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Fault Diagnosis with Statistical Methods

Contribution plots presented in Section 7.4 provide an indirect approach to fault diagnosis by first determining process variables that have inflated the detection statistics. These variables are then related to equipment and disturbances. A direct approach would associate the trends in process data to faults explicitly. HMMs discussed in the first three sections of this chapter is one way of implementing this approach. Use of statistical discriminant analysis and classification techniques discussed in this section and in Section 7.6 provides alternative methods for implementing direct fault diagnosis. [Pg.179]

PC models for specific faults can be developed using historical data sets collected when the process was experiencing that fault. When current measurements indicate out-of-control behavior, a likely cause for this behavior is assigned by pattern matching by using scores, residuals, angles or their combination. [Pg.182]

Score Discriminant Assuming that PC models retain sufficient variation to discriminate between possible causes in scores that have independent Normal distributions, the maximum likelihood that data x collected at a specific sampling time are from fault model i is indicated by the minimum distance. This minimum can be determined for example by the maximum of di expressed by quadratic discrimination (Eq. 3.41) [Pg.182]

Residual Discriminant For situations where the data collected are not described well by PC models of other faults but will be within the residual threshold of their own class, it is most likely that x is from the fault model i with minimum [Pg.183]

Combined Distance Discriminant Combining the information available in scores and residuals usually improves the diagnosis accuracy [206]. Comparing the combined information to the confidence limits of each fault model, X is most likely to be from the fault model i with minimum [Pg.183]


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