The enhancement of a block-oriented modeling method to improve inference and prediction

Abstract

In process identification (i.e., dynamic model development) information on the precision and reliability of a parameter estimate is conveyed by a confidence interval. The best confidence interval is the one with the shortest width for a given level of confidence. Confidence interval widths widen as the standard error increases or as the number of estimated parameters increases. This article focuses on minimizing the width of confidence intervals by reducing the number of estimated dynamic parameters in the context of blockoriented modeling. This objective is accomplished by the development of a procedure that finds parameter equivalencies within (intra) and between (inter) the functional forms for the responses (i.e., outputs). It is important to recognize that the least squares estimation criterion is not valid under inter-parameter equivalency. However, the multiresponse criterion does not have this limitation and is used in this work. For the seven (7) input, five (5) output, simulated CSTR from Bhandari and Rollins (2003), the number of estimated dynamic parameters was reduced from 84 to 23. This reduction resulted in a 50% decrease in confidence interval width for a given level of confidence or, equivalently, an increase in confidence level from 50% to 99.9% for a fixed interval width.