# Presentation: 326685

## Online Failure Detection and Identification for IFCS through Statistical Learning

- Yan Liu, Srikanth Gururajan, Bojan Cukic
**NASA OSMA SAS '04**
- July 2004

## Outline

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

## NASA IFCS Architecture

- NASA IFCS Architecture

**New V&V Techniques**** **

**Failure Detection and Identification **

## A Schematic of an Aircraft

- Elevators

- Ailerons

- Rudder

- Primary control surfaces on F-15 Aircraft

## 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

## A Validation Framework

- Feedback Control
- Adaptive NN

- Learning
- Rule

- Desired
- Response

- Physical Process

- Reference Model

-  Command

- Error

- Actual
- Response

- +

- -

**Failure Detection and Failure Identification**

**Monitor **
**Stability**
**of Learning**

**Estimate Trustworthiness of Outputs**

**1.**

**2.**

**3.**

**Notes:**
Pre-filter - block the penetration of unreliable or unreasonable training data from entering the online adaptive component and provide backward and forward recovery capabilities. 
Run-time monitor – deal with the real-time stability and convergence analysis of the learning device indicating the current confidence measure.
Post-filter - disallow the propagation of unsafe control adjustments into the controller, based on its knowledge of system safety requirements.

## Flight Section Division for Failure Detection and Identification

| 4 | 8 | 12 | 16 |
| --- | --- | --- | --- |
| 3 | 7 | 11 | 15 |
| 2 | 6 | 10 | 14 |
| 1 | 5 | 9 | 13 |

- Mach (0.2 – 1.6)

- Altitude (0 ft –70,000 ft )

## Failure Detection Using Support Vector Data Description (SVDD)

## 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.

## 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. **

## Previously...

- We demonstrate that SVDD can be used as an effective tool for novelty detection.

- SVDD can provide novelty measures for online monitoring.

## 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?

| Data size | Time (sec) |
| --- | --- |
| 100 | 2 |
| 200 | 240 |
| 400 | 1257 |

## Two Lemmas - 1

**Two Lemmas - 1**

- 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).

## Support Vectors = Extreme Points

- Outliers = Violators

- Data Description -

- (S)

- 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).

## Slide 15

## Two Lemmas - 2

-      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) .

**Two Lemmas - 2**

## 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.

**One Important Observation**

## A Fast Algorithm – Decompose and Combine

- 	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.

- A Fast Algorithm –** **Decompose and Combine

## A decomposing example 

## Time Advantage  (n=100)

- O(n log n ) << O(n3)

## Complexity of the Algorithm

- Space complexity is highly reduced because of the decomposing.
- Time complexity can be reduced to *O(d**3**+nlogn)* for normal cases where data is normally distributed and the number of support vectors is just a small fraction of n.
- The selection of working set size *d* can be decided upon system configuration and other requirements through empirical runs.
- This algorithm can also be used for sequential learning. However, it is likely that running of this algorithm on two very differently distributed data sets will give a tighter DD than the DD on the union.

## Fast SVDD - on nominal flight condition simulations

## 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

## Time Recorded

| Method | Time (sec) |
| --- | --- |
| Sequential Decomposition | 36 |
| Random Decomposition | 37 |
| No decomposition | 3752 |

**Time Recorded**

## 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)

## Slide 26

## Failure Identification by Cross-Correlation Analysis

## 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.

## Cross-correlation Analysis

- Statistically, we inspect the correlations through the following steps:
- Calculate the correlation coefficient between two variables.
- Based on the p-value of our statistical hypothesis testing on the observed correlation coefficient, we decide on whether the coef is significant. (p<0.05, and can be adjusted.)
- In general, a coefficient that is greater than 0.8 or less than –0.8 indicates that these two variables are highly correlated.

## 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

## Experimental Results – Failure identification

## Experimental Results – No failure

## 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.

## Future Work

- 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.