A Regularized Mixture of Linear Experts for Quality Prediction in Multimode and Multiphase Industrial Processes

Abstract

This paper proposes the use of a regularized mixture of linear experts (MoLE) for predictive modeling in multimode-multiphase industrial processes. For this purpose, different regularized MoLE were evaluated, namely, through the elastic net (EN), Lasso, and ridge regression (RR) penalties. Their performances were compared when trained with different numbers of samples, and in comparison to other nonlinear predictive models. The models were evaluated on real multiphase polymerization process data. The Lasso penalty provided the best performance among all regularizers for MoLE, even when trained with a small number of samples.

Contextual Mixture of Experts: Integrating Knowledge into Predictive Modeling

“…multiphase processes) [5]. These modes can be represented in a multi-model (ensemble) structure [6]. This work focuses on modeling processes with multiple operating modes, and the proposed method was created with this in mind.…”

“…The modeling of multiple operating modes processes follows from rule-based expert systems [7]- [10], clustering [11], Mixture models (MM) [12]- [14], Gaussian mixture regression (GMR) [15], [16], or mixture of experts (MoE) [6], [17] strategies to identify the groups that represent each operational regime, then combine them according to the process's regime. Apart from rule-based expert models, none of the above works discuss using domain knowledge from operators.…”

“…In order to avoid instability in the learning of gating coefficients (typically followed by a softmax function), the authors in [23] proposed the use of a proximal-Newton expectationmaximization (EM). The elastic-net penalty was used by the authors of [6], who employed a regularization penalty for the inverse of Hessian matrix along the gates learning. In the proposed cMoE, the 1 penalty is employed to promote sparsity in the gates and experts.…”

“…In the proposed cMoE, the 1 penalty is employed to promote sparsity in the gates and experts. The solution for the gates and experts follows from the coordinate gradient descent together with the EM framework, as used in [6]. However, there are two significant differences between the method presented here and the work of [6].…”

Correction: Souza et al. A Regularized Mixture of Linear Experts for Quality Prediction in Multimode and Multiphase Industrial Processes. Appl. Sci. 2021, 11, 2040

“…We, the authors, wish to make the following corrections to our paper [1]. We have found that Equations ( 16), ( 21) and ( 22) were stated wrong in the manuscript.…”