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16 pages, 1322 KiB  
Article
Simplified Model for the Behaviour of Asphalt Mixtures Depending on the Time and the Frequency Domain
by Péter Primusz and Csaba Tóth
Materials 2025, 18(2), 466; https://doi.org/10.3390/ma18020466 (registering DOI) - 20 Jan 2025
Abstract
Sigmoid functions are widely used for the description of viscoelastic material properties of asphalt mixtures. Unfortunately, there are still no known closed functions for describing connections among model parameters in the time and the frequency domains. In most cases, complicated interconversion methods are [...] Read more.
Sigmoid functions are widely used for the description of viscoelastic material properties of asphalt mixtures. Unfortunately, there are still no known closed functions for describing connections among model parameters in the time and the frequency domains. In most cases, complicated interconversion methods are applied for the conversion of viscoelastic material properties. To solve this problem, an empirical material model with four parameters has been developed. Parameters of the model can be quickly determined in the frequency domain and can be used in an unchanged way for the description of the material behaviour of the asphalt mixture in the time domain. The new model starts from the mathematical formula of the Ramberg–Osgood material model (short form RAMBO) and its main advantage is that its parameters are totally independent. Model calculations have been performed for the determination of factors necessary for the interconversion in the time and the frequency domains, applying the approximate procedure of Ninomiya and Ferry. The analysis of data has indicated that the interconversion factors in the time and the frequency domains depend only on the slope of the new empirical model function. Consequently, there is no need for further calculations, since the RAMBO model parameters determined in the frequency domain provide an excellent characterisation of the analysed mixture in the time domain as well. The developed new empirical material model has been verified using laboratory data and exact numerical calculations. Full article
15 pages, 27241 KiB  
Article
Compact Quantum Cascade Laser-Based Noninvasive Glucose Sensor Upgraded with Direct Comb Data-Mining
by Liying Song, Zhiqiang Han, Hengyong Nie and Woon-Ming Lau
Sensors 2025, 25(2), 587; https://doi.org/10.3390/s25020587 (registering DOI) - 20 Jan 2025
Abstract
Mid-infrared spectral analysis has long been recognized as the most accurate noninvasive blood glucose measurement method, yet no practical compact mid-infrared blood glucose sensor has ever passed the accuracy benchmark set by the USA Food and Drug Administration (FDA): to substitute for the [...] Read more.
Mid-infrared spectral analysis has long been recognized as the most accurate noninvasive blood glucose measurement method, yet no practical compact mid-infrared blood glucose sensor has ever passed the accuracy benchmark set by the USA Food and Drug Administration (FDA): to substitute for the finger-pricking glucometers in the market, a new sensor must first show that 95% of their glucose measurements have errors below 15% of these glucometers. Although recent innovative exploitations of the well-established Fourier-transform infrared (FTIR) spectroscopy have reached such FDA accuracy benchmarks, an FTIR spectrometer is too bulky. The advancements of quantum cascade lasers (QCLs) can lead to FTIR spectrometers of reduced size, but compact QCL-based noninvasive blood glucose sensors are not yet available. This work reports on two compact sensor system designs, both reaching the FDA accuracy benchmark. Each design commonly comprises a mid-infrared QCL for emission, a multiple attenuation total reflection prism (MATR) for data acquisition, and a computer-controlled infrared detector for data analysis. The first design translates the comb-like signals into conventional spectra, and then data-mines the resultant spectra to yield blood glucose concentrations. When a pressure actuator is employed to press the patient’s hypothenar against the MATR, the sensor accuracy is considered to reach the FDA accuracy benchmark. The second design abandons the data processing step of translating combs-to-spectra and directly data-mines the “first-hand” comb signal. Beyond increasing the measurement accuracy to the FDA accuracy benchmark, even without a pressure actuator, direct comb data-mining upgrades the sensor system with speed and data integrity, which can impact the healthcare of diabetic patients. Specifically, the sensor performance is validated with 492 glucose absorption scans in the time domain, each with 20 million datapoints measured from four subjects with glucose concentrations of 3.9–7.9 mM. The sensor data-mines 164 sets of critical singularity strengths, each comprising 4 critical singularity strengths directly from the 9840 million raw signal datapoints, and the 656 critical singularity strengths are subjected to a machine-learning regression model analysis, which yields 164 glucose concentrations. These concentrations are correlated with those measured with a standard finger-pricking glucometer. An accuracy of 99.6% is confirmed from the 164 measurements with errors not more than 15% from the reference of the standard glucometer. Full article
(This article belongs to the Section Biomedical Sensors)
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<p>(<b>a</b>) Schematic of an FTIR-based sensor equipped with a single-pass ATR plus a pressure actuator [<a href="#B17-sensors-25-00587" class="html-bibr">17</a>]. (<b>b</b>) The Clarke error grid plot for such a sensor with spectral analysis of the region of 1000 to 1040 cm<sup>−1</sup> for reducing spectral interference, with data collection from the hypothenar replacing that from the finger [<a href="#B18-sensors-25-00587" class="html-bibr">18</a>] (the blue circles are the data of the training set, and the orange crosses are the data of the testing set).</p>
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<p>Schematic diagram of a QCL-based noninvasive blood glucose sensor.</p>
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<p>Schematics of the operation of QCL-Sensor-System #1: (<b>a</b>) Interface between the patient’s hypothenar and the sensor; (<b>b</b>) the route from raw comb signal, to comb-to-spectrum translation, and finally to statistical analysis of glucose concentration.</p>
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<p>Schematics of the operation of QCL-Sensor-System #2: (<b>a</b>) Simplified interface hardware between the patient’s hypothenar and the sensor; (<b>b</b>) the simplified software route from generation of raw comb signal, to direct MFDFA data-mining of the four critical singularity strengths associated with MFDFA singularity plots, and finally to statistical analysis of glucose concentration.</p>
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<p>Conversion of raw data to continuous line spectrum (envelope). (<b>a</b>) Raw time signals of 36 full cycles. (<b>b</b>) An example showing 1 (in the red box) of these 36 full cycles. (<b>c</b>) Overlapping result for 36 full cycles. (<b>d</b>) A continuous emission spectrum from merging these two axisymmetric spectra of (<b>c</b>).</p>
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<p>Conversion of raw data to continuous line spectrum (envelope). (<b>a</b>) Raw time signals of 36 full cycles. (<b>b</b>) An example showing 1 (in the red box) of these 36 full cycles. (<b>c</b>) Overlapping result for 36 full cycles. (<b>d</b>) A continuous emission spectrum from merging these two axisymmetric spectra of (<b>c</b>).</p>
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<p>The comb-to-spectrum-translation results of 41 photoabsorption spectra (painted in color) from Patient-Subject #1, with a photoabsorption spectrum (painted in blue) collected by an FTIR spectrometer as a reference.</p>
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<p>The singularity spectra generated by MFDFA of the same 41 comb trains the comb-to-spectrum translation of which give the 41 photoabsorption spectra shown in <a href="#sensors-25-00587-f006" class="html-fig">Figure 6</a>.</p>
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<p>Clarke error grid plots corresponding to (<b>a</b>) Sensor-System #1 without a pressure actuator; (<b>b</b>) Sensor-System #1 with a pressure actuator; (<b>c</b>) Sensor-System #2 without a pressure actuator. (The blue circles are the data of the training set, and the orange crosses are the data of the testing set.)</p>
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29 pages, 4378 KiB  
Article
Analysis of Sparse Trajectory Features Based on Mobile Device Location for User Group Classification Using Gaussian Mixture Model
by Yohei Kakimoto, Yuto Omae and Hirotaka Takahashi
Appl. Sci. 2025, 15(2), 982; https://doi.org/10.3390/app15020982 (registering DOI) - 20 Jan 2025
Abstract
Location data collected from mobile devices via global positioning system often lack semantic information and can form sparse trajectories in space and time. This study investigates whether user age groups can be accurately classified solely from such sparse spatial–temporal trajectories. We propose a [...] Read more.
