An Unrestricted Algorithm for Accurate Prediction of Multiple-Input Multiple-Output (MIMO) Wiener Processes

Abstract

Previous research [N. Bhandari and D. K. Rollins, Ind. Eng. Chem. Res., 2003, 42, 5583] introduced a methodology for obtaining accurate continuous-time multiple-input, multiple-output (MIMO) models for Wiener processes with nonlinear static and dynamic behavior. This methodology consists of a model-building procedure for estimation of model forms in the Wiener structure and a choice of two algorithms for exact predictions of true Wiener systems. One algorithm uses only the most-recent input changes but is restricted to approximately steady-state conditions between input changes. The other algorithm has no restricted conditions but is dependent on all past input changes and, thus, requires a fading memory treatment. This article extends the former algorithm by proposing a new continuous-time algorithm that is not restricted by steady-state conditions between input changes. In addition, the proposed algorithm is dependent only on the most-recent input changes. Evaluation of the proposed algorithm is conducted using a simulated continuously stirred tank reactor (CSTR) that closely follows a Wiener process; the results of this study are compared with the other two previously mentioned algorithms. Results are given for two basic cases: (i) no noise and (ii) independently, identically, and normally distributed noise. Res., 2003, 42, 5583] introduced a methodology for obtaining accurate continuous-time multiple-input, multiple-output (MIMO) models for Wiener processes with nonlinear static and dynamic behavior. This methodology consists of a model-building procedure for estimation of model forms in the Wiener structure and a choice of two algorithms for exact predictions of true Wiener systems. One algorithm uses only the most-recent input changes but is restricted to approximately steadystate conditions between input changes. The other algorithm has no restricted conditions but is dependent on all past input changes and, thus, requires a fading memory treatment. This article extends the former algorithm by proposing a new continuous-time algorithm that is not restricted by steady-state conditions between input changes. In addition, the proposed algorithm is dependent only on the most-recent input changes. Evaluation of the proposed algorithm is conducted using a simulated continuously stirred tank reactor (CSTR) that closely follows a Wiener process; the results of this study are compared with the other two previously mentioned algorithms. Results are given for two basic cases: (i) no noise and (ii) independently, identically, and normally distributed noise. IntroductionThe nature of chemical processes in industry has become increasingly complicated. Linear modeling is no longer as useful in obtaining accurate models as nonlinear modeling. As one of the popular nonlinear techniques, block-oriented modeling has received a significant amount of attention. 1-3 Hammerstein and Wiener systems are two block-oriented structures that have been widely used to model chemical processes. Both of these systems have a ...

Continuous-time block-oriented nonlinear modeling with complex input noise structure

“…Both Uryson and projection-pursuit models have only one common input u(t). (1998, 1999a) and also to an industrial C2-splitter (1999b Bhandari and Rollins, 2003) are introduced, and then the continuous-time classical, restricted and unrestricted algorithms for the step input change sequences (Chin et al, 2004) are presented. As Chen and Rollins (2000) have shown, the discrete-time models can have critical drawbacks when sampling is infrequent, non-constant, or not online, while the continuous-time methods, like H-BEST and W-BEST, do not suffer from these limitations.…”

“…1.10. Bhandari and Rollins (2003) Later on, the algorithms for the MIMO Wiener processes were further investigated by Chin et al (2004). They defined the classical, restricted and unrestricted algorithm for a MIMO Wiener system clearly for the first time.…”

“…To overcome this limitation, an unrestricted algorithm was proposed by Chin et al (2004). Assume that the linear dynamic function is with n poles and m zeros and can be written as…”