Self-active and recursively selective Gaussian process models for nonlinear distributed parameter systems

Abstract

Modeling a nonlinear distributed parameter system (DPS) is difficult because it is usually hard to obtain the first-principle models in DPS with strong spatiotemporal characteristics. In this paper, a novel data-driven model, called KL–GP, is proposed based on Karhunen–Loève (KL) decomposition and Gaussian process (GP) models. First, KL decomposition is employed for the time/space separation and dimension reduction. The spatiotemporal output is projected onto a low-dimensional KL space. Subsequently, GP models are used to build the temporal system relationships. Thus, the nonlinear spatiotemporal dynamics can be reconstructed after the time/space synthesis. The advantage of the proposed model is that KL–GP provides the predictive distribution of the outputs and the estimate of the variance of its predicted outputs. The “active data” in the DPS region can be found for model improvement according to the predicted variances. Then the developed self-active KL–GP model is extended to include adaptation and on-line implementation in real time. Systematic design procedures are needed so that the DPS modeling problems can be solved because there are no guidelines to define the architecture needed for evolution in the traditional method. This is particularly good when reducing the computational demand of the DPS model. Simulation results of DPS are presented to demonstrate the effectiveness of the self-active KL–GP modeling method and the recursively selective KL–GP modeling method.