Location data collected from mobile devices via global positioning system often lack semantic information and can form sparse trajectories in space and time. This study investigates whether user age groups can be accurately classified solely from such sparse spatial–temporal trajectories. We propose a feature extraction method based on a Gaussian mixture model (GMM), which assigns representative points (RPs) by clustering the location data and aggregating user trajectories into these RPs. We then construct three machine learning (ML) models—support vector classifier (SVC), random forest (RF), and deep neural network (DNN)—using the GMM-based features and compare their performance with that of the improved DNN (IDNN), which is an existing feature extraction approach. In our experiments, we introduced a missing value ratio θth to quantify trajectory sparsity and analyzed the effect of trajectory sparsity on the classification accuracy and generalizability performance of the ML models. The results indicate that GMM-based features outperform IDNN-based features in both classification accuracy and generalization performance. Notably, the RF model achieved the highest accuracy, whereas the SVC model displayed stable generalizability. As the missing value ratio θth increases, the IDNN becomes more susceptible to overfitting, whereas the GMM-based approach preserves accuracy and robustness. These findings suggest that sparse trajectories can still offer meaningful classification performance with appropriate feature design and model selection even without semantic information. This approach holds promise for domains where large-scale, sparse trajectory data are common, including urban planning, marketing analysis, and public policy. Full article
(This article belongs to the Special Issue Data Analysis and Data Mining for Knowledge Discovery)
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<p>Data distribution for missing value ratio <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>k</mi> </msub> <mo>,</mo> <mo>∀</mo> <mi>k</mi> <mo>∈</mo> <mi>K</mi> </mrow> </semantics></math> for the PTDP data. These data were acquired from January to June 2021 in Narashino, Chiba, Japan. There are differences in the quantities of data among the missing value ratios. In particular, because the data range of 0.99–1.00 accounts for 60% of all user data, this figure shows that the user trajectories obtained from mobile devices in the area and in that period are very sparse.</p>
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<p>Imputation method based on the assumption as described in <a href="#sec3dot3-applsci-15-00982" class="html-sec">Section 3.3</a>. Data between two temporally continuous nodes are linearly imputed.</p>
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<p>Procedure for generating feature vectors <math display="inline"><semantics> <msubsup> <mrow> <mi mathvariant="bold-italic">f</mi> </mrow> <mi>k</mi> <mi>GMM</mi> </msubsup> </semantics></math> from <math display="inline"><semantics> <msub> <mi>L</mi> <mi>k</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>T</mi> <mi>k</mi> </msub> </semantics></math>.</p>
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<p>(<b>a</b>) SDA. (<b>b</b>) Fine-tuning of the DNN obtained via SDA.</p>
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<p>Data distribution by class and month. The raw location data are imbalanced. Undersampling is conducted based on the black line, i.e., <math display="inline"><semantics> <msup> <mi>S</mi> <mo>′</mo> </msup> </semantics></math>.</p>
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<p>Data distribution for the missing value rate <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>k</mi> </msub> <mo>,</mo> <mo>∀</mo> <mi>k</mi> <mo>∈</mo> <mi>K</mi> </mrow> </semantics></math> by month. Although there are differences in the data quantity, the distributions’ shapes for each missing value rate between months are almost the same.</p>
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<p>Diagram of fivefold GS+SV for tuning the hyperparameters of the ML models. This process increases the model performance and reduces overfitting of the model on the training data.</p>
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<p>Summary of a series of experimental procedures.</p>
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<p>Average and standard deviation (1SD) of 20 accuracies on test data by month for the <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>th</mi> </msub> <mo>=</mo> <mn>1.00</mn> </mrow> </semantics></math> and ML models. Each graph title indicates the maximum average and its standard deviation by components <span class="html-italic">n</span> in the form of average (1SD) and the <span class="html-italic">p</span>-value for the Shapiro–Wilk test for the accuracy distribution of 20 seeds obtained by components <span class="html-italic">n</span>. There is a tendency that the higher the number of GMD components is, the higher the accuracy across all months. Additionally, for all months, distribution normality for 20 accuracies is confirmed with <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>0.050</mn> </mrow> </semantics></math>, and accuracies are higher than those of random classification (<math display="inline"><semantics> <mrow> <mi>accuracy</mi> <mo>≈</mo> <mn>0.170</mn> </mrow> </semantics></math>) in the range of 3SD on components <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>&gt;</mo> <mn>2</mn> </mrow> </semantics></math>, with any accuracy average by SVC and RF.</p>
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<p>Average and standard deviation (1SD) of 20 accuracies on training data by month in <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>th</mi> </msub> <mo>=</mo> <mn>1.00</mn> </mrow> </semantics></math> and ML models. This metric is used to evaluate the generalization performance of the ML models, and the lower the difference in the accuracy of the test data is, the higher the generalization performance. Compared with the test data, SVC and DNN exhibit a gradual increase in accuracy with respect to the number of components <span class="html-italic">n</span>, whereas RF shows an increase in accuracy from smaller values of <span class="html-italic">n</span> compared with the other two models.</p>
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<p>This figure illustrates the trends in classification accuracy for the missing value ratio <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>th</mi> </msub> </semantics></math> based on the combinations of feature extraction methods and ML models for each month. Averages of 20 accuracies on test data. The dashed horizontal line indicates the best accuracy among the combinations. The title shows the month with the best average accuracy (standard deviation), the combinations of the feature extraction method and the ML model provide the best accuracy, and the results of the Shapiro–Wilk test for the accuracy distribution of 20 seeds, where n.s. is <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>≥</mo> <mn>0.050</mn> </mrow> </semantics></math>. The best average accuracy values are higher than those of random classification (<math display="inline"><semantics> <mrow> <mi>accuracy</mi> <mo>≈</mo> <mn>0.170</mn> </mrow> </semantics></math>) in the range of 3SD in any month.</p>
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<p>Average of 20 accuracies on training data by <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>th</mi> </msub> </semantics></math> for each month. The lower the difference between the accuracies of the training and test data is, the higher the generalization performance. The ML models using the IDNN show a wider range of accuracy differences between the training and test data than those using the GMM. This shows that features based on the GMM are more robust to overfitting than those based on the IDNN.</p>
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20 pages, 4425 KiB  
Article
Feature Analysis and Fault Diagnosis of Internal Leakage in Dual-Cylinder Parallel Balance Oil Circuit
by Haiqing Yao and Xuan Wu
Appl. Sci. 2025, 15(2), 972; https://doi.org/10.3390/app15020972 (registering DOI) - 20 Jan 2025
Viewed by 172
Abstract
The dual-cylinder parallel balance oil circuit is an important heavy-duty support mechanism. Driven by the automation and unmanned trend of equipment in various industries, the internal leakage analysis and corresponding fault diagnosis for this mechanism are increasingly being valued. To solve this problem, [...] Read more.
