Optimization of Levenberg Marquardt Algorithm Applied to Nonlinear Systems
Abstract
:1. Introduction
2. Related Work
3. Optimization and Identification of NS Model Based on LM-BPNN
3.1. Construction of NS Strategic Control Method Based on BPNN
3.2. Construction of NS Strategic Control Method Based on Optimized BPNN
4. Simulation Analysis Based on LM-BP Optimization Algorithm in Nss
4.1. Performance Analysis of LM-BP-Based Optimization Algorithms
4.2. Application Analysis of LM-BP Optimization Algorithm in NSs
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Term | Definition |
---|---|
CSTR | Continuous stirred tank reactor |
LM | Levenberg–Marquardt |
BPNN | Back Propagation Neural Network |
NN | Neural Network |
PI | Proportional-Integral |
Ca | Reactant concentration |
RMSE | Root mean square error |
MAE | Maximum absolute error |
AAE | Average absolute error |
GN-BP | Gauss–Newton-Back Propagation |
ANN | Artificial neural network |
NS | Nonlinear system |
Test Conditions | Parameter Value |
---|---|
Input signal | |
Output signal | |
Training function | Trainlm function |
Number of hidden layer nodes | 7 |
Learning Rate | θ = 0.5 |
Maximum Number of Iterations | 500 |
Target error accuracy | 10−4 |
Inertial coefficient | 0.05 |
Input reference trajectory | 10 Hz square wave signal |
Model Type | RMSE | MAE | AAE |
---|---|---|---|
LM-BPNN | 0.0451 | 0.0958 | 0.0351 |
BPNN | 0.0744 | 0.1775 | 0.0536 |
GN-BPNN | 0.0539 | 0.1108 | 0.0443 |
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Huang, X.; Cao, H.; Jia, B. Optimization of Levenberg Marquardt Algorithm Applied to Nonlinear Systems. Processes 2023, 11, 1794. https://doi.org/10.3390/pr11061794
Huang X, Cao H, Jia B. Optimization of Levenberg Marquardt Algorithm Applied to Nonlinear Systems. Processes. 2023; 11(6):1794. https://doi.org/10.3390/pr11061794
Chicago/Turabian StyleHuang, Xinyi, Hao Cao, and Bingjing Jia. 2023. "Optimization of Levenberg Marquardt Algorithm Applied to Nonlinear Systems" Processes 11, no. 6: 1794. https://doi.org/10.3390/pr11061794
APA StyleHuang, X., Cao, H., & Jia, B. (2023). Optimization of Levenberg Marquardt Algorithm Applied to Nonlinear Systems. Processes, 11(6), 1794. https://doi.org/10.3390/pr11061794