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Search Results (622)

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14 pages, 4346 KiB  
Article
Robust Sparse Bayesian Learning Source Localization in an Uncertain Shallow-Water Waveguide
by Bing Zhang, Rui Jin, Longyu Jiang, Lei Yang and Tao Zhang
Electronics 2024, 13(23), 4789; https://doi.org/10.3390/electronics13234789 - 4 Dec 2024
Viewed by 374
Abstract
Conventional matched-field processing (MFP) for acoustic source localization is sensitive to environmental mismatches because it is based on the wave propagation model and environmental information that is uncertain in reality. In this paper, a mode-predictable sparse Bayesian learning (MPR-SBL) method is proposed to [...] Read more.
Conventional matched-field processing (MFP) for acoustic source localization is sensitive to environmental mismatches because it is based on the wave propagation model and environmental information that is uncertain in reality. In this paper, a mode-predictable sparse Bayesian learning (MPR-SBL) method is proposed to increase robustness in the presence of environmental uncertainty. The estimator maximizes the marginalized probability density function (PDF) of the received data at the sensors, utilizing the Bayesian rule and two hyperparameters (the source powers and the noise variance). The replica vectors in the estimator are reconstructed with the predictable modes from the decomposition of the pressure in the representation of the acoustic normal mode. The performance of this approach is evaluated and compared with the Bartlett processor and original sparse Bayesian learning, both in simulation and using the SWellEx-96 Event S5 dataset. The results illustrate that the proposed MPR-SBL method exhibits better performance in the two-source scenario, especially for the weaker source. Full article
(This article belongs to the Special Issue Research on Cooperative Control of Multi-agent Unmanned Systems)
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Figure 1

Figure 1
<p>Two range-independent acoustic models of shallow-water waveguide in simulations: (<b>a</b>) A conventional mismatch scene (genlmis), which is divided into three layers from top to bottom: water layer, sediment layer, and half space; (<b>b</b>) SWellEx-96 acoustic model of shallow sea waveguide, which is divided into four layers from top to bottom: water layer, sediment layer, mudstone layer, and half space. The gray part of the first layer indicates the range of sound velocity.</p>
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<p>Accuracy (PCL) as a function of the SNR, evaluated for 4 different models (the four markers and colors in the figure), on 2 different scenarios: (<b>a</b>) the gelmis mismatch; (<b>b</b>) the SWellEx-96 mismatch.</p>
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<p>Root mean square errors (RMSE) as a function of the SNR, evaluating the error variation trend of weak source in depth and range for 4 different models (the four markers and colors in the figure) under the scenario of a genlmis mismatch: (<b>a</b>) the range; (<b>b</b>) the depth.</p>
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<p>Root mean square errors (RMSE) as a function of the SNR, evaluating the error variation trend of weak source in depth and range for 4 different models (the four markers and colors in the figure) under the scenario of a SWellEx-96 mismatch: (<b>a</b>) the range; (<b>b</b>) the depth.</p>
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<p>Localization results of 4 different models on the SWellEx-96 dataset for two sources: (<b>a</b>) MPR-Bartlett; (<b>b</b>) MPR-SBL; (<b>c</b>) Bartlett; (<b>d</b>) SBL.</p>
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30 pages, 15218 KiB  
Article
Robust Nonlinear Model Predictive Control for the Trajectory Tracking of Skid-Steer Mobile Manipulators with Wheel–Ground Interactions
by Katherine Aro, Leonardo Guevara, Miguel Torres-Torriti, Felipe Torres and Alvaro Prado
Robotics 2024, 13(12), 171; https://doi.org/10.3390/robotics13120171 - 3 Dec 2024
Viewed by 567
Abstract
This paper presents a robust control strategy for trajectory-tracking control of Skid-Steer Mobile Manipulators (SSMMs) using a Robust Nonlinear Model Predictive Control (R-NMPC) approach that minimises trajectory-tracking errors while overcoming model uncertainties and terra-mechanical disturbances. The proposed strategy is aimed at counteracting the [...] Read more.
This paper presents a robust control strategy for trajectory-tracking control of Skid-Steer Mobile Manipulators (SSMMs) using a Robust Nonlinear Model Predictive Control (R-NMPC) approach that minimises trajectory-tracking errors while overcoming model uncertainties and terra-mechanical disturbances. The proposed strategy is aimed at counteracting the effects of disturbances caused by the slip phenomena through the wheel–terrain contact and bidirectional interactions propagated by mechanical coupling between the SSMM base and arm. These interactions are modelled using a coupled nonlinear dynamic framework that integrates bounded uncertainties for the mobile base and arm joints. The model is developed based on principles of full-body energy balance and link torques. Then, a centralized control architecture integrates a nominal NMPC (disturbance-free) and ancillary controller based on Active Disturbance-Rejection Control (ADRC) to strengthen control robustness, operating the full system dynamics as a single robotic body. While the NMPC strategy is responsible for the trajectory-tracking control task, the ADRC leverages an Extended State Observer (ESO) to quantify the impact of external disturbances. Then, the ADRC is devoted to compensating for external disturbances and uncertainties stemming from the model mismatch between the nominal representation and the actual system response. Simulation and field experiments conducted on an assembled Pioneer 3P-AT base and Katana 6M180 robotic arm under terrain constraints demonstrate the effectiveness of the proposed method. Compared to non-robust controllers, the R-NMPC approach significantly reduced trajectory-tracking errors by 79.5% for mobile bases and 42.3% for robot arms. These results highlight the potential to enhance robust performance and resource efficiency in complex navigation conditions. Full article
(This article belongs to the Section Sensors and Control in Robotics)
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<p>Skid-Steer Mobile Manipulator (SSMM) model: The left figure depicts the local coordinate systems and Denavit–Hartenberg (DH) parameters for the SSMM, while the right image shows the physical robot used in this study.</p>
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<p>Scheme of the proposed Robust Nonlinear Model Predictive Control (R-NMPC) strategy.</p>
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<p>Characterization of disturbances used in tests using circular-type reference trajectory.</p>
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<p>Results of performance indexes. Tracking tests for circular trajectory considering linear and angular speed disturbances in the mobile base. The indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>b</mi> </msub> <mo>,</mo> <mi>C</mi> <msub> <mi>u</mi> <mi>b</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>b</mi> </msub> </mrow> </semantics></math> correspond to the mobile base and the indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>a</mi> </msub> <mo>,</mo> <mi>C</mi> <msub> <mi>u</mi> <mi>a</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>a</mi> </msub> </mrow> </semantics></math> correspond to the robotic arm of the SSMM.</p>
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<p>Tracking tests were also considered on a circular trajectory, profiling linear and angular speed disturbances on the mobile base and the robotic arm motion. The first top row from left to right depicts the results of tracking a reference trajectory for the mobile base and robot arm. In the next two figures are shown the tracking error in the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>, and the control effort on the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>. The orange point and arrow stands for initial position and orientation of the mobile base. The second row from left to right shows the tracking error in the x-coordinate of the mobile base, the control effort for the linear displacement of the mobile base, the tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>, the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>. The third row from left to right presents the tracking error in the y-coordinate of the mobile base, the control effort for the angular displacement of the mobile base, tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>.</p>
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<p>Disturbances used while testing the Lemniscata-type trajectory.</p>
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<p>Tracking tests on a Lemniscata trajectory considering linear and angular speed disturbances on the mobile base and the influence of the robotic arm motion. The first top row from left to right consists of the trajectory of the mobile base, the trajectory of the robotic arm, the tracking error in the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>. The orange point and arrow stands for initial position and orientation of the mobile base. The second row from left to right has the tracking error in the x-coordinate of the mobile base, the control effort for the linear displacement of the mobile base, the tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>. The third row from left to right consists of the tracking error in the y-coordinate of the mobile base, the control effort for the angular displacement of the mobile base, tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>.</p>
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<p>Performance index: Tracking tests for Lemniscata trajectory considering linear and angular speed disturbances in the mobile base. The indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>b</mi> </msub> <mo>,</mo> <mi>C</mi> <msub> <mi>u</mi> <mi>b</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>b</mi> </msub> </mrow> </semantics></math> correspond to the mobile base and the indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>a</mi> </msub> <mo>,</mo> <mi>C</mi> <msub> <mi>u</mi> <mi>a</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>a</mi> </msub> </mrow> </semantics></math> correspond to the robotic arm of the SSMM.</p>
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<p>Robustness tests on a circular trajectory considering linear and angular speed disturbances on the mobile base, the influence of the robotic arm motion, and parameter variation. The first top row from left to right consists of the trajectory of the mobile base, the trajectory of the robotic arm, the tracking error in the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>, and the control effort in the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>. The orange point and arrow stands for initial position and orientation of the mobile base. The second row from left to right has the tracking error in the x-coordinate of the mobile base, the control effort for the linear displacement of the mobile base, the tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>. The third row from left to right consists of the tracking error in the y-coordinate of the mobile base, the control effort for the angular displacement of the mobile base, tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>.</p>
