Model Uncertainty-Aware Residual Generators for SISO LTI Systems Based on Kernel Identification and Randomized Approaches

Robustness of residual signals to model uncertain-ties and noise in the measurements is of paramount importance in model-based fault diagnosis. Model uncertainty has been mainly represented in a structured way by considering known bounds on the model parameters, thus relying on prior knowledge about the plant structure and values of its physical parameters. When the plant is completely unknown, system identification techniques must be used for model-based diagnosis. In this work, we present a data-driven approach to represent the uncertainty in the identified model. This uncertainty is described in the frequency domain using kernel-based identification and robust control tools. The estimated model uncertainty region overlaps with the true uncertainty region with a probability specified by the user. The user choices are thus reduced to the selection of only some interpretable hyperparameters. Then, a residual generator robust to the es-timated model uncertainty and measurements noise is designed by a standard $H_{\infty}$ approach. Simulation results on SISO LTI systems show the effectiveness of the approach in producing a residual signal viable for the detection of additive faults.