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Asynchronous Fuzzy Cognitive Networks Modeling and Control for Goethite Iron Precipitation Process

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Abstract

Goethite iron precipitation process is a key step in direct leaching process of zinc, whose aim is to remove ferrous ions from zinc sulphate solution. The process consists of several cascade reactors, and each of them contains complex chemical reactions featured by strong nonlinearity and large time delay. Therefore, it is hard to build up an accurate mathematical model to describe the dynamic changes in the process. In this paper, by studying the mechanism of these reactions and combining historical data and expert experience, the modeling method called asynchronous fuzzy cognitive networks (AFCN) is proposed to solve the various time delay problem. Moréover, the corresponding AFCN model for goethite iron precipitation process is established. To control the process according to fuzzy rules, the nonlinear Hebbian learning algorithm (NHL) terminal constraints is firstly adopted for weights learning. Then the model parameters of equilibrium intervals corresponding to different operating conditions can be calculated. Finally, the matrix meeting the expected value and the weight value of steady states is stored into fuzzy rules as prior knowledge. The simulation shows that the AFCN model for goethite iron precipitation process could precisely describe the dynamic changes in the system, and verifies the superiority of control method based on fuzzy rules.

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References

  1. Deng Y G, Chen Q Y, Yin Z L, et al., Iron removal from zine leaching solution by goethite method, Non-Ferrous Metal, 2010, 62(33): 80–84.

    Google Scholar 

  2. Luo C Y, Application practice of iron removal technology of goethite in Danxia smelter, Non-Ferrous Metal Engineering, 2011, 3(1): 44–46.

    MathSciNet  Google Scholar 

  3. Li D B and Jiang J M, Present situation and development trend of zinc smelting technology at home and abroad, China Metal Bulletin, 2015, (6): 41–44.

  4. Chen N, Yang S, Peng J J, et al., Fuzzy cognitive network control of goethite process, Proceddings of 35th Chinese Control Conference, Chengdu, 2016, 325–330.

  5. Chen N, Dai J Y, Zhou X J, et al., Distributed model predictive control of iron precipitation process by goethite based on dual iterative method, International Journal of Control Automation and Systems, 2019, 17(5): 1233–1245.

    Article  Google Scholar 

  6. Chen N, Dai J Y, Gui W H, et al., A hybrid prediction model with a selectively updating strategy for iron removal process in zinc hydrometallurgy, Science China Information Sciences, 2020, 63(1): 119205.

    Article  Google Scholar 

  7. Kosko B, Fuzzy cognitive maps, International Journal of Man Machine Studie, 1986, 24(1): 65–75.

    Article  MATH  Google Scholar 

  8. Solanagutierrez J, Rincon G, Alonso C, et al., Using fuzzy cognitive maps for predicting river managementresponses: A case study of the Esla River basin, Spain, Ecological Modelling, 2017, (360): 260–269.

  9. Marchal P C, Garca J G, and Ortega J G, Application of fuzzy cognitive maps and run-to-run control to a decision support system for global set-point determination, IEEE Transactions on Systems Man & Cybernetics Systems, 2017, 47(8): 2256–2267.

    Article  Google Scholar 

  10. Mourhir A, Papageorgiou E, Kokkinos K, et al., Exploring precision farming scenarios using fuzzy cognitive maps, Sustainability, 2017, 9(7): 1241–1264.

    Article  Google Scholar 

  11. Albe S, Neural networks and fuzzy systems, Journal of the Acoustical Society of America, 1992, 103(6): 49–71.

    Google Scholar 

  12. Stylios C D and Groumpos P P, Fuzzy cognitive maps: A soft computing technique for intelligent control, Proc. International Symposium on Intelligent Control Patas, 2000, 97–102.

  13. Papageorgiou E I, Yield prediction in apples using fuzzy cognitive map learning approach, Computers and Electronics, 2013, 91(2): 19–29.

    Article  Google Scholar 

  14. Stylios C D and Groumpos P P, Modeling complex systems using fuzzy cognitive maps, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2004, 34(1): 155–162.

    Article  Google Scholar 

  15. Stylios C D and Groumpos P P, Fuzzy cognitive maps in modeling supervisory control systems, Journal of Intelligent and Fuzzy Systems, 2000, 8(2): 83–98.

    MATH  Google Scholar 

  16. Park K S and Kim S H, Fuzzy cognitive maps considering time relationships, International Journal of Human-Computer Studies, 1995, 42(2): 157–168.

    Article  Google Scholar 

  17. Zhang W, Liu L, and Zhu Y, Using fuzzy cognitive time maps for modeling and evaluating trust dynamics in the virtual enterprises, Exper System with Applications, 2008, 35(4): 1583–1592.

    Article  Google Scholar 

  18. Kottas T L, Boutalis Y S, and Christodoulou M A, Fuzzy cognitive networks: A general framework, Intelligent Decision Technologies, 2007, 1(4): 183–196.