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<p>Performance index: Robustness tests for circular trajectory considering linear and angular speed disturbances and parameter variations in the mobile base. The indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>b</mi> </msub> <mo>,</mo> <mi>C</mi> <msub> <mi>u</mi> <mi>b</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>b</mi> </msub> </mrow> </semantics></math> correspond to the mobile base and the indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>a</mi> </msub> <mo>,</mo> <mi>C</mi> <msub> <mi>u</mi> <mi>a</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>a</mi> </msub> </mrow> </semantics></math> correspond to the robotic arm of the SSMM.</p>
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<p>Robustness tests on a Lemniscata trajectory considering linear and angular speed disturbances on the mobile base, the influence of the robotic arm motion, and parameter variation. The first top row from left to right consists of the trajectory of the mobile base, the trajectory of the robotic arm, the tracking error in the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>, and the control effort in the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>1</mn> </msub> </semantics></math>. The orange point and arrow stands for initial position and orientation of the mobile base. The second row from left to right has the tracking error in the x-coordinate of the mobile base, the control effort for the linear displacement of the mobile base, the tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>2</mn> </msub> </semantics></math>. The third row from left to right consists of the tracking error in the y-coordinate of the mobile base, the control effort for the angular displacement of the mobile base, tracking error of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>, and the control effort of the joint coordinate <math display="inline"><semantics> <msub> <mi>θ</mi> <mn>3</mn> </msub> </semantics></math>.</p>
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<p>Performance index to assess robustness while tracking the Lemniscata trajectory, considering linear and angular speed disturbances and parameter variations in the mobile base. The indices <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>b</mi> </msub> <mo>,</mo> <mspace width="4pt"/> <mi>C</mi> <msub> <mi>u</mi> <mi>b</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mspace width="4pt"/> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>b</mi> </msub> </mrow> </semantics></math> are associated with the mobile base, whereas <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>ζ</mi> <mi>a</mi> </msub> <mo>,</mo> <mspace width="4pt"/> <mi>C</mi> <msub> <mi>u</mi> <mi>a</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mspace width="4pt"/> <mi>C</mi> <mi>t</mi> <mi>o</mi> <msub> <mi>t</mi> <mi>a</mi> </msub> </mrow> </semantics></math> are associated with the arm of the SSMM.</p>
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<p>Snapshots of the SSMM during field experiments. From left to right: the Pioneer 3P-AT mobile base is mechanically coupled with a Katana 6M180 robotic arm. The middle and right images show the experimental field setup used for tracking and regulation trials with the three test controllers.</p>
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<p>Field results for the three test controllers (PID, NMPC, and R-NMPC). The top right figures show the lonitudinal and lateral trajectory-tracking errors for the mobile base, whereas the bottom right plot presents the height tracking errors for the robotic arm. The gray dashed lines indicate when the height of the reference trajectory has changed.</p>
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<p>Field results for three test controllers tracking a curved reference trajectory on terrain unevenness acting as disturbance (gray shaded area). The top right figures show the trajectory-tracking errors for the mobile base, while the bottom right figure presents the tracking errors for the robotic arm.</p>
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30 pages, 2746 KiB  
Article
Optimizing Microgrid Performance: Integrating Unscented Transformation and Enhanced Cheetah Optimization for Renewable Energy Management
by Ali S. Alghamdi
Electronics 2024, 13(22), 4563; https://doi.org/10.3390/electronics13224563 - 20 Nov 2024
Viewed by 438
Abstract
The increased integration of renewable energy sources (RESs), such as photovoltaic and wind turbine systems, in microgrids poses significant challenges due to fluctuating weather conditions and load demands. To address these challenges, this study introduces an innovative approach that combines Unscented Transformation (UT) [...] Read more.
The increased integration of renewable energy sources (RESs), such as photovoltaic and wind turbine systems, in microgrids poses significant challenges due to fluctuating weather conditions and load demands. To address these challenges, this study introduces an innovative approach that combines Unscented Transformation (UT) with the Enhanced Cheetah Optimization Algorithm (ECOA) for optimal microgrid management. UT, a robust statistical technique, models nonlinear uncertainties effectively by leveraging sigma points, facilitating accurate decision-making despite variable renewable generation and load conditions. The ECOA, inspired by the adaptive hunting behaviors of cheetahs, is enhanced with stochastic leaps, adaptive chase mechanisms, and cooperative strategies to prevent premature convergence, enabling improved exploration and optimization for unbalanced three-phase distribution networks. This integrated UT-ECOA approach enables simultaneous optimization of continuous and discrete decision variables in the microgrid, efficiently handling uncertainty within RESs and load demands. Results demonstrate that the proposed model significantly improves microgrid performance, achieving a 10% reduction in voltage deviation, a 10.63% decrease in power losses, and an 83.32% reduction in operational costs, especially when demand response (DR) is implemented. These findings validate the model’s efficacy in enhancing microgrid reliability and efficiency, positioning it as a viable solution for optimized performance under uncertain renewable inputs. Full article
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<p>Flowchart of the proposed UT-based ECOA for optimal solving of EM problems.</p>
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<p>The mean values of (<b>a</b>) wind speed, (<b>b</b>) solar irradiance, and (<b>c</b>) load demand.</p>
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<p>Microgrid’s Optimal generation scheduling.</p>
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<p>DR’s effect on the hourly load curve.</p>
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<p>Optimal results of the PV’s power generation, bus, and phase locations.</p>
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<p>Optimal results of the grid’s power generation, bus, and phase locations.</p>
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<p>Optimal results of the WT’s power generation, bus, and phase locations.</p>
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<p>Optimal results of the DG’s power generation, bus, and phase locations.</p>
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<p>Optimal results of the MT’s power generation, bus, and phase locations.</p>
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<p>Optimal results of the BESS’s power generation, bus, and phase locations.</p>
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<p>Voltage deviations before and after the proposed optimization EM model.</p>
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<p>Microgrid losses before and after the proposed optimization EM model.</p>
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<p>Convergence curves of the comparative algorithms in solving the problem.</p>
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9 pages, 537 KiB  
Article
Estimation of the Real Incidence of a Contagious Disease Through a Bayesian Multilevel Model: Study of COVID-19 in Spanish Provinces
by David Hervás and Patricia Carracedo
Healthcare 2024, 12(22), 2308; https://doi.org/10.3390/healthcare12222308 - 19 Nov 2024
Viewed by 570
Abstract
Background: Pandemic outbreaks have emerged as a significant global threat, with the potential to cause waves of infections that challenge public health systems and disrupt societal norms. Understanding the underlying behavior of disease transmission can be of great use in the design of [...] Read more.
Background: Pandemic outbreaks have emerged as a significant global threat, with the potential to cause waves of infections that challenge public health systems and disrupt societal norms. Understanding the underlying behavior of disease transmission can be of great use in the design of informed and timely public health policies. It is very common for many contagious diseases not to have actual incidence but rather incidence in a given subgroup. For example, in Spain, as of 28 March 2022, the incidence of COVID-19 in people under 60 years of age is not registered. Methods: This work provides a Bayesian methodology to model the incidence of any infectious disease in the general population when its cases are only registered in a specific subgroup of that population. The case study used was the coronavirus disease (COVID-19), with data for 52 Spanish provinces during the period of 1 January 2020 to 29 August 2022. Results: Explicitly, two multilevel models were proposed, one for people over or of 60 years of age and the other for people under 60 years of age. Performance of the models was 5.9% and 12.7% MAPE, respectively. Conclusions: Despite the limitations of the data and the complexity and uncertainty in the propagation of COVID-19, the models were able to fit the data well and predict incidence with very low MAPE. Full article
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<p>Accumulated number of COVID-19 cases by Spanish province.</p>
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<p>Prediction of the number of cases per 100,000 for people over or of 60 years of age.</p>
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<p>Prediction of the ratio by province.</p>
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23 pages, 2713 KiB  
Article
Incorporating Forest Mapping-Related Uncertainty into the Error Propagation of Wall-to-Wall Biomass Maps: A General Approach for Large and Small Areas
by Hassan C. David, Alexander C. Vibrans, Rorai P. Martins-Neto, Ana Paula Dalla Corte and Sylvio Péllico Netto
Remote Sens. 2024, 16(22), 4295; https://doi.org/10.3390/rs16224295 - 18 Nov 2024
Viewed by 662
Abstract
The sources of uncertainty in wall-to-wall AGB maps propagate from the tree to pixel, but uncertainty due to forest cover mapping is rarely incorporated into the error propagation process. This study aimed to (1) elaborate an analytical procedure to incorporate forest-mapping-related uncertainty into [...] Read more.
