An Improved Detection Statistic for Systems with Unsteady Trend

Abstract The object of this paper is to address data-driven fault detection design for systems with unsteady trend, which shows cyclicity, monotonicity and non-zero mean. Firstly, mean theorem and covariance theorem are proposed and proved. The former is the mean property of projection matrix, and the latter is the recursive formula for covariance matrix of regression residual. Secondly, an improved fault detection statistic, called Least Square T 2 (LST 2 ), is proposed. It can partly solve the detection problem for systems with unsteady trend. The improvement can also partly cope with the limitations of the traditional multivariate detection methods, such as Principal Component Analysis (PCA). Thirdly, based on the two theorems, a recursive algorithm and a moving window algorithm of LST 2 are given, thus both time and space complexity are greatly reduced for online detection. The effectiveness of the presented detection statistic is evaluated with an application of monitoring satellite attitude control system. The case study result shows that the false alarm rate of LST 2 is much lower than that of T 2 based on PCA, while LST 2 is more sensitive to fault.