Diagnosis of poor control-loop performance using higher-order statistics

Higher-order statistical (HOS) techniques were first proposed over four decades ago. This paper is concerned with higher-order statistical analysis of closed-loop data for diagnosing the causes of poor control-loop performance. The main contributions of this work are to utilize HOS tools such as cumulants, bispectrum and bicoherence to develop two new indices: the non-Gaussianity index (NGI) and the nonlinearity index (NLI) for detecting and quantifying non-Gaussianity and nonlinearity that may be present in regulated systems, and to use routine operating data to diagnose the source of nonlinearity. The new indices together with some graphical plots have been found to be useful in diagnosing the causes of poor performance of control loops. Successful applications of the proposed method are demonstrated on simulated as well as industrial data. This study clearly shows that HOS-based methods are promising for closed-loop performance monitoring.