The sources of uncertainty in wall-to-wall AGB maps propagate from the tree to pixel, but uncertainty due to forest cover mapping is rarely incorporated into the error propagation process. This study aimed to (1) elaborate an analytical procedure to incorporate forest-mapping-related uncertainty into the error propagation from plot and pixel predictions; (2) develop a stratified estimator with a model-assisted estimator for small and large areas; and (3) estimate the effect of ignoring the mapping uncertainty on the confidence intervals (CIs) for totals. Data consist of a subset of the Brazilian national forest inventory (NFI) database, comprising 75 counties that, once aggregated, served as strata for the stratified estimator. On-ground data were gathered from 152 clusters (plots) and remotely sensed data from Landsat-8 scenes. Four major contributions are highlighted. First, we describe how to incorporate forest-mapping-related uncertainty into the CIs of any forest attribute and spatial resolution. Second, stratified estimators perform better than non-stratified estimators for forest area estimation when the response variable is forest/non-forest. Comparing our stratified estimators, this study indicated greater precision for the stratified estimator than for the regression estimator. Third, using the ratio estimator, we found evidence that the simple field plot information provided by the NFI clusters is sufficient to estimate the proportion forest for large regions as accurately as remote-sensing-based methods, albeit with less precision. Fourth, ignoring forest-mapping-related uncertainty erroneously narrows the CI width as the estimate of proportion forest area decreases. At the small-area level, forest-mapping-related uncertainty led to CIs for total AGB as much as 63% wider in extreme cases. At the large-area level, the CI was 5–7% wider. Full article
(This article belongs to the Special Issue Remote Sensing of Carbon Fluxes and Stocks II)
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Graphical abstract

Graphical abstract
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<p>Distribution of clusters within the study area following the NFI regular 20 km <span class="html-italic">×</span> 20 km grid. Black lines represent county boundaries.</p>
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<p>Analytical procedure for propagating errors in forest AGB mapping.</p>
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<p>Illustration of the NFI cluster overlapping a 30 m spatial resolution satellite image.</p>
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<p>Relationship between predicted vs. observed plot AGB. Blackline is the 1:1 relation. Data are from the validation dataset (15% from the total).</p>
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<p>Spatial distribution of forest AGB in Mg ha<sup>−1</sup> stocked in the study area and counties. Numbers 1–10 rank the 10 most biomass-stocked counties.</p>
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<p>Differences while estimating confidence intervals for AGB (in Mg) with and without adding the forest-mapping-related uncertainty. Markers represent the 75 counties (small areas).</p>
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12 pages, 1743 KiB  
Article
Standard Cell Sizing for Worst-Case Performance Optimization Considering Process Variation in Subthreshold Region
by Peng Cao and Jingjing Guo
Electronics 2024, 13(22), 4477; https://doi.org/10.3390/electronics13224477 - 14 Nov 2024
Viewed by 430
Abstract
Ultra-low-voltage design brings considerable outcomes in power reduction and energy efficiency improvement at the cost of performance degradation and uncertainty. Conventional standard cell design methodology cannot guarantee optimal performance for subthreshold operations due to the lack of consideration of process variation. In this [...] Read more.
Ultra-low-voltage design brings considerable outcomes in power reduction and energy efficiency improvement at the cost of performance degradation and uncertainty. Conventional standard cell design methodology cannot guarantee optimal performance for subthreshold operations due to the lack of consideration of process variation. In this paper, an effective subthreshold cell sizing method is proposed to minimize the worst-case propagation delay by deriving the optimal pMOS-to-nMOS width ratio (β) analytically, which reveals the relation between the minimal worst-case delay and the process parameters and provides distinct guidance for standard cell library design. The proposed method demonstrated good agreement with the Monte Carlo SPICE simulation results and was validated at the cell level and the circuit level. At the cell level, the logic cells designed with the proposed method show at least 8.6% and 7.4% improvement, on average, for worst-case delay and energy-delay product (EDP), respectively, with an additional 3.2% energy overhead compared to the prior approaches. At the circuit level, the proposed method improves the worst-case performance and worst-case EDP of the ring oscillator by at least 15.5% and 15.0%, respectively, with a 0.9% energy penalty. Moreover, the ISCAS’89 and OpenCores circuits synthesized with the optimized cells achieve at least 6.6% worst-case performance enhancement, 6.9% power reduction, and 9.4% area saving. Full article
(This article belongs to the Section Microelectronics)
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<p>SPICE simulation results of the nominal and worst-case propagation delay for inverter under TSMC 28 nm (<b>a</b>) super-threshold region (1.1 V) and (<b>b</b>) subthreshold region (0.35 V).</p>
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<p>Inverter driving an identical inverter.</p>
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<p>Derivation of the signs of <span class="html-italic">S<sub>μ</sub></span> and <span class="html-italic">S<sub>σ</sub></span> by the relation of <span class="html-italic">h<sub>σ</sub></span>(<span class="html-italic">β</span>) and <span class="html-italic">g<sub>σ</sub></span>(<span class="html-italic">β</span>).</p>
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26 pages, 7065 KiB  
Article
From Envelope Spectra to Bearing Remaining Useful Life: An Intelligent Vibration-Based Prediction Model with Quantified Uncertainty
by Haobin Wen, Long Zhang and Jyoti K. Sinha
Sensors 2024, 24(22), 7257; https://doi.org/10.3390/s24227257 - 13 Nov 2024
Viewed by 663
Abstract
Bearings are pivotal components of rotating machines where any defects could propagate and trigger systematic failures. Once faults are detected, accurately predicting remaining useful life (RUL) is essential for optimizing predictive maintenance. Although data-driven methods demonstrate promising performance in direct RUL prediction, their [...] Read more.
