Gas Turbine Engine Identification Based on a Bank of Self-Tuning Wiener Models Using Fast Kernel Extreme Learning Machine
Abstract
:1. Introduction
2. Self-Tuning Wiener Model
2.1. Block-Oriented Self-Tuning Wiener Model
2.2. Improved KELM for Self-Tuning Wiener Model
- Step 1:
- Initialize model parameters, Let p = 1; Empirically produce a set of M candidates including the regressor factors na, nb, and kernel parameter γ; Select the KELM feature parameter combination (na, nb, γ)k from candidate set, and k = 1.
- Step 2:
- Train the KELM using N samples to generate the matrices A and A−1 with full dimensions as the KELM parameter combination (na, nb, γ)k.
- Step 3:
- Calculate the simplified output weight vector αp by Equation (15) and by Equation (8).
- Step 4:
- If p < N, then p = p + 1 and return to step 3; otherwise, compute the generalization performance index of KELM: align
- Step 5:
- If k < M, then k = k + 1 and go back to step 2; otherwise, stop the procedure and select the optimal KELM feature parameter combination (na, nb, γ) and the output weight vector α who has the minimum value of RMSEk.
3. Aircraft Engine Identification by Self-Tuning Wiener Models
4. Simulation and Analysis
4.1. FKELM Performance Evaluation
4.2. Engine Identification Application of the Methodology
5. Conclusions
Acknowledgment
Author Contributions
Conflicts of Interest
References
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Label | Description | Value |
---|---|---|
H | Altitude | 0 m |
Ma | Mach number | 0 |
Wf | Fuel flow | 2.48 kg/s |
A8 | Throttle area | 0.2597 m2 |
NL | Physical low pressure spool speed | 10,302 r/min |
NH | Physical high pressure spool speed | 13,340 r/min |
W3 | Air flow | 75.6594 kg/s |
EGT | Exhaust gas temperature | 1157.34 K |
Method | 500 | 1000 | 1500 | 2000 | 2500 | 3000 |
---|---|---|---|---|---|---|
LOOC | 0.7491 | 7.7227 | 33.8026 | 74.1476 | 151.0138 | 277.2857 |
KC | 0.1641 | 0.7006 | 3.1656 | 2.9968 | 5.1389 | 8.0324 |
FLOOC | 0.0851 | 0.2268 | 1.2960 | 1.4037 | 2.5874 | 3.8879 |
Dataset | γ | Gaussian Kernel | Asymptotic Kernel | ||||
---|---|---|---|---|---|---|---|
LOOC-KELM | KC-KELM | FKELM | LOOC-KELM | KC-KELM | FKELM | ||
Boston housing | 10−2 | 0.41620 | 0.43200 | 0.45100 | 0.20877 | 0.19978 | 0.22111 |
10−1 | 0.26079 | 0.37001 | 0.27346 | 0.10276 | 0.11424 | 0.11406 | |
100 | 0.09068 | 0.16412 | 0.09078 | 0.08604 | 0.10308 | 0.07717 | |
101 | 0.07475 | 0.10137 | 0.07676 | 0.07375 | 0.10302 | 0.07170 | |
102 | 0.10673 | 0.11301 | 0.10885 | 0.07493 | 0.10328 | 0.07259 | |
Abalone | 10−2 | 0.26021 | 0.26153 | 0.26066 | 0.17534 | 0.18383 | 0.18874 |
10−1 | 0.12178 | 0.12364 | 0.11851 | 0.09174 | 0.09939 | 0.09623 | |
100 | 0.09149 | 0.09912 | 0.09316 | 0.08744 | 0.09720 | 0.09188 | |
101 | 0.08934 | 0.09720 | 0.09218 | 0.08961 | 0.09930 | 0.09215 | |
102 | 0.09441 | 0.09888 | 0.09493 | 0.09367 | 0.09941 | 0.09308 |
