Self-Organized Fuzzy Neural Network Nonlinear System Modeling Method Based on Clustering Algorithm
Abstract
:1. Introduction
2. Preliminary Knowledge
2.1. K-Means Clustering Algorithm
2.2. Fuzzy Neural Network
3. Implementation of Modeling Methods
3.1. Self-Organizing Mechanism
3.1.1. Neuronal Growth
3.1.2. Adjustment of Neuron Width
3.1.3. Neuron Deletion
3.1.4. Merging of Network-Rule Neurons
3.2. Adaptive Second-Order Learning Algorithm
Algorithm 1: Pseudocodes for constructing SOFNN-CA network |
Input: The input data in the training set are generally four inputs. Output: Single output datum in training set. |
|
3.3. Convergence Analysis
3.3.1. Under a Fixed Structure
3.3.2. Structural Dynamic Adjustment Phase
4. Simulation Analysis
4.1. Mackey–Glass Time-Series Forecasting
4.2. Identification of Nonlinear Systems
4.3. Combined Cycle Power-Plant Power-Output Forecast
4.4. Prediction of Benzene Levels in Air
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Method | Rule Neurons | Testing RMSE | Testing APE | CPU Times (s) |
---|---|---|---|---|
SOFNN-CA | 5 | 0.0058 | 0.0055 | 6.62 |
SOFNN-ALA [20] | 6 | 0.0066 | 0.0058 | 7.24 |
SOFNN-AGA [10] | 6 | 0.0119 | 0.0076 | 21.20 |
SOFNN-ACA [14] | 7 | 0.0201 | 0.0076 | 27.33 |
SOFNN-GA [19] | 7 | 0.0132 | 0.0094 | 168.35 |
FNN-EBP [37] | 8 | 0.0142 | 0.0131 | 37.05 |
Method | Rule Neurons | Testing RMSE | Testing APE | CPU Times (s) |
---|---|---|---|---|
SOFNN-CA | 8 | 0.0171 | 0.0490 | 5.11 |
SOFNN-ALA [20] | 6 | 0.0297 | 0.0954 | 3.73 |
SOFNN-AGA [10] | 6 | 0.0090 | 0.0464 | 13.10 |
RSEFNN-LF [38] | 4 1 | 0.0280 1 | 0.0652 1 | 35.31 1 |
FWNN [39] | 5 1 | 0.0201 1 | 0.0904 1 | 37.72 1 |
Method | Rule Neurons | Training RMSE | Testing RMSE | CPU Times (s) |
---|---|---|---|---|
SOFNN-CA | 3 | 4.1616 | 3.6034 | 11.26 |
SOFNN-HPS [8] | 7 | 4.0718 | 3.7469 | - |
GEBF-OSFNN [41] | 9 1 | 4.2483 1 | 3.8327 1 | - |
GD-FNN [11] | 15 1 | 3.8945 1 | 4.8510 1 | - |
D-FNN [12] | 19 1 | 3.7485 1 | 4.2545 1 | - |
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Zhang, T.; Wang, Z. Self-Organized Fuzzy Neural Network Nonlinear System Modeling Method Based on Clustering Algorithm. Appl. Sci. 2022, 12, 11435. https://doi.org/10.3390/app122211435
Zhang T, Wang Z. Self-Organized Fuzzy Neural Network Nonlinear System Modeling Method Based on Clustering Algorithm. Applied Sciences. 2022; 12(22):11435. https://doi.org/10.3390/app122211435
Chicago/Turabian StyleZhang, Tong, and Zhendong Wang. 2022. "Self-Organized Fuzzy Neural Network Nonlinear System Modeling Method Based on Clustering Algorithm" Applied Sciences 12, no. 22: 11435. https://doi.org/10.3390/app122211435