Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models
Abstract The present investigation employs relevance vector machine (RVM) and long short-term memory (LSTM) models to predict the time-dependent bearing capacity of concrete piles. Each RVM model (SRVM) is configured by each linear, polynomial, gaussian, sigmoid, laplacian, and exponential kernel fu...
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Nature Portfolio
2024-12-01
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| Online Access: | https://doi.org/10.1038/s41598-024-83784-8 |
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| author | Jitendra Khatti Mohammadreza Khanmohammadi Yewuhalashet Fissha |
| author_facet | Jitendra Khatti Mohammadreza Khanmohammadi Yewuhalashet Fissha |
| author_sort | Jitendra Khatti |
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| description | Abstract The present investigation employs relevance vector machine (RVM) and long short-term memory (LSTM) models to predict the time-dependent bearing capacity of concrete piles. Each RVM model (SRVM) is configured by each linear, polynomial, gaussian, sigmoid, laplacian, and exponential kernel function. Each SRVM model has been optimized by each genetic (GA_SRVM) and particle swarm optimization (PSO_RVM) algorithm. Moreover, the double kernel-based RVM models (DRVM) have been employed and optimized by each GA (GA_DRVM) and PSO (PSO_DRVM) algorithm. Thus, an extensive comparison among 33 RVM (6SRVM + 6GA_RVM + 6PSO_RVM + 5DRVM + 5GA_DRVM + 5PSO_DRVM) has been carried out. Conversely, the Adam, root mean squared propagation and stochastic gradient descent with momentum algorithms have optimized the LSTM model. Each optimized RVM and LSTM model has been trained and tested by 100 and 26 datasets. In addition, the effect of structural and database multicollinearities has been analyzed on models’ prediction capabilities. The performance index (PI), the variance accounted for (VAF), performance (R), mean absolute error (MAE), normalized mean bias error (NMBE), and root mean square error (RMSE) matrices have analyzed the prediction capabilities of each model. The comparison of 33 RVM and 3 LSTM models reveals that the genetic algorithm-optimized Gaussian kernel function-based SRVM model, i.e., UBC7, has been recognized as the optimal performance model with the RMSE = 146.3962 kPa, PI = 1.85, VAF = 94.60, NMBE = 30.1379 kPa, MAE = 105.7009 kPa, and R = 0.9727, close to the ideal values. Furthermore, the score (= 56), Wilcoxon (= 94.95% confidence), uncertainty (= 1st rank), generalizability (= close to ideal values), and Anderson Darling (= 9.435 ≈ 9.336) tests confirm the superiority of model UBC7. Still, structural and database multicollinearity has drastically impacted dual kernel-based RVM and stochastic gradient descent optimized LSTM models. |
| format | Article |
| id | doaj-art-220d819f91a44e018e6d810be6a4d3bc |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-220d819f91a44e018e6d810be6a4d3bc2025-01-05T12:25:34ZengNature PortfolioScientific Reports2045-23222024-12-0114113710.1038/s41598-024-83784-8Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory modelsJitendra Khatti0Mohammadreza Khanmohammadi1Yewuhalashet Fissha2Department of Civil Engineering, Rajasthan Technical UniversityDepartment of Civil Engineering, Isfahan University of TechnologyDepartment of Geosciences, Geotechnology, and Materials Engineering for Resources, Graduate School of International Resource Sciences, Akita UniversityAbstract The present investigation employs relevance vector machine (RVM) and long short-term memory (LSTM) models to predict the time-dependent bearing capacity of concrete piles. Each RVM model (SRVM) is configured by each linear, polynomial, gaussian, sigmoid, laplacian, and exponential kernel function. Each SRVM model has been optimized by each genetic (GA_SRVM) and particle swarm optimization (PSO_RVM) algorithm. Moreover, the double kernel-based RVM models (DRVM) have been employed and optimized by each GA (GA_DRVM) and PSO (PSO_DRVM) algorithm. Thus, an extensive comparison among 33 RVM (6SRVM + 6GA_RVM + 6PSO_RVM + 5DRVM + 5GA_DRVM + 5PSO_DRVM) has been carried out. Conversely, the Adam, root mean squared propagation and stochastic gradient descent with momentum algorithms have optimized the LSTM model. Each optimized RVM and LSTM model has been trained and tested by 100 and 26 datasets. In addition, the effect of structural and database multicollinearities has been analyzed on models’ prediction capabilities. The performance index (PI), the variance accounted for (VAF), performance (R), mean absolute error (MAE), normalized mean bias error (NMBE), and root mean square error (RMSE) matrices have analyzed the prediction capabilities of each model. The comparison of 33 RVM and 3 LSTM models reveals that the genetic algorithm-optimized Gaussian kernel function-based SRVM model, i.e., UBC7, has been recognized as the optimal performance model with the RMSE = 146.3962 kPa, PI = 1.85, VAF = 94.60, NMBE = 30.1379 kPa, MAE = 105.7009 kPa, and R = 0.9727, close to the ideal values. Furthermore, the score (= 56), Wilcoxon (= 94.95% confidence), uncertainty (= 1st rank), generalizability (= close to ideal values), and Anderson Darling (= 9.435 ≈ 9.336) tests confirm the superiority of model UBC7. Still, structural and database multicollinearity has drastically impacted dual kernel-based RVM and stochastic gradient descent optimized LSTM models.https://doi.org/10.1038/s41598-024-83784-8Concrete pilesMulticollinearityTime-dependent bearing capacityHybrid relevance vector machineLong short-term memory |
| spellingShingle | Jitendra Khatti Mohammadreza Khanmohammadi Yewuhalashet Fissha Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models Scientific Reports Concrete piles Multicollinearity Time-dependent bearing capacity Hybrid relevance vector machine Long short-term memory |
| title | Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models |
| title_full | Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models |
| title_fullStr | Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models |
| title_full_unstemmed | Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models |
| title_short | Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models |
| title_sort | prediction of time dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short term memory models |
| topic | Concrete piles Multicollinearity Time-dependent bearing capacity Hybrid relevance vector machine Long short-term memory |
| url | https://doi.org/10.1038/s41598-024-83784-8 |
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