Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

doi:10.1016/j.cjche.2023.09.010

中国化学工程学报 ›› 2024, Vol. 66 ›› Issue (2): 167-179.DOI: 10.1016/j.cjche.2023.09.010

• Full Length Article • 上一篇下一篇

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Zhiqiang Wang¹, Dakuo He^1,2, Haotian Nie¹

1. College of Information Science and Engineering, Northeastern University, Shenyang 110004, China;
2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China

收稿日期:2022-09-30 修回日期:2023-09-19 出版日期:2024-02-28 发布日期:2024-04-20
通讯作者: Dakuo He,E-mail:hedakuo@ise.neu.edu.cn
基金资助:
This work was supported in part by the National Key Research and Development Program of China (2021YFC2902703) and the National Natural Science Foundation of China (62173078, 61773105, 61533007, 61873049, 61873053, 61703085 and 61374147).

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Zhiqiang Wang¹, Dakuo He^1,2, Haotian Nie¹

1. College of Information Science and Engineering, Northeastern University, Shenyang 110004, China;
2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China

Received:2022-09-30 Revised:2023-09-19 Online:2024-02-28 Published:2024-04-20
Contact: Dakuo He,E-mail:hedakuo@ise.neu.edu.cn
Supported by:
This work was supported in part by the National Key Research and Development Program of China (2021YFC2902703) and the National Natural Science Foundation of China (62173078, 61773105, 61533007, 61873049, 61873053, 61703085 and 61374147).

摘要/Abstract

摘要： Concentrate copper grade (CCG) is one of the important production indicators of copper flotation processes, and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes. This paper addresses the fluctuation problem of CCG through an operational optimization method. Firstly, a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties. Next, a Bayesian network (BN) is applied to explore the relationship between the operational variables and the CCG. Based on the analysis results of BN, a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained. To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results, an index-oriented adaptive differential evolution (IOADE) algorithm is proposed, and the convergence performance of IOADE is superior to the traditional differential evolutionand adaptive differential evolutionmethods. Finally, the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

关键词: Weighted Gaussian process regression, Index-oriented adaptive differential evolution, Operational optimization, Copper flotation process

Abstract: Concentrate copper grade (CCG) is one of the important production indicators of copper flotation processes, and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes. This paper addresses the fluctuation problem of CCG through an operational optimization method. Firstly, a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties. Next, a Bayesian network (BN) is applied to explore the relationship between the operational variables and the CCG. Based on the analysis results of BN, a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained. To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results, an index-oriented adaptive differential evolution (IOADE) algorithm is proposed, and the convergence performance of IOADE is superior to the traditional differential evolutionand adaptive differential evolutionmethods. Finally, the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

Key words: Weighted Gaussian process regression, Index-oriented adaptive differential evolution, Operational optimization, Copper flotation process

Zhiqiang Wang, Dakuo He, Haotian Nie. Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm[J]. 中国化学工程学报, 2024, 66(2): 167-179.

