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Prediction of Three-Dimensional Fractal Dimension of Hematite Flocs Based on Particle Swarm Optimization Optimized Back Propagation Neural Network

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Abstract

The three-dimensional (3D) fractal dimension is an important parameter to analyze the 3D structure and flocculation effect of the hematite flocs. In this work, the 3D fractal dimension of hematite flocs was predicted by establishing the particle swarm optimization (PSO) algorithm optimized with the back propagation (BP) neural network (PSO-BP). The proposed model considers four factors, namely, the flocculant quantity, flocculation time, stirring speed, and temperature, as the input parameters. We normalize the input data during the preprocessing stage. The BP neural network was optimized by using the PSO algorithm for realizing the 3D fractal dimension. The prediction accuracy and effectiveness of the model were evaluated. The experimental results showed that the predictions performed by the proposed PSO-BP neural network were better than that of BP neural network. In addition, the root mean square error (RMSE), mean squared relative error (MSRE), mean absolute error (MAE), and mean absolute relative error (MARE) of the proposed model are lower, compared with the errors of the BP network. Similarly, the measurement coefficient R2 of the proposed model is higher, compared with the BP network. The maximum absolute error of the model is 0.0772, the maximum relative error is 0.02405, and the regression coefficient r is 0.98592. These results showed that the proposed model has a good performance and high prediction accuracy. When verifying the practicability and the effectiveness of the proposed PSO-BP model, the prediction results of 10 groups of hematite flocculation experimental data under different conditions showed that the prediction value of the proposed PSO-BP model was closer to the ground truth as compared to the BP model. Therefore, the proposed model is suitable for predicting the 3D fractal dimension of hematite flocculation.

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References

  1. Tian J, Gao H, Guan J, Ren Z (2017) Modified floc-flotation in fine sericite flotation using polymethylhydrosiloxane. Sep Purif Technol 174:439–444

    Article  Google Scholar 

  2. Zhang T, Qin W, Yang C, Huang S (2014) Floc flotation of marmatite fines in aqueous suspensions induced by butyl xanthate and ammonium dibutyl dithiophosphate. Trans Nonferrous Met Soc China 24(5):1578–1586

    Article  Google Scholar 

  3. Fox JM, Hill PS, Ogston AS et al (2004) Floc fraction in the waters Po River prodelta. Cont Shelf Res 24(15):1699–1715

    Article  Google Scholar 

  4. Li T, Zhu Z, Wang DS et al (2007) The strength and fractal dimension characteristics of alum–kaolin flocs. Int J Miner Process 82(1):23–29

    Article  Google Scholar 

  5. Son M, Hsu TJ (2009) The effect of variable yield strength and variable fractal dimension on flocculation of cohesive sediment. Water Res 43:3582–3592

    Article  Google Scholar 

  6. Zhao J, Fu X, Wang J et al (2016) Effect of shear force field on the separation effect of ultra-clean coal based on fractal dimension of flocs. J China Coal Soc 41(8):2078–2085

    Google Scholar 

  7. Wei W, Du M, Zhu J et al (2014) Multifractal behavior of flocs growth in flocculation processes. Acta Sci Circum 34(1):79–84

    Google Scholar 

  8. Berrezueta E, Cuervas-Mons J, Rodríguez-Rey Á, Ordóñez-Casado B (2019) Representativity of 2D shape parameters for mineral particles in quantitative petrography. Minerals 9(12):768

    Article  Google Scholar 

  9. Vojislav M, Cristina S, Ivana I, Markus M, HansJörg F (2021) Fractal nature of advanced Ni-based superalloys solidified on board the International Space Station. Remote Sensing 13(9):1724

    Article  Google Scholar 

  10. Xi Z, Wang J, Hu J, Tang S, Xiao H, Zhang Z, Xing Y (2018) Experimental investigation of evolution of pore structure in Longmaxi marine shale using an anhydrous pyrolysis technique. Minerals 8(6):226

    Article  Google Scholar 

  11. Fu H, Li H (2020) Prediction model of air pollution index in Anyang City in winter based on BP neural network. World Sci Res J 6(10):265–275

    Google Scholar 

  12. Han I, Yuan T, Lee J, Yoon Y, Kim J (2019) Learned prediction of compressive strength of GGBFS concrete using hybrid artificial neural network models. Materials 12(22):3708

    Article  Google Scholar 

  13. Xu Z, Ye D, Chen J, Zhou H (2020) Novel terahertz nondestructive method for measuring the thickness of thin oxide scale using different hybrid machine learning models. Coatings 10(9):805

    Article  Google Scholar 

  14. Wang Q (2020) Application of BP neural network model in data analysis. Electron Technol Softw Eng 12:189–190

    Google Scholar 

  15. Chen J, Hsieh H, Do Q (2014) Forecasting Hoabinh reservoir’s incoming flow: an application of neural networks with the Cuckoo Search algorithm. Information 5(4):570–586

