Hybrid Representations of Coupled Nonparametric and Parametric Models for Dynamic Systems

Abstract

Parametric modeling of stochastic systems has proven useful for systems with well-defined and well-structured sources of uncertainty. The suitability of such models is usually indicated by small levels of uncertainty associated with their parameters. The parametric model may not be efficiently employed to deal with problems associated with a high level of uncertainty, particularly due to the modeling uncertainty. The class of so-called nonparametric stochastic models has recently been introduced to address this specific issue and found to be useful to some extent. This paper presents a coupling technique adapted to the receptance frequency-response-function matrix that will be useful for analyzing a complex dynamic system, particularly when it consists of several stochastic subsystems, each of which is individually deemed to be suitable for either a parametric model or a nonparametric model. Such a complex dynamic system is otherwise difficult to analyze. The existing nonparametric approach was, to date, applied to the real-valued positive-definite/semidefinite random system matrix: for example, mass, damping, and stiffness matrices. In the present work, the nonparametric approach is also employed with the complex-valued symmetric receptance frequency-response-function matrix, now acting as the system matrix, by having recourse to Takagi's factorization.