Virtual sensors of nonlinear industrial processes based on neighborhood preserving regression model

Abstract

The micro perspective of manifold proximity would indicate local relationships with their unique spatial geometric distribution characteristics among the data samples, which are usually neglected by traditional data-driven virtual sensors. This would not guarantee a good prediction performance. In this paper, a regression model with localized construction named neighborhood preserving regression (NPR) model is proposed. It extends the unsupervised neighborhood preserving embedding (NPE) to the supervised form. The projection vector is learned from input process variables and the output quality variable, synchronously exploring the manifold structure of the input process variables for the dimension reduction and developing the regression relationship between the projected input process variables and the output quality variable. The model is developed as a novelly designed optimization whose analytical solution would be compactly and directly calculated without any iterative procedures. The effectiveness of the proposed algorithm is demonstrated by case studies carried out on a simulated penicillin production process.