New spatial basis functions for the model reduction of nonlinear distributed parameter systems

The selection of spatial basis functions is important for the model reduction of nonlinear distributed parameter systems (DPSs). Such a selection will significantly affect the accuracy and efficiency of modeling. The current study proposes new spatial orthogonal basis functions for the model reduction of nonlinear DPSs. Each new spatial basis function is a linear combination of the orthogonal eigenfunctions of such systems. The basis function transformation matrix is obtained using the balanced truncation method, which results in a straightforward derivation of the transformation matrix and low computation cost. This performance is proven theoretically. A numerical example is used to demonstrate the effectiveness of the proposed method.