A Semi-supervised Stochastic Configuration Network Based on Hessian Regularization for Industrial Soft Sensing Regression Modeling

A latest semi-supervised stochastic configuration network (SCN)-locality preserving SCN (LPSCN) has been proposed for soft sensing regression modeling to address the issue of insufficient labeled samples in real industrial processes. However, Laplacian regularization lacks extrapolation capabilities and biases the solution towards a constant function, leading to poor network performance in certain scenarios. To address this issue, a semi-supervised stochastic configuration network based on Hessian regularization (HSCN) is proposed. First, this paper presents the limitations of LPSCN. Then, by redefining the optimization function and reformulating the constraint mechanism, the algorithm of HSCN is proposed. Compared to LPSCN, HSCN can leverage its extrapolation capability to have better performance in the absence of labeled samples. The method was applied to the prediction of effluent biochemical oxygen demand (BOD) in a wastewater treatment plant and the results showed that HSCN outperformed LPSCN and SCN in terms of performance.