Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China
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 o...
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| Format: | Article |
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MDPI AG
2024-02-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/14/5/1748 |
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| author | Huabin Chai Hui Xu Jibiao Hu Sijia Geng Pengju Guan Yahui Ding Yuqiao Zhao Mingtao Xu Lulu Chen |
| author_facet | Huabin Chai Hui Xu Jibiao Hu Sijia Geng Pengju Guan Yahui Ding Yuqiao Zhao Mingtao Xu Lulu Chen |
| author_sort | Huabin Chai |
| collection | DOAJ |
| description | 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 R<sup>2</sup> 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. |
| first_indexed | 2024-04-25T00:35:18Z |
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| id | doaj.art-4732250488c6495292a1be350a5ace43 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-04-25T00:35:18Z |
| publishDate | 2024-02-01 |
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| series | Applied Sciences |
| spelling | doaj.art-4732250488c6495292a1be350a5ace432024-03-12T16:38:47ZengMDPI AGApplied Sciences2076-34172024-02-01145174810.3390/app14051748Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in ChinaHuabin Chai0Hui Xu1Jibiao Hu2Sijia Geng3Pengju Guan4Yahui Ding5Yuqiao Zhao6Mingtao Xu7Lulu Chen8School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, ChinaTo 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 R<sup>2</sup> 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.https://www.mdpi.com/2076-3417/14/5/1748subsidence predictiontrust region reflection algorithm (TRF)time functioncombined modelvariable weight |
| spellingShingle | Huabin Chai Hui Xu Jibiao Hu Sijia Geng Pengju Guan Yahui Ding Yuqiao Zhao Mingtao Xu Lulu Chen Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China Applied Sciences subsidence prediction trust region reflection algorithm (TRF) time function combined model variable weight |
| title | Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China |
| title_full | Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China |
| title_fullStr | Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China |
| title_full_unstemmed | Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China |
| title_short | Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China |
| title_sort | application of a variable weight time function combined model in surface subsidence prediction in goaf area a case study in china |
| topic | subsidence prediction trust region reflection algorithm (TRF) time function combined model variable weight |
| url | https://www.mdpi.com/2076-3417/14/5/1748 |
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