Geometric Approach to Fault Detection and Isolation in Multivariate Dynamical Systems

The purpose of this study is to develop a geometric approach to fault detection and isolation (FDI) in the multivariate dynamical systems. This development is validated by applying this approach to a frame, and the FDI results for multiple-input multiple-output (MIMO), multiple-input single-output (MISO), single-input multiple-output (SIMO), and single-input single-output (SISO) systems with stochastic inputs and in deterministic and probabilistic spaces have been compared. A proper distance function based on the estimated parameters obtained from the parametric system identification method is used in the geometric approach. ARX (Auto Regressive with exogenous input) and VARX (Vector Auto Regressive with exogenous input) models with the same number of estimated parameters are used in all of the above-mentioned models. The obtained results reveal that by increasing the number of inputs and/or outputs and/or using probabilistic distance function, the classification errors reduce.