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A Bayesian model averaging based multi-kernel gaussian process regression framework for nonlinear state estimation and quality prediction of multiphase batch processes with transient dynamics and uncertainty

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CHEMICAL ENGINEERING SCIENCE 2013年 93卷 96-109页

作者： Yu, Jie Chen, Kuilin Rashid, Mudassir M. McMaster Univ Dept Chem Engn Hamilton ON L8S 4L7 Canada

Batch processes are characterized by inherent nonlinearity, multiplicity of operating phases, between-phase transient dynamics and batch-to-batch uncertainty that pose significant challenges for accurate state estimation and quality prediction. Conventional multi-model strategies, however, may be ill-suited for multiphase batch processes because the localized models do not specially take into account the complex transient dynamics between two consecutive operating phases. In this study, a novel Bayesian model averaging based multi-kernel gaussian process regression (BMA-MKGPR) approach is proposed for state estimation and quality prediction of nonlinear batch processes with multiple operating phases and between-phase transient dynamics. A kernel mixture model strategy is first used to identify the different operating phases of batch processes and then the multi-kernel GPR models are built for all the identified phases. Further, the between-phase transitional stage is determined by the posterior probabilities of measurement samples with respect to the two consecutive phases so that the Bayesian model averaging strategy can be designed to incorporate the two localized GPR models for handling the between-phase transient dynamics. For an arbitrary test sample within the transitional stage, its posterior probabilities with respect to the local models corresponding to the two consecutive phases are set as the adaptive weightings to integrate the corresponding local GPR models for state estimation and quality prediction. The proposed BMA-MKGPR approach is applied to a multiphase batch polymerization process and the result comparison demonstrates that the presented method can effectively handle multiple nonlinear operating phases, between-phase transient dynamics and process uncertainty with fairly high prediction accuracies. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Nonlinear state estimation Quality prediction multiphase batch process Between-phase transient dynamics multi-kernel gaussian process regression Bayesian model averaging

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Optimizing surfactant-enhanced aquifer remediation based on gaussian process surrogate model in DNAPL-contaminated sites considering different wells patterns

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GROUNDWATER FOR SUSTAINABLE DEVELOPMENT 2021年 15卷

作者： Shams, Reza Alimohammadi, Saeed Yazdi, Jafar Shahid Beheshti Univ Civil Water & Environm Engn Fac POB 16765-1719Bahar Blvd Tehran *** Iran

Surfactant-enhanced aquifer remediation (SEAR) is an appropriate method for Dense non-aqueous phase liquids (DNAPLs) remediation. However, due to the high cost of chemicals used, choosing the suitable wells pattern and the optimal pumping scenario is necessary. In this study, the SEAR method performance for Regular (convergent) and Inverted (divergent) patterns with different wells numbers have been evaluated. The performance of 5 categories of patterns, including 35 different sub-patterns, was evaluated in a PCE-contaminated aquifer. The results show that the uniformity and appropriate surfactant distribution in the contaminated area significantly improves remediation performance. The distribution of surfactants in Regular patterns was better than Inverted patterns, and Regular patterns had lower remediation duration and cost. The best patterns that achieved a 95 % removal rate at the lowest cost were Regular. To find the optimal pumping scenario, a simulation-optimization model based on the gaussian process regressor (GPR), as a surrogate model, has been used to reduce the optimization model's computational burden. Nine different kernels were applied and evaluated to find the best GPR. Also, the Bayesian hyperparameter optimization (BHO) method was used to optimize the surrogate model, and its performance was compared with the conventional grid search method. The results showed that the use of the Chi(2) kernel and the BHO method are the best choices. A BHO-optimized multi-kernel gaussian process (BHOMK-GP) model has also been developed, and its performance has been compared with single-kernel GPR surrogate models. The BHOMK-GP model's accuracy was significantly higher than single-kernel GPR models. The test and cross-validation RMSE of the BHOMK-GP model were 0.0385 and 0.0435, respectively. Finally, the optimal remediation scenario has been obtained by substituting the BHOMK-GP model as a surrogate model instead of the SEAR simulation model. The cost of remediat

关键词： Surfactant-enhanced aquifer remediation (SEAR) Dense non-aqueous phase liquid (DNAPL) Wells patterns multi-kernel gaussian process regression Bayesian hyperparameter optimization

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