Incremental Modeling of Nonlinear Distributed Parameter Processes via Spatiotemporal Kernel Series Expansion

In this article, an incremental modeling approach is proposed to model nonlinear distributed parameter systems, with the help of the newly constructed spatiotemporal Volterra kernels. The complex spatiotemporal process is first decomposed into a series of spatiotemporal kernels, upon which the time−space separation can be further conducted with the spatial Karhunen−Loève and temporal Laguerre basis function expansions. These two decompositions can gradually separate the nonlinear time/space coupled dynamics. Finally, the kernels in the spatiotemporal model are estimated from the experimental data incrementally, which can easily achieve satisfactory modeling performance. Simulations of two transport−reaction processes demonstrate the effectiveness of the proposed modeling approach.