Engineering with Computers

, Volume 35, Issue 1, pp 305–314 | Cite as

The effect of ICA and PSO on ANN results in approximating elasticity modulus of rock material

  • Hua Tian
  • Jisen ShuEmail author
  • Liu Han
Original Article


Reliable determination/evaluation of the rock deformation can be useful prior any structural design application. Young’s modulus (E) affords great insight into the characteristics of the rock. However, its direct determination in the laboratory is costly and time-consuming. Therefore, rock deformation prediction through indirect techniques is greatly suggested. This paper describes hybrid particle swarm optimization (PSO)–artificial neural network (ANN) and imperialism competitive algorithm (ICA)–ANN to solve shortcomings of ANN itself. In fact, the influence of PSO and ICA on ANN results in predicting E was studied in this research. By investigating the related studies, the most important parameters of PSO and ICA were identified and a series of parametric studies for their determination were conducted. All models were built using three inputs (Schmidt hammer rebound number, point load index and p-wave velocity) and one output which is E. To have a fair comparison and to show the capability of the hybrid models, a pre-developed ANN model was also constructed to estimate E. Evaluation of the obtained results demonstrated that a higher ability of E prediction is received developing a hybrid ICA–ANN model. Coefficient of determination (R2) values of (0.952, 0.943 and 0.753) and (0.955, 0.949 and 0.712) were obtained for training and testing of ICA–ANN, PSO–ANN and ANN models, respectively. In addition, VAF values near to 100 (95.182 and 95.143 for train and test) were achieved for a developed ICA–ANN hybrid model. The results indicated that the proposed ICA–ANN model can be implemented better in improving performance capacity of ANN model compared to another implemented hybrid model.


Young’s modulus PSO ICA ANN Hybrid model 



This work was financially supported by the National Key Research and Development Plan (2016YFC0501103), Natural Science Foundation of Jiangsu Province (BK20160259), National Natural Science Foundation of China (51774271), National Natural Science Foundation of China (No. 51674245), Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), the Fundamental Research Funds for the Central Universities (No. 2014XT01).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MinesChina University of Mining and TechnologyXuzhouChina
  2. 2.Shenghua Xinjiang Energy Co., LtdUrumqiChina
  3. 3.School of MinesChina University of Mining and TechnologyXuzhouChina
  4. 4.School of MinesChina University of Mining and TechnologyXuzhouChina

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