A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM
Abstract
:1. Introduction
2. Temperature Effect on Piezoresistive Pressure Sensor
3. Hybrid Kernel LSSVM
3.1. LSSVM
3.2. Hybrid Kernel Function
4. Chaotic Ions Motion Algorithm
4.1. Ions Motion Algorithm
Algorithm 1 |
if (CbestFit ≥ CworstFit/2 and AbestFit ≥ AworstFit/2) |
if rand() > 0.5 |
Ai = Ai + Φ1 * (Cbest − 1) |
else |
Ai = Ai + Φ1 * Cbest |
end |
if rand() > 0.5 |
Ci = Ci + Φ2 * (Abest − 1) |
else |
Ci = Ci + Φ2 * Abest |
end |
if rand() < 0.05 |
Re - initialized Ai and Ci |
end |
end |
4.2. Chaotic Initialization and Searching
- (1)
- Chaotic initializationThe initialization of the ions group is one of the key points regarding whether the convergence speed is acceptable and the final solution quality is pleased. Even though the initial position of each ions is random in original ions motion algorithm, ions might be located far away from the optimal ion. Chaotic initialization is for the purpose of increasing the diversity among the population and accelerating the convergence speed.
- (2)
- Chaotic searchingRestart with the last ion position in the latest generation and replace all other ion positions by generating a new chaotic sequence. Continuing to generate new ion positions by chaotic sequence rather than by probability distributions could avoid stagnation and speed the convergence in the optimization searching process.
4.3. Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM (CIMA-Hybrid-LSSVM)
- (1)
- Chaotic initialization
- Chaotically distribute the seeds according to the dimension number of an ion by logistic map within the range of (0, 1).
- Calculate the chaotic sequence with chaotic seeds until the chaotic sequence length reaches the ions population size.
- Transform the chaotic sequence members into every parameter’s range, and take the transforming of as an example:
- (2)
- Generate the initial ion population by Equation (23) and divide it randomly into an anion group and a cation group at the same size.
- (3)
- Evaluate each ion in liquid phase and rank them in terms of fitness. Record the best fitness and position of anion group, cation group and the ion population. If the best fitness of the ion population can neither satisfy the predetermined estimation precision nor reach the maximum searching generation number, then go to Step 4.
- (4)
- Take the last seed of the chaotic sequence generated by Step 1 and repeat the procedure as in Step 1 to obtain a new chaotic sequence. Compute each ion fitness according to the rules stated in crystal phase with the new chaotic sequence. The computation comes to an end as the best fitness satisfies the predetermined estimation precision or reaches the maximum searching generation number. If the stop criterion can not be met, then take the last ion position as the chaotic seed and go back to Step 1.
5. Data Calibration Experiment and Result Analysis
5.1. Data Calibration
