Stochastic assessment of hard rock pillar stability based on the geological strength index system

Li, Chuanqi; Zhou, Jian; Armaghani, Danial Jahed; Cao, Wenzhuo; Yağız, Saffet

doi:10.1007/s40948-021-00243-8

Cited by 14 publications

(5 citation statements)

References 64 publications

(74 reference statements)

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“…The mean squared error (MSE) especially was considered separately as the fitness function to evaluate the optimization performance of all used MHO algorithms. These performance indices were introduced in several references [61][62][63][64][65][66][67][68][69] and are defined as follows:…”

Section: Rock Data Preparation and Performance Indicesmentioning

confidence: 99%

Comparative Evaluation of Empirical Approaches and Artificial Intelligence Techniques for Predicting Uniaxial Compressive Strength of Rock

Li,

Zhou,

Dias

et al. 2023

Geosciences

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The uniaxial compressive strength (UCS) of rocks is one of the key parameters for evaluating the safety and stability of civil and mining structures. In this study, 386 rock samples containing four properties named the load strength (PLS), the porosity (Pn), the P-wave velocity (Vp), and the Schmidt hardness rebound number (SHR) are utilized to predict the UCS using several typical empirical equations (EA) and artificial intelligence (AI) methods, i.e., 16 single regression (SR) equations, 2 multiple regression (MR) equations, and the random forest (RF) models optimized by grey wolf optimization (GWO), moth flame optimization (MFO), lion swarm optimization (LSO), and sparrow search algorithm (SSA). The root mean square error (RMSE), determination coefficient (R2), Willmott’s index (WI), and variance accounted for (VAF) are used to evaluate the predictive performance of all developed models. The evaluation results show that the overall performance of AI models is superior to empirical approaches, especially the LSO-RF model. In addition, the most important input variable is the Pn for predicting the UCS. Therefore, AI techniques are considered as more efficient and accurate approaches to replace the empirical equations for predicting the UCS of these collected rock samples, which provides a reliable and effective idea to predict the rock UCS in the filed site.

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Section: Rock Data Preparation and Performance Indicesmentioning

confidence: 99%

Comparative Evaluation of Empirical Approaches and Artificial Intelligence Techniques for Predicting Uniaxial Compressive Strength of Rock

Li,

Zhou,

Dias

et al. 2023

Geosciences

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“…In order to compare the performance of UCS predicted by the KELM-GWO model and other AI models or empirical equations, such as ELM, initial KELM, DELM, BPNN, and an empirical formula were developed in this study. The principle of DELM and BPNN can found in the literature [26,48,[80][81][82][83][84][85].…”

Section: Novel Hybrid Kelm-gwomentioning

confidence: 99%

“…BPNN is a typically and widely used neural network model for prediction problems in geotechnical engineering [80,81]. To develop an effective BPNN model for predicting UCS of rock samples, the numbers of hidden layers and neurons should be determined to prevent overfitting and reduce the computation time.…”

Section: Bpnnmentioning

confidence: 99%

A Kernel Extreme Learning Machine-Grey Wolf Optimizer (KELM-GWO) Model to Predict Uniaxial Compressive Strength of Rock

Zhou

Dias

et al. 2022

Applied Sciences

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Uniaxial compressive strength (UCS) is one of the most important parameters to characterize the rock mass in geotechnical engineering design and construction. In this study, a novel kernel extreme learning machine-grey wolf optimizer (KELM-GWO) model was proposed to predict the UCS of 271 rock samples. Four parameters namely the porosity (Pn, %), Schmidt hardness rebound number (SHR), P-wave velocity (Vp, km/s), and point load strength (PLS, MPa) were considered as the input variables, and the UCS is the output variable. To verify the effectiveness and accuracy of the KELM-GWO model, extreme learning machine (ELM), KELM, deep extreme learning machine (DELM) back-propagation neural network (BPNN), and one empirical model were established and compared with the KELM-GWO model to predict the UCS. The root mean square error (RMSE), determination coefficient (R2), mean absolute error (MAE), prediction accuracy (U1), prediction quality (U2), and variance accounted for (VAF) were adopted to evaluate all models in this study. The results demonstrate that the proposed KELM-GWO model was the best model for predicting UCS with the best performance indices. Additionally, the identified most important parameter for predicting UCS is the porosity by using the mean impact value (MIV) technique.

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“…Thus, four evaluation indices were adopted in this study, namely: mean absolute error (MAE), root mean squared error (RMSE), variance accounted for (VAF) and Pearson correlation coefficient (R 2 ). Explanations of these indices are given in the literature (Le et al 2019;Bui et al 2020;Ding et al 2020;Han et al 2020;Jahed Armaghani et al 2020;Li et al 2020aLi et al , 2021aDehghanbanadaki et al 2021;Fang et al 2021;Nguyen et al 2021a, b;Paji et al 2021).…”

Section: Model Verification and Evaluationmentioning

confidence: 99%

Performance of Hybrid SCA-RF and HHO-RF Models for Predicting Backbreak in Open-Pit Mine Blasting Operations

et al. 2021

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Backbreak is an adverse phenomenon in blasting operation, which can cause, among others, mine walls instability, falling down of machinery, drilling efficiency reduction and stripping ratio enhancement. Therefore, this research aimed to develop two hybrid RF (Random Forest) prediction models of random forest, which are optimized by Harris hawks optimizer (HHO) and sine cosine algorithm (SCA), for estimation of the backbreak distance. The HHO and SCA algorithms were adopted to determine two hyper-parameters (mtry and ntree) in the RF models, in which root mean square error (RMSE) was utilized as a fitness function. A database with 234 samples was established, in which six variables (i.e., hole length (L), burden (B), spacing (S), stemming (T), special drilling (SD), and powder factor (PF)) were used as input variables, and backbreak was defined as output variable. Additionally, three classical regression models (i.e., extreme learning machine, radial basis function network and general regression neural network) were adopted to verify the superiority of the hybrid RF prediction models. The predictive reliability of the proposed models was assessed by the combination of mean absolute error (MAE), RMSE, variance accounted for (VAF), and Pearson correlation coefficient (R 2 ). The results revealed that the SCA-RF model outperformed all the other prediction models with MAE of (0.0444 and 0.0470), RMSE of (0.0816 and 0.0996), VAF of (96.82 and 95.88) and R 2 of (0.9876 and 0.9829) in training and testing stages, respectively. A Gini index generated internally in the RF model showed that backbreak was significantly more sensitive to L and T than to SD.

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Stochastic assessment of hard rock pillar stability based on the geological strength index system

Cited by 14 publications

References 64 publications

Comparative Evaluation of Empirical Approaches and Artificial Intelligence Techniques for Predicting Uniaxial Compressive Strength of Rock

Comparative Evaluation of Empirical Approaches and Artificial Intelligence Techniques for Predicting Uniaxial Compressive Strength of Rock

A Kernel Extreme Learning Machine-Grey Wolf Optimizer (KELM-GWO) Model to Predict Uniaxial Compressive Strength of Rock

Performance of Hybrid SCA-RF and HHO-RF Models for Predicting Backbreak in Open-Pit Mine Blasting Operations

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