The dual-cylinder parallel balance oil circuit is an important heavy-duty support mechanism. Driven by the automation and unmanned trend of equipment in various industries, the internal leakage analysis and corresponding fault diagnosis for this mechanism are increasingly being valued. To solve this problem, verified by numerous simulation analyses and theoretical deduction, the pressure signal in the rodless chamber during the pressure maintenance stage was used innovatively to construct the fault features of the internal leakage, which is common and low-cost to be obtained. Then, the wavelet packet decomposition was used to extract three energy features and two time-domain features. Finally, an internal leakage diagnosis was performed based on the five features extracted from the experimental data, and the accuracy and robustness of the proposed five features were verified, which indicated that the proposed fault features and diagnosis method are practical in engineering. Full article
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<p>An illustration of the dual-cylinder parallel balanced oil circuit.</p>
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<p>The cantilever beam support structure.</p>
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<p>The rodless chamber pressure of hydraulic cylinder A and B with different internal leakage conditions.</p>
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<p>The pressure fluctuation amplitude at the main frequency with different internal leakage levels.</p>
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<p>The energy distribution of the wavelet packet decomposition of the rodless chamber pressure.</p>
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<p>Variation curves of wavelet packet energy entropy and energy variance of the rodless chamber pressure.</p>
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<p>Slope and increase rate of pressure under pressure maintaining state.</p>
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<p>Schematic diagram of hydraulic system.</p>
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<p>Three orifices for different internal leakages.</p>
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<p>The rodless chamber pressure of leakage cylinder with different working conditions.</p>
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<p>The T<sup>2</sup> and SPE statistics of three features and five features: (<b>a</b>) T<sup>2</sup> statistics of internal leakage in different severity; (<b>b</b>) SPE statistics of internal leakage in different severity.</p>
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<p>The feature matrix obtained by PCA dimensionality reduction.</p>
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<p>The Euclidean distance between healthy data and internal leakage data.</p>
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<p>The accuracy of T<sup>2</sup> statistics and SPE statistics based on three features and five features under different training sets: (<b>a</b>) Accuracy of T<sup>2</sup> statistics in different data sets; (<b>b</b>) Accuracy of SPE statistics in different data sets.</p>
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<p>The accuracy of three features and five features based on three diagnosis methods under different training sets: (<b>a</b>) Accuracy of different methods obtained with Data 2; (<b>b</b>) Accuracy of different methods obtained with Data 3.</p>
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<p>The average accuracy of different methods with different sample sets.</p>
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18 pages, 731 KiB  
Review
Computational Methods for Information Processing from Natural Language Complaint Processes—A Systematic Review
by J. C. Blandón Andrade, A. Castaño Toro, A. Morales Ríos. and D. Orozco Ospina
Computers 2025, 14(1), 28; https://doi.org/10.3390/computers14010028 - 20 Jan 2025
Viewed by 329
Abstract
Complaint processing is of great importance for companies because it allows them to understand customer satisfaction levels, which is crucial for business success. It allows them to show the real perceptions of users and thus visualize the problems, which are regularly processed from [...] Read more.
Complaint processing is of great importance for companies because it allows them to understand customer satisfaction levels, which is crucial for business success. It allows them to show the real perceptions of users and thus visualize the problems, which are regularly processed from oral or written natural language, derived from the provision of a service. In addition, the treatment of complaints is relevant because according to the laws of each country, companies have the obligation to respond to these complaints in a specified time. The specialized literature mentions that enterprises lost USD 75 billion due to poor customer service, highlighting that companies need to know and understand customer perceptions, especially emotions, and product reviews to gain insight and learn about customer feedback because of the importance of the voice of the customer for an organization. In general, it is evident that there is a need for research related to computational language processing to handle user requests. The authors show great interest in computational techniques for the processing of this information in natural language and how this could contribute to the improvement of processes within the productive sector. This work searches in indexed journals for information related to computational methods for processing relevant data from user complaints. It is proposed to apply a systematic literature review (SLR) method combining literature review guides by Kitchenham and the PRISMA statement. The systematic process allows the extraction of consistent information, and after applying it, 27 articles were obtained from which the analysis was conducted. The results show various proposals using linguistic, statistical, machine learning, and hybrid methods. We find that most authors combine Natural Language Processing (NLP) and Machine Learning (ML) to create hybrid methods. The methods extract relevant information from complaints of the customers in natural language in various domains, such as government, medical, banks, e-commerce, public services, agriculture, customer service, environmental, and tourism, among others. This work contributes as support for the creation of new systems that can give companies a significant competitive advantage due to their ability to reduce the response time of the complaints as established by law. Full article
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<p>PRISMA-statement-based screening and filtering flow chart.</p>
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19 pages, 12045 KiB  
Article
A Topological Approach to Enhancing Consistency in Machine Learning via Recurrent Neural Networks
by Muhammed Adil Yatkin, Mihkel Kõrgesaar and Ümit Işlak
Appl. Sci. 2025, 15(2), 933; https://doi.org/10.3390/app15020933 (registering DOI) - 18 Jan 2025
Viewed by 348
Abstract
The analysis of continuous events for any application involves the discretization of an event into sequences with potential historical dependencies. These sequences represent time stamps or samplings of a continuous process collectively forming a time series dataset utilized for training recurrent neural networks [...] Read more.
