Probabilistic Fault Diagnosis in Networked Systems

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Probabilistic Fault Diagnosisin Networked
Systems

• ECE 499 Senior Thesis

Sumanth Kidambi Advisor Dr. C.N.
Hadjicostis July 30th, 2005 Department of
Electrical and Computer Engineering University of
Illinois at Urbana Champaign
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Outline

• Introduction
• Definitions and Notation
• Maximum Likelihood Schemes
• Threshold Analysis
• Algorithm VertexDiag
• Algorithm EdgeDiag
• Results
• Future work
• Summary and Contribution

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Introduction

• Use of networks
• Safety-critical applications (defense, medicine)
• Commercial infrastructure
• Evolution of networks
• Increasing size and complexity
• Greater likelihood of a fault propagating
  throughout the entire network
• A single fault affects a large number of users
• Need for advanced fault management and
  correlation techniques

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Fault Identification Process
Fault Diagnosis

• Fault Diagnosis Process
• Correlate observed failure indications
• Propose hypotheses to explain the alarm set

Katzela, Schwartz, 95
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Categories of Algorithms

• Deterministic
• Guarantees that entire fault set is uniquely
  identified given a syndrome
• Requires certain assumptions be made on the
  structure of the network, behavior of faulty and
  non-faulty systems.
• Friedman and Simoncini1980, Kime1986
• Probabilistic
• Attempt to diagnose faulty processing elements
  with high probability
• No restrictive assumptions
• Work by Blough, Dahbura, Lee, Pelc

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System Model

• Random graph G(V,E) with N vertices
• Vertices represent nodes
• Two vertices connected with probability c
• Nodes fail independently of each other with
  probability f.

Number of faulty nodes Bernouilli RV with
parameter f ENumFaulty Nf
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Testing Model

• Each node tests its neighbors according to
  probability parameters defined a priori
• 0-information tester model (Lee, Shin, 1993)

1 - r
e
1 - e
t
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Algorithm VertexDiag
Threshold
Greedy Approach
iterate
Seclude faulty nodes
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Threshold Analysis

• Given local syndrome information
• T1-1(ui) nodes that diagnose ui as faulty
• T0-1(ui) nodes that diagnose ui as faulty

gt
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Threshold Analysis
N
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VertexDiag Finding max P_diag

• For each node ui, Evaluate HF(ui)
• Find Set M such that
• Isolate tests by elements in Set M
• Repeat until SteadyState or max_iterations is
  reached

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VertexDiag Results
Fault Coverage
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Algorithm EdgeDiag
Scenario Evaluation
Greedy Approach
iterate
Seclude faulty nodes
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EdgeDiag Unaccounted Negative Tests

• Get Syndrome
• For each negative test (occurs when a node
  diagnoses another to be faulty)
• Determine if negative test is accounted for
• Negative test is accounted for if
• Test is incident on a node has been labeled as
  faulty
• Test is efferent from a node which has been
  labeled as faulty

Unaccounted
Accounted
1
1
2
2
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EdgeDiag Evaluating Most Likely Scenario

• For each unaccounted test, evaluate J(ui)
  PScenarioSyndrome

2. u1 and u2 are non-faulty
1. u1 and u2 are faulty
3. u1 is non-faulty and u2 is faulty
3. u1 is faulty and u2 is non-faulty
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EdgeDiag Greedy Approach

• For each node ui, Evaluate JF(ui)
• Find Set M such that
• Isolate tests by elements in Set M
• Repeat until SteadyState or max_iterations is
  reached

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EdgeDiag - Results
Fault Coverage
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Algorithm CombDiag

• Run VertexDiag
• Periodically check for fluctuations in diagnosis
  state of VertexDiag
• If fluctuating, then return
• Run EdgeDiag to detect residual faulty nodes

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CombDiag Results
Fault Coverage
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Possibilities for future extensions

• Parameter modelling
• Currently assigned a priori
• Based on empirical data
• Possibility for a heuristic scheme to refresh
  probability parameters based on some belief
  revision scheme
• Use of syndrome information
• Algorithm currently requires entire syndrome
  information (Category 1 probabilistic diagnosis
  algorithm Lee,Shin1993)

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Contribution

• A generalized algorithm
• No assumptions on structure of the network Pelc
• No limit on the number of faulty nodes
• Does not assume complete fault coverage
• High diagnostic accuracy

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Acknowledgements

• Dr. Christoforos Hadjicostis
• Vodafone
• Prof. Swenson

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Thank youQuestions?