(587e) Input Design for Active Fault Diagnosis Using Zonotopes

In chemical processes, aerospace systems, and many other applications, the trend toward increasing complexity and automation has made component malfunctions and other abnormal events (i.e., faults) increasingly frequent and difficult to diagnose. Without corrective action, such faults lead to performance degradation and potentially critical situations. Thus, maintaining safe and profitable operation requires fast and accurate determination of whether a fault has occurred (fault detection) and which component has failed (fault diagnosis).

Approaches to automatic fault diagnosis can be classified as either active or passive. In the passive approach, input-output data are collected in real-time and faults are diagnosed based on comparisons with a process model or historical data. In contrast, the active approach involves injecting a signal into the system to improve the diagnosability of potential faults. Compared to passive methods, research on active fault diagnosis has been very limited.

This presentation discusses a deterministic, set-based approach for active fault diagnosis. The process of interest, under nominal and various faulty conditions, is described by a set of linear discrete-time models subject to bounded disturbances and measurement noise. Faults are modeled by discrete switches between these models. Given deterministic bounds on the disturbances and measurement noise, the objective is to compute an input that is guaranteed to lead to outputs that are consistent with at most one model. First, a method is presented for computing the set of all such inputs using computations with zonotopes (a class of centrally symmetric convex polytopes). These computations are very efficient and scalable to high dimensions. Second, a method is presented for choosing an input from this set that is minimally harmful with respect to other control objectives. Although this leads to a difficult nonconvex optimization problem, it is shown to be equivalent to a mixed-integer quadratic program that can be solved efficiently. The resulting input design method is significantly more efficient than other existing methods that provide a guarantee of diagnosis. Finally, the design of active inputs within a closed-loop framework is discussed using a moving horizon approach. All methods are demonstrated for examples with multiple fault models.