Xi‐Ming Sun

Tianju Sui, Damian Marelli, Ximing Sun et al.

This paper focuses on a networked state estimation problem for a spatially large linear system with a distributed array of sensors, each of which offers partial state measurements, and the transmission is lossy. We propose a measurement coding scheme with two goals. Firstly, it permits adjusting the communication requirements by controlling the dimension of the vector transmitted by each sensor to the central estimator. Secondly, for a given communication requirement, the scheme is optimal, within the family of linear causal coders, in the sense that the weakest channel condition is required to guarantee the stability of the estimator. For this coding scheme, we derive the minimum mean-square error (MMSE) state estimator, and state a necessary and sufficient condition with a trivial gap, for its stability. We also derive a sufficient but easily verifiable stability condition, and quantify the advantage offered by the proposed coding scheme. Finally, simulations results are presented to confirm our claims.

Aina Wang, Pan Qin, Xi-Ming Sun

Partial differential equations (PDEs) are a model candidate for soft sensors in industrial processes with spatiotemporal dependence. Although physics-informed neural networks (PINNs) are a promising machine learning method for solving PDEs, they are infeasible for the nonhomogeneous PDEs with unmeasurable source terms. To this end, a coupled PINN (CPINN) with a recurrent prediction (RP) learning strategy (CPINN- RP) is proposed. First, CPINN composed of NetU and NetG is proposed. NetU is for approximating PDEs solutions and NetG is for regularizing the training of NetU. The two networks are integrated into a data-physics-hybrid loss function. Then, we theoretically prove that the proposed CPINN has a satisfying approximation capability for solutions to nonhomogeneous PDEs with unmeasurable source terms. Besides the theoretical aspects, we propose a hierarchical training strategy to optimize and couple NetU and NetG. Secondly, NetU-RP is proposed for compensating information loss in data sampling to improve the prediction performance, in which RP is the recurrently delayed outputs of well-trained CPINN and hard sensors. Finally, the artificial and practical datasets are used to verify the feasibility and effectiveness of CPINN-RP for soft sensors.

Aina Wang, Pan Qin, Xi-Ming Sun

Soft sensors have been extensively used to monitor key variables using easy-to-measure variables and mathematical models. Partial differential equations (PDEs) are model candidates for soft sensors in industrial processes with spatiotemporal dependence. However, gaps often exist between idealized PDEs and practical situations. Discovering proper structures of PDEs, including the differential operators and source terms, can remedy the gaps. To this end, a coupled physics-informed neural network with Akaike's criterion information (CPINN-AIC) is proposed for PDE discovery of soft sensors. First, CPINN is adopted for obtaining solutions and source terms satisfying PDEs. Then, we propose a data-physics-hybrid loss function for training CPINN, in which undetermined combinations of differential operators are involved. Consequently, AIC is used to discover the proper combination of differential operators. Finally, the artificial and practical datasets are used to verify the feasibility and effectiveness of CPINN-AIC for soft sensors. The proposed CPINN-AIC is a data-driven method to discover proper PDE structures and neural network-based solutions for soft sensors.