Model Reduction for the Spatially Distributed Systems Using the Combined Eigenfunctions and Empirical Eigenfunctions

Mian JIANG*, Yong GUO, Jigang WU, Wenyun WANG

Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, Hunan University of Science and Technology, XiangTan 411201, China

Abstract: The selection of spatial basis functions will significantly affect the accuracy and efficiency of modeling for nonlinear spatially distributed processes (SDP). The performance using the general spatial basis functions is not good enough which restricts the applications of the approximated models. The current study compares the model reduction performance of empirical eigenfunctions (EEFs) and a kind of new basis functions for the spatially distributed processes, which are obtained from general spatial basis functions by linear transformation, and the transformation matrix is derived using empirical balanced truncation. The EEFs are assumed the optimal in the sense of the least squares errors for the model reduction of spatially distributed processes, however, the results of the simulations show that the accuracy of the modeling based on the present new basis functions is better than that based on the EEFs derived from the measured spatio-temporal data.

Keywords: Spatially Distributed Process; Basis Functions; Empirical Eigenfunctions; Linear Transformation; Empirical Balanced Truncation