    Article  Google Scholar 

  19. Zhang J, Liu Z Q, and Zhou S, Dynamic domination in fuaay causal networks, IEEE Translations on Fuzzy Systems, 2006, 14(1): 42–57.

    Article  Google Scholar 

  20. Liu Z Q and Zhang J Y, Interroating the structure of fuzzy cognitive maps, Soft Computing, 2003, 7(3): 148–153.

    Article  Google Scholar 

  21. Kottas T, Stimoniaris D, Tsiamitros D, et al., New operation scheme and control of smart grids using fuzzy cognitive networks, Power Tech., 2015 IEEE Eindhoven, 2015, 151: 1–5.

    Google Scholar 

  22. Kheirandish A, Motlagh F, Shafiabady N, et al., Dynamic fuzzy cognitive network approach for modelling and control of PEM fuel cell for power electric bicycle system, Applied Energy, 2017, 202(9): 20–31.

    Article  Google Scholar 

  23. Kottas T L, Boutalis Y S, and Christodoulou M A, Fuzzy Cognitive Networks: Adaptive Network Estimation and Control Paradigms, Springer, Berlin Heidelberg, 2010, 247: 89–134.

    Book  Google Scholar 

  24. Papageorgiou E, Stylios C D, and Groumpos P P, Fuzzy cognitive map learning based on nonlinear Hebbian rule, Proc. Aust. Conf. Artif. Intell., 2003, 256–268.

  25. Lindsay G W, Rigotti M, Warden M R, et al., Hebbian learning in a random network captures selectivity properties of prefrontal cortex, Journal of Neuroscience, 2017, 37(45): 1222–1217.

    Article  Google Scholar 

  26. Born J, Galeazzi J M, and Stringe S M, Hebbian learning of hand-centred representations in a hierarchical neural network model of the primate visual system, Plos One, 2017, 12(5): e0178304.

    Article  Google Scholar 

  27. Zenke F, Gerstner W, and Ganguli S, The temporal paradox of Hebbian learning and homeostatic plasticity, Current Opinion in Neurobiology, 2017, 43: 166–176.

    Article  Google Scholar 

  28. Papageorgiou E, Stylios C D, and Groumpos P P, Active Hebbian learning algorithm to train fuzzy cognitive maps, Int. J. Approx. Reason, 2004, 37(3): 219–249.

    Article  MathSciNet  MATH  Google Scholar 

  29. Chen N, Wang L, Peng J J, et al., Improved nonlinear Hebbian learning algorithm based on fuzzy cognitive networks model, Control Theory and Applications, 2017, 33(10): 1273–1280 (in Chinese).

    MATH  Google Scholar 

  30. Wu K and Liu J, Robust learning of large-scale fuzzy cognitive maps via the lasso from noisy time series, Knowledge-Based Systems, 2016, 113(12): 23–38.

    Article  Google Scholar 

  31. Natarajan R, Subramanian J, and Papageorgiou E I, Hybrid learning of fuzzy cognitive maps for sugarcane yield classification, Computers & Electronics in Agriculture, 2016, 127(9): 147–157.

    Article  Google Scholar 

  32. Chen N, Peng J J, Wang L, et al., Fuzzy grey cognitive networks modeling and its application, Acta Automatica Sinica, 2018, 44(7): 1227–1236 (in Chinese).

    MATH  Google Scholar 

  33. Chen N, Zhou J Q, Peng J J, et al., Modeling of goethite iron precipitation process based on time-delay fuzzy gray cognitive network, Journal of Central South University, 2019, 26(1): 63–74.

    Article  Google Scholar 

  34. Boutalis Y and Christocloulou M, Adaptive estimation of fuzzy cognitive maps with proven stability and parameter convergence, IEEE Transactions on Fuzzy Systems, 2009, 17(4): 874–889.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Automation, Central South University, Changsha, 410083, China

    Ning Chen, Junjie Peng, Weihua Gui, Jiaqi Zhou & Jiayang Dai

  2. School of Electrical Engineering, Guangxi University, Nanning, 530004, China

    Jiayang Dai

Authors
  1. Ning Chen
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  2. Junjie Peng
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  3. Weihua Gui
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  4. Jiaqi Zhou
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  5. Jiayang Dai
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Corresponding authors

Correspondence to Ning Chen, Jiaqi Zhou or Jiayang Dai.

Additional information

This work was supported in part by the Program of the National Natural Science Foundation of China under Grant No. 61673399, in part by the Program of National Natural Science Foundation of Hunan Province under Grant No. 2017JJ2329, and in part by Fundamental Research Funds for Central Universities of Central South University under Grant No. 2018zzts550.

This paper was recommended for publication by Editor SUN Jian.

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Chen, N., Peng, J., Gui, W. et al. Asynchronous Fuzzy Cognitive Networks Modeling and Control for Goethite Iron Precipitation Process. J Syst Sci Complex 33, 1422–1445 (2020). https://doi.org/10.1007/s11424-020-9120-1

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  • DOI: https://doi.org/10.1007/s11424-020-9120-1

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