Model Type | Number of Regressors (na, nb) | |||
---|---|---|---|---|
NL | NH | W3 | EGT | |
NN-WM | (1, 1) | (1, 1) | (1, 2) | (0, 2) |
EWM | (1, 1) | (1, 1) | (1, 1) | (0, 2) |
GA-SWM | (1, 1) | (1, 2) | (1, 1) | (0, 2) |
FSWM | (1, 1) | (1, 2) | (1, 2) | (1, 1) |
Outputs | Methods | Train Mode | Test Mode | ||||||
---|---|---|---|---|---|---|---|---|---|
PC % | EPmean % | EPmax % | Ttrain (s) | PC % | EPmean % | EPmax % | Ttest (s) | ||
NL | WM | 89.3425 | 1.2931 | 3.1574 | 6.5430 | 89.1452 | 1.3952 | 4.6521 | 0.0666 |
NN-WM | 91.6513 | 0.7611 | 3.2982 | 13.6896 | 91.0735 | 0.8211 | 3.3837 | 0.0980 | |
EWM | 91.8945 | 0.6088 | 3.5432 | 25.4344 | 91.5883 | 0.6401 | 3.5615 | 0.1830 | |
GA-SWM | 92.1245 | 0.5042 | 2.3628 | 19.5433 | 91.9654 | 0.5942 | 2.5627 | 0.0790 | |
FSWM | 92.0860 | 0.4948 | 2.4983 | 12.5448 | 92.9837 | 0.5401 | 2.5875 | 0.0772 | |
NH | WM | 91.5461 | 0.1288 | 1.3294 | 6.8910 | 91.5142 | 0.2547 | 1.9017 | 0.0762 |
NN-WM | 92.8771 | 0.1093 | 1.0712 | 13.8384 | 92.0011 | 0.3223 | 1.4396 | 0.0991 | |
EWM | 93.1091 | 0.0412 | 0.9093 | 26.0196 | 92.7981 | 0.2198 | 1.3015 | 0.1855 | |
GA-SWM | 93.2503 | 0.0461 | 0.8872 | 20.3589 | 93.0218 | 0.2021 | 1.0637 | 0.0903 | |
FSWM | 93.3025 | 0.0485 | 0.9016 | 13.0118 | 92.9824 | 0.1977 | 1.1174 | 0.0896 | |
W3 | WM | 91.3657 | 1.8426 | 3.1154 | 7.0230 | 90.7521 | 2.3594 | 5.4214 | 0.0649 |
NN-WM | 94.1293 | 1.4875 | 3.5860 | 14.0188 | 93.3703 | 2.3100 | 4.8191 | 0.0973 | |
EWM | 94.4033 | 1.2421 | 3.0077 | 25.8054 | 93.1342 | 1.9801 | 4.8994 | 0.1896 | |
GA-SWM | 95.4259 | 1.2543 | 2.6931 | 19.7997 | 94.6555 | 1.8224 | 4.2287 | 0.0815 | |
FSWM | 95.3912 | 1.2104 | 2.8706 | 12.3192 | 94.7123 | 1.8753 | 4.0411 | 0.0797 | |
EGT | WM | 89.5422 | 2.5423 | 6.3922 | 6.5970 | 88.2763 | 3.2452 | 7.4682 | 0.0674 |
NN-WM | 90.3145 | 1.5593 | 4.7812 | 14.1670 | 89.8872 | 1.8557 | 5.9163 | 0.0986 | |
EWM | 90.6713 | 1.2431 | 4.0913 | 26.0361 | 90.2201 | 1.7411 | 5.0617 | 0.1879 | |
GA-SWM | 91.1222 | 1.2933 | 3.7534 | 20.1074 | 90.1244 | 1.8875 | 4.9018 | 0.0833 | |
FSWM | 91.0479 | 1.2706 | 3.7921 | 13.0536 | 90.1975 | 1.9452 | 4.9533 | 0.0819 |
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Lu, F.; Ye, Y.; Huang, J. Gas Turbine Engine Identification Based on a Bank of Self-Tuning Wiener Models Using Fast Kernel Extreme Learning Machine. Energies 2017, 10, 1363. https://doi.org/10.3390/en10091363
Lu F, Ye Y, Huang J. Gas Turbine Engine Identification Based on a Bank of Self-Tuning Wiener Models Using Fast Kernel Extreme Learning Machine. Energies. 2017; 10(9):1363. https://doi.org/10.3390/en10091363
Chicago/Turabian StyleLu, Feng, Yu Ye, and Jinquan Huang. 2017. "Gas Turbine Engine Identification Based on a Bank of Self-Tuning Wiener Models Using Fast Kernel Extreme Learning Machine" Energies 10, no. 9: 1363. https://doi.org/10.3390/en10091363