Variable selection procedures and efficient suboptimal mask search algorithms in fuzzy inductive reasoning

Abstract

This paper describes two new suboptimal mask search algorithms for Fuzzy inductive reasoning (FIR), a technique for modelling dynamic systems from observations of their input/output behaviour. Inductive modelling is by its very nature an optimisation problem. Modelling large-scale systems in this fashion involves solving a high-dimensional optimisation problem, a task that invariably carries a high computational cost. Suboptimal search algorithms are therefore important. One of the two proposed algorithms is a new variant of a directed hill-climbing method. The other algorithm is a statistical technique based on spectral coherence functions. The utility of the two techniques is demonstrated by means of an industrial example. A garbage incinerator process is inductively modelled from observations of 20 variable trajectories. Both suboptimal search algorithms lead to similarly good models. Each of the algorithms carries a computational cost that is in the order of a few percent of the cost of solving the complete optimisation problem. Both algorithms can also be used to filter out variables of lesser importance, i.e. they can be used as variable selection tools.