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Online Failure Detection and Online Failure Detection and Identification for IFCS through Identification for IFCS through

Statistical LearningStatistical Learning

Yan Liu, Srikanth Gururajan, Bojan Cukic

NASA OSMA SAS '04July 2004

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Outline Introduction A Validation Framework Failure Detection

SVDD A Fast Learning Algorithm Online detection for different flight sections

Failure Identification Summary and Future Work

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R e a l-T im e P ID

e s tim a te dd e r iv a tiv e s

d e r iv a tiv ee rro rs

C o n tro lle rp ilo tin p u ts

S e n s o rs

c o n tro lc o m m a n d s

b a s e lin ed e r iv a tiv e s

B a s e lin eN e u ra l N e tw o rk

O n lin eN e u ra lN e tw o rk

d e r iv a tiv ec o rre c t io n s

a n a lo g

NASA IFCS Architecture

New V&V Techniques

Failure Detection and Identification

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A Schematic of an Aircraft

Elevators

Ailerons

Rudder

Primary control surfaces on F-15 Aircraft

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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

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A Validation Framework

Feedback ControlAdaptive NN

LearningRule

Desired Response

Physical Process

Reference Model

Command

Error

ActualResponse

+-

Failure Detection and Failure Identification

Monitor Stabilityof Learning

Estimate Trustworthiness of Outputs

1.

2.

3.

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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)

Altit

ude

(0 ft

–70,

000

ft )

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Failure Detection Using Support Vector Data Description (SVDD)

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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.

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HighlightsHighlights 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.

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Previously… We demonstrate that

SVDD can be used as an effective tool for novelty detection.

SVDD can provide novelty measures for online monitoring.

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Limitations of SVDDLimitations 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 2200 240400 1257

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A simple sampling lemmaTwo 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).

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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).

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A U B

A

Violators of ASVs of A

Data of A

B

Violators of BSVs of B

Data of B

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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. (a)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(b)V(C) is a subset of V(A U B), where

V(AUB) = V(A)^V(B) .

Two Lemmas - 2

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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

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1. 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.

A Fast Algorithm – Decompose and Combine

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A decomposing example A decomposing example

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Time Advantage Time Advantage (n=100)(n=100)

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

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Fast SVDDFast SVDD - - on nominal flight condition simulationson nominal flight condition simulations

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Compare results with/without Compare results with/without decompositiondecomposition

Normalized data of parameters (alpha , Cz_alpha), nominal flight condition, 20hz, running for 40 secs, n=800.

SVDD for whole dataset SVDD using decomposition

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Failure Detection TestsFailure 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)

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Failure Identification by Cross-Correlation

Analysis

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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.

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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

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Experimental Results – Failure identification

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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.

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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.

Future Work