An ensemble tree-based machine learning model for predicting the uniaxial compressive strength of travertine rocks

  • Rahim BarzegarEmail author
  • Masoud Sattarpour
  • Ravinesh Deo
  • Elham Fijani
  • Jan Adamowski
Original Article


Estimating the uniaxial compressive strength (UCS) of travertine rocks with an indirect modeling approach and machine learning algorithms is useful as models can reduce the cost and time required to obtain accurate measurements of UCS, which is important for the prediction of rock failure. This approach can also address the limitations encountered in preparing detailed measured samples using direct measurements. The current paper developed and compared the performance of three standalone tree-based machine learning models (random forest (RF), M5 model tree, and multivariate adaptive regression splines (MARS)) for the prediction of UCS in travertine rocks from the Azarshahr area of northwestern Iran. Additionally, an ensemble committee-based artificial neural network (ANN) model was developed to integrate the advantages of the three standalone models and obtain further accuracy in UCS prediction. To date, an ensemble approach for estimating UCS has not been explored. To construct and validate the models, a set of rock test data including p-wave velocity (Vp (Km/s)), Schmidt Hammer (Rn), porosity (n%), point load index (Is (MPa)), and UCS (MPa) were acquired from 93 travertine core samples. To develop the ensemble tree-based machine learning model, the input matrix representing Vp, Rn, n%, and Is data with the corresponding target variable (i.e., UCS) was incorporated with a ratio of 70:15:15 (train: validate: test). Results indicated that a standalone MARS model outperformed all other standalone tree-based models in predicting UCS. The ANN-committee model, however, obtained the best performance with an r-value of approximately 0.890, an RMSE of 3.980 MPa, an MAE of 3.225 MPa, a WI of 0.931, and an LMI of 0.537, demonstrating the improved accuracy of the ensemble model for the prediction of UCS relative to the standalone models. The results suggest that the proposed ensemble committee-based model is a useful approach for predicting the UCS of travertine rocks with a limited set of model-designed datasets.


Uniaxial compressive strength Tree-based machine learning Travertine Ensemble model Iran 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Rahim Barzegar
    • 1
    Email author
  • Masoud Sattarpour
    • 2
  • Ravinesh Deo
    • 3
  • Elham Fijani
    • 4
  • Jan Adamowski
    • 1
  1. 1.Department of Bioresource EngineeringMcGill UniversitySainte-Anne-de-BellevueCanada
  2. 2.Department of Engineering GeologyTarbiat Modares UniversityTehranIran
  3. 3.Institute of Agriculture and Environment (IAg&E), School of Agricultural Computational and Environmental SciencesUniversity of Southern QueenslandSpringfieldAustralia
  4. 4.School of Geology, College of ScienceUniversity of TehranTehranIran

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