Application of the Time Function Model for Dynamic Deformation Prediction in Mining Areas under Characteristic Constraints
Zhihong Wang,
Huayang Dai,
Yueguan Yan
et al.
Abstract:The fundamental model for dynamically predicting surface subsidence is the time influence function. However, current research and the application of time functions often neglect the comprehensive characteristics of the entire surface deformation process, leading to a less systematic representation of the actual deformation law. To rectify this, we explore ground point deformation along the strike line from two perspectives: dynamic subsidence and dynamic horizontal movement. Moreover, we develop prediction mod… Show more
“…Based on a substantial amount of measured data [21,[41][42][43][44][45], it was evident that during a complete subsidence process, a ground point typically undergoes three phases as depicted in Figure 1.…”
Section: Mining Subsidence Dynamic Process Analysismentioning
confidence: 99%
“…However, this time function falls short in effectively describing the sinking speed and acceleration of surface points, leading to disparities with actual surface subsidence processes. Consequently, many scholars have continuously refined the Knothe time function model and proposed new time function models, including Usher [11,12], Weibull [13][14][15][16][17], Richards [18][19][20][21], and MMF [22][23][24], among others. While these models partially reflect the dynamic process of surface movement and deformation to some extent, they also have their own limitations.…”
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.
“…Based on a substantial amount of measured data [21,[41][42][43][44][45], it was evident that during a complete subsidence process, a ground point typically undergoes three phases as depicted in Figure 1.…”
Section: Mining Subsidence Dynamic Process Analysismentioning
confidence: 99%
“…However, this time function falls short in effectively describing the sinking speed and acceleration of surface points, leading to disparities with actual surface subsidence processes. Consequently, many scholars have continuously refined the Knothe time function model and proposed new time function models, including Usher [11,12], Weibull [13][14][15][16][17], Richards [18][19][20][21], and MMF [22][23][24], among others. While these models partially reflect the dynamic process of surface movement and deformation to some extent, they also have their own limitations.…”
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.
“…After initial testing of several commonly used interpolation methods for discrete points (such as inverse distance weighting, natural neighbor interpolation, ordinary Kriging, radial basis function interpolation, etc. ), it is known from existing research that ordinary Kriging and radial basis function interpolation are relatively convenient and effective methods [23][24][25][26][27][28][29][30]. The specific usage of these two methods in this problem is described as follows.…”
Section: Interpolation Of Surface Horizontal Displacement Field At Di...mentioning
confidence: 99%
“…Furthermore, there is little systematic description regarding the monitoring interpolation method at present. Overall, as a calculation method for surface deformation, the main advantage of the monitoring interpolation method is that it can quickly obtain the entire surface deformation field based on monitoring data, bypassing the need for complex constitutive relationships and rock mechanics parameters, and it often achieves good results [26,27]. However, its main disadvantage is that it cannot predict surface deformation [28,29]; thus, it can only be used for calculating assessment of surface deformation in mining areas or studying the historical patterns of surface deformation [30].…”
Considering the importance of calculating surface deformation based on monitoring data, this paper proposes a method for calculating horizontal deformation based on horizontal displacement monitoring data. This study first analyzes the characteristics of horizontal displacement monitoring data, then proposes a scheme for obtaining the surface horizontal displacement field through corresponding discrete point interpolation. Subsequently, the calculation method for surface horizontal strain is introduced, along with relevant examples. The study also systematically summarizes the calculation methods for surface curvature and surface tilt deformation values, forming a set of surface deformation calculation methods based on monitoring data. The research results indicate that when there is a large number of on-site monitoring points, effective monitoring points can be selected based on the direction of horizontal displacement. When interpolating the surface horizontal displacement field, the interpolation accuracy of the radial basis function method is slightly higher than that of ordinary Kriging. The form of coordinate expression has a significant impact on interpolation accuracy. The accuracy of interpolation using horizontal displacement vectors expressed in polar coordinates is higher than that using vectors expressed in Cartesian coordinates. The calculated surface horizontal strain has effective upper and lower limits, with lower-limit strain on the contour line conforming to the typical surface deformation patterns around mined-out areas.
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