Online Failure Detection and Identification for IFCS through Statistical Learning

1. Online Failure Detection and Identification for IFCS through Statistical Learning Yan Liu, Srikanth Gururajan, Bojan Cukic NASA OSMA SAS '04 July 2004

2. Outline • Introduction • A Validation Framework • Failure Detection • SVDD • A Fast Learning Algorithm • Online detection for different flight sections • Failure Identification • Summary and Future Work

3. NASA IFCS Architecture Failure Detection and Identification New V&V Techniques

4. A Schematic of an Aircraft Ailerons Elevators Rudder Primary control surfaces on F-15 Aircraft

5. Actuator Failures • Primary Control Surfaces • Elevators, Ailerons, Rudders • Two kinds of actuator failures • Locked surface • Control surface locked at current or predefined deflection • Results in coupling of lateral and longitudinal dynamics • Loss of surface • Part of control surface is lost • Results in loss of efficiency on the surface

6. A Validation Framework Desired Response Reference Model Error Actual Response + Command Physical Process - 3. Feedback Control Adaptive NN Estimate Trustworthiness of Outputs Learning Rule 2. Monitor Stability of Learning 1. Failure Detection and Failure Identification

7. Flight Section Division for Failure Detection and Identification Altitude (0 ft –70,000 ft ) Mach (0.2 – 1.6)

8. Failure Detection Using Support Vector Data Description (SVDD)

9. The TOOL - Support Vector Data Description • Based on SVM, Developed by Tax et. al., • Finds a sphere with the minimal volume that contains all data points. • Basically a one class classifier.

10. Highlights • Misclassification error and the function complexity bound generalization error. • Maximizing “volume” minimizes complexity – typical quadratic programming. • “Eliminates” over-fitting. • Solution depends only on Support Vectors, not the number of attributes. • Evaluation and implementation are fast and simple.

11. Previously… • We demonstrate that SVDD can be used as an effective tool for novelty detection. • SVDD can provide novelty measures for online monitoring.

12. Limitations of SVDD • Time is of essence in real-time (flight) control! • Optimization takes time! - O(n3). space complexity is high due to matrix operation. • Running on 1.6Ghz, 256M RAM, How much time does it take?

13. Two Lemmas - 1 • A simple sampling lemma Let S be a set of size n and a function that maps any subset of S, denoted by R to some value f(R). The violators of R is defined as V(R):={ s in S\R| (R U {s}) (R) }. The extreme elements in R is defined as X(R):={ s in R | ( R\{s}) (R)}. For a random sample R of size r, the expected number of violators and extremes of R,denoted by vr and xr respectively, has the following relationship: vr / (n-r) = xr+1 / (r+1).

14. Support Vectors = Extreme Points Data Description - (S) Outliers = Violators Based on the sampling lemma, it has been proven that for an LP-type problem, SVM in particular, a fast random sampling working set selection algorithm can achieve running time complexity O(m logn).

15. Data of B Data of A Violators of A Violators of B SVs of A SVs of B A B A U B

16. Two Lemmas - 2 • A lemma of combining • For two sets A and B, where both A and B are subset of S, let C = A U B. Let X(R) and V(R) denote the extremes and violators of a set R respectively. • X(C) is a subset of X(A U B), where • X(A U B) = (X(A)^X(B)) U (X(A)^V(B)) U (V(A)^X(B)); • and • V(C) is a subset of V(A U B), where • V(AUB) = V(A)^V(B) .

17. One Important Observation Only SV’s are relevant for the final form of the classifier. ( by Vapnik) - This means if we were given only the SV’s, we would obtain EXACTLY the identical classifier as if we dispose all other data points.

18. A Fast Algorithm –Decompose and Combine • Decompose: • Sequentially decompose the training set (flight data) into small working sets of fixed size. Apply SVDD for the subsets. • 2. Combine: • Combine the SVDDs of current and previously learned data subsets to obtain the global solution.

19. A decomposing example

20. Time Advantage (n=100) O(n log n ) << O(n3)

21. Fast SVDD - on nominal flight condition simulations

22. Compare results with/without decomposition Normalized data of parameters (alpha , Cz_alpha), nominal flight condition, 20hz, running for 40 secs, n=800. SVDD for whole dataset SVDD using decomposition

23. Failure Detection Tests • Normalized data of parameters (alpha , Cz_alpha). • Control failure flight condition, 20hz, running for 40 secs, 800 data frames collected. • Failure occurs at 600th data frame. • Examine data every second = 20 data frames. (Online Detection)

25. Failure Identification by Cross-Correlation Analysis

26. Nominal vs. Off-nominal • Under nominal flight conditions - • No significant interaction between longitudinal and lateral dynamics. • Under off-nominal flight conditions - • Failure results in loss of symmetry and thus significant couplings between longitudinal and lateral dynamics becomes highly probable.

27. Failure Identification by Correlation Analysis • Research results suggest that failures can be identified by studying the correlation between certain longitudinal and lateral dynamics parameters. • p (RollRate) vs. q (PitchRate) • DeltaE vs. p • p (RollRate) vs. q (PitchRate) • DeltaA vs. q Longitudinal Failure Lateral Failure

28. Experimental Results –Failure identification

29. Summary • With the fast SVDD algorithm, possible failures can be detected efficiently and effectively. • The correlation analysis provides us with accurate results and thus can be implemented as an online failure identification tool.

30. Future Work • Explore flight sections and build a SVDD database of vectors for online failure detection. • Embed the SVDD tools and cross-correlation analysis into the IFCS simulation environment for future testing. • Continue building tools. • Inclusion into VV of NN guidebook.