Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.