Probabilistic evaluation of drilling rate index based on a least square support vector machine and Monte Carlo simulation

  • Zhongliang Ru
  • Hongbo ZhaoEmail author
  • Changxing Zhu
Original Paper


Drilling rate index (DRI) is an important index for evaluating the drillability of rock in mining, tunneling, and underground excavation. Various studies have been implemented to predict DRI based on the relationship between DRI and its influence factors. Meanwhile, many uncertainties are associated with the evaluation of DRI because of the complexity and nonlinearity of rock mechanical and physical properties. But the uncertainty has not been considered in previous studies. In this study, a novel method was proposed to evaluate DRI considering the uncertainty through combining the least square support vector machine (LSSVM) and Monte Carlo simulation (MCS). The LSSVM was adopted to map the relationship between DRI and rock strength index. Latin hypercube sampling (LHS) was used to produce the sample sets based on the uncertainty distribution of rock strength index. MCS was utilized to simulate the uncertainty of DRI. The proposed method was verified by three testing examples with the uncertainties. Interaction effects of DRI’s influence factors were analyzed and discussed. The results show the proposed method can evaluate the DRI reasonably. Compared with the determinate method, the proposed method is more rational and scientific and conforms to the rock engineering practice. Interaction effects should be considered while predicting or evaluating the DRI. LSSVM can not only present well the nonlinear relationship between DRI and its influence factors, but also deal with the interaction effects of the DRI’s influence factors. The proposed method provides a scientific tool to predict and evaluate the DRI and its uncertainty.


Drilling rate index Rock strength index Uncertainty Least square support vector machine Monte Carlo simulation 



The authors gratefully acknowledge financial support from the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (no. 15IRTSTHN029).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Resources and Material SciencesTaiyuan University of Science and TechnologyTaiyuanPeople’s Republic of China
  2. 2.School of Civil EngineeringHenan Polytechnic UniversityJiaozuoPeople’s Republic of China

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