Probabilistic Weighted Copula Regression Model With Adaptive Sample Selection Strategy for Complex Industrial Processes

With complicated structures and complex physicochemical reactions, most industrial processes are intrinsically characterized by high dimensionality, nonlinearity, non-Gaussianity, and self-correlation. In this article, a novel probabilistic generative model, called weighted copula regression (WCR), is developed for complex processes. This method employs a probabilistic graphical tool (vine copula) to flexibly handle the underlying patterns via the factorization of complex dependence structures into multiple bivariate copulas. Monte Carlo estimation is incorporated for establishing a fast and reliable computing framework. To avoid overinterpretation of the industrial data, an adaptive sample selection strategy is proposed to explore the underlying distribution of the sample space and to select the most “informative” samples. By considering the copula weights that carry crucial information on the local data, the probabilistic WCR method can provide fast point estimate with prediction uncertainty for every predicted sample. The proposed WCR method is compared with six state-of-the-art methods, and the efficiency is validated using a numerical example and the ethylene cracking furnace process.