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<p>To address the issue of machine learning methods requiring large amounts of high-quality historical data and computational resources for predicting mine groundwater levels, this study proposes a coupled model integrating an Improved Grey Wolf Optimizer (IGWO) with the Boussinesq equation. The model is based on the Boussinesq equation describing groundwater movement, treating key parameters such as <i>ε</i> (controlling nonlinearity) and source/sink term <i>φ</i> as optimization variables for IGWO. Through intelligent search for optimal parameter combinations, these values are then substituted into the physical equation to achieve groundwater level prediction in mining areas. This model enhances the Grey Wolf Optimizer (GWO) algorithm by incorporating a chaotic Tent mapping, a non-linear control parameter “<i>a</i>”, and the influence of introducing a global optimum solution. The optimization performance of IGWO and the original GWO was compared using 24 classical benchmark functions and the CEC 2022 benchmark suite; the inversion performance of the Boussinesq equation coupled with four algorithms (IGWO, GWO, Whale Optimization Algorithm (WOA), Genetic Algorithm (GA)) for phreatic water level prediction in mining blocks of a Fujian rare earth mine was further investigated. Results show that the IGWO algorithm outperforms the GWO algorithm in terms of both the mean and standard deviation of optimization results for 19 out of the 24 classical benchmark functions and 9 out of the 12 CEC 2022 benchmark functions, with the mean value of the classical unimodal function F1 reduced to 5.08 × 10<sup>− 31</sup>, the classical composite function F24 optimized to − 10.36, and the CEC 2022 composite function F9 decreased to 2.61 × 10<sup>3</sup>. Among the four coupled models, the IGWO-Boussinesq model achieves the optimal prediction accuracy with the best comprehensive matching degree to the measured data in the Taylor diagram analysis: for Block 1, the coefficient of determination (R²), mean absolute error (MAE) and root mean squared error (RMSE) are 0.84, 0.68 and 0.78, respectively, with a correlation coefficient (R) of 0.92, a centered root mean square deviation (CRMSD) of 0.78 and a standard deviation (STD) of 1.72 relative to the measured data; for Block 2, the corresponding R², MAE and RMSE are 0.87, 0.44 and 0.52, with the correlation coefficient (R) reaching 0.94, a CRMSD of 0.49 and an STD of 1.30. Meanwhile, the IGWO algorithm exhibits a faster convergence rate in the parameter inversion process and outperforms GWO, WOA and GA in terms of convergence accuracy. The IGWO-Boussinesq coupled model enables more efficient identification of optimal solutions to problems and provides reasonable predictions of mine groundwater level under limited monitoring data. This research may provide assistance and technical support for monitoring and managing groundwater levels in mines.</p>

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Research on mine groundwater level prediction based on coupled model of improved grey wolf algorithm and Boussinesq equation

  • 期刊论文

  • 发表日期：

    2026年4月16日

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  • Yujun Luo,
  • Guanshi Wang,
  • Wei Zeng,
  • Qiang Wang

摘要

To address the issue of machine learning methods requiring large amounts of high-quality historical data and computational resources for predicting mine groundwater levels, this study proposes a coupled model integrating an Improved Grey Wolf Optimizer (IGWO) with the Boussinesq equation. The model is based on the Boussinesq equation describing groundwater movement, treating key parameters such as ε (controlling nonlinearity) and source/sink term φ as optimization variables for IGWO. Through intelligent search for optimal parameter combinations, these values are then substituted into the physical equation to achieve groundwater level prediction in mining areas. This model enhances the Grey Wolf Optimizer (GWO) algorithm by incorporating a chaotic Tent mapping, a non-linear control parameter “a”, and the influence of introducing a global optimum solution. The optimization performance of IGWO and the original GWO was compared using 24 classical benchmark functions and the CEC 2022 benchmark suite; the inversion performance of the Boussinesq equation coupled with four algorithms (IGWO, GWO, Whale Optimization Algorithm (WOA), Genetic Algorithm (GA)) for phreatic water level prediction in mining blocks of a Fujian rare earth mine was further investigated. Results show that the IGWO algorithm outperforms the GWO algorithm in terms of both the mean and standard deviation of optimization results for 19 out of the 24 classical benchmark functions and 9 out of the 12 CEC 2022 benchmark functions, with the mean value of the classical unimodal function F1 reduced to 5.08 × 10− 31, the classical composite function F24 optimized to − 10.36, and the CEC 2022 composite function F9 decreased to 2.61 × 103. Among the four coupled models, the IGWO-Boussinesq model achieves the optimal prediction accuracy with the best comprehensive matching degree to the measured data in the Taylor diagram analysis: for Block 1, the coefficient of determination (R²), mean absolute error (MAE) and root mean squared error (RMSE) are 0.84, 0.68 and 0.78, respectively, with a correlation coefficient (R) of 0.92, a centered root mean square deviation (CRMSD) of 0.78 and a standard deviation (STD) of 1.72 relative to the measured data; for Block 2, the corresponding R², MAE and RMSE are 0.87, 0.44 and 0.52, with the correlation coefficient (R) reaching 0.94, a CRMSD of 0.49 and an STD of 1.30. Meanwhile, the IGWO algorithm exhibits a faster convergence rate in the parameter inversion process and outperforms GWO, WOA and GA in terms of convergence accuracy. The IGWO-Boussinesq coupled model enables more efficient identification of optimal solutions to problems and provides reasonable predictions of mine groundwater level under limited monitoring data. This research may provide assistance and technical support for monitoring and managing groundwater levels in mines.