The analysis of continuous events for any application involves the discretization of an event into sequences with potential historical dependencies. These sequences represent time stamps or samplings of a continuous process collectively forming a time series dataset utilized for training recurrent neural networks (RNNs) such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) for pattern prediction. The challenge is to ensure that the estimates from the trained models are consistent in the same input domain for different discretizations of the same or similar continuous history-dependent events. In other words, if different time stamps are used during the prediction phase after training, the model is still expected to give consistent predictions based on the knowledge it has learned. To address this, we present a novel RNN transition formula intended to produce consistent estimates in a wide range of engineering applications. The approach was validated with synthetically generated datasets in 1D, 2D, and 3D spaces, intentionally designed to exhibit high non-linearity and complexity. Furthermore, we have verified our results with real-world datasets to ensure practical applicability and robustness. These assessments show the ability of the proposed method, which involves restructuring the mathematical structure and extending conventional RNN architectures, to provide reliable and consistent estimates for complex time series data. Full article
(This article belongs to the Special Issue Deformation and Fracture Behaviors of Materials)
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<p>The comprehensive research process followed in this study, outlining the key stages and the methodology employed to achieve the research objectives.</p>
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<p>Representation of an incremental update during the learning process of recurrent neural networks (RNNs) in 2D, shown in (<b>A</b>). The condition in Equation (<a href="#FD2-applsci-15-00933" class="html-disp-formula">2</a>) must hold on the RNN transition function to provide consistent predictions. The <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>β</mi> </semantics></math> values in Equation (<a href="#FD2-applsci-15-00933" class="html-disp-formula">2</a>) is illustrated through one incremental update. As shown in (<b>B</b>), an incremental difference <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> </semantics></math> is divided by the norm of the input vector, expressed as <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mo>Δ</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mi>v</mi> </mfrac> </mstyle> </semantics></math>. At the introduced transition formula in Equation (<a href="#FD4-applsci-15-00933" class="html-disp-formula">4</a>), while the <math display="inline"><semantics> <mrow> <msub> <mi>g</mi> <mi>W</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mo>Δ</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mi>v</mi> </mfrac> </mstyle> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>h</mi> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> learns the update effect of <math display="inline"><semantics> <mi>β</mi> </semantics></math> on the previous state vector, multiplying this difference with the norm as <span class="html-italic">v</span> gives the total update.</p>
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<p>Consistency results in 1D-Space: As seen in the figures, while the number of increments increases, the ConsRNN-based NN architecture provides consistent estimates, whereas the GRU-based NN architecture loses accuracy and deviates from the ground truth.</p>
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<p>Consistency analysis results in 2D-Space with the transformation of input paths through the objective function. As shown in the figures, as the number of increments increases along the input paths, the GRU-based architecture’s predictions deviate from the ground truth. In contrast, the ConsRNN-based architecture’s estimations remain consistent.</p>
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<p>Consistency analysis results in 2D-Space with the transformation of input path through the objective non-smooth continuous function.</p>
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<p>The 3D results with continuous functional mapping. The black lines represent the input paths and the red lines represent the output paths that are expected to be estimated by NN architectures. As can be seen from both the visual results and MSE scores, while the number of increments increases, the GRU estimations deviate from the ground truth in contrast to the ConsRNN-based NN architecture. In the left MSE figure, the change in MSE value is indicated with reference to 20 increment case as a multiple. The ‘x’ values correspond to the MSE value multiples for different numbers of increments.</p>
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<p>Generated shape in 3D with different number of points. These points are mapped by the function in Equation (<a href="#FD9-applsci-15-00933" class="html-disp-formula">9</a>), resulting in the transformation of output shapes.</p>
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<p>Visual estimation results of two different NN architectures built from GRU and ConsRNN layer for 100 and 1000 points.</p>
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<p>Bilinear Forming Limit Curve (FLC) results. As the number of increments increases, predictions from the GRU-built NN architecture increasingly deviate from the actual FLC curve, in contrast to those from the ConsRNN-built architecture.</p>
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<p>As can be seen from the figure (<b>A</b>), while the number of increments increasing the MSE for the GRU-trained model is increasing, the trained ConsRNN-based NN architecture still gives similar results, even with the changing number of increments.</p>
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18 pages, 2041 KiB  
Article
A Wavelet Transform-Based Transfer Learning Approach for Enhanced Shaft Misalignment Diagnosis in Rotating Machinery
by Houssem Habbouche, Tarak Benkedjouh, Yassine Amirat and Mohamed Benbouzid
Electronics 2025, 14(2), 341; https://doi.org/10.3390/electronics14020341 - 17 Jan 2025
Viewed by 260
Abstract
Rotating machines are vital for ensuring reliability, safety, and operational availability across various industrial sectors. Among the faults that can affect these machines, shaft misalignment is particularly critical due to its impact on other components connected to the shaft, making it a key [...] Read more.
Rotating machines are vital for ensuring reliability, safety, and operational availability across various industrial sectors. Among the faults that can affect these machines, shaft misalignment is particularly critical due to its impact on other components connected to the shaft, making it a key focus for diagnostic systems. Misalignment can lead to significant energy losses, and therefore, early detection is crucial. Vibration analysis is an effective method for identifying misalignment at an early stage, enabling corrective actions before it negatively impacts equipment efficiency and energy consumption. To improve monitoring efficiency, it is essential that the diagnostic system is not only intelligent but also capable of operating in real-time. This study proposes a methodology for diagnosing shaft misalignment faults by combining wavelet transform for feature extraction and transfer learning for fault classification. The accuracy of the proposed soft real-time solution is validated through a comparison with other time-frequency transformation techniques and transfer learning networks. The methodology also includes an experimental procedure for simulating misalignment faults using a laser measurement tool. Additionally, the study evaluates the thermal impacts and vibration signature of each type of misalignment fault through multi-sensor monitoring, highlighting the effectiveness and robustness of the approach. First, wavelet transform is used to obtain a good representation of the signal in the time-frequency domain. This step allows for the extraction of key features from multi-sensor vibration signals. Then, the transfer learning network processes these features through its different layers to identify the faults and their severity. This combination provides an intelligent decision-support tool for diagnosing misalignment faults, enabling early detection and real-time monitoring. The proposed methodology is tested on two datasets: the first is a public dataset, while the second was created in the laboratory to simulate shaft misalignment using a laser alignment tool and to demonstrate the effect of this defect on other components through thermal imaging. The evaluation is carried out using various criteria to demonstrate the effectiveness of the methodology. The results highlight the potential of implementing the proposed soft real-time solution for diagnosing shaft misalignment faults. Full article
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<p>Flowchart of the proposed shaft misalignment fault diagnosis.</p>
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<p>AlexNet architecture.</p>
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<p>WT of different signals classes: (<b>a</b>) no misalignment, (<b>b</b>) horizontal misalignment with 0.5 mm, (<b>c</b>) horizontal misalignment with 1.15 mm, (<b>d</b>) vertical misalignment with 0.34 mm, (<b>e</b>) vertical misalignment with 0.8 mm, and (<b>f</b>) vertical misalignment with 1.09 mm.</p>
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<p>Statistical features evolution for normal state: (<b>a</b>) RMS, (<b>b</b>) kurtosis, (<b>c</b>) skewness, and (<b>d</b>) crest factor.</p>
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<p>Confusion matrix, the blue color represents correctly classified samples, while other colors indicate misclassified ones.</p>
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<p>Misalignment test bench: (<b>a</b>) model; (<b>b</b>) real.</p>
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<p>Misalignment control parts, (<b>a</b>) Soft foot, (<b>b</b>) Flexible coupling, and (<b>c</b>) Motor support.</p>
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<p>Experimental setup and data acquisition system for shaft misalignment fault diagnosis using shaft misalignment system Easy-Laser E540.</p>
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<p>Thermal image in the case of Defaut N°1: speed of rotation 3000 RPM using infrared camera Fluke Ti32.</p>
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<p>(<b>a</b>) Vibration signal of the misalignment fault; (<b>b</b>) spectrum of the vibration signal.</p>
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<p>Sketch of the test bench and acquisition chain.</p>
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<p>WT of signal from sensor 3: (<b>a</b>) Fault N°1; (<b>b</b>) Fault N°6.</p>
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<p>Confusion matrix of Data N°1, the blue color represents correctly classified samples, while other colors indicate misclassified ones.</p>
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<p>Confusion matrix of Data N°2, the blue color represents correctly classified samples, while other colors indicate misclassified ones.</p>
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<p>Confusion matrix of Data N°3, the blue color represents correctly classified samples, while other colors indicate misclassified ones.</p>
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13 pages, 4312 KiB  
Article
Numerical Simulation Study of Electromagnetic Pulse in Low-Altitude Nuclear Explosion Source Regions
by Zhaomin Li, Jiarong Dong, Bing Wei and Xinbo He
Electronics 2025, 14(2), 337; https://doi.org/10.3390/electronics14020337 - 16 Jan 2025
Viewed by 380
Abstract
A nuclear electromagnetic pulse (NEMP) is the fourth effect of a nuclear explosion, characterized by a strong electromagnetic field that can instantly damage electronic devices. To investigate the spatial field value distribution characteristics of the source region of low-altitude NEMPs, this study employed [...] Read more.
