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L1-norm minimization-based spatiotemporal modeling for distributed parameter systems
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DOI：10.1016/j.aei.2025.104068.png)
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Abstract
En 中文
Data-based spatiotemporal modeling methods are widely used in modeling distributed parameter systems (DPSs). However, they are usually based on the L2-norm criterion and may thus be susceptible to outliers. Furthermore, they do not explicitly consider the local and global structure of the spatiotemporal data in the time/space separation process, which leads to the loss of crucial spatial information. This paper proposes an L1-norm minimization-based spatiotemporal modeling method to solve these problems. First, a global and local spatial basis function learning method with L1-norm minimization (GLSBF-L1) is developed to separate the infinite-dimensional spatiotemporal data of DPSs into spatial basis functions (SBFs) and low-dimensional time coefficients. Due to the utilization of the L1-norm, GLSBF-L1 is not sensitive to outliers, making the proposed method promising for the robust modeling of DPSs. Furthermore, by integrating the locality preserving projections (LPP) and the principal component analysis (PCA), GLSPF-L1 preserves both local and global information. Second, a Lyapunov-based broad learning system (L-BLS) is proposed based on time coefficients and system input to construct a temporal model. Since a novel Lyapunov theory-based update strategy is introduced, L-BLS can be adjusted in real-time according to the system’s variation. Finally, through the integration of SBFs with the temporal model, the spatiotemporal output of DPSs is effectively reconstructed. The experimental findings from a 32Ah ternary lithium-ion battery thermal process and a chip curing process in the snap oven demonstrate our method’s strong stability and effectiveness.
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