>
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<p>Induction motor thermal network [<a href="#B25-modelling-05-00083" class="html-bibr">25</a>].</p>
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<p>IM model and quantum fuzzy controller.</p>
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<p>Membership functions.</p>
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<p>Evolution of torque (<b>a</b>) and speed (<b>b</b>).</p>
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<p>The transition from classical vector control to quantum speed control by Schrödinger.</p>
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<p>DT implementation level of integration for Induction Motors in Industry 4.0.</p>
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14 pages, 2765 KiB  
Article
Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
by Roman Kvit, Petro Pukach, Tetyana Salo and Myroslava Vovk
Modelling 2024, 5(4), 1568-1581; https://doi.org/10.3390/modelling5040082 - 19 Oct 2024
Viewed by 687
Abstract
Based on the solutions of deterministic fracture mechanics and the methods of probability theory, the algorithm for calculating the probabilistic strength characteristics of plate elements of structures with an arbitrary stochastic distribution of surface defects is outlined. On the plate surface, there are [...] Read more.
Based on the solutions of deterministic fracture mechanics and the methods of probability theory, the algorithm for calculating the probabilistic strength characteristics of plate elements of structures with an arbitrary stochastic distribution of surface defects is outlined. On the plate surface, there are uniformly distributed cracks that do not interact with each other, the plane of which is normal to the surface, and the depth is much less than its length on the surface. The cracks’ depth and angle of orientation are random values, and their joint distribution density is specified. Plates made of this material are under the influence of biaxial loading. The probability of failure, along with the mean value, the dispersion, and the variation coefficient of the plate’s strength, taking into account the surface defects under different types of stress, were determined. Their dependence on the type of loading, the size of the plate, and the surface structural heterogeneity of the material were studied graphically. Joint consideration of the influence of the interrelated properties of real materials, such as defectiveness and stochasticity, on strength and fracture, opens up new opportunities in creating a theory of strength and fracture of deformable solids. Full article
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<p>Model of a plate weakened by a surface crack extending to a certain depth <math display="inline"><semantics> <mi>l</mi> </semantics></math>.</p>
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<p>Marginal crack in the strip of width <math display="inline"><semantics> <mi>H</mi> </semantics></math> equal to the thickness of the plate under the action of tensile stresses <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>n</mi> </msub> </mrow> </semantics></math>.</p>
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<p>A plate model with stochastically distributed surface defects of random size and orientation, which are uniformly scattered in such a way that they do not interact with each other.</p>
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<p>Probability of failure (<math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> for the green line, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> for the purple line) for a given loading <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>=</mo> <mn>1.3</mn> </mrow> </semantics></math> on the number of surface cracks <math display="inline"><semantics> <mi>N</mi> </semantics></math> and the type of stress state (<math display="inline"><semantics> <mi>η</mi> </semantics></math>).</p>
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<p>Failure loading mean value (<math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> for the green line, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> for the purple line) for different types of stress states (<math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>—equal biaxial tension, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>—uniaxial tension, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>—tension-compression).</p>
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<p>Dispersion of failure loading (<math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> for the green line, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> for the purple line) for different types of stress states (<math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>—equal biaxial tension, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>—uniaxial tension, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>—tension-compression).</p>
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<p>Coefficient of strength variation (<math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> for the green line, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> for purple line) for different types of stress states (<math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>—equal biaxial tension, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>—uniaxial tension, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>—tension-compression).</p>
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18 pages, 7447 KiB  
Article
Modeling and Simulation of Material Type Effects on the Mechanical Behavior of Crankshafts in Internal Combustion Engines
by Hasan Mhd Nazha, Muhsen Adrah, Thaer Osman, Maysaa Shash and Daniel Juhre
Modelling 2024, 5(4), 1550-1567; https://doi.org/10.3390/modelling5040081 - 19 Oct 2024
Viewed by 1024
Abstract
This research aims to study the mechanical behavior of the materials most commonly used in crankshaft manufacturing by designing a four-piston crankshaft, analyzing the stresses and displacements resulting from the applied load, and determining vibration frequencies. Additionally, this study examines the thermal behavior [...] Read more.
