Real-Time Parameter ID Using Polynomial Chaos Expansions

Abstract

A novel real-time parameter identification algorithm has been developed that exploits polynomial chaos expansion (PCE) representations of uncertain parameters. Dynamic system models inevitably contain parameters whose values are rarely known with absolute certainty. In many cases, such parameters are either not measurable, or they are slowly time varying. In some cases, the dynamic system model is inadequate and parameter values are simply chosen to provide a “best fit” representation. For the method proposed here, we assume apriori knowledge of the probability distributions associated with the uncertain parameters. Within the PCE framework, the uncertain parameter distribution is explicitly propagated through the dynamic system equations using a Galerkin projection onto an orthogonal polynomial basis. The probabilistic PCE model is then collapsed to a deterministic model where an adaptive algorithm is designed to effectively reduce the uncertainty. For illustration, this algorithm is numerically demonstrated using a simple first order dynamic system with only a single uncertain parameter.