Bearings are pivotal components of rotating machines where any defects could propagate and trigger systematic failures. Once faults are detected, accurately predicting remaining useful life (RUL) is essential for optimizing predictive maintenance. Although data-driven methods demonstrate promising performance in direct RUL prediction, their robustness and practicability need further improvement regarding physical interpretation and uncertainty quantification. This work leverages variational neural networks to model bearing degradation behind envelope spectra. A convolutional variational autoencoder for regression (CVAER) is developed to probabilistically predict RUL distributions with confidence measures. Enhanced average envelope spectra (AES) are used as network input for its physical robustness in bearing condition assessment and fault detection. The use of the envelope spectrum ensures that it contains only bearing-related information by removing other rotor-related frequencies, hence it improves the RUL prediction. Unlike traditional variational autoencoders, the probabilistic regressor and latent generator are formulated to quantify uncertainty in RUL estimates and learn meaningful latent representations conditioned on specific RUL. Experimental validations are conducted on vibration data collected using multiple accelerometers whose natural frequencies cover bearing resonance ranges to ensure fault detection reliability. Beyond conventional bearing diagnosis, envelope spectra are extended for statistical RUL prediction integrating physical knowledge of actual defect conditions. Comparative and ablation studies are conducted against benchmark models to demonstrate their effectiveness. Full article
(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)
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<p>The architecture of AE and VAE networks.</p>
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<p>Schematic diagram of the probabilistic CVAER model for RUL prediction.</p>
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<p>Network architecture of the CVAER.</p>
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<p>The schematic diagram of the bearing test rig for run-to-failure experiments.</p>
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<p>Raw vibration acceleration signals of Bearing 1–3.</p>
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<p>The AES around fault detection time. (<b>a</b>–<b>d</b>): Horizontal AES of Bearing 1–3 from the 58th to 61st minute. The outer-race fault components, BPFO and its harmonics, are observed from the 59th minute, indicating the initiation of the outer-race fault.</p>
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<p>The AES around fault detection time. (<b>a</b>–<b>d</b>): Horizontal AES of Bearing 1–3 from the 58th to 61st minute. The outer-race fault components, BPFO and its harmonics, are observed from the 59th minute, indicating the initiation of the outer-race fault.</p>
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<p>The horizontal AES contours with respect to machine operation time for (<b>a</b>) Bearing 1–3 and (<b>b</b>) Bearing 3–1. The onsets of the BPFO components are, respectively, identified as the 59th minute and the 2386th minute, as indicated by the red solid lines.</p>
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<p>The generation of the RUL targets of ground truth (illustrated via Bearing 1–3).</p>
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<p>RUL prediction results based on CVAER at the bearing degradation stage for (<b>a</b>) Bearing 1–1, (<b>b</b>) Bearing 1–3, (<b>c</b>) Bearing 2–2, (<b>d</b>) Bearing 2–5, (<b>e</b>) Bearing 3–4, and (<b>f</b>) Bearing 3–5. The mean predicted RULs for the test bearings are shown in blue solid lines with the standard deviation (STD). The error bar plots present the prediction error between the mean prediction and the RUL of ground truth (in red solid line).</p>
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<p>RUL prediction results based on CVAER at the bearing degradation stage for (<b>a</b>) Bearing 1–1, (<b>b</b>) Bearing 1–3, (<b>c</b>) Bearing 2–2, (<b>d</b>) Bearing 2–5, (<b>e</b>) Bearing 3–4, and (<b>f</b>) Bearing 3–5. The mean predicted RULs for the test bearings are shown in blue solid lines with the standard deviation (STD). The error bar plots present the prediction error between the mean prediction and the RUL of ground truth (in red solid line).</p>
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<p>The 2D embedding based on t–SNE using the envelope spectra of the test bearings under Condition 1. The projection of (<b>a</b>) the AES from the horizontal channel into a 2D plane, and (<b>b</b>) the AES from the vertical channel into a 2D plane. (<b>c</b>) The projection of the latent representations learned by the CVAER using the network parameters from Group 3.</p>
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<p>RUL prediction results of CVAER with comparisons against other benchmark models. (<b>a</b>) Bearing 1–1, (<b>b</b>) Bearing 1–3, (<b>c</b>) Bearing 2–2, (<b>d</b>) Bearing 2–5, (<b>e</b>) Bearing 3–4, and (<b>f</b>) Bearing 3–5.</p>
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<p>RUL prediction results of CVAER with comparisons against other benchmark models. (<b>a</b>) Bearing 1–1, (<b>b</b>) Bearing 1–3, (<b>c</b>) Bearing 2–2, (<b>d</b>) Bearing 2–5, (<b>e</b>) Bearing 3–4, and (<b>f</b>) Bearing 3–5.</p>
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17 pages, 20240 KiB  
Article
Foundational Aspects for Incorporating Dependencies in Copula-Based Bayesian Networks Using Structured Expert Judgments, Exemplified by the Ice Sheet–Sea Level Rise Elicitation
by Dorota Kurowicka, Willy Aspinall and Roger Cooke
Entropy 2024, 26(11), 949; https://doi.org/10.3390/e26110949 - 5 Nov 2024
Viewed by 692
Abstract
The work presented here marks a further advance in expert uncertainty quantification. In a recent probabilistic evaluation of ice sheet process contributions to sea level rise, tail dependence was elicited and propagated through an uncertainty analysis for the first time. The elicited correlations [...] Read more.
The work presented here marks a further advance in expert uncertainty quantification. In a recent probabilistic evaluation of ice sheet process contributions to sea level rise, tail dependence was elicited and propagated through an uncertainty analysis for the first time. The elicited correlations and tail dependencies concerned pairings of three processes: Accumulation, Discharge and Run-off, which operate on major ice sheets in the West and East Antarctic and in Greenland. The elicitation enumerated dependencies between these processes under selected global temperature change scenarios over different future time horizons. These expert judgments allowed us to populate a Paired Copula Bayesian network model to obtain the estimated contributions of these ice sheets for future sea level rise. Including positive central tendency dependence and tail dependence increases the fatness of the upper tails of projected sea level rise distributions, an amplification important for designing and evaluating possible mitigation strategies. Detailing and jointly computing distributional dependencies and tail dependencies can be crucial components of good practice for assessing the influence of uncertainties on extreme values when modelling stochastic multifactorial processes. Full article
(This article belongs to the Special Issue Bayesian Network Modelling in Data Sparse Environments)
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<p>DAG with 4 nodes.</p>
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<p>Gaussian and Gumbel copula densities both with correlation 0.7.</p>
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<p>Cdf plots of marginal distributions of sea level contributions of West Antarctica due to Discharge assessed by experts 3, 6, 8, 9, 12, 14, 24 and 27, and the performance-based combination PWWD. The latter black dashed line is mainly hidden in the central region of the various expert Cdfs.</p>
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<p>Graph of bivariate relationships assessed by experts.</p>
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<p>PCBN models of all experts with non-zero weights. Types of copulas and conditional copulas (in red) and values of copula parameters are assigned to arks of each graph.</p>
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<p>PCBN models of all experts with non-zero weights. Types of copulas and conditional copulas (in red) and values of copula parameters are assigned to arks of each graph.</p>
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<p>Violin plots of sea level rise distributions obtained with performance-based weights combination with dependence (DepSLR—green) and without (IndSLR—yellow).</p>
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<p>Bar plots of exceedance probabilities for SLR with (green) and without (yellow) dependence.</p>
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<p>Scatter plot matrix of E, G, W and SLR.</p>
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<p>Scatter plot of G and SLR for experts 3 and 14.</p>
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<p>Effect of eliciting dependence and tail dependence of 8 weighted experts. Bars represent 5%, 50% and 95% of SLR distributions of the experts combined with equal (EW) and performance-based (PW) weights in the case of independence (I), Gaussian copulas corresponding to 50% ExcProb assessed by experts (NTD) and with copulas with tail dependence (TD), as discussed in the paper. Experts 3 and 14 with weights 0.28 and 0.3, respectively, are the most important experts.</p>
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<p>Effect of adding eliciting dependence and tail dependence on EW and PW DMs. Bars represent 5%, 50% and 95% of SLR distributions combined with equal (EW) and performance-based (PW) weights in case of independence (I), Gaussian copulas corresponding to 50% ExcProb assessed by experts (NTD) and with copulas with tail dependence (TD), as discussed in the paper.</p>
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20 pages, 899 KiB  
Article
A Koopman Reachability Approach for Uncertainty Analysis in Ground Vehicle Systems
by Alok Kumar, Bhagyashree Umathe and Atul Kelkar
Machines 2024, 12(11), 753; https://doi.org/10.3390/machines12110753 - 24 Oct 2024
Viewed by 2317
Abstract
Recent progress in autonomous vehicle technology has led to the development of accurate and efficient tools for ensuring safety, which is crucial for verifying the reliability and security of vehicles. These vehicles operate under diverse conditions, necessitating the analysis of varying initial conditions [...] Read more.
