Gray-box models via approximate steady-state matching

Gray-box modeling attempts to combine both fundamental knowledge and empirical data to obtain a useful model of process dynamics. This idea may be implemented in various ways, and we have previously considered an implementation based on the idea of exact steady-state matching: the steady-state locus of the physical system to be modelled is assumed to be known, a model structure capable of matching that locus is chosen, and the steady-state of the model is forced to exactly match this locus. This constraint represents the fundamental knowledge incorporated in the model, and the remaining model parameters are then optimized to best fit available empirical data, obtained from typical (i.e., dynamic) process operation. This paper considers the question of what happens when our steady-state knowledge is not exact. In particular, we briefly consider the following topics: the extent of steady-state variability we might reasonably expect in practice, the consequences of that variability on our gray-box identification results, and some ideas for dealing with this variability based on the notions of set-theoretic parameter estimation.