An Optimized Neural Network Acoustic Model for Porous Hemp Plastic Composite Sound-Absorbing Board
Abstract
:1. Introduction
2. Literature Review
3. Materials and Methods
3.1. Obtaining Data
3.2. Proposed Model
3.2.1. Design of the Neural Network Structure
3.2.2. Data Processing
3.2.3. Improved Genetic Algorithm
- (1)
- Initialization and Encoding
- (2)
- Fitness function design
- (3)
- Selection operator
- (4)
- Crossover operator
- (5)
- Mutation operator
3.2.4. Training of the Neural Network Model
- (1)
- Set the allowable training error , damping constant , number of iterations , initial value = , and let . Then input the weight and threshold obtained by the genetic algorithm into the network, together with the training data, as the initialized weight and threshold vector.
- (2)
- Calculate the network output and error. The error function is shown in Equation (14), where the mean squared error (MSE) is adopted. represents the ideal network output in the formula, , the actual network output, p, the number of specimens, , the vector composed of the weight and threshold of iteration , and , the error generated by specimen .
- (3)
- Calculate the Jacobian matrix according to Equation (15).
- (4)
- Calculate the increment of weight and threshold using the method shown in Equation (16), where represents the unit matrix, is the error matrix of all the specimens, and is the Jacobian matrix.
- (5)
- If is smaller than , the set error value, end the training. If not, continue to step (6).
- (6)
- Update the weight and threshold vector according to Equation (17), calculate the error according to Equation (14), and if , update and according to Equations (18) and (19), respectively, and continue to step (2). Otherwise, update and according to Equations (18) and (20), and then progress to step (4).
3.2.5. Model Testing
4. Experiment Results and Discussion
4.1. Test Output Results
4.2. Comparison of Output Results
4.3. Validating Efficacy
4.4. Performance Analysis of the Proposed Model
4.4.1. Enhanced Solution Generation
4.4.2. Performance Analysis of Trained Model
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Center Frequency/Hz | Maximum Sound Pressure/dB | Minimum Sound Pressure/dB |
---|---|---|
200 | 96.9 | 71.8 |
250 | 100.7 | 79.8 |
315 | 109.6 | 88.3 |
400 | 106 | 85.4 |
500 | 105 | 85.4 |
630 | 90.8 | 73.5 |
800 | 90.8 | 74.2 |
1000 | 87 | 72.3 |
1250 | 73.8 | 61.6 |
1600 | 74.5 | 62.1 |
2000 | 63.5 | 52.6 |
2500 | 54 | 39.8 |
3150 | 49.6 | 37.2 |
4000 | 47.4 | 37.4 |
Evolutional Epochs | Population Size | Crossover Probability | Mutation Probability |
---|---|---|---|
100 | 30 | 0.3 | 0.1 |
Evaluation Index | Our Model | Our Model +10-fold Cross-Validation | 1D CA | Unoptimized Neural Network | Support Vector | Random Forest | XGBoost |
---|---|---|---|---|---|---|---|
RMSE | (1.1728 ± 0.312) × 10−6 | (1.1366 ± 0.543) × 10−6 | 2.1846 × 10−4 | (8.691 ± 1.136) × 10−3 | (8.783 ± 1.826) × 10−3 | (5.2765 ± 2.138) × 10−3 | (7.1863 ± 0.768) × 10−3 |
R2 | 0.95 ± 0.046 | 0.94 ± 0.041 | 0.91 | 0.82 ± 0.06 | 0.65 ± 0.06 | 0.75 ± 0.07 | 0.72 ± 0.06 |
Convergence time/s | 85 + 6.25 | 121 ± 10.95 | 65.1 | 85 ± 10.9 | 78 ± 7.5 | 83 ± 10.8 | 55 ± 4.75 |
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Wang, H.; Zhao, H.; Lian, Z.; Tan, B.; Zheng, Y.; E, E. An Optimized Neural Network Acoustic Model for Porous Hemp Plastic Composite Sound-Absorbing Board. Symmetry 2022, 14, 863. https://doi.org/10.3390/sym14050863
Wang H, Zhao H, Lian Z, Tan B, Zheng Y, E E. An Optimized Neural Network Acoustic Model for Porous Hemp Plastic Composite Sound-Absorbing Board. Symmetry. 2022; 14(5):863. https://doi.org/10.3390/sym14050863
Chicago/Turabian StyleWang, Haizhen, Hong Zhao, Zuozheng Lian, Bin Tan, Yongjie Zheng, and Erdun E. 2022. "An Optimized Neural Network Acoustic Model for Porous Hemp Plastic Composite Sound-Absorbing Board" Symmetry 14, no. 5: 863. https://doi.org/10.3390/sym14050863
APA StyleWang, H., Zhao, H., Lian, Z., Tan, B., Zheng, Y., & E, E. (2022). An Optimized Neural Network Acoustic Model for Porous Hemp Plastic Composite Sound-Absorbing Board. Symmetry, 14(5), 863. https://doi.org/10.3390/sym14050863