A nuclear electromagnetic pulse (NEMP) is the fourth effect of a nuclear explosion, characterized by a strong electromagnetic field that can instantly damage electronic devices. To investigate the spatial field value distribution characteristics of the source region of low-altitude NEMPs, this study employed a finite-difference time-domain (FDTD) method based on a rotating ellipsoidal hyperbolic coordinate system. Due to intense field variations near the explosion center, non-uniform grids were employed for both spatial and temporal steps, and an OpenMP parallel algorithm was utilized to enhance computational efficiency. Analysis focused on the following two scenarios: varying angles at a constant distance and varying distances at a constant angle, considering both transverse magnetic (TM) and transverse electric (TE) waves. The results indicate that the spatial field value distribution characteristics differ between the two wave types. For TM waves, the electric and magnetic fields share the same polarity, but their waveform polarities are opposite above and below the explosion center. A TE wave is exactly the opposite. Compared with a TM wave, a TE wave has stronger peak electromagnetic fields but narrower pulse widths and lower overall energy. This research provides significant support for the development of nuclear explosion detection technology and offers theoretical foundations for the protection of surrounding environmental facilities. Full article
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<p>Comparison of the relative occurrence rates of three processes as a function of photon energy and atomic number the medium.</p>
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<p>Schematic diagram of low–altitude NEMP generation.</p>
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<p>The geometric schematic diagram of the spherical coordinate system (<math display="inline"><semantics> <mrow> <mi>r</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </semantics></math>) and the rotating ellipsoid–hyperbolic orthogonal coordinate system (<math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>,</mo> <mi>ζ</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </semantics></math>) at the field point P.</p>
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<p>Comparison of results between the study and existing literature.</p>
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<p>Distribution map of source area under specific conditions.</p>
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<p>Schematic diagram of nuclear explosion points and observation points from different angles at the same distance.</p>
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<p>Comparison of field time–domain waveforms during angle variation of TM wave. (<b>a</b>) Electric field; (<b>b</b>) magnetic field.</p>
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<p>Comparison of field time–domain waveforms during angle variation of TE Wave. (<b>a</b>) Electric field; (<b>b</b>) magnetic field.</p>
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<p>Schematic diagram of nuclear explosion points and observation points from different distances at the same angle.</p>
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<p>Comparison of field time–domain waveforms during distance variation of TM wave. (<b>a</b>) Electric field above the explosion center; (<b>b</b>) magnetic field above the explosion center; (<b>c</b>) electric field below the explosion center; (<b>d</b>) magnetic field below the explosion center.</p>
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<p>Comparison of field time–domain waveforms during distance variation of TE wave. (<b>a</b>) Electric field; (<b>b</b>) magnetic field.</p>
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14 pages, 13519 KiB  
Article
Study on the Coarsening Behavior of Interphase Precipitates and Random Precipitates in Steel Under the High-Temperature Environment of Fire
by Jinghua Cong, Yongzhe Yang, Haibin Zhu, Xueliang Shang, Hongyu Wu, Zhendong Song, Xuemin Wang and Xiangyu Xu
Metals 2025, 15(1), 73; https://doi.org/10.3390/met15010073 - 16 Jan 2025
Viewed by 266
Abstract
In the domain of fire-resistant steels, the characteristics of precipitates significantly influence material properties. This study developed a novel heat treatment protocol to concurrently achieve both interphase precipitation and random precipitation. Samples were subjected to isothermal treatments at various temperatures and durations, while [...] Read more.
In the domain of fire-resistant steels, the characteristics of precipitates significantly influence material properties. This study developed a novel heat treatment protocol to concurrently achieve both interphase precipitation and random precipitation. Samples were subjected to isothermal treatments at various temperatures and durations, while techniques such as scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were employed to thoroughly analyze the coarsening behavior of the two types of precipitate and reveal their thermal stability differences. The results show that the growth and coarsening rates of interphase precipitates are substantially lower than random precipitates. Coarsening kinetics analysis reveals that the radius of random precipitates follows a 1/3 power law with time at 600 °C and 650 °C, whereas the radius of interphase precipitates adheres to a 1/6 power law at 600 °C and a 1/5 power law at 650 °C. Furthermore, interphase precipitation demonstrates excellent size uniformity, which hinders the formation of a concentration gradient, thereby reducing the coarsening rate and enhancing thermal stability. After prolonged tempering treatment, interphase precipitation maintains a higher strengthening contribution than random precipitation. This study provides novel insights and theoretical foundations for the design and development of fire-resistant steels. Full article
(This article belongs to the Special Issue Design, Preparation and Properties of High Performance Steels)
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<p>Schematic diagram illustrating the heat treatment process of the microalloyed steels.</p>
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<p>SEM micrographs of sample S0.</p>
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<p>TEM micrographs (<b>a</b>) and EDS analysis (<b>b</b>) of the precipitates in sample S0.</p>
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<p>SEM micrographs (<b>a</b>,<b>c</b>,<b>e</b>,<b>g</b>) and binarized images (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>) of precipitates with different isothermal holdings time at 600 °C in the microalloyed steels. (<b>a</b>,<b>b</b>) S0 (<b>c</b>,<b>d</b>) S0-600 °C-1 h, (<b>e</b>,<b>f</b>) S0-600 °C-3 h, (<b>g</b>,<b>h</b>) S0-600 °C-10 h.</p>
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<p>SEM micrographs (<b>a</b>,<b>c</b>,<b>e</b>,<b>g</b>) and binarized images (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>) of precipitates with different isothermal holding times at 650 °C in the microalloyed steels. (<b>a</b>,<b>b</b>) S0, (<b>c</b>,<b>d</b>) S0-650 °C-1 h, (<b>e</b>,<b>f</b>) S0-650 °C-3 h, (<b>g</b>,<b>h</b>) S0-650 °C-10 h.</p>
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<p>Variation of the average diameter of precipitates with different isothermal holding times at 600 °C (<b>a</b>) and 650 °C (<b>b</b>) in the microalloyed steels.</p>
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<p>Plot of the mean radius of different precipitates against time at 600 °C: (<b>a</b>) is interphase precipitation; (<b>b</b>) is random precipitation.</p>
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<p>Plot of the mean radius of different precipitates against time at 650 °C: (<b>a</b>) is interphase precipitation; (<b>b</b>) is random precipitation.</p>
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<p>Variation of the average density of precipitates with different isothermal holding times at 600 °C in the microalloyed steels.</p>
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<p>Distributions of precipitate diameter determined from the SEM images of the microalloyed steels held at 600 °C for various times: (<b>a</b>–<b>d</b>) are the statistical diagrams of random precipitation; (<b>e</b>–<b>h</b>) are the statistical diagrams of interphase precipitation (FWHM: the full width at half-maximum).</p>
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<p>Schematic diagram of the diffusion of Ti atoms between interphase precipitation and random precipitation.</p>
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<p>Schematic illustration of changes in the morphology and nature of precipitates during different processes.</p>
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17 pages, 4934 KiB  
Article
Implementing a Wide-Area Network and Low Power Solution Using Long-Range Wide-Area Network Technology
by Floarea Pitu and Nicoleta Cristina Gaitan
Technologies 2025, 13(1), 36; https://doi.org/10.3390/technologies13010036 - 16 Jan 2025
Viewed by 437
Abstract
In recent decades, technology has undergone significant transformations, aimed at optimizing and enhancing the quality of human life. A prime example of this progress is the Internet of Things (IoT) technology. Today, the IoT is widely applied across diverse sectors, including logistics, communications, [...] Read more.
