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Predicting Elastic Modulus of Rocks Using Metaheuristic-Optimized Ensemble Regression Models

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Rock Mechanics and Rock Engineering
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Niaz Muhammad Shahani at China University of Mining and Technology
Niaz Muhammad Shahani
Xigui Zheng
Xigui Zheng
Xigui Zheng
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Xin Wei
Xin Wei
Xin Wei
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Abstract and Figures

The elastic modulus (E) of rocks is an essential parameter in mining and rock engineering projects, as it directly affects their stability and structural integrity. This study investigates the application of metaheuristic optimization algorithms, specifically Cuckoo Search (CS) and Harris Hawks Optimization (HHO), to fine-tune the hyperparameters of ensemble regression models, including extreme gradient boosting (XGBoost), decision tree (DT), and adaptive boosting (AdaBoost). A dataset of 122 rock samples, including input parameters such as wet density, moisture, dry density, Brazilian tensile strength, and uniaxial compressive strength, was used to predict E. A dataset was split into training and testing datasets with a 70:30 ratio. Model performance was evaluated using metrics like coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) in %, and severity index (SI). The results show that CS-HHO-optimized models significantly outperformed the unoptimized models, with the optimized stacking model providing superior prediction accuracy for predicting E. Both the unoptimized and optimized Stacking Models exhibited superior performance on the test data. The unoptimized Stacking Model achieved an R² of 0.980, RMSE of 0.0483, MAE of 0.0223, MAPE of 12.412%, and SI of 0.1737, while the CS-HHO-optimized Stacking Model yielded a similar R² of 0.980, with slight variations in RMSE (0.0497), MAE (0.0234), MAPE (13.5736%), and SI (0.1786). This study provides a robust predictive framework for rock behavior analysis, contributing to the field of mining and rock engineering project design.
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Vol.:(0123456789)
Rock Mechanics and Rock Engineering
https://doi.org/10.1007/s00603-025-04499-4
ORIGINAL PAPER
Predicting Elastic Modulus ofRocks Using Metaheuristic‑Optimized
Ensemble Regression Models
NiazMuhammadShahani1 · XiguiZheng1· XinWei1· YueWei1
Received: 10 December 2024 / Accepted: 27 February 2025
© The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025
Abstract
The elastic modulus (E) of rocks is an essential parameter in mining and rock engineering projects, as it directly affects their
stability and structural integrity. This study investigates the application of metaheuristic optimization algorithms, specifi-
cally Cuckoo Search (CS) and Harris Hawks Optimization (HHO), to fine-tune the hyperparameters of ensemble regression
models, including extreme gradient boosting (XGBoost), decision tree (DT), and adaptive boosting (AdaBoost). A dataset
of 122 rock samples, including input parameters such as wet density, moisture, dry density, Brazilian tensile strength, and
uniaxial compressive strength, was used to predict E. A dataset was split into training and testing datasets with a 70:30 ratio.
Model performance was evaluated using metrics like coefficient of determination (R2), root mean square error (RMSE),
mean absolute error (MAE), mean absolute percentageerror (MAPE) in %, and severity index (SI). The results show that
CS-HHO-optimized models significantly outperformed the unoptimized models, with the optimized stacking model provid-
ing superior prediction accuracy for predicting E. Both the unoptimized and optimized Stacking Models exhibited superior
performance on the test data. The unoptimized Stacking Model achieved an R2 of 0.980, RMSE of 0.0483, MAE of 0.0223,
MAPE of 12.412%, and SI of 0.1737, while the CS-HHO-optimized Stacking Model yielded a similar R2 of 0.980, with slight
variations in RMSE (0.0497), MAE (0.0234), MAPE (13.5736%), and SI (0.1786). This study provides a robust predictive
framework for rock behavior analysis, contributing to the field of mining and rock engineering project design.
Highlights
• This study introduces a metaheuristic-optimized ensemble framework for accurately predicting the elastic modulus of
rocks at the Thar Coalfield.
• The proposed ensemble method compares the performance of base models, including XGBoost, decision tree, and Ada-
Boost, in both their unoptimized and optimized forms.
• Advanced metaheuristic algorithms, such as Cuckoo Search and Harris Hawks Optimization, are utilized to enhance the
predictive capabilities of the base models.
• Stacking models are constructed using both unoptimized and optimized base models, demonstrating superior performance.
• The study presents a robust predictive framework for analyzing rock behavior, offering valuable insights for mining
operations and rock engineering design.
Keywords Elastic modulus· Ensemble regression models· Stacking method· Metaheuristic optimization algorithms·
Mining and rock engineering project design
1 Introduction
The mechanical properties of rock samples, particularly
the elastic modulus (E), are crucial for predicting material
behavior under stress and play a significant role in various
* Niaz Muhammad Shahani
shahani.niaz@cumt.edu.cn
* Xigui Zheng
ckzxg@cumt.edu.cn
1 School ofMines, China University ofMining
andTechnology, Xuzhou221116, China
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
ResearchGate has not been able to resolve any citations for this publication.
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