Soft-Sensor Model for Chemical Processes Based on D-Vine Copula with Rolling Pin Transformation

Abstract

Soft-sensing methods have been widely used in recent years to predict key variables that are difficult to measure or involve costly and time-consuming in chemical processes. Owing to the increasing complexity of industrial processes, industrial data often exhibit strong nonlinearities and self-correlation, and the data distribution fails to satisfy the Gaussian assumption. To address these problems, a vine copula-based soft-sensor model combined with the rolling pin method is proposed. This approach uses a D-vine copula to model a joint probability distribution of auxiliary variables and a key variable. In accordance with the joint distribution, the predicted value of the key variable can be determined by weighting the training samples. During modeling, the Bayesian information criterion is adopted to select the best-fitted copula pairs. Given the nonmonotonicity between variables of actual industrial data, the rolling pin monotonic transformation is simultaneously introduced to improve the suitability of transformed data for vine copula modeling. The efficiency of the proposed method was verified using a numerical example and ethylene cracking.

Process Monitoring Based on the Multiblock Rolling Pin Vine Copula

“…Vine copula can effectively process non-Gaussian nonlinear data, but it cannot accurately characterize nonmonotonic data; however, monotony is difficult to guarantee for complex industrial data . For this reason, Ahooyi et al proposed the rolling pin method, which maps data to the same dimensional space using a monotonic transformation.…”

“…Vine copula can effectively process non-Gaussian nonlinear data, but it cannot accurately characterize nonmonotonic data; however, monotony is difficult to guarantee for complex industrial data. 25 For this reason, Ahooyi et al 26 proposed the rolling pin method, which maps data to the same dimensional space using a monotonic transformation. This conversion process requires a reference variable according to which the remaining variables are converted; however, it is difficult to find reference variables that are strongly correlated with other variables.…”