Offline identification and output prediction for a class of SISO Wiener process

Abstract

AbstractIn this paper, a simplified Wiener structure (SWS) for single‐input‐single‐output (SISO) Wiener processes and an identification method based on Gaussian mixture model (GMM) and expectation maximization (EM) algorithm are proposed. The vast majority of industrial processes can be regarded as approximately monotonic non‐linear processes. Approximately, a monotonic characteristic is introduced into the non‐linear module and a rich dynamic characteristic is added into the linear module of the Wiener model. Thus, SWS is exploited and has strong generalization ability. Because GMM can describe the arbitrary distribution of sample data in theory, it is used to accurately describe the output data, including the system error term of SWS. Hence, a statistical model (Equation (17)) is obtained. Then, the EM algorithm is introduced to identify the parameters of the statistical model that contains the parameters of SWS. In the end, two numerical examples demonstrate the effectiveness of both the SWS and the GMM‐EM‐based iterative offline identification algorithm.