Ensemble Correntropy‐Based Mooney Viscosity Prediction Model for an Industrial Rubber Mixing Process

Abstract

Development of accurate soft sensors for online prediction of Mooney viscosity in industrial rubber mixing processes is a difficult task because the modeling data set often contains various outliers. A correntropy kernel learning (CKL) method for robust soft sensor modeling of nonlinear industrial processes with outlier samples is proposed. Simultaneously, the candidate outliers can be found out once the CKL-based soft sensor model is built. An index for description of the uncertainty of the CKL model is designed. Furthermore, to obtain more robust and accurate predictions, an ensemble CKL (ECKL) method is formulated by introducing the simple bagging strategy. Consequently, by detecting the outliers in a sequent manner, the database becomes more reliable for long-term use. The application results in an industrial rubber mixing process exhibit the superiority of ECKL in terms of better prediction performance.

Robust Soft Sensor with Deep Kernel Learning for Quality Prediction in Rubber Mixing Processes

“…where y i and e i are the process output and noise for ith sample, respectively; f is the DCKR model with its parameters β, and bias b, respectively. The following optimization problem is formulated to solve the DCKR model [31,32]:…”

“…. , N into [0,1]), the candidate outliers can be identified and removed out [32]. Interestingly, although the candidate outliers are kept in the DCKR model, they cannot degrade the prediction performance mainly because of their negligible effects.…”

“…where y t andŷ t are the assayed and predicted values of the Mooney viscosity, respectively, for N tst test samples. For comparison studies, four robust soft sensors, including CKR [31,32], PCA-CKR, DCKR, and EDCKR, are investigated. Their main characteristics are described briefly in Table 1.…”

“…This is mainly because the modeling dataset often contains various outliers caused by instrument degradation, process disturbances, transmission problems, etc. [4,[30][31][32]. Robust data mining approaches are necessary and more attractive for development of a reliable soft sensor in industrial processes [33,34].…”

“…To address the two above-mentioned issues simultaneously, this work aims to develop a robust DNN soft sensor for the modeling of nonlinear processes with outliers. Specially, the proposed ensemble deep correntropy kernel regression (EDCKR) framework integrates the ensemble learning [35], DBN structure [22], and correntropy kernel regression (CKR) [31,32]. The DBN-based unsupervised learning is adopted as a multilevel nonlinear feature extractor to absorb the information in related input variables.…”