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To attain precise forecasts of surface displacements and deformations in goaf areas (a void or cavity that remains underground after the extraction of mineral resources) following coal extraction, this study based on the limitations of individual time function models, conducted a thorough analysis of how the parameters of the model impact subsidence curves. Parameter estimation was conducted using the trust-region reflective algorithm (TRF), and the time function models were identified. Then we utilized a combined model approach and introduced the sliding window mechanism to assign variable weights to the model. Based on this, the combined model was used for prediction, followed by the application of this composite prediction to engineering scenarios for the dynamic forecasting of surface movements and deformations. The results indicated that, in comparison with DE, GA, PSO algorithms, the TRF exhibited superior stability and convergence. The parameter models obtained using this method demonstrated a higher level of predictive accuracy. Moreover, the predictive precision of the variable-weight time function combined model surpassed that of corresponding individual time function models. When employing six different variable-weight combination prediction models for point C22, the Weibull-MMF model demonstrated the most favorable fitting performance, featuring a root mean square error (RMSE) of 32.98 mm, a mean absolute error (MAE) of 25.66 mm, a mean absolute percentage error (MAPE) of 7.67%; the correlation coefficient R2 reached 0.99937. These metrics consistently outperformed their respective individual time function models. Additionally, in the validation process of the combined model at point C16, the residuals were notably smaller than those of individual models. This reaffirmed the accuracy and reliability of the proposed variable-weight combined model. Given that the variable-weight combination model was an evolution from individual time function models, its applicability extends to a broader range, offering valuable guidance for the dynamic prediction of surface movement and deformation in mining areas.

In this study conducted in the Shendong mining area, this paper tackles the challenge of estimating mining subsidence parameters in the absence of empirical values. The study employs a tailored pattern recognition method specifically designed for mining subsidence in a specific working face. The goal is to determine a globally approximate optimal solution for these parameters. Subsequently, this study utilizes the approximate optimal solution as an initial exploration value and harnesses the modular vector method to obtain stable, accurate, optimal solutions for the parameters. The results of the study demonstrate the effectiveness of the improved modular vector method. In simulation tests involving the subsidence coefficient, the main influence angle tangent value, the propagation angle of mining influence, and the deviation of the inflection point, the relative errors do not exceed 1.2%, 1.9%, 1.7%, and 7.9%, respectively. Furthermore, when subjected to random errors of less than 20 mm, the relative errors for each parameter remain below 2%. Even in conditions with 200 mm gross error, the relative error for each parameter does not exceed 5.1%, indicating high precision. In an engineering example, the root mean square error of the improved modular vector method’s fitting result is 64.31 mm, constituting a mere 1.79% of the maximum subsidence value. This performance surpasses that of the genetic algorithm (70.47 mm), particle swarm algorithm (72.82 mm), and simulated annealing algorithm (75.45 mm). Notably, the improved modular vector method exhibits superior stability and reduced reliance on the quantity of measured values compared to the three aforementioned algorithms. The inversion analysis of predicted parameters based on the improved modular vector method, coupled with the probability integral method, holds practical significance for enhancing the accuracy of mining subsidence prediction.

Investigating the spatiotemporal variations in the Normalized Difference Vegetation Index (NDVI) in the Shanxi section of the Yellow River Basin and its coal mining areas holds significant importance for dynamic vegetation monitoring and mining area management. This study employs MODIS NDVI data and combines various analytical methods, including trend analysis and coefficient of variation analysis, to reveal the characteristics of NDVI spatiotemporal variations and their response to climatic factors in the study area. The results indicate the following: (1) The overall NDVI in the Shanxi section of the Yellow River Basin exhibits a growth trend with an annual growth rate of 1.82% and a 36% increase. Among the mining areas, the NDVI increase is most prominent in the Hebaopian mining area with a 100% growth, while the QinYuan mining area shows the lowest increase at 21%; (2) The NDVI in the Shanxi section of the Yellow River Basin displays high fluctuations, with areas of moderate and high fluctuations accounting for 54.39% of the total. The Hebaopian mining area has a substantial portion of high-fluctuation areas at 38.85%; (3) According to the Hurst index analysis, future vegetation changes in the Shanxi section of the Yellow River Basin are uncertain, with approximately 9.77% of areas expected to continue improving; (4) The variations in the NDVI and climatic factors across the Shanxi section of the Yellow River Basin display spatial heterogeneity. The NDVI exhibits a positive correlation with both temperature and precipitation, with the correlation with precipitation being more pronounced than that with temperature. Precipitation exerts a more significant influence on the NDVI than temperature. These findings not only provide scientific guidance for vegetation restoration and area management in the Shanxi section of the Yellow River Basin and its mining areas but also serve as a scientific basis for decision making regarding vegetation management under the influence of climate change and human activities.