Introduction to Fault Diagnosis and Isolation(FDI) By Hariharan 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 Analysis Our approach analyze measurements individually. Transient Response of a signal (can be approximated by Taylor series of order k) y(t) = y(t 0 ) + y ' (t 0 )(t- t 0 )/ 1! + y '' (t 0 )(t- t 0 )2 / 2! + …… + y (k) (t 0 )(t- t 0 )k / k! + R k (t), where R k (t) is the remainder term based on y (k+1) (t). Signal transient due to a fault at t 0 can be expressed as discontinuous magnitude change, y(t 0 ), plus first and higher order derivative changes, y ' (t 0 ), y '' (t 0 ), ….., y (k) (t 0 ).

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(0 th order), slope(1 st 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 System Response to Faults It seems one measurement is enough but not really…. (especially if analysis is qualitative) & discontinuities not reliably detected... f5: Faults: R b1, R b2, R 12 Discontinuity Faults: C 1, C 2 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(0 th order) of a variable but it may affect its 1 st 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 C 1 - and R 12 + 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