Spatio-Temporal Regularized Stochastic Configuration Network for Supervised and Semi-Supervised Soft Sensor Development

Abstract

Stochastic configuration network (SCN) has become a favorable soft sensor model due to its innovative random parameter construction approach under inequality constraint. However, it may suffer from the disadvantage of model overfitting with the increase of hidden nodes. To handle this issue, an improved Regularized SCN based on Spatio-Temporal nearest neighbors (ST-RSCN) is presented for better nonlinear soft sensor development. Different from regularized SCN only with L2 regularization, a dually-regularized SCN optimization framework is designed, where the L2 regularization term and manifold regularization (MR) term are applied to enforce the constraints from the perspectives of model parameters and data structure. Peculiarly, considering the data dynamic property, the traditional spatial nearest neighbor selection method is upgraded by integrating temporal searching strategy. Two spatio-temporal neighbor searching strategies are formed by designing different neighbor determination orders in spatial and temporal domains. The efficiency of the developed ST-RSCNs is finally demonstrated by two industrial cases, including a debutanizer column process and a continuous stirred tank reactor. The outcomes in both supervised and semi-supervised scenarios indicate that ST-RSCNs have better prediction performance compared with several models with respect to stability and generalization. Note to Practitioners—Data structure characteristic is of great importance for soft sensor model performance in practice. However, this is omitted in the existing SCN models. This paper designs a new enhanced regularized SCN for soft sensing. Specifically, a unified optimization objective is established involving both L2 regularization for constraining output weight magnitude and manifold regularization for mining the underlying geometric structure information. Further, two spatio-temporal nearest neighbor strategies are introduced to better fit the dynamic data structure. ST-RSCN related principles and proofs are described in detail. The simulation results of DCP and CSTR cases show the proposed ST-RSCNs significantly reduce the model prediction root mean squared errors (RMSEs) and are applicable for supervised and semi-supervised domains. Additionally, the key parameters’ selection methods are discussed, which contributes to a sound understanding of this paper.