Introduction%20to%20Fault%20Diagnosis%20and%20Isolation(FDI)

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Introduction to Fault Diagnosis and Isolation(FDI)

• By
• Hariharan Kannan

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Fault Detection Isolation An Overview

• Goal of FDI
• To meet the requirements of reliability, Safety
  and low cost operation for todays engineering
  systems.
• To accurately isolate problems and make control
  changes to bring system behavior back to desired
  operating ranges or at least a safe mode of
  operation.

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Diagnosis- The Bigger Picture
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Idea of Model Based Diagnosis

• A set of variables called observations are
  measured.
• Residuals r, are computed as the difference
  between the observations y, and the predicted
  normal behavior y.
• Non-zero residuals imply that there is a fault in
  the system and this triggers the diagnosis
  algorithm.

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Types of Faults

• Incipient Faults
• Occur slowly over time
• Linked to wear and tear of components and drift
  in control parameters.
• Intermittent Faults
• Present only for very short periods in time
• Could have disastrous consequences in time
• Abrupt Faults
• Dramatic and persistent
• Cause significant deviations from steady state
  operations-Transients

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Steps in Fault Diagnosis

• Fault Detection- signaled by a non zero residual
• Fault Isolation
• Qualitative Fault Isolation
• Hypothesis Generation- Back Propagation Algorithm
• Generating Fault Signatures- Forward propagation
  Algorithm
• Progressive Monitoring
• Quantitative fault Isolation
• Parameter Estimation

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Modeling For Diagnosis

• The models should describe both normal and
  faulty system behavior.
• The model should generate dynamic behavior under
  faulty conditions, so fault transients can be
  predicted by the model.
• The model should incorporate sufficient
  behavioral details so that deviations in observed
  variables can be mapped back to system components
  and parameters.

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Temporal Causal Graph

• Dynamic Characteristics of system behavior
  derived from the bond graph are represented as a
  temporal causal graph
• Algorithms for monitoring, fault isolation and
  prediction are based on this representation.
• It is derived from the bond graph model.
• Incorporates cause effect relationship among the
  power variables shown in the bond graph.
• Component parameters and temporal information are
  added to individual causal edges.

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Transient Analysis

• Our approach analyze measurements individually.
• Transient Response of a signal (can be
  approximated by Taylor series of order k)
• y(t) y(t0) y'(t0)(t- t0)/ 1!
• y''(t0)(t- t0)2/ 2!
• y(k)(t0)(t- t0)k/ k! Rk(t),
• where Rk(t) is the remainder term based on
  y(k1)(t).
• Signal transient due to a fault at t0 can be
  expressed as discontinuous magnitude change,
  y(t0), plus first and higher order derivative
  changes, y'(t0), y''(t0), .., y(k)(t0).

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2 Tank System- Example
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Derivation of TCG from Bond Graph

• Effort and flow variables are vertices
• Relation between variables as directed edges
• implies that two variables associated with the
  edge take on equal values, 1 implies direct
  proportionality,-1 implies inverse
  proportionality.
• Edge associated with component represents the
  components constituent relation.

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Backward Propagation
Above Normal - Below Normal 0
Normal
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Fault Prediction-Establish Signature for system
variables

• The prediction module uses the system model to
  compute the dynamic, transient behavior of the
  observed variables and the eventual steady state
  behavior of the system under fault conditions.
• Future behavior is expressed in qualitative
  termsmagnitude(0th order), slope(1st order)
• The algorithm used propagates the effects of a
  hypothesized fault to measure a qualitative value
  for all measured system variables.
• Forward propagation along temporal edges implies
  an integral effect, the cause variable affects
  the derivative of the effect variable.
• Algorithm stops when signature of sufficient
  order is generated.
• Order depends on set of chosen measurement
  variables desired level of diagnosability.

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Monitoring Implementation

• Progressive Monitoring to track system dynamics
  after failure
• Higher-order derivatives as a predictor of future
  behavior (justified by Taylors series)
• Activated when there is a discrepancy between
  predicted and observed value.

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Diagnosability of a system

• Diagnosability is a function of the number of
  possible faults that can be uniquely identified
  by a fault isolation system.
• Completely Diagnosable system- A system which can
  uniquely isolate all possible hypothesized
  faults.
• Depends on selected observation set and chosen
  order of their signature.
• Consideration of higher order variable effects is
  likely to result in greater diagnosability.
• same diagnosabilty can be achieved- by
  considering higher order signatures but smaller
  number of total observations or using a large
  number of observations with lower order
  signatures.

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Two Tank SystemResponse to Faults
f5 Faults Rb1, Rb2, R12
Discontinuity
Faults C1, C2
Discontinuity
It seems one measurement is enough but not
really. (especially if analysis is
qualitative) discontinuities not reliably
detected...
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Progressive Monitoring

• Monitoring involves comparing predicted
  signatures of the hypothesized faults to actual
  measurements as they change dynamically.
• Choice of monitoring time step is vital-neither
  too low or too small
• Transient characteristics at the time of failure
  tend to change over time as other phenomena in
  the system affect the measured variables.
• Ex A fault may have no effect on initial
  magnitude(0th order) of a variable but it may
  affect its 1st derivative(slope), predicting that
  it will be above normal.
• Therefore immediately after fault occurs,
  variable value will be observed to be normal ,
  but as time progresses, the derivative effect
  will cause the variable to go above normal.
• This notion of employing higher order derivatives
  Progressive Monitoring.

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Progressive Monitoring..Contd
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Progressive Monitoring-Contd..
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Limitations of Purely Qualitative Schemes

• For the case where a signal does not undergo
  abrupt change, higher order derivatives beyond
  the first non-zero derivative have no
  discriminatory power.
• Consider 2 faults with second order
  signatures-(0,,) and (0,,-) for a particular
  measurement.
• signal shows no discontinuous change at point of
  failure, matches (,,.)
• Even if signal slope is measured to be -, the
  (,,) cant be eliminated as a higher order
  derivative not captured in the second order
  signature could be -. So faults cant be isolated.
• Solution- Quantitative diagnosis.

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Parameter Estimation
Consider system defined by
C1- and R12 are the fault candidates.
Estimate the parameter by substituting the
nominal values values for the variables in the
I-O model of the system.
If the error e converges to 0, for a particular
parameter, that parameter is the fault