Semi-supervised local manifold regularization model based on dual representation for industrial soft sensor development

Abstract

Data-driven soft sensors are crucial for predicting key quality variables in the process industry. In most processes, the dynamic characteristics are obvious, and the relationship between the primary and secondary variables is strongly nonlinear. Moreover, the worst thing is that labeled samples are usually scarce due to certain technical difficulties or measurement costs. To deal with these issues, this paper first proposes a semi-supervised manifold regularization model based on dual representation (SsMRM-DR). Then, a semi-supervised local manifold regularization model based on dual representation (SsLMRM-DR) is further proposed from the viewpoint of local manifold regularization. In the SsLMRM-DR, a space–time weighted similarity calculation method is designed to reduce the influence of measurement noise on similarity calculation. At the same time, a local manifold regularization method is developed to use unlabeled samples more efficiently and to improve the prediction accuracy and computational efficiency of the SsLMRM-DR. A numerical example and a real industrial process are used to evaluate the performance of the proposed schemes. The results show that SsLMRM-DR is effective and it has a good application prospect of soft sensors in the industry.