This research aims to study the mechanical behavior of the materials most commonly used in crankshaft manufacturing by designing a four-piston crankshaft, analyzing the stresses and displacements resulting from the applied load, and determining vibration frequencies. Additionally, this study examines the thermal behavior of the crankshaft. For this purpose, a three-dimensional model of the crankshaft was designed using CATIA V5 R18 software, and finite element analysis was subsequently performed using ANSYS 2019 R1 software under static, dynamic, and thermal conditions with four different materials in various orientations. To verify the effectiveness of the proposed design, it was compared with a reference design in terms of stresses and displacements. This study also explores improvements in crankshaft geometry and shape. The results indicate that selecting the appropriate material for the working conditions and optimizing the geometry and shape enhance engine performance and reduce the crankshaft’s weight by 20%. The findings were validated by comparing the designs, which support increased productivity and improved durability. Full article
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<p>A three-dimensional model of the crankshaft.</p>
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<p>Mesh sensitivity.</p>
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<p>Variation of pressure with crank angle.</p>
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<p>Finite element model of the crankshaft.</p>
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<p>Comparison between crankshaft designs: (<b>a</b>) design within the reference study [<a href="#B11-modelling-05-00081" class="html-bibr">11</a>], Solidworks (<b>b</b>) design within this study CATIA V5 R18.</p>
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<p>Von-Mises stress analysis results for the crankshaft.</p>
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<p>Von Mises stress of the studied materials.</p>
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<p>Results of displacement analysis of the crankshaft.</p>
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<p>Displacement analysis results for the studied crankshaft materials.</p>
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<p>Boundary conditions for vibratory behavior.</p>
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<p>Vibrational analysis of the four materials.</p>
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<p>Vibrational analysis of the four materials.</p>
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<p>Boundary conditions for thermal behavior.</p>
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<p>Output temperature of the studied materials.</p>
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<p>Heat flow of materials used for the crankshaft.</p>
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<p>Advanced concepts for weight loss.</p>
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<p>Crankshaft analysis results (<b>a</b>) von Misses stress and (<b>b</b>) displacement.</p>
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<p>Vibration analysis of Structural Steel.</p>
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<p>Thermal behavior analysis (<b>a</b>) Output temperature, and (<b>b</b>) Heat flow.</p>
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18 pages, 883 KiB  
Article
Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
by Vishal Singh, Dineshkumar Harursampath, Sharanjeet Dhawan, Manoj Sahni, Sahaj Saxena and Rajnish Mallick
Modelling 2024, 5(4), 1532-1549; https://doi.org/10.3390/modelling5040080 - 18 Oct 2024
Cited by 1 | Viewed by 1733
Abstract
Our objective in this work is to demonstrate how physics-informed neural networks, a type of deep learning technology, can be utilized to examine the mechanical properties of a helicopter blade. The blade is regarded as a one-dimensional prismatic cantilever beam that is exposed [...] Read more.
Our objective in this work is to demonstrate how physics-informed neural networks, a type of deep learning technology, can be utilized to examine the mechanical properties of a helicopter blade. The blade is regarded as a one-dimensional prismatic cantilever beam that is exposed to triangular loading, and comprehending its mechanical behavior is of utmost importance in the aerospace field. PINNs utilize the physical information, including differential equations and boundary conditions, within the loss function of the neural network to approximate the solution. Our approach determines the overall loss by aggregating the losses from the differential equation, boundary conditions, and data. We employed a physics-informed neural network (PINN) and an artificial neural network (ANN) with equivalent hyperparameters to solve a fourth-order differential equation. By comparing the performance of the PINN model against the analytical solution of the equation and the results obtained from the ANN model, we have conclusively shown that the PINN model exhibits superior accuracy, robustness, and computational efficiency when addressing high-order differential equations that govern physics-based problems. In conclusion, the study demonstrates that PINN offers a superior alternative for addressing solid mechanics problems with applications in the aerospace industry. Full article
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<p>Artificial neural network architecture.</p>
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<p>Physics-informed neural network architecture.</p>
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<p>Cantilever beam with triangular loading.</p>
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<p>Points over the length of beam.</p>
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<p>Loss curve for the ANN model.</p>
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<p>Loss curve for the PINN model.</p>
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<p>Comparing the solutions from PINN and ANN for predicting deflection.</p>
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<p>Comparing the solutions from PINN and ANN for predicting slope (<b>a</b>), bending moment (<b>b</b>), and shear force (<b>c</b>).</p>
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13 pages, 623 KiB  
Technical Note
The Influence of Harmonic Content on the RMS Value of Electromagnetic Fields Emitted by Overhead Power Lines
by Jozef Bendík, Matej Cenký and Žaneta Eleschová
Modelling 2024, 5(4), 1519-1531; https://doi.org/10.3390/modelling5040079 - 16 Oct 2024
Viewed by 828
Abstract
This paper investigates the influence of harmonic content on the root mean square value of electromagnetic fields emitted by overhead power lines. The paper presents a methodology to assess the intensity of electric field and magnetic flux density, incorporating both fundamental frequencies and [...] Read more.
