APPLICATIONS

1
Towards Distributed Diagnosis of Complex Physical Systems
J. Gandhe Embedded Hybrid Systems Laboratory, EECS Dept ISIS, Vanderbilt University Collaborators G. Biswas, X. Koutsoukos, S. Abdelwahed, E. Manders
APPLICATIONS
Motivation 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.
FAULT DETECTION ISOLATION FROM TRANSIENTS Fault Detection robust detection of small changes detecting fault onset Fault Isolation hypothesis generation hypothesis refinement Hypothesis 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 k1 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.

6-tank fluid system
Methodology We 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 dont 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.
Design 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)
Bond Graph Model 6th order system
Tradeoffs between independence of faults and measurements 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.
Heuristics of approximating algorithm for independent fault subsets 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
Model of Diagnosis Energy based modeling of physical systems.
TCG of Example 6-tank System
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

• Temporal Causal Graph

One Tank System
Bond Graph Energy-storage elements C,
I Dissipaters R Sources Sf, Se Junctions
conserve energy 0 Constant-effort (Parallel) 1
Constant-flow (Series)

• Derived systematically from BG
  
• Nodes effort, flow variables from BG
• Links labeled
• 1,-1 Direct, Inverse proportionality
• 1/R algebraic
• 1/C (1/I) integrating edges
• -- introduce delays

FUTURE WORK Extension to deal with cases where faults and measurements cannot be completely decoupled Extension to diagnosis of hybrid systems.
Acknowledgement This work was supported in part through the NASA-ALS grant NCC 9-159 and NSF ITR grant CCR- 022 5610.
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