1. Identification of Reduced-Oder Dynamic Models of Gas Turbines
CSC Student Seminars
(Spring/Summer, 2006)
Identification of Reduced-Oder Dynamic Models of Gas Turbines
PhD Student: Xuewu Dai
Supervisor: Tim Breikin and Hong Wang

2. Introduction 1. Introduction 2. Reduced-order Model
3. Long-term Prediction
4. Dynamic Gradient Descent
5. Nonlinear Least-Squares Optimization
6. Future Works

3. 1. Introduction Modlling of Gas Turbines Fault Detection
Condition Monitoring

4. Aims Reducing Computational Complexity: Real time
Improving Prediction Accuracy:
Long-term prediction
Robustness

5. 2. Reduced Order Thermodynamic models: 1. High order : 26th
2. Non-linear
Linearisation
Our ARX models :
1. Reduced order: 1st, 2nd …
2. Linear:

6. 3. Long-term Prediction Model Model b. Long-term Prediction Model
a. One-step Ahead Prediction Model

7. Model Equations
One-step ahead prediction
2. Long-term prediction

8. Challenges Computational Burden
How many iterations need to identify the parameters?
Dependency of Prediction Errors (Non-Gaussian Noise)
MSE=9.1318
Autocorrelation of prediction errors

9. 4. Dynamic Gradient Descent
Objective Function
Global Gradient and local gradient

10. Dynamic Gradient Descent

11. Results 1: deepest direction

12. BFGS direction

13. 5. Nonlinear Least-squares Optimization (Gauss-Newton)

14. Search direction, step size and initial value
Deepest descent: inverse global gradient
Nonlinear Least Squares: Gauss-Newton
Step size:
fixed, adjustable, line search
Initial value:
Blind guess: [ ]
LSE: [ ]

15. Result 3 Gauss-Newton

16. Prediction of 1st Order Model

17. Comparison of 1st Order Model
Methods
MSE a b
Iterations
LSE 1
ANFIS
N/A
200 GD
0.9809
0.0376
Exhausted Search
10000
DGD1*
1000
DGD2*
101
DGD3* 98
DGD1: Deepest descent direction and adjusting step size
DGD2: BFGS direction and adjusting step size
DGD3: Gauss-Newton and line search

18. High Order Model initial (by LSE) : [1.2805 -0.29191 0.10582 0.15903]
final: [ ]

19. 6. Future Works Initial value Problem: Robustness Problem: ???
Applying such learning algorithm to Neural Networks
Model structure selection by autocorrelation of prediction errors
NARMX models

20. CSC Student Seminars
(Spring/Summer, 2006)
Thanks

21. Appendix

22. Initial value problem manual setting of initial value
[ ]
[ ]
Final MSE=
setting initial value by LSE
[ ]
[ ]
Final MSE=

23. appendix