Batch-to-batch optimization of cobalt oxalate synthesis process using modifier-adaptation strategy with latent variable model

Jia, Runda; Mao, Zhizhong; Wang, Fuli; He, Dakuo

doi:10.1016/j.chemolab.2014.11.007

Cited by 22 publications

(35 citation statements)

References 33 publications

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“…We preset γ in the range [0.1,0.5,1,5,10,50,100,1000]and preset σ in the range [0.1,0.5,1,5,10,50,100,1000]. Furthermore, the cross validation error for the subset {x i , y i } can be computed as 2 where y j andŷ j represent the real value and prediction value respectively. And N i is the number of samples is subset {x i , y i };…”

Section: B Prediction Results and Discussionmentioning

confidence: 99%

“…In the typical synthesis process which is characterized by high nonlinearity and multivariable, a fed-batch mode is utilized to synthesize the cobalt oxalate crystals. Compared to the batch operation model, the fed-batch mode can avoid the risk of reaction runaway [2]. Firstly, a certain volume of cobalt chloride is filled in the crystallizer and the ammonium oxalate is added at a preset flow rate to the crystallizer.…”

Section: A Description Of Cobalt Oxalate Synthesis Processmentioning

confidence: 99%

“…2) Build a LSSVR model using the initial training dataset, the prediction errors for the training dataset can be obtained; 3) Construct Gaussian mixture model based on the input variables and prediction error, and the indexδ 2 e|x can be obtained. 4) Select the data with the largestδ 2 e|x and introduce the newly selected data to the initial LSSVR model training dataset; 5) Rebuild the LSSVR model and error GMM model based on the updated training dataset; 6) Calculate the stopping index ε m to judge whether the active learning should be terminated. If ε m > ρ go to step (4).…”

Section: The Procedures Of Active Learning Approach Based On Gmmmentioning

confidence: 99%

“…Cobalt oxalate synthesis process is an important separation and purification unit operation of cobalt hydrometallurgy where cobalt oxalate powders are produced [1], [2]. The powder particle size distribution (PSD) which can determine the filtration and drying operation efficiency is a key quality variable.…”

Section: Introductionmentioning

confidence: 99%

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Active Learning Strategy for Online Prediction of Particle Size Distribution in Cobalt Oxalate Synthesis Process

2019

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Cobalt oxalate synthesis process is a nonlinear batch process. However, the lack of online sensors for the quality variable (e.g., average particle size) has become the main obstacle of controlling the process accurately and optimally. An active learning strategy for selecting the informative training data is proposed to improve the soft sensor prediction performance. First, an initial data set which is collected from the process is used to establish an LSSVR soft sensor model. Second, the LSSVR model prediction error is obtained and the joint probability distribution for the prediction error and input variables can be described through a Gaussian mixture model (GMM). Then, the conditional error variance, which can be calculated from the error GMM, is used to select the representative data which can be added to the initial data set and can improve the current LSSVR model for better performance. In addition, an evaluation index is presented to implement the active learning procedure. Finally, the proposed method applicability to an industrial cobalt oxalate synthesis process is demonstrated. INDEX TERMS Active learning, cobalt oxalate synthesis process, Gaussian mixture model, least squares support vector regression, soft sensor.

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Section: B Prediction Results and Discussionmentioning

confidence: 99%

Section: A Description Of Cobalt Oxalate Synthesis Processmentioning

confidence: 99%

Section: The Procedures Of Active Learning Approach Based On Gmmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Active Learning Strategy for Online Prediction of Particle Size Distribution in Cobalt Oxalate Synthesis Process

2019

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“…For CORC process, the fed-batch mode is employed by taking its advantage compared with the batch mode. The main objective of CORC process is to synthesize the cobalt oxalate through the reaction of cobalt chloride and ammonium oxalate which is described as [1], [35] (28) In the process, the important product quality index, i.e. average particle size, is measured by laboratory analysis.…”

Section: B Application To a Cobalt Oxalate Synthesis Pilot Plangmentioning

confidence: 99%

Soft Sensor Model Development for Cobalt Oxalate Synthesis Process Based on Adaptive Gaussian Mixture Regression

et al. 2019

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Average particle size is a critical quality variable for optimal operation of the cobalt oxalate synthesis process. However, the measurement for this variable is often achieved from offline laboratory assaying procedure with low sampling rate and low reliability. Therefore, a data-driven soft sensor model based on adaptive Gaussian mixture regression (AGMR) is presented in this paper. Firstly, a GMR based soft sensor model is developed for predicting the average particle size. Secondly, the prediction uncertainty obtained from the GMR model is used to assess the performance of the current soft sensor model. Thirdly, a dual updating algorithm based on the model performance assessment is constructed to track the timevarying behavior of the synthesis process. In the updating method, bias updating and moving window model updating methods are performed in turns based on the results of model performance assessment. The dual updating mechanism can avoid blind updating. Finally, a numerical example and a real industrial cobalt oxalate synthesis process application are used to demonstrate the effectiveness of the proposed method. INDEX TERMS Cobalt oxalate synthesis process, Gaussian mixture regression, soft sensor, model performance assessment, model updating.

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Self‐correcting modifier‐adaptation strategy for batch‐to‐batch optimization based on batch‐wise unfolded PLS model

2016

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The problem of optimizing a batch process under model uncertainty using a batch‐wise unfolded PLS (BW‐PLS) model‐based modifier‐adaptation (MA) strategy is described. The main idea behind the strategy is to use measurements and iteratively modify the model to compensate for the mismatch of the necessary condition of optimality (NCO) between the plant and the model‐based optimization problem. It is proven that the popular data‐driven model‐based iterative learning control (ILC) strategy is equivalent to the proposed MA strategy using only zero‐order modifier. Inspired by the effectiveness of the ILC being enhanced by rebuilding the data‐driven model, a more elaborate model updating scheme is proposed in this paper to improve the optimization performances. The heuristic rules for choosing filtering gain matrix are also presented to further accelerate the convergence rate and reduce the variation of the cost during the period of evolution. Finally, the efficacy of the proposed MA strategy is illustrated via a simulated typical batch reaction and a simulated cobalt oxalate synthesis process.

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Batch-to-batch optimization of cobalt oxalate synthesis process using modifier-adaptation strategy with latent variable model

Cited by 22 publications

References 33 publications

Active Learning Strategy for Online Prediction of Particle Size Distribution in Cobalt Oxalate Synthesis Process

Active Learning Strategy for Online Prediction of Particle Size Distribution in Cobalt Oxalate Synthesis Process

Soft Sensor Model Development for Cobalt Oxalate Synthesis Process Based on Adaptive Gaussian Mixture Regression

Self‐correcting modifier‐adaptation strategy for batch‐to‐batch optimization based on batch‐wise unfolded PLS model

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