Predicting the Young’s Modulus of granites using the Bayesian model selection approach

Yang, Lingqiang; Feng, Xianjin; Sun, Yang

doi:10.1007/s10064-018-1326-2

Cited by 16 publications

(4 citation statements)

References 48 publications

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“…FIGURE 7 | Relationship between the pressure change caused by the magma solidification and the ultimate load of the overlying crust. P c (max) and P c (min) are obtained from the average maximum and minimum Young's moduli of the main components of the crust (basalt and granite), respectively (Schultz, 1993;Yang et al, 2019). contributes to power plate tectonics and other geologic movements.…”

Section: Discussionmentioning

confidence: 99%

Geodynamics Based on Solidification of Liquid/Molten Substances in the Earth’s Interior

Tao

2022

Front. Earth Sci.

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Since its formation, the Earth has cooled from molten magma to the present layered structure. The liquid and molten substance in the interior of the Earth continuously solidifies, radiating heat to the outer space and causing changes in the pressure and density inside the Earth. Constrained by the rigid lithosphere, the change in density decreases the pressure at the bottom of the crust, and thereby supports the rigid lithosphere. Under the effect of gravity, there is an increased interaction between tectonic plates, which leads to local stress accumulation. Eventually, this stress exceeds the strength of the rock and makes the mechanical structure of the crustal lithosphere unstable. This process is iterative, and the Earth continuously adjusts to new mechanical equilibria by releasing the accumulated stress through geological events such as earthquakes. In this study, using three sets of observations (Global Positioning System data, length of day data, and the latent heat of Earth solidification), we show that these observations are consistent with the aforementioned assumption that the solidification of liquid cause changes in density and volume in the Earth’s interior. Mechanical analyses indicate that liquid solidification in the interior of the Earth leads to decrease in the Earth’s volume. This increases the intensity of plate interactions, which leads to the movement of large plates, triggering geological events such as earthquakes. Thus, it is determined that liquid solidification in the Earth’s interior is the main source for the movement of plates.

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Section: Discussionmentioning

confidence: 99%

Geodynamics Based on Solidification of Liquid/Molten Substances in the Earth’s Interior

Tao

2022

Front. Earth Sci.

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“…Singh et al (2012) introduced the ANFIS architecture as a method for predicting rock E. Cao et al (2022) adopted an innovative approach by combining XGBoost and the Firefly Algorithm (FA) in supervised ML to predict E. The results showed that this novel method was effective. Yang et al (2019) used a Bayesian method to predict intact granite's E, and the model produced suitable predictions. Rastegarnia et al (2018) predicted the mechanical characteristics of sedimentary rocks, especially UCS and E, using ANN with R 2 of 0.99 and 0.97, respectively.…”

Section: Related Workmentioning

confidence: 99%

Hybrid PSO with tree-based models for predicting uniaxial compressive strength and elastic modulus of rock samples

Shahani,

Xiaowei,

Wei

et al. 2024

Front. Earth Sci.

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The mechanical characteristics of rocks, specifically uniaxial compressive strength (UCS) and elastic modulus (E), serve as crucial factors in ensuring the integrity and stability of relevant projects in mining and civil engineering. This study proposes a novel hybrid PSO (particle swarm optimization) with tree-based models, such as gradient boosting regressor (GBR), light gradient boosting machine (LightGBM), random forest (RF), and extreme gradient boosting (XGBoost) for predicting UCS and E of rock samples from Block IX of the Thar Coalfield in Pakistan. A total of 122 datasets were divided into training and testing sets, with an 80:20 ratio, respectively, to develop the predictive models. Key performance metrics, including the coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE), were employed to assess the model’s predictive performance. The results indicate that the PSO-XGBoost model demonstrated the highest accuracy in predicting UCS and E, outperforming the other models, which exhibited inferior predictive performance. Furthermore, this study utilized the SHAP (Shapley Additive exPlanations) machine learning method to enhance our understanding of how each input feature variable influences the output values of UCS and E. In conclusion, the proposed framework offers significant advantages in evaluating the strength and deformation of rocks at Thar Coalfield, with promising applications in the field of mining and rock engineering.

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“…References Models Inputs Number of Samples Majdi and Beiki [30] GA-ANN UCS, GSI, RQD, ρ, n, NJ 120 Dehghan et al [29] ANN V p , Is (50) , R n , n 30 Khandelwal and Singh [31] ANN UCS, BTS 120 Ocak and Seker [32] ANN UCS, γ 195 Armaghani et al [17] ANFIS ρ, V p , content of Qtz, Kpr, Plg, and Bi 45 Bejarbaneh et al [33] ANN Is (50) , V p , R n 96 Saedi et al [34] ANFIS BPI, BTS, V p , Is (50) 120 Rezaei [35] MFIS H, ρ, n, DI 50 Yang et al [36] Bayesian I S(50) , R n , V p , n, UCS 71 Acar and Kaya [26] LS-SVM V p , γ, Is (50) , BTS 575 Cao et al [23] XGBoost-firefly ρ, V p , content of Qtz, Kpr, Plg, Bi 45 Pappalardo and Mineo [27] ANN n, γ, V p , E dyn , UCS / Meng and Wu [24] RF PF, SF, IAF, TF, NF / Abdi et al [25] RF n, ρ, V p , Id In comparison to other methods, ML approaches can yield dependable results by establishing the nonlinear relationship between input and output variables [37,38]. It is a promising method for estimating the E of rock.…”

Section: Yearmentioning

confidence: 99%

Developing Hybrid DMO-XGBoost and DMO-RF Models for Estimating the Elastic Modulus of Rock

Lin,

Liu,

Zhao

et al. 2023

Mathematics

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Accurate estimation of the elastic modulus (E) of rock is critical for the design of geotechnical projects such as mining, slopes, and tunnels. However, the determination of rock mechanical parameters usually involves high budget and time requirements. To address this problem, numerous researchers have developed machine learning models to estimate the E of rock. In this study, two novel hybrid ensemble learning models were developed to estimate the E of rock by optimizing the extreme gradient boosting (XGBoost) and random forest (RF) algorithms through the dwarf mongoose optimization (DMO) approach. Firstly, 90 rock samples with porosity, dry density, P-wave velocity, slake durability, and water absorption as input indicators were collected. Subsequently, the hyperparameters of XGBoost and RF were tuned by DMO. Based on the optimal hyperparameters configuration, two novel hybrid ensemble learning models were constructed using the training set (80% of the data). Finally, the performance of the developed models was evaluated by the coefficient of determination (R2 score), root mean squared error (RMSE), mean absolute error (MAE), and variance accounted for (VAF) on the test set (20% of the data). The results show that the DMO-RF model achieved the best comprehensive performance with an R2 score of 0.967, RMSE of 0.541, MAE of 0.447, and VAF of 0.969 on the test set. The dry density and slake durability were more influential indicators than others. Moreover, the convergence curves suggested that the DMO-RF model can reduce the generalization error and avoid overfitting. The developed models can be regarded as viable and useful tools in estimating the E of rock.

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Predicting the Young’s Modulus of granites using the Bayesian model selection approach

Cited by 16 publications

References 48 publications

Geodynamics Based on Solidification of Liquid/Molten Substances in the Earth’s Interior

Geodynamics Based on Solidification of Liquid/Molten Substances in the Earth’s Interior

Hybrid PSO with tree-based models for predicting uniaxial compressive strength and elastic modulus of rock samples

Developing Hybrid DMO-XGBoost and DMO-RF Models for Estimating the Elastic Modulus of Rock

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