Virtual Sensor Development for Multioutput Nonlinear Processes Based on Bilinear Neighborhood Preserving Regression Model With Localized Construction

The traditional data-driven virtual sensors mainly define the outer shape of the data, but they cannot provide any insight into the micro perspective of manifold proximity indicating the local relationships among the data samples. In this article, a regression model with localized construction named bilinear neighborhood preserving regression (BNPR) model is proposed by synchronously exploring the local manifold geometry among both the process variables and primary variables and developing the regression relationship for the estimates of the primary variables. The model is constructed under multi-output to discover the inherent relationships among the primary variables instead of building independent models for each primary variable. The effectiveness of the proposed algorithm is demonstrated by case studies carried out on a simulated penicillin production process and a real-life semiconductor process.