A functional pooling framework for the identification of systems under multiple operating conditions

The problem of identifying stochastic dynamical systems capable of operating under various conditions, with each condition maintained for the observation time interval, is tackled based on data corresponding to a sample of such conditions. The problem is important and encompasses a plethora of practical systems, including mechanical systems operating under different loading conditions, structures under different environmental conditions, and so on. It is tackled within a novel framework that consists of the class of functionally pooled (FP) models, data pooling for combining data records from the various operating conditions, and statistical inference. The FP models postulated are of the autoregressive with exogenous input (FP-ARX) type, and differ from their conventional counterparts in that i) their parameters and statistical characteristics are functions of a measurable variable characterizing the operating condition, and ii) cross-correlations among operating conditions (due to external and other factors) are accounted for. Model estimation is achieved via the least squares and maximum likelihood principles, and the asymptotic properties of the estimators are established. The methods' performance characteristics are assessed via a Monte Carlo study.