Recent progress in autonomous vehicle technology has led to the development of accurate and efficient tools for ensuring safety, which is crucial for verifying the reliability and security of vehicles. These vehicles operate under diverse conditions, necessitating the analysis of varying initial conditions and parameter values. Ensuring the safe operation of the vehicle under all these varying conditions is essential. Reachability analysis is an important tool to certify the safety and stability of the vehicle dynamics. We propose a reachability analysis approach for evaluating the response of the vehicle dynamics, specifically addressing uncertainties in the initial states and model parameters. Reachable sets illustrate all the possible states of a dynamical system that can be obtained from a given set of uncertain initial conditions. The analysis is crucial for understanding how variations in initial conditions or system parameters can lead to outcomes such as vehicle collisions or deviations from desired paths. By mapping out these reachable states, it is possible to design systems that maintain safety and reliability despite uncertainties. These insights help to ensure the stability and reliability of the vehicles, even in unpredictable conditions, by reducing accidents and optimizing performance. The nonlinearity of the model complicates the computation of reachable sets in vehicle dynamics. This paper proposes a Koopman theory-based approach that utilizes the Koopman principal eigenfunctions and the Koopman spectrum. By leveraging the Koopman principal eigenfunction, our method simplifies the computational process and offers a formal approximation for backward and forward reachable sets. First, our method effectively computes backward and forward reachable sets for a nonlinear quarter-car model with fixed parameter values. Furthermore, we applied our approach to analyze the uncertainty response for cases with uncertain parameters of the vehicle model. When compared to time-domain simulations, our proposed Koopman approach provided accurate results and also reduced the computational time by half in most cases. This demonstrates the efficiency and reliability of our proposed approach in dynamic systems uncertainty analysis using the reachable sets. Full article
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<p>Nonlinear quarter-car dynamic model.</p>
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<p>Flowchart for the complete process of our proposed Koopman approach for uncertainty analysis.</p>
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<p>Diagram for (<b>a</b>) forward reachable set starting from an initial set, (<b>b</b>) backward reachable set for the given target set.</p>
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<p>Forward reachable sets obtained using the proposed Koopman approach at different times (shown in different colors) for the chassis displacement <math display="inline"><semantics> <msub> <mi>x</mi> <mn>1</mn> </msub> </semantics></math> and chassis velocity <math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math>. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Forward reachable sets obtained using the proposed Koopman approach at different times (shown in different colors) for the wheel displacement <math display="inline"><semantics> <msub> <mi>x</mi> <mn>3</mn> </msub> </semantics></math> and wheel velocity <math display="inline"><semantics> <msub> <mi>x</mi> <mn>4</mn> </msub> </semantics></math>. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets obtained using the proposed Koopman approach at different times (shown in different colors) at different times for the chassis displacement <math display="inline"><semantics> <msub> <mi>x</mi> <mn>1</mn> </msub> </semantics></math> and chassis velocity <math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math>. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets obtained using the proposed Koopman approach at different times (shown in different colors) at different times for the wheel displacement <math display="inline"><semantics> <msub> <mi>x</mi> <mn>3</mn> </msub> </semantics></math> and wheel velocity <math display="inline"><semantics> <msub> <mi>x</mi> <mn>4</mn> </msub> </semantics></math>. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Forward reachable sets at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for varying suspension spring coefficient. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for varying suspension spring coefficient. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Forward reachable sets at a given fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for varying suspension damping coefficient. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> showing the impact of varying suspension damping coefficient. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Forward reachable sets at a given time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for varying wheel mass. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for varying wheel mass. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Forward reachable sets at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity (<math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math>) for varying chassis mass. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets shown at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for the case of varying chassis mass. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Forward reachable sets shown at a fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity (<math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math>) for varying tire spring coefficient. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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<p>Backward reachable sets at a given fixed time for the chassis displacement <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics></math> and chassis velocity <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> for varying tire spring coefficient. The gray tube shows the trajectories obtained from the time-domain simulation with some of the trajectories shown in cyan color.</p>
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27 pages, 1734 KiB  
Article
Model-Centric Integration of Uncertain Expert Knowledge into Importance Sampling-Based Parameter Estimation
by Éva Kenyeres and János Abonyi
Appl. Sci. 2024, 14(21), 9652; https://doi.org/10.3390/app14219652 - 22 Oct 2024
Viewed by 571
Abstract
This study presents a model-based parameter estimation method for integrating and validating uncertainty in expert knowledge and simulation models. The parameters of the models of complex systems are often unknown due to a lack of measurement data. The experience-based knowledge of experts can [...] Read more.
This study presents a model-based parameter estimation method for integrating and validating uncertainty in expert knowledge and simulation models. The parameters of the models of complex systems are often unknown due to a lack of measurement data. The experience-based knowledge of experts can substitute missing information, which is usually imprecise. The novelty of the present paper is a method based on Monte Carlo (MC) simulation and importance sampling (IS) techniques for integrating uncertain expert knowledge into the system model. Uncertain knowledge about the model parameters is propagated through the system model by MC simulation in the form of a discrete sample, while IS helps to weight the sample elements regarding imprecise knowledge about the outputs in an iterative circle. Thereby, the consistency of expert judgments can be investigated as well. The contributions of this paper include an expert knowledge-based parameter estimation technique and a method for the evaluation of expert judgments according to the estimation results to eliminate incorrect ones. The applicability of the proposed method is introduced through a case study of a Hungarian operating waste separation system. The results verify that the assessments of experts can be efficiently integrated into system models, and their consistency can be evaluated. Full article
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<p>Parameter estimation and evaluation of expert knowledge based on the integration of expert-based information into the system model. The expert knowledge is available in the form of probability distributions of the parameters and outputs. Outputs are estimated by Monte Carlo (MC) simulation based on the system model and the sampled probability distributions of parameters, and parameters are deduced and refined according to the expert-based outputs by importance sampling (IS), iteratively. Expert knowledge can also be evaluated according to the results. <math display="inline"><semantics> <mi mathvariant="bold">u</mi> </semantics></math>, <math display="inline"><semantics> <mi mathvariant="bold">Θ</mi> </semantics></math>, and <math display="inline"><semantics> <mi mathvariant="bold">y</mi> </semantics></math> are represent the input, parameter, and output vector of the system, respectively. They need to be estimated gathered to vector <math display="inline"><semantics> <mi mathvariant="bold">x</mi> </semantics></math>, and its elements are marked by <math display="inline"><semantics> <msub> <mi>x</mi> <mi>i</mi> </msub> </semantics></math>.</p>
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<p>The steps of the procedure used in this paper to integrate expert knowledge into the system model. The initial information from the experts is represented by uniform distributions (green), which are aggregated for each estimable <math display="inline"><semantics> <msub> <mi>x</mi> <mi>i</mi> </msub> </semantics></math> variable (red). Sample elements are drawn from the aggregated distributions of the parameters and are weighted (<math display="inline"><semantics> <msub> <mi>w</mi> <mi>i</mi> </msub> </semantics></math>) according to those of the outputs (<math display="inline"><semantics> <msub> <mi>y</mi> <mi>i</mi> </msub> </semantics></math>). Thereby, empirical distributions (blue) are generated and compared to the original expert-based distributions (green), thus creating goodness values (<math display="inline"><semantics> <msub> <mi>g</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>e</mi> </mrow> </msub> </semantics></math>) of expert judgments.</p>
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<p>The outline of MC simulation. Samples are drawn from the continuous distribution to represent it. The variable that the distribution belongs to is denoted by <math display="inline"><semantics> <msub> <mi>x</mi> <mi>i</mi> </msub> </semantics></math>.</p>
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<p>The schematic figure of the parameter estimation technique using expert knowledge. It is assumed that the input vector (<math display="inline"><semantics> <mi mathvariant="bold">u</mi> </semantics></math>) of the system is known. <math display="inline"><semantics> <mi mathvariant="bold">Θ</mi> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="bold">y</mi> </semantics></math> denote the parameter and output vector of the system with the elements of <math display="inline"><semantics> <msub> <mo>Θ</mo> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>y</mi> <mi>i</mi> </msub> </semantics></math>, respectively. <math display="inline"><semantics> <msub> <mi>w</mi> <mi>i</mi> </msub> </semantics></math> refers to the weights generated by importance sampling. The expert-based distributions are represented by red color and the empirical distributions by blue.</p>
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<p>Schematic figure of resampling. The generated <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>n</mi> </msub> <mo>∈</mo> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math> random numbers are represented by orange arrows and the weights of the sample elements are denoted by <math display="inline"><semantics> <msubsup> <mi>w</mi> <mi>i</mi> <mi>j</mi> </msubsup> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>N</mi> </mrow> </semantics></math>). If an arrow points to the interval of <math display="inline"><semantics> <msubsup> <mi>w</mi> <mi>i</mi> <mi>m</mi> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>x</mi> <mi>i</mi> <mi>m</mi> </msubsup> </semantics></math> is chosen as new sample element.</p>
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<p>Comparison of two probability distribution by calculating the Jaccard index. The <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </semantics></math> distributions are discretized by <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> </semantics></math> and probability density functions are evaluated at that points. The elements two datasets are compared pairwise: the maximum and minimum values are denoted with red and green color, respectively. Then, Equation (<a href="#FD12-applsci-14-09652" class="html-disp-formula">12</a>) is used to calculated Jaccard index, which is the ratio of the areas under the red and green curves, actually.</p>
