Dynamic Observer with Complex Coefficient Filter for Fault Detection

Aiming at robust fault detection problems subject to external disturbance with a specific spectrum, this paper proposes a new fault detection filter by combing the dynamic observer and a complex coefficient gain. In order to improve the performance of minor fault detection at an early stage, the focus of the proposed design is to reduce the adverse impacts caused by the external disturbance with a specific spectrum. This is achieved through a two-stage procedure. First, the additional zeros introduced by the dynamic observer’s integration actions are allocated to near the disturbance frequency, and the gain of the transfer function matrix relating from the disturbance to the fault indicator signals is minimized. Secondly, a novel complex coefficient gain matrix is proposed to attenuate further disturbance components in the fault indicator signal. The complex coefficients is to adjust the amplitude-frequency characteristics of each part of the residual vector such that the disturbance components in the residual signal can cancel each other as much as possible. The sufficient conditions for the convergence of the proposed fault detection filter is also given in this paper. The experimental results show the improved performance of the proposed method, which can effectively attenuate the disturbance at specific frequencies and detect minor faults earlier.