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Numerous industrial processes can be defined using distributed parametersystems (DPSs). This study introduces a two-stage spatial construction approachfor real-time modeling of DPSs in cases of limited sensors. Initially, adiscrete space-completion approach is created to recuperate the spatiotemporalpatterns of non-monitored locations under sparse sensing. The high-dimensionalspace construction method is employed to derive continuous spatial basisfunctions (SBFs). The identification and adjustment of the nonlinear temporalmodel are carried out via the long short-term memory (LSTM) neural network.Eventually, the amalgamation of the derived SBFs and temporal model results ina spatially continuous model. The use of a cubic B-spline surface is validatedas an effective solution for optimizing space construction in the sense ofleast squares approximation. Experimental tests conducted on a pouch-typeLi-ion battery demonstrate the efficacy of the proposed modeling techniqueunder sparse sensing. This work highlights the promise of sparse sensors inreal-time full-space modeling for large-scale battery energy storage systems.

Two-stage space construction for real-time modeling of distributed parameter systems under sparse sensing