In recent decades, technology has undergone significant transformations, aimed at optimizing and enhancing the quality of human life. A prime example of this progress is the Internet of Things (IoT) technology. Today, the IoT is widely applied across diverse sectors, including logistics, communications, agriculture, education, and infrastructure, demonstrating its versatility and profound relevance in various domains. Agriculture has historically been a fundamental sector for meeting humanity’s basic needs, and it is indispensable for survival and development. A critical factor in this regard is climatic and meteorological conditions directly influencing agricultural productivity. Therefore, real-time monitoring and analysis of these variables becomes imperative for optimizing production and reducing vulnerability to climate change. This paper presents the development and implementation of a low-power wide-area network (LPWAN) solution using LoRaWAN (long-range wide-area network) technology, designed for real-time environmental monitoring in agricultural applications. The system consists of energy-efficient end nodes and a custom-configured gateway, designed to optimize data transmission and power consumption. The end nodes integrate advanced sensors for temperature, humidity, and pressure, ensuring accurate data collection. Full article
(This article belongs to the Section Information and Communication Technologies)
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<p>The development module used as a gateway.</p>
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<p>System block diagram.</p>
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<p>Programming the gateway with the specific firmware.</p>
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<p>Gateway parameters.</p>
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<p>Adding the gateway to the LORIOT network.</p>
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<p>Setting the MAC address of the device.</p>
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<p>Gateway status and location.</p>
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<p>Results obtained in the Tera Term.</p>
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<p>The flowchart diagram for the end node.</p>
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<p>Transmission successful, as shown on the highlighted LED.</p>
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<p>LoRaWAN protocol initialization and parameter transmission to TTN.</p>
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17 pages, 4621 KiB  
Article
An Analysis of the Effect of Cavitation on Rotor–Stator Interaction in a Bidirectional Bulb Tubular Pump
by Yucheng Zhou, Wenyong Duan, Haiyu Liu, Xiaodong Yang, Jing Hu, Dawang Sun and Shikai Yan
J. Mar. Sci. Eng. 2025, 13(1), 138; https://doi.org/10.3390/jmse13010138 - 14 Jan 2025
Viewed by 317
Abstract
This study delves into rotor–stator interaction within a bidirectional bulb tubular pump under cavitation conditions. Using pressure pulsation tests on a model pump and numerical simulations performed with ANSYS CFX software, we analyzed pressure pulsation and flow field data across three distinct flow [...] Read more.
This study delves into rotor–stator interaction within a bidirectional bulb tubular pump under cavitation conditions. Using pressure pulsation tests on a model pump and numerical simulations performed with ANSYS CFX software, we analyzed pressure pulsation and flow field data across three distinct flow rates and multiple cavitation numbers. Both time-domain and frequency-domain analyses were conducted to examine the patterns of pressure pulsation influenced by flow rates and cavitation numbers at various monitoring locations. A numerical flow field analysis further validated the findings. The results reveal that rotor–stator interaction manifests in the vaneless spaces of the pump during cavitation. The onset of cavitation alters the amplitudes of dominant frequencies at different flow rates. Near the guide vane and impeller, the dominant frequencies shift toward the impeller frequency and guide vane frequency, respectively. Under low-flow conditions, the rotor–stator interaction effect is more conspicuous due to the deteriorated flow pattern. Pressure pulsations are more strongly influenced in the front vaneless space (FVP) than in the rear vaneless space (RVP). This difference arises because the front guide vane destabilizes rather than stabilizes the flow pattern, worsening the rotor–stator interaction. Additionally, the FVP is less affected by the impeller than the RVP, further amplifying the influence of rotor–stator interaction on pressure pulsation. These findings provide a theoretical foundation for mitigating the effects of rotor–stator interaction on the operational stability and efficiency of bidirectional bulb tubular pumps. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Model pump system.</p>
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<p>Model pump system.</p>
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<p>Grid diagram of inlet and outlet flow passages with bulb body.</p>
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<p>Grid diagram of typical guide vanes and impeller.</p>
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<p>Grid independence analysis.</p>
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<p>Comparison of external characteristic curves between experiments and numerical simulations.</p>
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<p>Time-domain signals of pressure pulsation under non-cavitating and cavitating conditions at different flow rates.</p>
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<p>Time-domain signals of pressure pulsation under non-cavitating and cavitating conditions at different flow rates.</p>
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<p>Frequency-domain signals of P1 and P2 influenced by different cavitation numbers at various flow rates.</p>
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<p>Frequency-domain signals of P3 and P4 influenced by different cavitation numbers at various flow rates.</p>
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<p>Guide vane unfolding diagram.</p>
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<p>Unfolding chart of impeller under different cavitation numbers.</p>
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<p>Cavitation bubble distribution on blade surface under different cavitation numbers.</p>
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12 pages, 834 KiB  
Article
A Post-Processing Method for Quantum Random Number Generator Based on Zero-Phase Component Analysis Whitening
by Longju Liu, Jie Yang, Mei Wu, Jinlu Liu, Wei Huang, Yang Li and Bingjie Xu
Entropy 2025, 27(1), 68; https://doi.org/10.3390/e27010068 - 14 Jan 2025
Viewed by 399
Abstract
Quantum Random Number Generators (QRNGs) have been theoretically proven to be able to generate completely unpredictable random sequences, and have important applications in many fields. However, the practical implementation of QRNG is always susceptible to the unwanted classical noise or device imperfections, which [...] Read more.
Quantum Random Number Generators (QRNGs) have been theoretically proven to be able to generate completely unpredictable random sequences, and have important applications in many fields. However, the practical implementation of QRNG is always susceptible to the unwanted classical noise or device imperfections, which inevitably diminishes the quality of the generated random bits. It is necessary to perform the post-processing to extract the true quantum randomness contained in raw data generated by the entropy source of QRNG. In this work, a novel post-processing method for QRNG based on Zero-phase Component Analysis (ZCA) whitening is proposed and experimentally verified through both time and spectral domain analysis, which can effectively reduce auto-correlations and flatten the spectrum of the raw data, and enhance the random number generation rate of QRNG. Furthermore, the randomness extraction is performed after ZCA whitening, after which the final random bits can pass the NIST test. Full article
(This article belongs to the Special Issue Network Information Theory and Its Applications)
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<p>The typical structure of a QRNG.</p>
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<p>The proposed post-processing scheme for QRNG.</p>
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<p>Data blocks when <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Experimental set up of ASE scheme to acquire the raw data. SLED: superluminescent light emitting diode; PD: photodetector; DSO: digital storage oscilloscope.</p>
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<p>Statistical histogram of raw data for the QRNG based on ASE noise.</p>
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<p>Auto-correlation coefficients before and after ZCA whitening.</p>
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<p>Power spectral density analysis before and after ZCA whitening.</p>
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<p>The results of the NIST-STS test.</p>
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<p>Auto-correlation coefficients of raw data2 and raw data3.</p>
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30 pages, 5973 KiB  
Article
Versatile LCL Inverter Model for Controlled Inverter Operation in Transient Grid Calculation Using the Extended Node Method
by Daniela Vorwerk and Detlef Schulz
Energies 2025, 18(2), 344; https://doi.org/10.3390/en18020344 - 14 Jan 2025
Viewed by 362
Abstract
Due to increasing decentralized power applications, power electronics are gaining importance, also in distribution grids. Since their scope of investigation is diverse, their versatile models and their use in grid calculations are important. In this work, a three-phase grid-synchronous inverter with an LCL [...] Read more.
