Temperature Compensation Method for Piezoresistive Pressure Sensors Based on Gated Recurrent Unit
Abstract
:1. Introduction
2. Failure Mechanism of Pressure Sensors
2.1. Introduction of Piezoresistive Pressure Sensors
2.2. Temperature Effects of Pressure Sensors
2.3. Factors for Temperature Compensation
3. Compensation Algorithms and Model
3.1. Random Forest
3.2. Gated Recurrent Unit Networks
3.3. WOA and IWOA
3.3.1. Whale Optimization Algorithm
- Contraction EncirclingThis process imitates the behavior of whales surrounding their prey through circular movement. The way the whales shrink their enclosures is modulated by .At , the algorithm performs a local search.At , the algorithm performs a global search.
- Spiral Updating positionThis process imitates the behavior of whales encircling a target through spiral movement.
3.3.2. Improved Whale Optimization Algorithm
- Chebyshev Chaotic MapThe Chebyshev chaotic map generates chaotic sequences through the repeated application of iterative functions. It exhibits nonlinearity, high sensitivity to initial values, excellent ergodicity, and unpredictability [42]. This map is frequently used for population initialization to enhance algorithmic diversity and randomness [43]. Based on the comparison of chaotic optimization algorithms, the Chebyshev chaotic map has a large Lyapunov exponent, which means its chaotic nature is pronounced, and its degree of chaos is high. Furthermore, considering the optimal, mean, and standard values, the Chebyshev chaotic map exhibits stability and high applicability. Therefore, considering all these factors, we chose the Chebyshev chaotic map to optimize the traditional whale algorithm. The formula is as follows:
- Adaptive WeightIn the case of contracting the encircling and spiral updating positions, a large weight value should be selected at the initial stage of the algorithm to improve the optimization speed and global search ability of the algorithm [44]. As the algorithm iterates continuously, the weight values should gradually decrease to reduce the fluctuation amplitude of the search and improve the convergence accuracy of the algorithm. Given the above situation, adaptive weight is introduced to optimize the algorithm so that the contraction encircling and spiral updating positions are adjusted according to the current iteration degree. The mathematical expression of can be expressed as follows:
3.4. RF-IWOA-GRU Model
4. Experiment and Results Analysis
4.1. Experiment and Data Collection
4.2. Data Preprocessing
4.2.1. Calculation of the Rate of Temperature Change
4.2.2. Interpolation of Missing Actual Pressure Data Values
4.3. Modeling and Training
4.4. Results and Discussions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
SVM | Support vector machine |
ANN | Artificial neural network |
RF | Random forest |
GRU | Gated recurrent unit |
WOA | Whale optimization algorithm |
IWOA | Improved whale optimization algorithm |
ELM | Extreme learning machines |
LSSVM | Least squares support vector machine |
BP | Backpropagation |
RBF | Radial basis function |
CSO | Chicken swarm optimization |
WNN | Wavelet neural network |
RNN | Recurrent neural network |
LSTM | Long–short-term memory |
CART | Classification and regression tree |
MA | Moving average |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
RMSE | Root mean square error |
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Model Parameter | Numerical Value |
---|---|
Initial learning rate | 0.001–0.01 |
Batch size | 10–250 |
Number of neurons | 2–50 |
Model | MAE | MAPE | RMSE |
---|---|---|---|
BP | 2.089 | 0.0129 | 2.616 |
RNN | 1.786 | 0.0103 | 2.169 |
LSTM | 0.976 | 0.0063 | 1.230 |
GRU | 0.928 | 0.0060 | 1.089 |
IWOA-GRU | 0.661 | 0.0043 | 0.826 |
Model | MAE | MAPE | RMSE |
---|---|---|---|
Uncompensated | 8.260 | 0.0402 | 10.18 |
BP | 4.259 | 0.0267 | 5.403 |
RNN | 3.561 | 0.0198 | 4.244 |
LSTM | 2.896 | 0.0156 | 3.616 |
GRU | 2.787 | 0.0172 | 3.338 |
IWOA-GRU | 2.027 | 0.0124 | 2.428 |
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Liu, M.; Wang, Z.; Jiang, P.; Yan, G. Temperature Compensation Method for Piezoresistive Pressure Sensors Based on Gated Recurrent Unit. Sensors 2024, 24, 5394. https://doi.org/10.3390/s24165394
Liu M, Wang Z, Jiang P, Yan G. Temperature Compensation Method for Piezoresistive Pressure Sensors Based on Gated Recurrent Unit. Sensors. 2024; 24(16):5394. https://doi.org/10.3390/s24165394
Chicago/Turabian StyleLiu, Mian, Zhiwu Wang, Pingping Jiang, and Guozheng Yan. 2024. "Temperature Compensation Method for Piezoresistive Pressure Sensors Based on Gated Recurrent Unit" Sensors 24, no. 16: 5394. https://doi.org/10.3390/s24165394