Soft Computing

, Volume 23, Issue 19, pp 9429–9437 | Cite as

Strength prediction of similar materials to ionic rare earth ores based on orthogonal test and back propagation neural network

  • Wen ZhongEmail author
  • Yunchuan Deng
  • J. A. Tenreiro Machado
  • Chao Zhang
  • Kui Zhao
  • Xiaojun Wang


This paper aims to predict the strength of materials similar to the ionic rare earth (IRE) ores [hereinafter referred as similar materials (SM)]. A 4 × Y × 2 back propagation neural network (BPNN) prediction model, based on 18 groups of samples of the SM with different mix proportions, was used to describe their strength. The BPNN modelling scheme includes four input layer neurons, representing the amounts of kaolinite, potassium feldspar, anorthose and mica, and two output layer neurons corresponding to the strength indices c and φ of the samples after 6 h leaching. Comparing the training and prediction errors, it is verified that the error in predicted strength is minimized when the number of hidden layer neurons Y equals 9. The correlation coefficient R of the prediction model is as high as 0.998, and the maximum relative errors of the strength indices (c and φ) are 4.11% and 4.26%, respectively. Orthogonal tests show that the BPNN is a reliable and accurate method to predict the strength of SM. Featuring uniform dispersion, comparability and nonlinear optimization, the proposed method sheds further light on the strength prediction of IRE ores.


Back propagation neural network (BPNN) Orthogonal test Ionic rare earth (IRE) Similar materials (SM) Strength prediction 


Author contributions

WZ was involved in conceptualization; YD was involved in data curation; YD and CZ was involved in formal analysis; WZ, ZK and XW were contributed to funding acquisition; WZ was involved in project administration; AC was involved in supervision; WZ and YD was involved in writing–original draft; AC was involved in writing–review and editing.


This study was funded by the National Natural Science Foundation of China (51504102, 51764014), the Postdoctoral Research Foundation of China (2017M622099), the National Key Technologies Research & Development Program (2017YFC0804601), the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering (Z017024), the China Scholarship Council (201708360152), the Program of Qingjiang Excellent Young Talents, Jiangxi University of Science and Technology (JXUSTQJYX2017002), the Program of Hundred People Voyage, Jiangxi Province (20180375).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Wen Zhong
    • 1
    • 2
    Email author
  • Yunchuan Deng
    • 1
    • 3
  • J. A. Tenreiro Machado
    • 4
  • Chao Zhang
    • 2
  • Kui Zhao
    • 1
  • Xiaojun Wang
    • 1
  1. 1.School of Resources and Environment EngineeringJiangxi University of Science and TechnologyGanzhouChina
  2. 2.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil MechanicsChinese Academy of SciencesBeijingChina
  3. 3.Chongyi Zhangyuan Tungsten Co., Ltd.GanzhouChina
  4. 4.Department of Electrical Engineering, Institute of EngineeringPolytechnic of PortoPortoPortugal

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