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<p>Outline of the outer iteration circle. The initial distributions from experts are merged again in every iteration according to the normalized goodness values (<math display="inline"><semantics> <msub> <mover accent="true"> <mi>g</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>e</mi> </mrow> </msub> </semantics></math>) gained by comparing these distributions to the estimated ones resulted in the inner circle.</p>
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<p>Block diagram of the waste processing technology, where <math display="inline"><semantics> <msub> <mi>m</mi> <mi>i</mi> </msub> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mn>14</mn> </mrow> </semantics></math>) represents the technological mass flows, and <math display="inline"><semantics> <msub> <mi>r</mi> <mi>j</mi> </msub> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mn>7</mn> </mrow> </semantics></math>) represents the set of the separation efficiencies of the <span class="html-italic">j</span>th unit on components. Each type of component is isolated by machines with related separation principles. For example, iron can be isolated by a magnetic separator; thus, <math display="inline"><semantics> <msub> <mi>m</mi> <mn>8</mn> </msub> </semantics></math> flow mainly contains this component. The titles of the arrows indicate in which component the related flow is rich, that is, why, e.g., <math display="inline"><semantics> <msub> <mi>m</mi> <mn>8</mn> </msub> </semantics></math> is called <b>Iron</b>. RDF: refuse-derived fuel, PET: polyethylene terephthalate, LDPE: low-density polyethylene, HDPE: high-density polyethylene.</p>
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<p>Effects of the parameters on the outputs. The four outputs about which expert-based information was obtained are referred to <math display="inline"><semantics> <msub> <mi>y</mi> <mi>i</mi> </msub> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mn>4</mn> </mrow> </semantics></math>). Green, yellow, red, and blue colors mark which units have an effect on the different outputs. <span class="html-italic">u</span> denotes to the input, and <math display="inline"><semantics> <msub> <mi>r</mi> <mi>i</mi> </msub> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mn>7</mn> </mrow> </semantics></math>) represents the parameters of the <span class="html-italic">i</span>th unit.</p>
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<p>Empirical cumulative density functions (CDFs) of the outputs along the iteration steps. The lines turn black from orange as the iteration is progressing.</p>
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<p>Empirical probability density functions (PDFs) of the outputs along the iteration steps. The lines turn black from orange as the iteration is progressing.</p>
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<p>Empirical cumulative density functions (CDFs) of the <math display="inline"><semantics> <msubsup> <mi>r</mi> <mn>3</mn> <mrow> <mi>A</mi> <mi>l</mi> <mi>u</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mi>i</mi> <mi>u</mi> <mi>m</mi> </mrow> </msubsup> </semantics></math> parameter along the iteration steps. The lines turn black from orange as the iteration is progressing.</p>
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<p>The estimated and the expert-based outputs. The former are represented by boxes with a red line in the median, and the latter by markers (red o, green x, and blue diamond) at the edges of the provided intervals by the three experts.</p>
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<p>Estimated and expert-based distributions of the estimable parameters and output belonging to LDPE.</p>
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<p>Q-Q plot for comparing the uniform distribution provided by Expert 2. and the estimated empirical distributions of <math display="inline"><semantics> <msubsup> <mi>r</mi> <mn>2</mn> <mrow> <mi>L</mi> <mi>D</mi> <mi>P</mi> <mi>E</mi> </mrow> </msubsup> </semantics></math>. If the two distributions were the same, the plot would appear linear. The 45° line as a reference is shown in red, and the quantiles of the two distributions in the function of each other in blue crosses.</p>
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<p>Goodness values belonging to the outputs.</p>
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<p>Goodness values belonging to the estimable parameters. The labels on the axes mark which parameter the goodness value belongs to.</p>
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<p>Convergence of the empirical distributions of the four outputs (<math display="inline"><semantics> <mi mathvariant="bold">y</mi> </semantics></math>) estimated in the inner circle. The lines turn black from orange as the iteration is progressing in the outer iteration circle.</p>
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<p>Normalized goodness values (<math display="inline"><semantics> <msub> <mover accent="true"> <mi>g</mi> <mo stretchy="false">˜</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>e</mi> </mrow> </msub> </semantics></math>) belonging to the system outputs (<math display="inline"><semantics> <mi mathvariant="bold">y</mi> </semantics></math>) and the number of inner iterations along the outer iterations. The three experts are marked with different line styles and the four outputs with different colors.</p>
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<p>Comparison of the results of different methods and the original aggregated expert knowledge. The estimated distributions of outputs are compared in case of a simple one-stage MC simulation, the proposed iterative MC-IS circle, and the MC-IS method with the outer circle for estimating the weight of expert judgment correctness.</p>
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17 pages, 1379 KiB  
Article
Range-Domain Subspace Detector in the Presence of Direct Blast for Forward Scattering Detection in Shallow-Water Environments
by Jiahui Luo, Chao Sun and Mingyang Li
J. Mar. Sci. Eng. 2024, 12(10), 1864; https://doi.org/10.3390/jmse12101864 - 17 Oct 2024
Viewed by 529
Abstract
This paper aims to detect a target that crosses the baseline connecting the source and the receiver in shallow-water environments, which is a special scenario for a bistatic sonar system. In such a detection scenario, an intense sound wave, known as the direct [...] Read more.
This paper aims to detect a target that crosses the baseline connecting the source and the receiver in shallow-water environments, which is a special scenario for a bistatic sonar system. In such a detection scenario, an intense sound wave, known as the direct blast, propagates directly from the source to the receiver without target scattering. This direct blast usually arrives at the receiver simultaneously with the forward scattering signal and exhibits a larger intensity than the signal, posing a significant challenge for target detection. In this paper, a range-domain subspace is constructed by the horizontal distance between the source/target and each element of a horizontal linear array (HLA) when the ranges of environmental parameters are known a priori. Meanwhile, a range-domain subspace detector based on direct blast suppression (RSD-DS) is proposed for forward scattering detection. The source and the target are located at different positions, so the direct blast and the scattered signal are in different range-domain subspaces. By projecting the received data onto the orthogonal complement subspace of the direct blast subspace, the direct blast can be suppressed and the signal that lies outside the direct blast subspace is used for target detection. The simulation results indicate that the proposed RSD-DS exhibits a performance close to the generalized likelihood ratio detector (GLRD) while requiring less prior knowledge of environments (only known are the ranges of the sediment sound speed and the bottom sound speed), and its robustness to environmental uncertainties is better than that of the latter. Moreover, the proposed RSD-DS exhibits better immunity against the direct blast than the GLRD, since it can still work effectively at a signal-to-direct blast ratio (SDR) of −30 dB, while the GLRD stops working in this case. Full article
(This article belongs to the Special Issue Applications of Underwater Acoustics in Ocean Engineering)
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<p>Schematic of forward scattering detection.</p>
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<p>Geometric relationship between the source, the target, and the HLA (the plane of <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>O</mi> <mi>y</mi> </mrow> </semantics></math> represents the sea surface and <span class="html-italic">z</span> represents the depth).</p>
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<p>Geometry of bistatic sonar in the plane of <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>O</mi> <mi>y</mi> </mrow> </semantics></math>.</p>
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<p>Environmental configuration of the GENLMIS model (the solid line and the dashed line, respectively, represent the mean parameters and the ranges of parameters).</p>
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<p><math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> average and coefficient of variation under 500 random environmental realizations with different spatial dimensions (SNR = 10 dB, SDR = −20 dB): (<b>a</b>) Average; (<b>b</b>) coefficient of variation.</p>
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<p><math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> under 500 random environmental realizations (SNR = 10 dB, SDR = −20 dB).</p>
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<p><math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> of RSD-DS and GLRD with different SNRs and SDRs: (<b>a</b>) <math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> vs. SDR (SNR = 10 dB); (<b>b</b>) <math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> vs. SNR (SDR = −20 dB).</p>
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<p>Correlation between the direct blast, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>source</mi> </msub> </semantics></math>, and the real signal, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>, as well as between the approximate signal, <math display="inline"><semantics> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi mathvariant="bold-italic">g</mi> <mi>tr</mi> </msub> </mrow> </semantics></math>, and the real signal, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>, in the areas along the source-HLA baseline: (<b>a</b>) Correlation between <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>source</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>; (<b>b</b>) correlation between <math display="inline"><semantics> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi mathvariant="bold-italic">g</mi> <mi>tr</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>.</p>
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<p><math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> in the areas along the source-HLA baseline (SNR = 10 dB): (<b>a</b>) RSD-DS, SDR = −20 dB; (<b>b</b>) RSD-DS, SDR = −30 dB; (<b>c</b>) GLRD, SDR = −20 dB.</p>
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<p>Correlation between the direct blast, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>source</mi> </msub> </semantics></math>, and the real signal, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>, as well as between the approximate signal, <math display="inline"><semantics> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi mathvariant="bold-italic">g</mi> <mi>tr</mi> </msub> </mrow> </semantics></math>, and the real signal, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>, in different horizontal positions: (<b>a</b>) Correlation between <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>source</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>; (<b>b</b>) correlation between <math display="inline"><semantics> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi mathvariant="bold-italic">g</mi> <mi>tr</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mi>target</mi> </msub> </semantics></math>.</p>
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<p><math display="inline"><semantics> <msub> <mi>P</mi> <mi mathvariant="normal">d</mi> </msub> </semantics></math> at different horizontal positions (SNR = 10 dB): (<b>a</b>) RSD-DS, SDR = −20 dB; (<b>b</b>) RSD-DS, SDR = −30 dB; (<b>c</b>) GLRD, SDR = −20 dB.</p>
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21 pages, 1883 KiB  
Article
Adaptive Point Learning with Uncertainty Quantification to Generate Margin Lines on Prepared Teeth
by Ammar Alsheghri, Yoan Ladini, Golriz Hosseinimanesh, Imane Chafi, Julia Keren, Farida Cheriet and François Guibault
Appl. Sci. 2024, 14(20), 9486; https://doi.org/10.3390/app14209486 - 17 Oct 2024
Viewed by 1466
Abstract
During a crown generation procedure, dental technicians depend on commercial software to generate a margin line to define the design boundary for the crown. The margin line generation remains a non-reproducible, inconsistent, and challenging procedure. In this work, we propose to generate margin [...] Read more.