Due to increasing decentralized power applications, power electronics are gaining importance, also in distribution grids. Since their scope of investigation is diverse, their versatile models and their use in grid calculations are important. In this work, a three-phase grid-synchronous inverter with an LCL filter is considered. It is defined as a component of the “Extended Node Method” to make it applicable in this node-based transient grid calculation method. Because the component stucture always looks the same and the construction of the grid system of equations always follows the same, straightforward process, the model can be applied easily and several times to large network calculations. Furthermore, an approach is developed for how inverter control algorithms are interconnected with the method’s results in the time domain. This allows for the fast analysis of converter control schemes in different grid topologies. To evaluate its accuracy, the developed approach is compared to equivalent calculations with Simulink and shows very good agreement, also for steep transients. In the long term, this model is intended to bridge the gap to other DC systems like electrochemical components and to gas and heating networks with the Extended Node Method. Full article
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<p>Two-level three-phase grid-tied inverter with LCL filter configuration.</p>
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<p>Single-phase electric circuit diagram of grid-tied inverter with LCL filter.</p>
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<p>Single-phase electric circuit diagram of grid-tied inverter with LCL filter and parallel damping conductance.</p>
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<p>Single-phase electric circuit diagram of grid-tied inverter with LCL filter and series damping resistor.</p>
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<p>Cascaded grid current control loop for inverter with basic LCL filter in dq frame.</p>
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<p>Synchronous reference frame phase-locked loop (PLL) for grid synchronization based on [<a href="#B49-energies-18-00344" class="html-bibr">49</a>].</p>
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<p>Combined grid calculation with the Extended Node Method and inverter control, basically taken from [<a href="#B36-energies-18-00344" class="html-bibr">36</a>] and expanded with the LCL inner states and the interface with the cascaded current controller.</p>
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<p>Bode plot of selected LCL filter design with exact values and <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>20</mn> </mrow> </semantics></math>% tolerance.</p>
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<p>Single-phase electric circuit diagram for single grid-connected inverter with LCL filter.</p>
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<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> with grid impedance <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>0.16</mn> </mrow> </semantics></math> mH and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>0.12</mn> <mspace width="0.166667em"/> <mo>Ω</mo> </mrow> </semantics></math>: (<b>a</b>) Inverter terminal current <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi>A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal current and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltage <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
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<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> with grid impedance <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>0.16</mn> </mrow> </semantics></math> mH and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>0.12</mn> <mspace width="0.166667em"/> <mo>Ω</mo> </mrow> </semantics></math>: (<b>a</b>) Inverter terminal current <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi>A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal current and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltage <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
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<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> with grid impedance <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> mH and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>1.51</mn> <mspace width="0.166667em"/> <mo>Ω</mo> </mrow> </semantics></math>: (<b>a</b>) Inverter terminal current <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal current and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltage <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
Full article ">Figure 12
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> with grid impedance <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math> mH and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>6.03</mn> <mspace width="0.166667em"/> <mo>Ω</mo> </mrow> </semantics></math>: (<b>a</b>) Inverter terminal current <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal current and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltage <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
Full article ">Figure 13
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> with grid impedance <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math> mH and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>6.03</mn> <mspace width="0.166667em"/> <mo>Ω</mo> </mrow> </semantics></math> for varying filter parameters with <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>L</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mi mathvariant="normal">f</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>ζ</mi> <msub> <mi>L</mi> <mrow> <mi mathvariant="normal">f</mi> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>L</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mi mathvariant="normal">f</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mi>ζ</mi> <msub> <mi>L</mi> <mrow> <mi mathvariant="normal">f</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>C</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mi>ζ</mi> <mi>C</mi> </mrow> </semantics></math>: (<b>a</b>) Inverter terminal current <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi mathvariant="normal">c</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal currents <math display="inline"><semantics> <msub> <mi>I</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>I</mi> <mi mathvariant="normal">q</mi> </msub> </semantics></math>. (<b>c</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
Full article ">Figure 14
<p>Grid topology of sample network ’Simbench rural’ with connected inverters at nodes 5 and 9.</p>
Full article ">Figure 15
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math> in the Simbench rural testgrid for study case 1. (<b>a</b>) Inverter terminal currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal currents and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltages <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
Full article ">Figure 15 Cont.
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math> in the Simbench rural testgrid for study case 1. (<b>a</b>) Inverter terminal currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal currents and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltages <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
Full article ">Figure 16
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math> in the Simbench rural testgrid for study case 1 (<b>a</b>) Inverter source currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi>sc</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter source currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">I</mi> <mrow> <mi>sc</mi> <mo>,</mo> <mi>dq</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>c</b>) Capacitor voltage reference <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">U</mi> <mrow> <mi mathvariant="normal">C</mi> <mo>,</mo> <mi>dq</mi> </mrow> <mo>*</mo> </msubsup> </mrow> </semantics></math> and actual voltage <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mrow> <mi mathvariant="normal">C</mi> <mo>,</mo> <mi>dq</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>d</b>) Inverter modulation signal <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">m</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 17
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math> in the Simbench rural testgrid for study case 2. (<b>a</b>) Inverter terminal currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter terminal currents and current references <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">I</mi> <mi>dq</mi> <mo>*</mo> </msubsup> </mrow> </semantics></math>. (<b>c</b>) PCC voltages <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">u</mi> <mi>abc</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>. (<b>d</b>) Grid active and reactive power references <math display="inline"><semantics> <msup> <mi>P</mi> <mo>*</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>Q</mi> <mo>*</mo> </msup> </semantics></math> and actual power <span class="html-italic">P</span> and <span class="html-italic">Q</span>.</p>
Full article ">Figure 18
<p>System responses to sudden changes in active and reactive inverter power references <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mn>2</mn> <mo>*</mo> </msubsup> </semantics></math> in the Simbench rural testgrid for study case 2. (<b>a</b>) Inverter source currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">i</mi> <mrow> <mi>sc</mi> <mo>,</mo> <mi>abc</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>b</b>) Inverter source currents <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">I</mi> <mrow> <mi>sc</mi> <mo>,</mo> <mi>dq</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>c</b>) Capacitor voltage reference <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="bold-italic">U</mi> <mrow> <mi mathvariant="normal">C</mi> <mo>,</mo> <mi>dq</mi> </mrow> <mo>*</mo> </msubsup> </mrow> </semantics></math> and actual voltage <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">U</mi> <mrow> <mi mathvariant="normal">C</mi> <mo>,</mo> <mi>dq</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>d</b>) Inverter modulation signal <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">m</mi> <mi>dq</mi> </msub> </mrow> </semantics></math>.</p>
Full article ">
21 pages, 985 KiB  
Study Protocol
A Protocol for AI-Powered Tools to Enhance Mobility and Function in Older Adults: An Evidence and Gap Map
by Mirella Veras, Jordi Pardo, Mê-Linh Lê, Cindy Jussup, José Carlos Tatmatsu-Rocha and Vivian Welch
J. Pers. Med. 2025, 15(1), 29; https://doi.org/10.3390/jpm15010029 - 14 Jan 2025
Viewed by 590
Abstract
Introduction: Artificial intelligence (AI) is transforming healthcare by enhancing diagnostic accuracy, treatment, and patient monitoring, benefiting older adults by offering personalized care plans. AI-powered tools help manage chronic conditions and maintain independence, making them a valuable asset in addressing aging challenges. Objectives [...] Read more.
