Decision Making System and Fault Isolation

After their generation, residuals must be processed in order to detect and isolate faults. The decision process usually comes down to the selection of suitable thresholds. In ideal conditions (i.e., residuals not affected by uncertainties and disturbances), thresholds can be set to zero. However, in practice, this condition cannot be achieved therefore, nonzero thresholds must be adopted. 

Sensitivity to faults can be improved by using adaptive thresholds, adjusted online on the basis of measurements [56], Adaptive thresholds may help in evaluating residuals, provided that suitable bounding functions for the uncertainties are devised. In the case of complex systems, the sources of uncertainties are often difficult to model hence, it can be quite challenging to derive reliable bounding functions. 

A different approach to threshold selection is based on fuzzy logic [14], By adopting this approach, the value that represents the crisp discriminant between faults and disturbances is replaced by a fuzzy set, characterized by a membership function. Hence, a yes-no decision is replaced by a continuous indication of the faulty level. 

Whilst a single residual may be sufficient to detect faults, a vector of residuals is usually required for fault isolation. For isolation purposes, structured residuals [8, 17] can be generated, i.e., each residual is affected only by a specific subset of faults, and each fault only affects a specific subset of residuals. This concept can be expressed in a mathematical form by introducing a boolean fault code vector and a boolean structure matrix [8], 

In this chapter, a bank of observers is adopted for isolation of process and actuator faults. Namely, it is assumed that only N different types of faults can occur. Then, 

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