Certifying Robustness of Separating Inputs and Outputs in Active Fault Diagnosis for Uncertain Nonlinear Systems

To ensure safe operation of technical processes, faults have to be reliably detected and isolated to provide information for process maintenance, shutdown, or reconfiguration. Fault detection and isolation can be achieved by invalidation of fault candidates, i.e. models of the system in fault-free and faulty condition. In order to enhance the performance of fault detection and isolation, so-called active approaches use input signals with the objective that the resulting system outputs are consistent with at most one fault candidate. Guaranteeing or analyzing robustness of active fault diagnosis with respect to input, output, and process uncertainties and nonlinearities is challenging. This paper provides certificates of robustness of input sequences with respect to the aforementioned uncertainties and nonlinearities. The certificates enable the determination of input and output uncertainties for which unique fault diagnosis results can still be guaranteed. In addition, a method is presented to select a minimal number of outputs that still guarantee robust fault diagnosis, thus reducing the measurement setup and cost. The approach employs nonlinear mixed-integer feasibility problems and a relaxation framework and does not require the explicit computation of reachable sets. The approach is applicable to polynomial discrete-time systems and is demonstrated for a numerical example.