Dissimilarity Analysis-Based Multimode Modeling for Complex Distributed Parameter Systems

For complex distributed parameter systems (DPSs) with strong nonlinearities and time-varying dynamics, the conventional spatiotemporal modeling methods become ill-suited since the elementary assumption that the process data follow a unimodal Gaussian distribution usually becomes invalid. In this paper, a multimode method is proposed for modeling of such systems. First, the original operating space is partitioned along the time dimension into several subspaces via modified dissimilarity analysis. Each subspace represents the local spatiotemporal characteristics of the original system. Second, the Karhunen-Loève decomposition (KLD)-based spatiotemporal modeling approach is applied to approximate the local dynamics of each subspace. Finally, an ensemble model is obtained using the soft weighting sum of the local ones, where the corresponding weights are calculated by principal component regression. By properly decomposing the original space into several local parts, the ensemble model is capable of handling the strong nonlinearities and time-varying dynamics of the system. The validity and efficiency of the proposed method are verified on two representative applications: 1) a one-dimensional parabolic catalytic rod and 2) a two-dimensional curing thermal process. The experimental results show that the proposed method provides a superior performance regarding modeling accuracy compared to several baselines.