An Improved Detection Statistic for Monitoring the Nonstationary and Nonlinear Processes

The objective of this paper is to address a data-driven fault detection design for the nonstationary and nonlinear processes. Firstly, an improved statistic is proposed for fault detection, which fits the data using the design functions. The fitted parameters are then used for computing the trend of the fault-free data, based on which the prediction residual is generated and the improved statistic is constructed. This method can cope with the limitations of the standard Hotelling statistic in the sense of adaptation and condition number. Secondly, based on the formula of the inverse of the calibration covariance matrix, an incremental and decremental algorithm is proposed for updating the improved statistic. Compared with the brute force algorithm, it can reduce the computational complexity significantly, which benefits the online detection. The effectiveness of the improved statistic is validated by a nonstationary and nonlinear numerical case. Also it is used for monitoring the satellite attitude control system. The results show that the improved statistic, compared with the standard Hotelling statistic, is more sensitive to the additive fault.