Locally weighted kernel partial least squares regression based on sparse nonlinear features for virtual sensing of nonlinear time-varying processes

Virtual sensing technology is crucial for monitoring product quality when real-time measurement is not available. To deal with both strong nonlinearity and time-varying dynamics of industrial processes, we propose a novel locally weighted kernel PLS (LW-KPLS) based on sparse nonlinear features in this research. Unlike the conventional locally weighted PLS (LW-PLS), the proposed method weights the training samples by using sparse kernel feature characterization factors (SKFCFs), which take account of the strength of nonlinear dependency between samples in the Hilbert feature space. By integrating the nonlinear features into the locally weighted regression framework, LW-KPLS not only can cope with the time-varying characteristics but also is more suitable for highly nonlinear processes. The proposed method was validated through a numerical example, a penicillin fermentation process, and a real industrial cleaning process for residual drug substances. The results have demonstrated that the proposed LW-KPLS outperforms the conventional PLS, KPLS, LW-PLS, and eLW-KPLS in the prediction performance.