Modeling of goethite iron precipitation process based on time-delay fuzzy gray cognitive network

Abstract

The goethite iron precipitation process consists of several continuous reactors and involves a series of complex chemical reactions, such as oxidation reaction, hydrolysis reaction and neutralization reaction. It is hard to accurately establish a mathematical model of the process featured by strong nonlinearity, uncertainty and time-delay. A modeling method based on time-delay fuzzy gray cognitive network (T-FGCN) for the goethite iron precipitation process was proposed in this paper. On the basis of the process mechanism, experts’ practical experience and historical data, the T-FGCN model of the goethite iron precipitation system was established and the weights were studied by using the nonlinear hebbian learning (NHL) algorithm with terminal constraints. By analyzing the system in uncertain environment of varying degrees, in the environment of high uncertainty, the T-FGCN can accurately simulate industrial systems with large time-delay and uncertainty and the simulated system can converge to steady state with zero gray scale or a small one.

Keywords

time-delay fuzzy gray cognitive network (T-FGCN) / iron precipitation process / nonlinear Hebbian learning

References

[1] LiD-b, JiangJ-mu. Present situation and development trend of zinc smelting technology at home and abroad [J]. China Metal Bulletin, 2015, 6: 41-44

[2] XieY F, XieS W, LiY G, YangC H, GuiW H. Dynamic modeling and optimal control of goethite process based on the rate-controlling step [J]. Control Engineering Practice, 2017, 58: 54-65

[3] ChenN, FanY, GuiW-h, YangC-h, JiangZ-hui. Hybrid modeling and control of iron precipitation by goethite process [J]. Chinese Journal of Nonferrous Metals, 2014, 24(1): 254-261

[4] AnninouP A, GroumposP P. Modeling of Parkinson’s disease using fuzzy cognitive maps and non-Linear Hebbian learning [J]. International Journal on Artificial Intelligence Tools, 2014, 23(5): 1450010-1450026

[5] FatahiS, MoradiH. A fuzzy cognitive map model to calculate a user’s desirability based on personality in e-learning environments [J]. Computers in Human Behavior, 2016, 63: 272-281

[6] ObiedatM, SamarasingheS. A novel semiquantitative Fuzzy Cognitive Map model for complex systems for addressing challenging participatory real life problems [J]. Applied Soft Computing, 2016, 48: 91-110

[7] JiangZ-h, LiX-m, GuiW-hua. All parameters adaptive predictive control strategy for long time-delay system [J]. Journal of Central South University (Science and Technology), 2012, 43(1): 200-206

[8] WangY Y, ChenJ W, GuL Y, LiX D. Time delay control of hydraulic manipulators with continuous nonsingular terminal sliding mode [J]. Journal of Central South University, 2015, 22(12): 4616-4624

[9] ChenF W, LiuT. Iterative identification of discrete-time output-error model with time delay [J]. Journal of Central South University, 2017, 24(3): 647-654

[10] BourganiE, StyliosC D, ManisG, GeorgoulosV C. Integrated approach for developing timed fuzzy cognitive maps [C]. 7th IEEE International Conference on Intelligent Systems., 2015, 322: 193-204

[11] NeocleousC, SchizasC N. Modeling socio-politicoeconomic systems with time-dependent fuzzy cognitive maps [C]. IEEE International Conference on Fuzzy Systems., 2012, 19: 1-7

[12] ParkK S, KimS H. Fuzzy cognitive maps considering time relationships [J]. International Journal of Human-Computer Studies, 1995, 42(2): 157-168

[13] BourganiE, StyliosC D, ManisG, GeorgoulosV C. Timed fuzzy cognitive maps for supporting obstetricians’ decisions [J]. IFMBE Proceedings, 2015, 45: 753-756

[14] LeeI K, KwonS H. Learning rule for time delay in fuzzy cognitive maps [J]. IEICE Transactions on Information & Systems, 2010, 93(11): 3153-3157

[15] ZhangW, LiuL, ZhuY C. Using fuzzy cognitive time maps for modeling and evaluating trust dynamics in the virtual enterprises [J]. Expert Systems with Applications, 2008, 35(4): 1583-1592

[16] ZhangJ Y, LiuZ Q, ZhouS. Dynamic domination in fuzzy causal networks [J]. IEEE Transactions on Fuzzy Systems, 2006, 14(1): 42-57

[17] KheirandishA, MotlaghF, ShafiabadyN, DahariM, WahabA K A. Dynamic fuzzy cognitive network approach for modelling and control of PEM fuel cell for power electric bicycle system [J]. Applied Energy, 2017, 202: 20-31

[18] KottasT L, BoutalisY S, ChristodoulouM A. Fuzzy cognitive network: A general framework [J]. Intelligent Decision Technologies, 2007, 1(4): 183-196

[19] KottasT, StimoniarisD, TsiamitrosD, KikisV, BoutalisY, DialynasE. New operation scheme and control of Smart Grids using Fuzzy Cognitive Networks [C]. IEEE Power Tech Eindhoven Conference., 2015, 151: 1-5

[20] DengJ-longGray system (Society*Economy) [M], 1985, National Defense Industry Press, Beijing: 36105

[21] JiP-rong. Unbiased gray prediction model [J]. Journal of Systems Engineering and Electronics, 2000, 22(6): 78-80

[22] JiP-rong. Research on the characteristics of gray prediction model [J]. System Engineering-Theory & Practice, 2001, 9: 105-108

[23] MaX, LiuZ. Application of a novel time-delayed polynomial grey model to predict the natural gas consumption in China [J]. Journal of Computational & Applied Mathematics, 2017, 324: 17-24

[24] DingS, DangY G, LiX M, WangJ J, ZhaoK. Forecasting Chinese CO₂ emissions from fuel combustion using a novel grey multivariable model [J]. Journal of Cleaner Production, 2017, 162: 1527-1538

[25] PapageorgiouE I, StyliosC D, GroumposP P. Active Hebbian learning algorithm to train fuzzy cognitive maps [J]. International Journal of Approximate Reasoning, 2004, 37(3): 219-249

[26] WuK, LiuJ. Robust learning of large-scale fuzzy cognitive maps via the lasso from noisy time series [J]. Knowledge-Based Systems, 2016, 113: 23-38

[27] NatarajanR, SubramanianJ, PapageorgiouE I. Hybrid learning of fuzzy cognitive maps for sugarcane yield classification [J]. Computers and Electronics in Agriculture, 2016, 127: 147-157

[28] ChenN, PengJ-j, WangL, GuoY-q, GuiW-hua. Fuzzy grey cognitive networks modeling and its application [J]. Acta Automatica Sinica, 2018, 44(7): 1227-1236

[29] ChenN, WangL, PengJ-j, LiuB, GuiW-hua. Improved nonlinear Hebbian learning algorithm based on fuzzy cognitive networks model [J]. Control Theory and Applications, 2016, 33(10): 1273-1280