During a crown generation procedure, dental technicians depend on commercial software to generate a margin line to define the design boundary for the crown. The margin line generation remains a non-reproducible, inconsistent, and challenging procedure. In this work, we propose to generate margin line points on prepared teeth meshes using adaptive point learning inspired by the AdaPointTr model. We extracted ground truth margin lines as point clouds from the prepared teeth and crown bottom meshes. The chamfer distance (CD) and infoCD loss functions were used for training a supervised deep learning model that outputs a margin line as a point cloud. To enhance the generation results, the deep learning model was trained based on three different resolutions of the target margin lines, which were used to back-propagate the losses. Five folds were trained and an ensemble model was constructed. The training and test sets contained 913 and 134 samples, respectively, covering all teeth positions. Intraoral scanning was used to collect all samples. Our post-processing involves removing outlier points based on local point density and principal component analysis (PCA) followed by a spline prediction. Comparing our final spline predictions with the ground truth margin line using CD, we achieved a median distance of 0.137 mm. The median Hausdorff distance was 0.242 mm. We also propose a novel confidence metric for uncertainty quantification of generated margin lines during deployment. The metric was defined based on the percentage of removed outliers during the post-processing stage. The proposed end-to-end framework helps dental professionals in generating and evaluating margin lines consistently. The findings underscore the potential of deep learning to revolutionize the detection and extraction of 3D landmarks, offering personalized and robust methods to meet the increasing demands for precision and efficiency in the medical field. Full article
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<p>Converting die meshes to point clouds and downsampling the point clouds to 10,000 points.</p>
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<p>Extracting ground truth margin lines. A crown bottom is first extracted from a crown designed by a dental technician. The internal edge of crown bottom lower horizontal thickness coincides with the margin line on the dental preparation. The internal points are extracted, projected on the die, and augmented to represent the margin line.</p>
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<p>AdaPoinTr architecture showing the forward pass in blue arrows and backpropagation pass in red.</p>
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<p>One case augmented 20 times.</p>
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<p>Identifying outliers with (<b>a</b>) local density only; (<b>b</b>) with local density and PCA; (<b>c</b>) first component of PCA. Purple represents outliers in (<b>a</b>,<b>b</b>). With both local density and PCA, less outliers are observed.</p>
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<p>Illustration of the post-processing procedures to remove outliers.</p>
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<p>Predicted margin line point clouds of four test cases of different positions compared with ground truth. Red is the prediction, green is the ground truth.</p>
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<p>Qualitative comparison of margin lines obtained using the proposed framework showing the predicted points with outliers highlighted, the predicted margin line splines with outliers (baseline), the predicted splines without outliers improvement, and the ground truth margin lines. The chamfer distance and confidence metric are also presented for each test case.</p>
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<p>Qualitative and quantitative results comparing the margin line predictions using our proposed model with the ground truth.</p>
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<p>Challenging test case showing margin line prediction (dotted) compared with ground truth (solid), both overlaid on the die. The contours of the mean curvatures values of the die mesh are shown. Blue represents high curvature and red represents low curvature. The die geometry is also shown without contours.</p>
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<p>Worst margin line point cloud prediction recorded on a test case considered as a special case.</p>
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<p>Representative frequencies of (<b>a</b>) CD values; (<b>b</b>) percentage of outliers, for the test set obtained using fold 2 model. CD values start from 0.062 mm because the prediction never matches the ground truth exactly.</p>
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<p>Representative CD training and validation loss curves.</p>
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<p>Ordering point cloud using travel sales person algorithm. The 10 lasts points of the point cloud are shown in red, and the first 10 are shown in blue. Notice that one red point is far from where it is supposed to be.</p>
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21 pages, 4421 KiB  
Article
Three-Stage Cascade Information Attenuation for Opinion Dynamics in Social Networks
by Haomin Wang, Youyuan Li and Jia Chen
Entropy 2024, 26(10), 851; https://doi.org/10.3390/e26100851 - 8 Oct 2024
Viewed by 644
Abstract
In social network analysis, entropy quantifies the uncertainty or diversity of opinions, reflecting the complexity of opinion dynamics. To enhance the understanding of how opinions evolve, this study introduces a novel approach to modeling opinion dynamics in social networks by incorporating three-stage cascade [...] Read more.
In social network analysis, entropy quantifies the uncertainty or diversity of opinions, reflecting the complexity of opinion dynamics. To enhance the understanding of how opinions evolve, this study introduces a novel approach to modeling opinion dynamics in social networks by incorporating three-stage cascade information attenuation. Traditional models have often neglected the influence of second- and third-order neighbors and the attenuation of information as it propagates through a network. To correct this oversight, we redefine the interaction weights between individuals, taking into account the distance of opining, bounded confidence, and information attenuation. We propose two models of opinion dynamics using a three-stage cascade mechanism for information transmission, designed for environments with either a single or two subgroups of opinion leaders. These models capture the shifts in opinion distribution and entropy as information propagates and attenuates through the network. Through simulation experiments, we examine the ingredients influencing opinion dynamics. The results demonstrate that an increased presence of opinion leaders, coupled with a higher level of trust from their followers, significantly amplifies their influence. Furthermore, comparative experiments highlight the advantages of our proposed models, including rapid convergence, effective leadership influence, and robustness across different network structures. Full article
(This article belongs to the Special Issue Dynamics in Biological and Social Networks)
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<p>Illustrations of three points A, B, and C.</p>
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<p>Opinion evolution of followers without a leader.</p>
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<p>Opinion evolution in Model I with different <span class="html-italic">N</span>1.</p>
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<p>Opinion evolution with different confidence levels.</p>
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<p>Opinion evolution under different intensities of the target opinion.</p>
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<p>Opinion evolution under different self-confidence and trust levels in Model I.</p>
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<p>Opinion evolution under different self-confidence and trust levels in Model II.</p>
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<p>Model I on small-world networks with the different rewiring probability <span class="html-italic">p</span>.</p>
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<p>Model I on scale-free networks with the different degree distribution <span class="html-italic">M</span>.</p>
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<p>Model I on growing networks with the different homophily coefficient <span class="html-italic">beta</span>.</p>
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<p>Model II on small-world network with the different rewiring probability <span class="html-italic">p</span>.</p>
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<p>Model II on scale-free networks with the different degree distribution <span class="html-italic">M</span>.</p>
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<p>Model II on growing networks with the different homophily coefficient <span class="html-italic">beta</span>.</p>
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<p>Comparative experimental results for single leader group [<a href="#B17-entropy-26-00851" class="html-bibr">17</a>,<a href="#B18-entropy-26-00851" class="html-bibr">18</a>,<a href="#B32-entropy-26-00851" class="html-bibr">32</a>,<a href="#B48-entropy-26-00851" class="html-bibr">48</a>].</p>
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<p>Comparative experiment results for two leader groups [<a href="#B17-entropy-26-00851" class="html-bibr">17</a>,<a href="#B18-entropy-26-00851" class="html-bibr">18</a>,<a href="#B32-entropy-26-00851" class="html-bibr">32</a>,<a href="#B48-entropy-26-00851" class="html-bibr">48</a>].</p>
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23 pages, 5492 KiB  
Article
Form Deviation Uncertainty and Conformity Assessment on a Coordinate Measuring Machine
by Nabil Habibi, Abdelilah Jalid and Abdelouahab Salih
Machines 2024, 12(10), 704; https://doi.org/10.3390/machines12100704 - 4 Oct 2024
Viewed by 616
Abstract
Coordinate measuring machines are widely used in the industrial field due to their ease of automation. However, estimating the measurement uncertainty is a delicate task, especially when controlling for deviation, given the large number of factors that influence the measurement. A precise estimate [...] Read more.
