Improved Empirical Eigenfunctions Based Model Reduction for Nonlinear Distributed Parameter Systems

摘要

Karhunen—Loeve (KL) decomposition is a popular approach for determining the principal spatial structures from the measured data. Empirical eigenfunctions (EEFs) can generally generate a relatively low-dimensional model among all linear expansions. The current study proposes improved EEFs for model reduction of the nonlinear distributed parameter systems (DPSs) by the basis function transformation from initial EEFs. The basis function transformation matrix is obtained using the balanced truncation method. This performance is proved theoretically. The numerical simulations for the rescaled Kuramoto— Sivashinsky equations show that using the improved EEFs has an evidently better performance than using the same number of the initial EEFs.