KPCA-ARX time-space modeling for distributed parameter system*

Modeling of distributed parameter systems (DPSs) is difficult because of their infinite dimensional time-space nature. For a class of nonlinear distributed parameter systems described by parabolic partial differential equations (PDEs), Kernel Principal Component Analysis (KPCA) method is utilized to extract the nonlinear basis functions in dominant space, and the time-space decomposition is carried out in terms of these basis functions to obtain the outputs in time domain. Since the dominant space extraction is influenced by the parameters of kernel functions, they are optimized by Genetic Algorithm (GA) to obtain more system information with less principal components. The input stimulation and time domain outputs are used to construct the ARX model, which is identified by the recursive least squares algorithm. The simulation results show that the proposed method can obtain more system information with less principal components and gain satisfying reconstruction accuracy.