Spatiotemporal kernel-local-embedding modeling approach for nonlinear distributed parameter systems

Abstract

In actual distributed parameter systems (DPSs), each spatial point has nonlinear energy transfer with its local neighbor points. Also, this energy transfer is affected by the past states. However, these properties are often ignored by most of modeling methods, which causes these methods ineffective in modeling of DPSs. Aiming for this problem, a spatiotemporal kernel-local-embedding (STKLLE) Modeling approach is proposed here to reconstruct the nonlinear spatiotemporal dynamics of DPSs. First, in order to present the complex dynamics on space, a STKLLE strategy is developed to extract space basis functions (SBFs). On the one hand, this STKLLE method represents the energy transfer relation with its neighboring points and maintains this local relation in model. On the other hand, it considers the influence of the adjacent past states to the current state. Then, using T–S fuzzy algorithm, a temporal model is designed to represent the temporal dynamics of DPSs in each sampling period. Integrating these SBFs and the temporal fuzzy model, a spatiotemporal model is constructed to well present and predict the nonlinear spatiotemporal dynamics in DPSs. Through the actual experiment on Lithium-ion batteries and heating oven, the effectiveness of this proposed model is detailly verified, and quantitative comparisons with several data-driven modeling algorithms are further carried out to demonstrate the model efficiency.