Estimating a minimum set of physically based dynamic parameters to enhance statistical inference in block-oriented modeling

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 intervals widen as the standard error increases or as the number of estimated parameters increases. When the value of a parameter is needed for physical understanding of process characteristics, its precision and reliability, i.e., certainty, is crucial. Parameter certainty increases as the number of estimated parameters decreases because this causes confidence intervals to shorten and confidence levels to increase. Hence, this article focuses on maximizing parameter certainty of physically interpretable dynamic parameters under block-oriented modeling by obtaining accurate values for all the dynamic parameters from a minimum set of estimated parameters. This objective is accomplished by the development of a procedure that identifies equivalent sets of parameters and estimates one parameter for each set. For a seven (7) input, five (5) output, simulated CSTR, its 84 physically based dynamic parameters were accurately determined from 23 estimated parameters that resulted in an increase in confidence level from 50% to 99.9% for a fixed interval width.