Equivalence of non-linear model structures based on Pareto uncertainty

In view of practical limitations, it is not always feasible to find the best model structure. In such situations, a more realistic problem to address seems to be the choice of a set of model structures that are not clearly distinguishable in view of the available data. This study proposes a procedure based on the bi-objective optimisation and hypothesis testing that, given a pool of candidate model structures, will select a subset that is consistent with the data given a user-defined confidence level. Such a subset carries an important information that no single most likely model structure can deliver: the unmodelled component of system behaviour, given the model structure uncertainty. The procedure is illustrated using simulated and measured data. For the sake of argument convex optimisation has been considered, although the procedure also applies to non-convex problems.