(552b) Sparse Nonlinear Features Based Locally Weighted Kernel Partial Least Squares for Virtual Sensing of Nonlinear Time-Varying Processes

Virtual sensing or soft-sensors are crucial for monitoring and controlling key product quality when it is not measured in real time. Although linear regression methods such as partial least squares (PLS) have been widely used, they do not show superior prediction performance owing to the complex characteristics of industrial processes such as nonlinearity and time-varying dynamics. To cope with the time-varying characteristics as well as nonlinearity, locally weighted PLS (LW-PLS) has been applied to various industrial processes. Even though LW-PLS can achieve high prediction performance in particular applications, it may not function well for highly nonlinear processes. The reason is that the weights used in the conventional LW-PLS model usually do not take account of the strength of nonlinearity, which may change with the time-varying nature of industrial processes. In addition, since input features used for LW-PLS are still the original process variables and the nonlinearity of the regression model only rests in the different treatment of samples, i.e., local weighting, LW-PLS may not be able to meet the demand of the prediction accuracy for industrial processes with strong nonlinearity. To deal with these issues, we propose a novel locally weighted kernel PLS (LW-KPLS) based on sparse kernel regression factors in this study. Unlike the conventional LW-PLS, the proposed method derives sparse nonlinear features, learns a regression function efficiently, and predicts the output variable for a query, which is a target sample. The sparse kernel regression factors (SKRFs), which are derived from a nonlinear kernelized Lasso model, show nonlinear dependency between the query and training samples in the Hilbert feature space. Hence, SKRFs are essential to understand which samples are important for the current query, and which samples provide irrelevant or redundant information and can be eliminated. Thus SKRFs can be assigned to weight the training samples to construct a LW-KPLS model in the Hilbert feature space. Furthermore, by integrating the nonlinear features into the locally weighted regression framework, the proposed LW-KPLS not only can cope with time-varying characteristics but also is more suitable for highly nonlinear processes. The reliability and validity of the proposed method were firstly verified through a nonlinear numerical example; its estimation accuracy was improved by 25%, 5%, and 3% in Root Mean Square Error of Prediction (RMSEP) compared with PLS, KPLS, and LW-PLS, respectively. Then the proposed method was applied to the estimation of the penicillin concentration in the penicillin fermentation process. The estimation accuracy was improved by 57%, 6%, and 3% in comparison with PLS, KPLS, and LW-PLS, respectively. The results clearly show that the proposed LW-KPLS is useful for the penicillin concentration estimation and is superior to the conventional methods.