Physical Informed Sparse Learning for Robust Modeling of Distributed Parameter System and Its Industrial Applications

With the development of information technologies, a large number of sensors have been deployed to obtain industrial data. As a result, data-driven approaches have become a crucial means for modeling of distributed parameter systems (DPS). However, due to harsh environments and unreliable sensors, data is often of low quality in practice, which in turn poses a challenge for data-driven modeling approaches. In order to address the challenge of inaccurate modeling of DPS induced by outliers, this paper proposes a physical-informed sparse learning method to overcome the adverse effects of outliers and achieve robust modeling of DPS by fully exploring the spatiotemporal dynamic of DPS. Specifically, this paper proposes an innovative method for robust modeling of DPS. The method incorporates the statistical features of contaminated data to restore the dynamic evolution structure of DPS, which weakens the adverse effects of outliers and address the problem of low modeling accuracy caused by contaminated observation data. Furthermore, the underlying partial differential equation (PDE) of DPS is incorporated into the constraint on the temporal deviation data, which leads to a physical-informed optimization objective and improves the reliability of outlier extraction and DPS modeling. Finally, an optimization algorithm based on the alternating direction method of multipliers (ADMM) with an adaptive penalty factor is proposed. This ensures the convergence of multivariate optimization problem and superior performance of the DPS modeling framework. Extensive experimental results have verified that the proposed method is effective in overcoming the adverse effects of outliers and achieving robust modeling of DPS. Note to Practitioners—The motivation of this paper is to develop an interpretable and robust modeling method for DPS. Considering the negative impact of outliers, the proposed method first restores the dynamic properties of the data based on the characteristics of the outliers. Then, the embedding of physical knowledge ensures the reliability of outlier removal and robustness of modeling. Extensive experimental results have verified that the proposed method can effectively overcome the adverse effects of outliers and outperform some state-of-the-art methods. Therefore, it is more suitable for real industrial systems.