A nonlinear industrial soft sensor modeling method based on locality preserving stochastic configuration network with utilizing unlabeled samples

Abstract

Stochastic configuration network (SCN) is an emerging incremental randomized regression modeling technology with the advantages of adaptively determining the hidden layer parameters, and has been successfully applied to industrial soft sensor modeling field. However, the traditional SCN model is intrinsically a supervised learner, which has the underlying assumption that all the training samples are labeled. In fact, most of process samples are unlabeled and the labeled samples are relatively rare in real industrial scenarios. To handle this issue, this paper presents one modified SCN model, called locality preserving SCN (LPSCN), for semi-supervised industrial soft sensor modeling. In this method, all the training samples, including the labeled and the unlabeled, are fed into the soft sensor model, where the labeled samples are used to capture the modeling error, while the unlabeled samples help construct the local adjacency graph. Based on these two kinds of samples, the supervised optimization objective in the traditional SCN is improved to be a semi-supervised version by minimizing the modeling error and preserving the local data relationship simultaneously. Furthermore, the random parameter configuration mechanism is deduced under the modified semi-supervised optimization framework. A new inequality constraint condition with considering the unlabeled samples is obtained to generate the hidden layer nodes incrementally so that the LPSCN model structure is determined automatically. Experiments on two real industrial systems demonstrate that the proposed LPSCN method outperforms the SCN method in terms of the soft sensor prediction performance.