Dec. 3 2010 2:30PM

Dec. 3 2010 2:40PM

Model-based prediction is frequently used for industrial control or monitoring purposes. It can be based on recursive Bayesian parameter estimation representing theoretically consistent treatment of uncertainty. In a special case -- under the assumption of normal probability distribution of all processed quantities and when restricted to the linear normal autoregressive model with external variables (ARX) - it leads to the very efficient and numerically robust algorithm. Industrial applications often work with a mathematical model, the structure of which is based, at least to some extent, on a physical model of the process. Recursive estimation can track parameter changes caused either by a real change of some physical parameter of the process or compensating imperfect matching of the process and its model. For unrestricted estimation, parameter estimates may occur in regions, which are formally correct but physically unreasonable. Then, especially in the case of an abrupt change of some physical parameter of the process, behavior of a corresponding predictor or controller can become undesirable. Intrinsic application of constraints to the parameter estimates could be beneficial in such cases.

Existence of bounded intervals for acceptable model parameters can be well respected within Bayesian framework. It suffices to restrict support of their prior distribution to this range. For recursive use, this possibility has been theoretically elaborated for a Gaussian parametric model and for a uniform parametric model. An alternative, albeit suboptimal solution has been sought to be practically applicable in metal processing industry. Possible solution is based on simultaneous run of two or more proven estimators different in applied process models. Simulated and real data tests outlined potential benefits of the algorithm.

Mezinárodní konference Výzkumného centra DAR 2010 pořádaná v Jindřichově Hradci v prostorách Fakulty managementu VŠE (Kontaktní osoba: Jiří Ivánek)