Minimizing the Number of Dynamic Parameters in Multiresponse Transfer Function Modeling

Reducing the number of model parameters without adversely affecting model accuracy narrows the width of confidence intervals for model parameters. That is, for a specific interval width, it raises the level of confidence. This article presents a new method for reducing the number of dynamic model parameters in transfer function modeling. The method involves determining sets of parameters within and across responses (i.e., outputs) that can be made equivalent without significantly affecting accuracy. This is done by exploiting multiresponse estimation, that allows outputs to depend on the same parameters. This appears to be the first application of multiresponse estimation to transfer function modeling. For the seven (7) input, five (5) output simulated CSTR from Bhandari and Rollins (2003), the number of dynamic parameters was reduced from 84 to 23. This reduction resulted in a 50% decrease in confidence interval width. Stated another way, this reduction in the number of parameters increases the confidence level from 50% to 99.9% for a fixed interval width.