Data-Driven Fault Detection and Identification of Nonlinear Systems Using Weighted Window Extended Dynamic Mode Decomposition

In this study, we designed a data-driven fault detection and identification method for time-varying nonlinear systems using the Koopman operator. Koopman operator is an infinite-dimensional linear operator that transforms a nonlinear dynamical system. In this paper, Weighted Window Extended Dynamic Mode Decomposition (WW-EDMD) is used to obtain the Koopman operator through a recursive procedure to reduce the computation time and memory usage. The forgetting factor is implemented to enhance the fault detection ability, weighting the latest data in the WW-EDMD framework. When the column vector norm of the matrix
$B$
is less than the designed threshold, the fault is detected and estimated. Through the data collection period, the performance of the obtained Koopman operator model is confirmed by comparing the true state of the model. Numerical simulation results show that the proposed method has better fault detection ability for time-varying nonlinear systems than window extended dynamic mode decomposition.