Maximum entropy approach to the identification of stochastic reduced-order models of nonlinear dynamical systems

Data-driven methodologies based on the restoring force method have been developed over the past few decades for building predictive Reduced-Order Models (ROMs) of nonlinear dynamical systems. These methodologies involve fitting a polynomial expansion of the restoring force in the dominant state variables to observed states of the system. ROMs obtained in this way are usually prone to modeling errors due to the approximate nature of the polynomial expansion. Also, uncertainties exist as a reflection of various limitations in experimental methods. We develop in this article a stochastic methodology that endows these errors and uncertainties with a probabilistic structure in order to obtain a quantitative description of the proximity between the ROM and the system that it purports to represent. Specifically, we propose an entropy maximization procedure for constructing a multi-variate probability distribution for the coefficients of power-series expansions of restoring forces. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed framework.