5.2. Data Preprocessing
5.3. Modeling Temperature Compensation and Result Analysis
5.3.1. Random Partition of the Sample
5.3.2. Fixed Partition of the Sample
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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P (Pa) | T (°C) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
−20 | −10 | 0 | 10 | 20 | 27 | 35 | 40 | 50 | 60 | 70 | |
TAD | |||||||||||
46113 | 45715 | 45268 | 44875 | 44445 | 44066 | 43834 | 43559 | 43255 | 42833 | 42449 | |
UAD | |||||||||||
−40000 | 225163 | 229882 | 235926 | 240350 | 245293 | 249365 | 251904 | 254585 | 257738 | 261883 | 265502 |
−35000 | 258948 | 263075 | 268467 | 272361 | 276787 | 280403 | 282638 | 285002 | 287807 | 291422 | 294694 |
−30000 | 292891 | 296416 | 301166 | 304587 | 308434 | 311591 | 313534 | 315581 | 318035 | 321166 | 324036 |
−25000 | 326975 | 329900 | 334016 | 336931 | 340227 | 342921 | 344579 | 346307 | 348415 | 351061 | 353526 |
−20000 | 361190 | 363517 | 367004 | 369421 | 372163 | 374394 | 375763 | 377152 | 378937 | 381095 | 383158 |
−15000 | 395535 | 397260 | 400131 | 402004 | 404232 | 406003 | 407086 | 408178 | 409595 | 411274 | 412937 |
−10000 | 429974 | 431111 | 433352 | 434705 | 436398 | 437712 | 438518 | 439281 | 440352 | 441555 | 442817 |
−5000 | 464508 | 465059 | 466694 | 467572 | 468680 | 469525 | 470046 | 470503 | 471221 | 471962 | 472818 |
0 | 499132 | 499093 | 500112 | 500490 | 501053 | 501453 | 501666 | 501827 | 502188 | 502462 | 502916 |
5000 | 533794 | 533200 | 533579 | 533466 | 533475 | 533419 | 533347 | 533205 | 533214 | 533028 | 533077 |
10000 | 568569 | 567362 | 567163 | 566524 | 566019 | 565509 | 565185 | 564690 | 564373 | 563699 | 563370 |
15000 | 603351 | 601564 | 600769 | 599619 | 598591 | 597628 | 597024 | 596217 | 595555 | 594429 | 593697 |
20000 | 638130 | 635788 | 634383 | 632731 | 631170 | 629766 | 628882 | 627762 | 626757 | 625174 | 624052 |
25000 | 672932 | 670020 | 668039 | 665862 | 663787 | 661936 | 660781 | 659345 | 657996 | 655939 | 654454 |
30000 | 707712 | 704235 | 701674 | 699016 | 696402 | 694107 | 692600 | 690934 | 689248 | 686760 | 684868 |
35000 | 742451 | 738421 | 735281 | 732121 | 728999 | 726261 | 724565 | 722513 | 720489 | 717537 | 715282 |
40000 | 777129 | 772552 | 768840 | 765221 | 761560 | 758380 | 756415 | 754060 | 751701 | 748336 | 745668 |
Parameters | PSO [29] | PSO [30] | IMA |
---|---|---|---|
swarm size | 50 | 50 | 50 |
maximum iteration number | 30 | 30 | 30 |
fitness | MSE | MSE | MSE |
maximum weight | 0.9 | 0.9 | |
minimum weight | 0.4 | 0.4 | |
social factor | [1, 3] | 2 | |
cognitive factor | [1, 3] | 2 |
Temperature Compensation Methods | eir (min) | eir (max) | eir (mean) | eir (variance) | MTT (s) |
---|---|---|---|---|---|
SVM | 4.814 × 10−3 | 5.026 × 10−3 | 4.973 × 10−3 | 2.237 × 10−9 | 1.499 × 10−2 |
PSO-RBF-SVM | 5.550 × 10−4 | 1.334 × 10−3 | 9.673 × 10−4 | 3.385 × 10−9 | 2.107 × 102 |
