Development of Self-Learning Kernel Regression Models for Virtual Sensors on Nonlinear Processes

Abstract

The prediction accuracy of the traditional kernel with data-driven regression methods strongly depends on the appropriate selection of the kernel function and aims at solving the nonlinearity of the input space. In this paper, a self-learning kernel regression model is proposed. A special kernel space from the measured data is learned and designed, so that combined with dimension reductions on the input variables, the regression behavior between the projected input variables and the output variable is found. The model is posed as a semidefinite programming problem with the objective function to find the maximum variance between the learned manifolds. The kernel is data dependent and can be generated online whenever a new data point is available. The effectiveness of the proposed algorithm is demonstrated through the case studies on a simple nonlinear system and a real semiconductor process. Note to Practitioners—Virtual sensing of quality/key variables is critical for the control and optimization of industrial processes. Traditional data-driven kernel regression methods cannot achieve guaranteed high prediction accuracy. This paper aims to develop a high-accuracy virtual sensor based on the self-learning kernel regression (SLKR) model, which simultaneously constructs the relationship between the input and the output data as well as represents the data in a low-dimensional manifold. For practical implementation, the following are necessary to: 1) select a historical data set with abundant information of the process; 2) preprocess industrial data well and eliminate irregular entries; 3) establish a self-learning regression kernel based on local manifold structure and regression relationship; 4) approximate the explicit data-dependent kernel function and determine suitable parameter; and 5) extract regression coefficients from the learned kernel matrix.