Introduction to Fault Diagnosis and Isolation(FDI)

ByHariharan Kannan

Fault Detection & Isolation – An Overview

Goal of FDI: To meet the requirements of reliability,

Safety and low cost operation for today’s 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.

Diagnosis- The Bigger Picture

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 ŷ.

Non-zero residuals imply that there is a fault in the system and this triggers the diagnosis algorithm.

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

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

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.

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.

Transient AnalysisOur 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(k+1)(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).

2 Tank System- Example

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 component’s constituent relation.

Backward Propagation

+ Above Normal

- Below Normal

0 Normal

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 terms:magnitude(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”.

Monitoring Implementation

Progressive Monitoring to track system dynamics after failure

Higher-order derivatives as a predictor of future behavior (justified by Taylor’s series)

Activated when there is a discrepancy between predicted and observed value.

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.

Two Tank SystemResponse to Faults

Rb2

It seems one measurement is enough but not really….(especially if analysis is qualitative)

& discontinuities not reliably detected...

f5:

Faults:Rb1, Rb2, R12

Discontinuity

Faults: C1, C2

Discontinuity

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.

Progressive Monitoring..Contd

Progressive Monitoring-Contd..

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.

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