PSO-RBF-LSSVM | 2.199 × 10−4 | 3.556 × 10−4 | 2.703 × 10−4 | 1.080 × 10−9 | 1.200 × 10−2 |
PSO-Hybrid-LSSVM | 2.586 × 10−4 | 3.588 × 10−4 | 3.126 × 10−4 | 4.996 × 10−10 | 1.478 × 10−2 |
IMA-Hybrid-LSSVM | 1.593 × 10−4 | 2.401 × 10−4 | 1.933 × 10−4 | 3.776 × 10−10 | 1.418 × 10−2 |
CIMA-Hybrid-LSSVM | 1.353 × 10−5 | 4.413 × 10−5 | 2.497 × 10−5 | 5.258 × 10−11 | 1.392 × 10−2 |
Temperature Compensation Methods | eir (min) | eir (max) | eir (mean) | eir (variance) |
---|---|---|---|---|
SVM | 2.106 × 10−1 | 3.197 × 10−1 | 2.648 × 10−1 | 5.562 × 10−4 |
PSO-RBF-SVM | 5.924 × 10−4 | 2.187 × 10−3 | 1.235 × 10−3 | 1.085 × 10−7 |
PSO-RBF-LSSVM | 2.422 × 10−4 | 6.706 × 10−4 | 4.011 × 10−4 | 6.286 × 10−9 |
PSO-Hybrid-LSSVM | 2.733 × 10−4 | 5.165 × 10−4 | 3.687 × 10−4 | 1.494 × 10−9 |
IMA-Hybrid-LSSVM | 1.841 × 10−4 | 3.424 × 10−4 | 2.517 × 10−4 | 9.659 × 10−10 |
CIMA-Hybrid-LSSVM | 1.155 × 10−4 | 2.559 × 10−4 | 1.770 × 10−4 | 1.104 × 10−9 |
Temperature Compensation Methods | eir (min) | eir (max) | eir (mean) | eir (variance) | MTT (s) |
---|---|---|---|---|---|
SVM | 3.272 × 10−4 | 5.220 × 10−3 | 4.722 × 10−3 | 1.227 × 10−6 | 1.507 × 10−2 |
PSO-RBF-SVM | 4.343 × 10−5 | 3.248 × 10−4 | 1.850 × 10−4 | 5.467 × 10−9 | 10.71 × 101 |
PSO-RBF-LSSVM | 8.946 × 10−6 | 1.111 × 10−3 | 1.927 × 10−4 | 3.692 × 10−8 | 2.448 × 10−2 |
PSO-Hybrid-LSSVM | 1.085 × 10−4 | 1.564 × 10−4 | 1.251 × 10−4 | 1.159 × 10−10 | 2.549 × 10−2 |
IMA-Hybrid-LSSVM | 4.095 × 10−7 | 6.063 × 10−5 | 1.444 × 10−5 | 1.844 × 10−10 | 2.641 × 10−2 |
CIMA-Hybrid-LSSVM | 9.921 × 10−6 | 6.401 × 10−5 | 2.029 × 10−5 | 1.210 × 10−10 | 2.568 × 10−2 |
Temperature Compensation Methods | eir (min) | eir (max) | eir (mean) | eir (variance) |
---|---|---|---|---|
SVM | 3.414 × 10−4 | 5.003 × 10−1 | 2.647 × 10−1 | 2.387 × 10−2 |
PSO-RBF-SVM | 7.647 × 10−5 | 1.154 × 10−3 | 3.290 × 10−4 | 6.368 × 10−8 |
PSO-RBF-LSSVM | 1.953 × 10−5 | 1.338 × 10−3 | 3.549 × 10−4 | 7.548 × 10−8 |
PSO-Hybrid-LSSVM | 1.082 × 10−4 | 1.074 × 10−3 | 3.555 × 10−4 | 5.374 × 10−8 |
IMA-Hybrid-LSSVM | 1.831 × 10−6 | 1.038 × 10−3 | 3.007 × 10−4 | 6.565 × 10−8 |
CIMA-Hybrid-LSSVM | 1.224 × 10−5 | 1.066 × 10−3 | 3.056 × 10−4 | 6.427 × 10−8 |
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Li, J.; Hu, G.; Zhou, Y.; Zou, C.; Peng, W.; Alam SM, J. A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM. Sensors 2016, 16, 1707. https://doi.org/10.3390/s16101707
Li J, Hu G, Zhou Y, Zou C, Peng W, Alam SM J. A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM. Sensors. 2016; 16(10):1707. https://doi.org/10.3390/s16101707
Chicago/Turabian StyleLi, Ji, Guoqing Hu, Yonghong Zhou, Chong Zou, Wei Peng, and Jahangir Alam SM. 2016. "A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM" Sensors 16, no. 10: 1707. https://doi.org/10.3390/s16101707
APA StyleLi, J., Hu, G., Zhou, Y., Zou, C., Peng, W., & Alam SM, J. (2016). A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM. Sensors, 16(10), 1707. https://doi.org/10.3390/s16101707