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This paper investigates the online learning problem of Lagrangian ε -twin support vector regression (L- ε -TSVR), with the goal of presenting incremental implementations. First, to solve the problem that the existing L- ε -TSVR cannot efficiently update the model under incremental scenarios, an incremental Lagrangian ε -twin support vector regression (IL- ε -TSVR) based on the semi-smooth Newton method is proposed. By utilizing the matrix inverse theorems to update the Hessian matrices incrementally, IL- ε -TSVR lowers the time complexity and expedites the training process. However, when solving the problem of nonlinear case, the training speed of IL- ε -TSVR rapidly decreases with the increasing size of the kernel matrix. Therefore, an incremental reduced Lagrangian ε -twin support vector regression (IRL- ε -TSVR) is presented. IRL- ε -TSVR employs the reduced technique to restrict the size of the inverse matrix at the cost of slightly lower the prediction accuracy. Next, to lighten the prediction accuracy loss caused by parameters reduction, a novel regularization term is introduced to replace the original one, and an improved incremental reduced Lagrangian ε -twin support vector regression (IIRL- ε -TSVR) is designed. The results on UCI benchmark datasets show that IL- ε -TSVR can effectively address the linear regression problem under incremental scenarios and obtain almost the same generalization capability as offline learning. Moreover, IRL- ε -TSVR and IIRL- ε -TSVR can reduce training time of nonlinear regression model and obtain sparse solution, and their generalization capabilities are close to those of offline ones. Particularly, the proposed algorithms can implement fast incremental learning of large-scale data. [ABSTRACT FROM AUTHOR]

Process nonlinearity, multiple operating modes and time-varying characteristics often deteriorate the prediction performance of process models. In this article, a multi-mode moving-window Gaussian process regression (MWGPR) based approach for ARX modeling is proposed to effectively capture process nonlinearity or switching dynamics. The Gaussian mixture model (GMM) is first introduced to separate the data into different operating modes. Then the MWGPR strategy is applied to identify the local ARX model. Just-in-time learning (JITL) and dual updating are applied for more effective tracking of process dynamics. A simulation of a continuous fermentation process and a pilot scale experiment are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Accurate and real-time quality prediction to realize the optimal process control at a competitive price is an important issue in Industrial 4.0. This paper shows a successful engineering application of how smart soft sensors can be combined with machine learning technique to significantly save human resources and improve performance under complex industrial conditions. Ensemble learning based soft sensors succeed in capturing complex nonlinearities, frequent dynamic changes, as well as time-varying characteristics in industrial processes. However, local model regions under traditional ensemble modelling methods are highly dependent on labeled data samples and, hence, their prediction accuracy might get affected when labeled samples are limited. A novel active learning (AL) framework upon the ensemble Gaussian process regression (GPR) model is proposed for smart soft sensor design in order to overcome this drawback. Firstly, to iteratively select the most informative unlabeled samples for labeling with hierarchical sampling based AL strategy, to then apply Gaussian mixture model (GMM) technique to autonomously identify operation phases, to further construct local GPR models without human involvement, and finally to integrate the base predictors by applying the Bayesian fusion strategy. Comparative studies for the penicillin fermentation process demonstrate the reliability and superiority of the recommended smart soft sensing. The cost of human annotation can be dramatically reduced by at least half while the prediction performance simultaneously keeps high. [ABSTRACT FROM AUTHOR]