Natural Resources Research

, Volume 28, Issue 1, pp 223–239 | Cite as

Comparison of LLNF, ANN, and COA-ANN Techniques in Modeling the Uniaxial Compressive Strength and Static Young’s Modulus of Limestone of the Dalan Formation

  • Maryam MokhtariEmail author
  • Mahmoud Behnia
Original Paper


The uniaxial compressive strength and static Young’s modulus are among the key design parameters typically used in geotechnical engineering projects. In this paper, three artificial intelligence techniques, namely the local linear neuro-fuzzy (LLNF) technique, artificial neural network (ANN) and the hybrid cuckoo optimization algorithm-artificial neural network (COA-ANN), were used to estimate the uniaxial compressive strength and the static Young’s modulus of limestone. For this purpose, 115 limestone samples were subjected to the tests of uniaxial compressive strength, ultrasonic velocity, and physical properties (density and porosity) tests. From the laboratory results obtained, the values of the P-wave velocity, density, porosity and dynamic Poisson’s ratio were tested as the model input parameters to determine the best input configuration for estimating the uniaxial compressive strength and the static Young’s modulus. Different models with different input combinations were practiced, and the models with the highest estimation accuracy are reported here. Performance evaluation was carried out using three criteria including coefficient of determination, variance accounted for, and normalized mean-square error. Evaluating the correlation coefficients and error criteria resulting from the three methods used demonstrates the superiority of LLNF method to ANN and COA-ANN methods. The developed ANN models display lower correlation coefficients and higher amount of error compared to the other models. However, using cuckoo optimization algorithm has led to significant improvement in accuracy and precision of estimations carried out by ANN and has improved its efficiency. Results have confirmed that the employed hybrid method outperforms in estimating untrained data (test data) compared to the LLNF and ANN methods.


Uniaxial compressive strength Static Young’s modulus Ultrasonic velocity Local linear neuro-fuzzy Artificial neural network Cuckoo optimization algorithm 



We would like to thank two anonymous reviewers and the Editor-in-Chief of Natural Resources Research, Dr. John Carranza, for their valuable and constructive comments that greatly helped to improve the quality of this paper.


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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering, Faculty of EngineeringYazd UniversityYazdIran
  2. 2.Department of Mining EngineeringIsfahan University of TechnologyIsfahanIran

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