参考文献

[1] Y. Jiang, J.L. Fan, T.Y. Chai, F.L. Lewis, Dual-rate operational optimal control for flotation industrial process with unknown operational model, IEEE Trans. Ind. Electron. 66(6)(2019)4587-4599.
[2] K.X. Bi, S.Y. Zhang, C. Zhang, H.R. Li, X.Y. Huang, H.Y. Liu, T. Qiu, Knowledge expression, numerical modeling and optimization application of ethylene thermal cracking:From the perspective of intelligent manufacturing, Chin. J. Chem. Eng. 38(2021)1-17.
[3] M.B. Sabeti, M.A. Hejazi, A. Karimi, Enhanced removal of nitrate and phosphate from wastewater by Chlorella vulgaris:Multi-objective optimization and CFD simulation, Chin. J. Chem. Eng. 27(3)(2019)639-648.
[4] H. Yan, F.L. Wang, D.K. He, Q.K. Wang, An operational adjustment framework for a complex industrial process based on hybrid Bayesian network, IEEE Trans. Autom. Sci. Eng. 17(4)(2020)1699-1710.
[5] F.Z. Liu, H.J. Gao, J.B. Qiu, S. Yin, J.L. Fan, T.Y. Chai, Networked multirate output feedback control for setpoints compensation and its application to rougher flotation process, IEEE Trans. Ind. Electron. 61(1)(2014)460-468.
[6] T.Y. Chai, L. Zhao, J.B. Qiu, F.Z. Liu, J.L. Fan, Integrated network-based model predictive control for setpoints compensation in industrial processes, IEEE Trans. Ind. Inform. 9(1)(2013)417-426.
[7] J. Zhang, Z.H. Tang, Y.F. Xie, M.X. Ai, G.Y. Zhang, W.H. Gui, Data-driven adaptive modeling method for industrial processes and its application in flotation reagent control, ISA Trans. 108(2021)305-316.
[8] W. Dai, T.Y. Chai, S.X. Yang, Data-driven optimization control for safety operation of hematite grinding process, IEEE Trans. Ind. Electron. 62(5)(2015)2930-2941.
[9] M. Ellis, P.D. Christofides, Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems, Contr. Eng. Pract. 22(2014)242-251.
[10] C.X. Mu, D. Wang, H.B. He, Novel iterative neural dynamic programming for data-based approximate optimal control design, Automatica 81(2017)240-252.
[11] B.Y. Li, H.P. Du, W.H. Li, B.J. Zhang, Integrated dynamics control and energy efficiency optimization for overactuated electric vehicles, Asian J. Contr. 20(5)(2018)1952-1966.
[12] C.E. Rasmussen, C.K.I. Williams, Gaussian processes for machine learning. Cambridge, Mass.:MIT Press, 2006.
[13] T. Krivec, G. Papa, J. Kocijan, Simulation of variational Gaussian process NARX models with GPGPU, ISA Trans. 109(2021)141-151.
[14] H.J. Huang, Y.D. Song, X. Peng, S.X. Ding, W.M. Zhong, W. Du, A sparse nonstationary trigonometric Gaussian process regression and its application on nitrogen oxide prediction of the diesel engine, IEEE Trans. Ind. Inform. 17(12)(2021)8367-8377.
[15] L. Yang, K. Wang, L. Mihaylova, Online sparse multi-output Gaussian process regression and learning, IEEE Trans. Signal Inf. Process. Netw. 5(2)(2019)258-272.
[16] D. Yang, X. Zhang, R. Pan, Y.J. Wang, Z.H. Chen, A novel Gaussian process regression model for state-of-health estimation of lithium-ion battery using charging curve, J. Power Sources 384(2018)387-395.
[17] K.L. Liu, Y. Li, X.S. Hu, M. Lucu, W.D. Widanage, Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries, IEEE Trans. Ind. Inform. 16(6)(2019)3767-3777.
[18] X. Zhao, Y. Fu, Y.C. Liu, Human motion tracking by temporal-spatial local Gaussian process experts, IEEE Trans. Image Process. 20(4)(2011)1141-1151.
[19] A. Ranganathan, M.H. Yang, J. Ho, Online sparse Gaussian process regression and its applications, IEEE Trans. Image Process. 20(2)(2011)391-404.
[20] A. Gijsberts, G. Metta, Real-time model learning using Incremental Sparse Spectrum Gaussian Process Regression, Neural Netw. 41(2013)59-69.
[21] X.L. Wu, Q. Yuan, L. Wang, Multiobjective differential evolution algorithm for solving robotic cell scheduling problem with batch-processing machines, IEEE Trans. Autom. Sci. Eng. 18(2)(2021)757-775.
[22] L.M. Zheng, S.X. Zhang, S.Y. Zheng, Y.M. Pan, Differential evolution algorithm with two-step subpopulation strategy and its application in microwave circuit designs, IEEE Trans. Ind. Inform. 12(3)(2016)911-923.
[23] Y. Wang, H. Liu, H. Long, Z.J. Zhang, S.X. Yang, Differential evolution with a new encoding mechanism for optimizing wind farm layout, IEEE Trans. Ind. Inform. 14(3)(2017)1040-1054.
[24] S.M. Guo, C.C. Yang, Enhancing differential evolution utilizing eigenvector-based crossover operator, IEEE Trans. Evol. Comput. 19(1)(2015)31-49.
[25] N.M. Hamza, D.L. Essam, R.A. Sarker, Constraint consensus mutation-based differential evolution for constrained optimization, IEEE Trans. Evol. Comput. 20(3)(2016)447-459.
[26] H. Zhao, Z.H. Zhan, Y. Lin, X.F. Chen, X.N. Luo, J. Zhang, S. Kwong, J. Zhang, Local binary pattern-based adaptive differential evolution for multimodal optimization problems, IEEE Trans. Cybern. 50(7)(2019)3343-3357.
[27] Y. Yang, S.C. Tan, S.Y.R. Hui, Front-end parameter monitoring method based on two-layer adaptive differential evolution for SS-compensated wireless power transfer systems, IEEE Trans. Ind. Inform. 15(11)(2019)6101-6113.
[28] X.F. Liu, Z.H. Zhan, Y. Lin, W.N. Chen, Y.J. Gong, T.L. Gu, H.Q. Yuan, J. Zhang, Historical and heuristic-based adaptive differential evolution, IEEE Trans. Syst. Man Cybern. 49(12)(2018)2623-2635.
[29] Z.H. Zhan, Z.J. Wang, H. Jin, J. Zhang, Adaptive distributed differential evolution, IEEE Trans. Cybern. 50(11)(2019)4633-4647.
[30] Z.J. Wang, Z.H. Zhan, Y. Lin, W.J. Yu, H. Wang, S. Kwong, J. Zhang, Automatic niching differential evolution with contour prediction approach for multimodal optimization problems, IEEE Trans. Evol. Comput. 24(1)(2019)114-128.
[31] Q.Q. Fan, X.F. Yan, Self-adaptive differential evolution algorithm with zoning evolution of control parameters and adaptive mutation strategies, IEEE Trans. Cybern. 46(1)(2016)219-232.
[32] Q.Q. Fan, Y.L. Zhang, Self-adaptive differential evolution algorithm with crossover strategies adaptation and its application in parameter estimation, Chemom. Intell. Lab. Syst. 151(2016)164-171.

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价