The Data-Driven Homogenization of Mohr–Coulomb Parameters Based on a Bayesian Optimized Back Propagation Artificial Neural Network (BP-ANN)
Abstract
:1. Introduction
2. Methodology
2.1. Back Propagation Artificial Neural Networks
2.2. Bayesian Optimization
2.3. Back Propagation Artificial Neural Network Based on Bayesian Optimization
- (1)
- Divide the dataset into training and testing sets.
- (2)
- Set the hyperparameters that need to be optimized and the range of values for each hyperparameter. In this work, we selected hyperparameters such as learning rate, dropout rate, the number of hidden layers, and the number of neurons in each hidden layer.
- (3)
- Set the initial values of hyperparameters, perform Bayesian optimization, and obtain the optimal hyperparameters.
- (4)
- Substitute the optimal hyperparameters into the back propagation artificial neural network to determine the final architecture of the back propagation artificial neural network.
- (5)
- Train models on the training set.
- (6)
- Test the model on the test set.
3. Generation of the Training Dataset
3.1. Problem Formulation
3.2. Finite Element Simulation of the Heterogeneous Model
3.3. Finite Element Simulation of the Homogenized Model
3.4. Matching the Homogenized Parameters to the Heterogeneous Parameters
4. Network Architecture and Parameter Optimization
4.1. Data Pre-Processing
4.2. Dataset Partitioning
4.3. The Bayesian Optimized Neural Network
5. Results
5.1. Training Loss of the BP-ANN Model
5.2. Verification of Our Model on an Independent Dataset
5.3. Discussion
- (1)
- The proposed method exhibits generalizability and can be applied in various fields of geotechnical mechanics.
- (2)
- The established model accurately predicts the displacement difference. The mean absolute percentage error (MAPE) between the predicted and actual displacement difference is only 5.3% for the test set, and 2.6% for the independent validation set. This again demonstrates the model’s strong generalization ability for the geotechnical problems examined in this study.
- (3)
- Utilizing the trained model for practical geotechnical problems significantly reduces the need for computational resources and time costs when compared to traditional approaches.
6. Conclusions
- Bayesian optimization, in our work, managed to optimize our network architecture as well as the hyperparameters.
- Applying the BP-ANN to predict the yields of the corresponding sets of predicted parameters and the good agreement between the difference in displacement computed using the predicted parameters and the simulation data of the heterogeneous model verify the superiority of our model.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Min | Max | Avg | STD |
---|---|---|---|---|
15.00 | 20.00 | 17.63 | 2.50 | |
15.00 | 20.00 | 17.65 | 2.50 | |
8.00 | 48.00 | 34.50 | 11.86 |
Neuron | Dropout_Rate | Learning_Rate | Hidden Layers |
---|---|---|---|
25 | 0.6 | 0.006 | 7 |
MSE | RMSE | MAE | |
---|---|---|---|
E | 0.06 | 0.24 | 0.18 |
0.036 | 0.19 | 0.14 | |
C | 0.10 | 0.32 | 0.27 |
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Gao, Y.; Huang, G.; Li, Y.; Zhang, J.; Yang, Z.; Wang, M. The Data-Driven Homogenization of Mohr–Coulomb Parameters Based on a Bayesian Optimized Back Propagation Artificial Neural Network (BP-ANN). Appl. Sci. 2023, 13, 11966. https://doi.org/10.3390/app132111966
Gao Y, Huang G, Li Y, Zhang J, Yang Z, Wang M. The Data-Driven Homogenization of Mohr–Coulomb Parameters Based on a Bayesian Optimized Back Propagation Artificial Neural Network (BP-ANN). Applied Sciences. 2023; 13(21):11966. https://doi.org/10.3390/app132111966
Chicago/Turabian StyleGao, Yunfei, Guogui Huang, Yinxi Li, Junyuan Zhang, Zeng Yang, and Meng Wang. 2023. "The Data-Driven Homogenization of Mohr–Coulomb Parameters Based on a Bayesian Optimized Back Propagation Artificial Neural Network (BP-ANN)" Applied Sciences 13, no. 21: 11966. https://doi.org/10.3390/app132111966
APA StyleGao, Y., Huang, G., Li, Y., Zhang, J., Yang, Z., & Wang, M. (2023). The Data-Driven Homogenization of Mohr–Coulomb Parameters Based on a Bayesian Optimized Back Propagation Artificial Neural Network (BP-ANN). Applied Sciences, 13(21), 11966. https://doi.org/10.3390/app132111966