Detection and Diagnosis of System Nonlinearities Using Higher Order Statistics

This paper is concerned with the statistical analysis of closed loop data for diagnosing the causes of poor control loop performance. Higher Order Statistical (HOS) techniques have been developed over the last two decades, but until now have not been applied to the area of process monitoring. The main contribution of this work is to utilize the higher order statistical tools such as cumulants and their frequency domain counterparts (bispectrum, bicoherence, trispectrum) to detect and quantify the non-Gaussianity and nonlinearity of regulated processes or control error variables which are sometimes the main contributors to the poor performance of many of the control loops. The bicoherence index together with the process and manipulated variable plots are used to diagnose the sources of system nonlinearities. Successful application of the proposed method is demonstrated on simulated as well as industrial data.