Introduction: Artificial intelligence (AI) is transforming healthcare by enhancing diagnostic accuracy, treatment, and patient monitoring, benefiting older adults by offering personalized care plans. AI-powered tools help manage chronic conditions and maintain independence, making them a valuable asset in addressing aging challenges. Objectives: The objectives are as follows: 1. To identify and describe AI-power-based exercise programs for older adults. 2. To highlight primary evidence gaps in AI interventions for functional improvement and mobility. 3. To evaluate the quality of existing reviews on this topic. Methods: The evidence gap map (EGM) will follow the five-step method, adhering to the Campbell Collaboration guidelines and, if available at the time of reporting, PRISMA-AI standards. Guided by the Metaverse Equitable Rehabilitation Therapy framework, this study will categorize findings across domains like equity, health service integration, interoperability, governance, and humanization. The study will include systematic reviews, randomized controlled trials, and pre-and post-intervention designs. Results will be reported following PRISMA-AI guidelines. We will use AMSTAR-2 Checklist for Analyzing Systematic Reviews on AI Interventions for Improving mobility and function in Older Adults to evaluate the reliability of systematic reviews and focus on internal validity. Conclusions: This comprehensive analysis will act as a critical resource for guiding future research, refining clinical interventions, and influencing policy decisions to enhance AI-driven solutions for aging populations. The EGM aims to bridge existing evidence gaps, fostering a more informed, equitable, and effective approach to AI solutions for older adults. Full article
(This article belongs to the Special Issue Ehealth, Telemedicine, and AI in the Precision Medicine Era)
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Figure 1

Figure 1
<p>Evidence-gap-map 5-step method with AI Extension for AI-powered tools to enhance mobility and function in older adults.</p>
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<p>Metaverse Equitable Rehabilitation Therapy (MERTH) framework [<a href="#B21-jpm-15-00029" class="html-bibr">21</a>].</p>
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19 pages, 6477 KiB  
Article
Numerical Investigation and Experimental Verification of Vibration Behavior for a Beam with Cantilever-Hertzian Contact Boundary Conditions
by Yinnan Zhang, Chao Zhang, Yuan Meng and Wanbin Ren
Machines 2025, 13(1), 52; https://doi.org/10.3390/machines13010052 - 13 Jan 2025
Viewed by 280
Abstract
The simple spring structure, with detachable electrical contacts, is a very suitable solution for many applications, such as electromechanical relays and connectors. However, they are prone to exhibit instantaneous interruption faults under mechanical vibration environments. In this paper, the governing equations of the [...] Read more.
The simple spring structure, with detachable electrical contacts, is a very suitable solution for many applications, such as electromechanical relays and connectors. However, they are prone to exhibit instantaneous interruption faults under mechanical vibration environments. In this paper, the governing equations of the modal analysis of a beam with cantilever-Hertzian contact boundary conditions are presented. Then, the time domain analysis method and frequency domain analysis method for solving the forced vibration response are described explicitly. Next, the effect of the axial force on the modal frequency of a detailed model sourced from the practical relay is investigated by using commercial ANSYS Workbench 2021R1 software. Afterward, the harmonic response of the beam is numerically solved individually by using the transient analysis model and the harmonic analysis model in ANSYS Workbench 2021R1 software. Then, the influences of the damping coefficient and excited frequency on the contact force response are investigated. The experimental results of transient displacement and contact resistance of the beam structure agree well with the simulation outcomes. It is proven that there is a linear relationship between the stiffness coefficient and the mass coefficient, which are used for characterizing the damping of the structures in the time domain method and frequency domain methods. Full article
(This article belongs to the Section Machine Design and Theory)
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Figure 1

Figure 1
<p>Normally closed contact pairs within the typical electromechanical relay.</p>
Full article ">Figure 2
<p>Schematic of the flexible beam structure within the electromechanical relay. The set vertical offset causes a static beam deflection, <span class="html-italic">y</span>(<span class="html-italic">x</span>). The dynamic displacement, <span class="html-italic">y</span>(<span class="html-italic">x</span>,<span class="html-italic">t</span>), is defined relative to <span class="html-italic">y</span>(<span class="html-italic">x</span>). The contact between the two electrodes is assumed to be Hertzian contact.</p>
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<p>Flexible beam structure model.</p>
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<p>Modal shape of a beam with cantilever-Hertzian contact boundary conditions (<span class="html-italic">f</span> = 1354.5 Hz).</p>
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<p>Modal frequencies under combination conditions of different free end length and overtravel.</p>
Full article ">Figure 6
<p>Simulation results obtained by time domain analysis method (<span class="html-italic">f</span> = 1000 Hz, <span class="html-italic">β</span> = 3.1831 × 10<sup>−3</sup>).</p>
Full article ">Figure 7
<p>Variations in contact force amplitude as a function of excited frequency by using the time domain method.</p>
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<p>Deviation of the displacement amplitude obtained by the time domain method.</p>
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<p>Variations in contact force amplitude as a function of exciting vibration frequency by using the frequency domain simulation method.</p>
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<p>Contour map of contact surface measured by a laser confocal microscope.</p>
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<p>The relationship between contact resistance and contact force.</p>
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<p>Experiment system.</p>
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<p>Contact spring specimen.</p>
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<p>Displacement results (<span class="html-italic">f</span> = 1000 Hz). (Note: the distance between the displacement testing model and the measurement sample is 1.003 mm).</p>
Full article ">Figure 15
<p>Deviation of displacement amplitude.</p>
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<p>Experimental test contact resistance results (<span class="html-italic">f</span> = 1000 Hz). (<b>a</b>) 10 s contact resistance waveform. (<b>b</b>) Local contact resistance waveform within 10 ms.</p>
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<p>Deviation between time domain simulation results and experimental results. (<b>a</b>) Deviation of maximum value. (<b>b</b>) Deviation of minimum value.</p>
Full article ">Figure 18
<p>Deviation of maximum value between frequency domain simulation results and experimental results.</p>
Full article ">Figure 19
<p>The amplitude results of contact force obtained by time domain analysis method and frequency domain analysis method.</p>
Full article ">
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