Towards Distributed Diagnosis of Complex Physical SystemsTowards Distributed Diagnosis of Complex Physical Systems

J. GandheEmbedded & Hybrid Systems Laboratory, EECS Dept & ISIS, Vanderbilt University

Collaborators: G. Biswas, X. Koutsoukos, S. Abdelwahed, E. Manders

APPLICATIONSAPPLICATIONS

TCG of Example 6-tank System

6-tank fluid system

Heuristics of approximating algorithm for independent fault Heuristics of approximating algorithm for independent fault subsetssubsets

Measurements with Discontinuities have the most discriminatory power for a fault. (Manders, et Al Safeprocess 2000)

Initial fault partitions are established by placing those faults in different independent sets which can be distinguished with measurement sets containing different Measurements with Discontinuities.

After initial partitions are established, to obtain a maximum number of partitions, add the next fault to a partition by

-- creating a new partition for it

-- or if that is not possible, then choose the best available partition for that the fault.

Best Partition to which a fault should be added is the one whose measurement set most overlaps with measurements that uniquely identify this fault and also causes the least number of combinations with other partitions.

Complexity of the partition procedure - O (f * m4) f, m – Number of faults and measurements respectively

MotivationMotivation

Large Scale , Complex Systems deployed in mission-critical and safety-critical applications should be reliable, dependable, available, and operationally robust. Online Model based fault diagnosis with composed model of overall complex system makes diagnosis task computationally difficult Hard to analyze complex nonlinearities online. Develop qualitative reasoning techniques to make diagnostic analysis computationally simpler and robust

Develop Distributed Diagnosis Algorithm so a large computationally expensive diagnosis task is decomposed into a set of smaller tasks that can be performed independently, thus reducing the overall complexity of online diagnosis.

http://macs.vuse.vanderbilt.edu

http://www.isis.vanderbilt.edu

FUTURE WORKFUTURE WORK Extension to deal with cases where faults and measurements cannot be completely decoupled Extension to diagnosis of hybrid systems.

Measured variables (encircled): Flows through pipes modeled as linear resistances

Three Independent fault sets are enclosed in red boxes.

Measurements available {f4, f7, f14, f17, f24, f27}

Faults { C1, R1, C2, R2, C3, R3, C4, R4, C5, R5, C6, R6}

Three independent Fault subsets are – • {C1, R1, C2, R2}• {C3, R3, C4, R4}• {C5, R5, C6, R6}

Tradeoffs between independence of faults and Tradeoffs between independence of faults and measurementsmeasurements

With fewer measurements, the number of possible independent

fault subsets will be smaller, and the number of faults

in each subset will be larger.

Measurements tend to make faults more independent.

Higher the number of measurements, higher the number of

independent fault subsets.

But making a large number of measurements is costly and infeasible.

We assume presence of measurements that ensures complete diagnosability and then try to find maximum number of independent fault sets. This is equivalent to a form of the set covering problem, which is NP-Complete.

Design of the algorithmDesign of the algorithm

Two steps

-- Establish measurements that uniquely distinguish a fault : For a given set of faults and a set of available measurements, find the subsets of measurements for each fault that can uniquely distinguish the fault from all other faults.

-- Group faults to obtain maximum number of independent fault subsets : Given the uniquely distinguishing measurement set, generate independent fault sets such that faults in the two independent fault sets do need same measurements for their isolation.

Step 2 is NP-Complete. (Reduction from Set Packing)

Model of DiagnosisModel of Diagnosis

Energy based modeling of physical systems.

Bond Graph Model 6th order system

Sf 0

C1

R1

1

R12

0

C2

R2

1

R23

0

C3

R3

1

R34

0

C4

R4

1

R45

0

C5

R5

1

R56

0

C6

R6

01

2

34

56

7

89

1011

12

1314

1516

17

1819

2021

22

2324

2526

27

f0+1

f11/C1 dt

e2f2

=

1/R1

-1

e3 e4

=

+1 1/R12

f3

=

-1

=f5

+1f6

1/C2 dt

e7

=

1/R2

-1

e8 e9

=

+1 1/R23

f8

=

-1

f9

f10+1

f111/C3 dt

e12 f121/R3

-1=

=

e13e14f15= =1/R34 +1

f13

+1f16

1/C4 dt

e171/R4

-1=

e18e19f19=1/R45 +1

f18

= = -1-1

f20+1

f211/C5 dt

e22f22

=

1/R5

-1

e23 e24

=

+1 1/R56

f23

=

-1

=f25

+1f26

1/C6 dt

e27

=

1/R6

-1

=

-1 =

=

-1

= -1

=-1 e25

e5

e15

e10

=

-1

e1 e6

e11e16

e20

e21 e26

f4

f17

f14

f7

f27

f24

One Tank System Bond GraphEnergy-storage elements: C, IDissipaters: RSources: Sf, SeJunctions – conserve energy0: Constant-effort (Parallel)1: Constant-flow (Series)

Derived systematically from BG Nodes: effort, flow variables from BGLinks labeled:1,-1: Direct, Inverse proportionality1/R: algebraic1/C (1/I): integrating edges

-- introduce delays

Temporal Causal Graph

Complete Diagnosability

Faults Measurements

Independence of faults

MethodologyMethodologyWe start with - A set of possible faults in the system and a set of available measurements.

Our Goal - Distributed and Complete Diagnosis ( i.e., all faults of interest can be uniquely identified)

Our Method- Partition the set of faults into subsets such that we can construct non-interacting diagnosers for each subset. Two diagnosers do not interact if they don’t share information in establishing unique diagnosis results that are globally valid. This is done by ensuring that the fault subsets corresponding the two diagnosers are independent i.e. they do not require the same set of measurements to achieve complete diagnosability.

FAULT DETECTION & ISOLATION FROM TRANSIENTSFAULT DETECTION & ISOLATION FROM TRANSIENTS

Fault Detection – robust detection of small changes + detecting fault onset

Fault Isolation – hypothesis generation + hypothesis refinementHypothesis Generation – On fault detection, breadth first backward propagation algorithm is invoked which generates possible fault candidates (parameter values in TCG) .Signature Generation – For every fault hypothesis, fault signatures are generated. Fault signature is a set of k+1 feature values consisting of the magnitude and 1st through kth order derivative computed from the signal residual.

Hypothesis Refinement For every fault hypothesis, a progressive monitoring scheme is applied on the temporal causal graph to drop inconsistent fault hypothesis and converge on the true fault.

Acknowledgement

This work was supported in part through the NASA-ALS grant NCC 9-159 and NSF ITR grant CCR- 022 5610.