Coordinate measuring machines are widely used in the industrial field due to their ease of automation. However, estimating the measurement uncertainty is a delicate task, especially when controlling for deviation, given the large number of factors that influence the measurement. A precise estimate of the uncertainty is crucial to avoid incorrect conformity assessments. The purpose of this study is to control geometrical-form tolerance specifications, taking into consideration their associated uncertainty. A surface fitting model based on the least squares criterion is proposed, allowing one to obtain the variance–covariance matrix by iterative calculation according to the Levenberg–Marquard optimization method. The form deviation is then evaluated following the Geometrical Product Specifications (GPS) Standard, and its associated uncertainty is estimated using the guide to the expression of uncertainty in measurement (GUM) propagation of the uncertainty law. Finally, the conformity assessment is performed based on the measured deviation and its associated uncertainty. Different results for the measurement of straightness, flatness, circularity, roundness, and cylindricity are presented and detailed. This model is thereafter validated by a Monte Carlo simulation, and interlaboratory comparisons of the obtained results were performed, which showed satisfactory outcome. This contribution is of great use to manufacturing companies and metrology laboratories, allowing them to meet the normative guidelines, which stipulates that each measurement result must be accompanied by its associated uncertainty. Full article
(This article belongs to the Section Machine Design and Theory)
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<p>Proposed model.</p>
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<p>Form tolerance control model.</p>
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<p>CMM measurement uncertainty sources.</p>
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<p>Parametrization of the studied elements: line, plane, circle, sphere and cylinder.</p>
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<p>Orthogonal distance <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> between the point and the fitting feature.</p>
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<p>The surface fitting model.</p>
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<p>Form deviation uncertainty estimation model.</p>
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<p>The coordinate measuring machine used for probing the inspected parts.</p>
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<p>Line fitting.</p>
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<p>Plane fitting.</p>
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<p>Circle fitting.</p>
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<p>Sphere fitting.</p>
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<p>Cylinder fitting.</p>
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<p>NIST reference elements with the highest deviations.</p>
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<p>Flatness deviation generated distribution.</p>
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32 pages, 30650 KiB  
Article
A Novel Strategy Coupling Optimised Sampling with Heterogeneous Ensemble Machine-Learning to Predict Landslide Susceptibility
by Yongxing Lu, Honggen Xu, Can Wang, Guanxi Yan, Zhitao Huo, Zuwu Peng, Bo Liu and Chong Xu
Remote Sens. 2024, 16(19), 3663; https://doi.org/10.3390/rs16193663 - 1 Oct 2024
Viewed by 1233
Abstract
The accuracy of data-driven landslide susceptibility prediction depends heavily on the quality of non-landslide samples and the selection of machine-learning algorithms. Current methods rely on artificial prior knowledge to obtain negative samples from landslide-free regions or outside the landslide buffer zones randomly and [...] Read more.
The accuracy of data-driven landslide susceptibility prediction depends heavily on the quality of non-landslide samples and the selection of machine-learning algorithms. Current methods rely on artificial prior knowledge to obtain negative samples from landslide-free regions or outside the landslide buffer zones randomly and quickly but often ignore the reliability of non-landslide samples, which will pose a serious risk of including potential landslides and lead to erroneous outcomes in training data. Furthermore, diverse machine-learning models exhibit distinct classification capabilities, and applying a single model can readily result in over-fitting of the dataset and introduce potential uncertainties in predictions. To address these problems, taking Chenxi County, a hilly and mountainous area in southern China, as an example, this research proposes a strategy-coupling optimised sampling with heterogeneous ensemble machine learning to enhance the accuracy of landslide susceptibility prediction. Initially, 21 landslide impact factors were derived from five aspects: geology, hydrology, topography, meteorology, human activities, and geographical environment. Then, these factors were screened through a correlation analysis and collinearity diagnosis. Afterwards, an optimised sampling (OS) method was utilised to select negative samples by fusing the reliability of non-landslide samples and certainty factor values on the basis of the environmental similarity and statistical model. Subsequently, the adopted non-landslide samples and historical landslides were combined to create machine-learning datasets. Finally, baseline models (support vector machine, random forest, and back propagation neural network) and the stacking ensemble model were employed to predict susceptibility. The findings indicated that the OS method, considering the reliability of non-landslide samples, achieved higher-quality negative samples than currently widely used sampling methods. The stacking ensemble machine-learning model outperformed those three baseline models. Notably, the accuracy of the hybrid OS–Stacking model is most promising, up to 97.1%. The integrated strategy significantly improves the prediction of landslide susceptibility and makes it reliable and effective for assessing regional geohazard risk. Full article
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<p>Geographical position of the investigated region and landslide inventory: (<b>a</b>) locations of the hilly and mountainous terrains in southern China; (<b>b</b>) landslide inventory; (<b>c</b>–<b>f</b>) images depicting various examples of typical landslides, and red arrows in the images indicating the main slide direction of the landslides.</p>
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<p>Flowchart of the methodology.</p>
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<p>Procedure flowchart of the optimised sampling method.</p>
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<p>Schematic diagram of the random forest (RF) process.</p>
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<p>Principle of support vector machine (SVM): the red and blue dots are two different datasets in separate categories, and the two data points aligned with the dash lines are used to determine the marginal area of the hyperplane of support vectors.</p>
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<p>Architecture of back propagation neural network (BPNN).</p>
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<p>Framework of stacking ensemble machine learning.</p>
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<p>Impact factors for landslide susceptibility prediction: (<b>a</b>) Elevation; (<b>b</b>) Slope; (<b>c</b>) Aspect; (<b>d</b>) Curvature; (<b>e</b>) Plane curvature; (<b>f</b>) Profile curvature; (<b>g</b>) Terrain roughness; (<b>h</b>) TRI; (<b>i</b>) TPI; (<b>j</b>) RDLS; (<b>k</b>) Distance to faults; (<b>l</b>) Engineering rock group; (<b>m</b>) Distance to roads; (<b>n</b>) Population density; (<b>o</b>) LULC; (<b>p</b>) Distance to rivers; (<b>q</b>) Rainfall; (<b>r</b>) SPI; (<b>s</b>) TWI; (<b>t</b>) Soil types; and (<b>u</b>) NDVI.</p>
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<p>Frequency analysis of the impact factors: (<b>a</b>) Elevation; (<b>b</b>) Slope; (<b>c</b>) Aspect; (<b>d</b>) Curvature; (<b>e</b>) Plane curvature; (<b>f</b>) Profile curvature; (<b>g</b>) Terrain roughness; (<b>h</b>) TRI; (<b>i</b>) TPI; (<b>j</b>) RDLS; (<b>k</b>) Distance to faults; (<b>l</b>) Engineering rock group; (<b>m</b>) Distance to roads; (<b>n</b>) Population density; (<b>o</b>) LULC; (<b>p</b>) Distance to rivers; (<b>q</b>) Rainfall; (<b>r</b>) SPI; (<b>s</b>) TWI; (<b>t</b>) Soil types; and (<b>u</b>) NDVI.</p>
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<p>PPCs of all the impact factors.</p>
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<p>Distribution of sample locations: the red dot stands for the positive samples, and the green star indicates the negative samples. (<b>a</b>) The non-landslide samples via the RS approach. (<b>b</b>) The non-landslide samples via the CF approach. (<b>c</b>) The non-landslide samples via the OS approach.</p>
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<p>Landslide susceptibility mapping by 12 prediction models: (<b>a</b>) LSM by RS-RF model; (<b>b</b>) LSM by RS-SVM model; (<b>c</b>) LSM by RS-BPNN model; (<b>d</b>) LSM by RS-Stacking model; (<b>e</b>) LSM by CF-RF model; (<b>f</b>) LSM by CF-SVM model; (<b>g</b>) LSM by CF-BPNN model; (<b>h</b>) LSM by CF-Stacking model; (<b>i</b>) LSM by OS-RF model; (<b>j</b>) LSM by OS-SVM model; (<b>k</b>) LSM by OS-BPNN model; (<b>l</b>) LSM by OS-Stacking model.</p>
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<p>AUC and ROCC for 12 prediction models. (<b>a</b>) AUC and ROCC for the baseline models using various sampling approaches. (<b>b</b>) AUC and ROCC results for the stacking ensemble machine-learning using different sampling methods. The dot line is the reference line or the diagonal line.</p>
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<p>Feature importance ranking of impact factors.</p>
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<p>Statistical analysis of the landslide susceptibility zoning: (<b>a</b>) coverage of the area in each landslide susceptibility class; (<b>b</b>) proportion of landslide in each landslide susceptibility class; (<b>c</b>) frequency ratio of landslides in each landslide susceptibility class; (<b>d</b>) landslide density in each landslide susceptibility class.</p>
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