    Article  Google Scholar 

  16. Zhang L, Wang F, Sun T, Xu B (2018) A constrained optimization method based on BP neural network. Neural Comput Appl 29:413–421

    Article  Google Scholar 

  17. Deng C, Feng Y, Shu J, Huang Z, Tang Q (2020) Prediction of tool point frequency response functions within machine tool work volume considering the position and feed direction dependence. Symmetry 12(7):1073

    Article  Google Scholar 

  18. Hossain Lipu MS, Hannan MA, Hussain A, Saad MHM (2017) Optimal BP neural network algorithm for state of charge estimation of lithium-ion battery using PSO with PCA feature selection. J Renew Sustain Energy 9(6):1063

    Article  Google Scholar 

  19. Chen N, Xiong C, Du W, Wang C, Lin X, Chen Z (2019) An improved genetic algorithm coupling a back-propagation neural network model (IGA-BPNN) for water-level predictions. Water 11(9):1795

    Article  Google Scholar 

  20. Xiang T, Wang H (2018) Research on distributed 5G signal coverage detection algorithm based on PSO-BP-kriging. Sensors (Basel, Switzerland) 18(12):4390

    Article  Google Scholar 

  21. Parsopoulos KE, Vrahatis MN (2002) Recent approaches to global optimization problems through Particle Swarm Optimization. Nat Comput 1:235–306

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhan X (2022) Construction of TCM syndrome prediction model for psoriasis based on PSO-BP. Mod Comput 28(06):52–55

    Google Scholar 

  23. Gao M, Yu S, Zheng J, Xu C, Liu W, Luan H (2016) Research on resistivity imaging using neural network based on immune genetic algorithm. Chin J Geophys 59(11):4372–4382

    Google Scholar 

  24. Amar MN, Zeraibi N, Redouane K (2018) Bottom hole pressure estimation using hybridization neural networks and grey wolves optimization. Petroleum 4(4):419–429

    Article  Google Scholar 

  25. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. MHS’95. Proc Sixth Int Symp Micro Mach Hum Sci 10(6):39–43

    Article  Google Scholar 

  26. Liu X, Liu Z, Liang Z, Zhu S, Correia JAFO, De Jesus AMP (2019) PSO-BP neural network-based strain prediction of wind turbine blades. Materials 12(12):1889

    Article  Google Scholar 

  27. Shao D, Nong X, Tan X, Chen S, Xu B, Hu N (2018) Daily water quality forecast of the south-to-north water diversion project of China based on the Cuckoo Search-back propagation neural network. Water 10(10):1471

    Article  Google Scholar 

  28. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1:33–57

    Article  Google Scholar 

  29. Kshirsagar P, Akojwar S (2016) Optimization of BPNN parameters using PSO for EEG signals. Proc Int Conf Commun Signal Process 2016 (ICCASP 2016) 12:384–393

    Google Scholar 

  30. Jin C, Jin S, Qin L (2012) Attribute selection method based on a hybrid BPNN and PSO algorithms. Appl Soft Comput J 12(8):2147–2155

    Article  Google Scholar 

Download references

Funding

This work is financially supported by the National Natural Science Foundation of China (51874135, 51904106), Natural Science Foundation of Hebei Province (E2019209347), and Tangshan Basic Innovation Team Project (19130207C).

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Authors and Affiliations

  1. College of Mining Engineering, North China University of Science and Technology, Tangshan, 063210, China

    Hongmei Zhang, Fusheng Niu, Jinxia Zhang & Xiaodong Yu

  2. Hebei Province Mining Industry Develops With Safe Technology Priority Laboratory, Tangshan, 063210, Hebei, China

    Fusheng Niu & Jinxia Zhang

Authors
  1. Hongmei Zhang
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  2. Fusheng Niu
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  3. Jinxia Zhang
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  4. Xiaodong Yu
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Contributions

Conceptualization, H.Z. and F.N.; investigation, H.Z., F.N., and J.Z.; methodology, H.Z. and X.Y.; formal analysis, J.Z. and X.Y.; data curation, H.Z., F.N., J.Z., and X.Y.; writing—original draft preparation, H.Z. and J.Z.; writing—review and editing, F.N., J.Z., and X.Y.; project administration, F.N. and J.Z.; funding acquisition, F.N.

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Correspondence to Hongmei Zhang.

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Zhang, H., Niu, F., Zhang, J. et al. Prediction of Three-Dimensional Fractal Dimension of Hematite Flocs Based on Particle Swarm Optimization Optimized Back Propagation Neural Network. Mining, Metallurgy & Exploration 39, 2503–2515 (2022). https://doi.org/10.1007/s42461-022-00684-z

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  • DOI: https://doi.org/10.1007/s42461-022-00684-z

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