This paper investigates the influence of harmonic content on the root mean square value of electromagnetic fields emitted by overhead power lines. The paper presents a methodology to assess the intensity of electric field and magnetic flux density, incorporating both fundamental frequencies and harmonics. The results of our calculations indicate that harmonic distortion in current waveforms can significantly increase the RMS value of magnetic flux density but its effect on electric field intensity is minimal. Additionally, our findings highlight a potential increase in induced voltages on buried or overhead steel pipelines in the vicinity of OPLs, which could pose risks such as pipeline damage and increased corrosion. This underscores the importance of considering harmonic content in EMF exposure evaluations to address both health risks and potential infrastructure impacts comprehensively. Effective harmonic management and rigorous infrastructure monitoring are essential to prevent potential hazards and ensure the reliability of protective systems. Full article
(This article belongs to the Topic EMC and Reliability of Power Networks)
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<p>Graph showing the dependency of exposure limit <math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </semantics></math> from frequency.</p>
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<p>Graph showing the dependency of exposure limit <math display="inline"><semantics> <msub> <mi>B</mi> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </semantics></math> from frequency.</p>
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<p>Illustration of position of EMF calculation, red line perpendicular to span axis.</p>
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<p>The positions of the vectors <math display="inline"><semantics> <mover accent="true"> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </semantics></math>, <math display="inline"><semantics> <mover accent="true"> <msub> <mi>r</mi> <mi>o</mi> </msub> <mo stretchy="false">→</mo> </mover> </semantics></math>, <math display="inline"><semantics> <mover accent="true"> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo stretchy="false">→</mo> </mover> </semantics></math> around catenary curve in relation to the observer P.</p>
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<p>The levels of harmonic distortion relative to the fundamental frequency of 50 Hz.</p>
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<p>Results of magnetic flux density calculation for power frequency current, and with consideration of harmonics current distortion.</p>
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<p>Results of intensity fo the electric field calculation for power frequency voltage, and with consideration of harmonics voltage distortion.</p>
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<p>Change in the magnetic flux density RMS value as a function of current THD.</p>
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14 pages, 2841 KiB  
Article
Improving Patient Experience in Outpatient Clinics through Simulation: A Case Study
by Abdullah Alrabghi and Abdullah Tameem
Modelling 2024, 5(4), 1505-1518; https://doi.org/10.3390/modelling5040078 - 15 Oct 2024
Viewed by 1159
Abstract
This research aims to present a case study on the use of simulation to support operational decision-making and improve the patient experience in outpatient clinics. A simulation model was developed to represent patient flow through the endocrine clinics of the internal medicine department [...] Read more.
