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 T2 (LST2), 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 LST2 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 LST2 is much lower than that of T2 based on PCA, while LST2 is more sensitive to fault.