This research aims to present a case study on the use of simulation to support operational decision-making and improve the patient experience in outpatient clinics. A simulation model was developed to represent patient flow through the endocrine clinics of the internal medicine department in a large hospital in Saudi Arabia. The research evaluated the impact of using simulation models on different aspects of healthcare facility operations, such as patient flow, resource utilization, and staffing. Potential bottlenecks and inefficiencies in the clinic’s processes were identified. Furthermore, improvements were suggested and evaluated that could significantly reduce patient waiting times and increase the number of patients served. Different scenarios and strategies were evaluated without the need for real-world implementation, which can be costly and time consuming. The model can also be easily modified and adapted to accommodate changes in patient demand, staffing levels, or other factors that may impact clinic operations. The findings demonstrate the utility of simulation models in healthcare management. Overall, the use of simulation models in healthcare management has the potential to revolutionize the way clinics and hospitals operate, leading to improved patient outcomes and more efficient use of resources. Full article
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<p>Patient flow through the internal medicine department.</p>
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<p>Visualization of patient flow through internal medicine department using Simio simulation software 14.230.25895.0.</p>
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<p>Average waiting times in reception, triage, and endocrine clinics.</p>
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<p>Utilization of reception, triage, and endocrine clinics.</p>
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<p>Average number waiting in reception and triage.</p>
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<p>Work schedule of reception workers.</p>
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<p>Average time in system in 30:70 patient arrival.</p>
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<p>Number of patients served in 30:70 patient arrival.</p>
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<p>Average time in system in 50:50 patient arrival.</p>
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<p>Number of patients served in 50:50 patient arrival.</p>
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15 pages, 1496 KiB  
Article
Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
by Benedetta Calusi and Liviu Iulian Palade
Modelling 2024, 5(4), 1490-1504; https://doi.org/10.3390/modelling5040077 - 9 Oct 2024
Cited by 1 | Viewed by 711
Abstract
We investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure [...] Read more.
We investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on the method of separation of variables and does not depend on a specific choice of the expression for the pressure-dependent viscosity. Therefore, we show the existence of a general procedure to investigate the behavior of piezo-viscous fluids in Hele-Shaw flow and its solution near a sharp corner. The results are applied to the case of an exponential dependence of viscosity on pressure as an example of exact solutions for the pressure field. Full article
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<p>Sketches of the problem geometry when the edge angle is such that the region close to the tip is a sharp edge (re-entrant plane sector) or a hollow-shaped cavity (non re-entrant plane sector).</p>
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<p>Schematic diagram of the three-dimensional flow domain geometry.</p>
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<p>Plot of <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </semantics></math> as a function of <span class="html-italic">p</span> for classical Newtonian fluid (blue line) and piezo−viscous fluids given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) for different values of <math display="inline"><semantics> <mi>δ</mi> </semantics></math>.</p>
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<p>Plots of the pressure field (<b>left</b>) and of the viscosity given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) (<b>right</b>) in Cartesian coordinates for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math> (i.e., classical Newtonian fluid) and for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> </mrow> </semantics></math> (i.e., piezo−viscous fluid) in the case of antisymmetric flows when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mi>π</mi> <mo>/</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Plots of the pressure field (<b>left</b>) and of the viscosity given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) (<b>right</b>) in Cartesian coordinates for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math> (i.e., classical Newtonian fluid) and for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> </mrow> </semantics></math> (i.e., piezo−viscous fluid) in the case of symmetric flows when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mi>π</mi> <mo>/</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Plots of the pressure field (<b>left</b>) and of the viscosity given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) (<b>right</b>) in Cartesian coordinates for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math> (i.e., classical Newtonian fluid) and for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> </mrow> </semantics></math> (i.e., piezo−viscous fluid) in the case of antisymmetric flows when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>3</mn> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Plots of the pressure field (<b>left</b>) and of viscosity given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) (<b>right</b>) in Cartesian coordinates for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math> (i.e., classical Newtonian fluid) and for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> </mrow> </semantics></math> (i.e., piezo−viscous fluid) in the case of symmetric flows when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>3</mn> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Comparison of fluxes in Cartesian coordinates for classical Newtonian fluid (i.e., <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math>) and piezo−viscous fluid with the viscosity given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> </mrow> </semantics></math> in the case of antisymmetric (<b>left</b>) and symmetric (<b>right</b>) flows when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mi>π</mi> <mo>/</mo> <mn>3</mn> </mrow> </semantics></math>. The corresponding magnification is reported from the maximum to the minimum value.</p>
Full article ">Figure 9
<p>Comparison of fluxes in Cartesian coordinates for classical Newtonian fluid (i.e., <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math>) and piezo−viscous fluid with the viscosity given by (<a href="#FD14-modelling-05-00077" class="html-disp-formula">14</a>) for <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> </mrow> </semantics></math> in the case of antisymmetric (<b>left</b>) and symmetric (<b>right</b>) flows when <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>3</mn> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math>. The corresponding magnification is reported from the maximum to the minimum value.</p>
Full article ">
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