Research on a dynamic early warning model for gas outbursts using adaptive fractal dimension characterization

Abstract

To address the issues of single warning indicators, fixed thresholds, and insufficient adaptability in coal and gas outburst early warning models, this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization. By analyzing the nonlinear characteristics of gas concentration data, an adaptive window fractal analysis method is introduced. Combined with box-counting dimension and variation of box dimension metrics, a cross-scale dynamic warning model for disaster prevention is established. The implementation involves three key phases: First, wavelet denoising and interpolation methods are employed for raw data preprocessing, followed by validation of fractal characteristics. Second, an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration, enabling effective capture of multi-scale complex features. Finally, dynamic threshold partitioning is achieved through membership functions and the 3σ principle, establishing a graded classification standard for the mine gas disaster (M_GD) index. Validated through engineering applications at Shoushan #1 Coal Mine in Henan Province, the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods, with local feature detection capability improved and warning accuracy reaching 86.9%. The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multi-indicator fusion and threshold optimization, providing both theoretical foundation and practical tool for coal mine gas outburst early warning.

Keywords

Gas outburst / Fractal characteristics / Adaptive fractal method / Dynamic warning model

Acknowledgement

This study is funded by the National Key Research and Development Program, Fund for Young Scientists (No.2021YFC2900400), the National Natural Science Foundation of China (No. 52304123), Fundamental Research Funds for the Central Universities (No. 2024CDJXY025), Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project (No. CSTB2024TIAD-CYKJCXX0016), Postdoctoral Research Foundation of China (No. 2023M730412), Postdoctoral Fellowship Program of China Postdoctoral Science Foundation (No. GZB20230914), and Chongqing Outstanding Youth Science Foundation Program (No. CSTB2023NSCQ-JQX0027).

References

[1] Wang K, Du F. Coal-gas compound dynamic disasters in China: A review. Process Saf Environ Prot 2020; 133:1-17.

[2] Zhang X, Tang JP, Pan YS, Yu HH. Experimental study on intensity and energy evolution of deep coal and gas outburst. Fuel 2022; 324:124484.

[3] Qiao MY, Ma XP, Qiao TZ, Tao H. Study on gas emission value time sequence fractal features of coal mining face. Coal Sci Technol 2011; 39(12):51-5. in Chinese.

[4] An FH, Yuan Y, Chen XJ, Li ZQ, Li LY. Expansion energy of coal gas for the initiation of coal and gas outbursts. Fuel 2019; 235:551-7.

[5] Xie XC, Fu G, Xue Y, Zhao ZQ, Chen P, Lu BJ, Jiang S. Risk prediction and factors risk analysis based on IFOA-GRNN and apriori algorithms: Application of artificial intelligence in accident prevention. Process Saf Environ Prot 2019; 122:169-84.

[6] Zhang CL, Wang EY, Wang YB, Zhou XF. Spatial-temporal distribution of outburst accidents from 2001 to 2020 in China and suggestions for prevention and control. Coal Geol Explor 2021; 49(4):134-41. in Chinese.

[7] Fan CJ, Li S, Luo MK, Du WZ, Yang ZH. Coal and gas outburst dynamic system. Int J Min Sci Technol 2017; 27(1):49-55.

[8] Qi QX, Pan YS, Shu LY, Li HY, Jiang DY, Zhao SK, Zou YH, Pan JF, Wang KJ, Li HT. Theory and technical framework of prevention and control with different sources in multi-scales for coal and rock dynamic disasters in deep mining of coal mines. J China Coal Soc 2018; 43(7):1801-10. in Chinese.

[9] Yuan L. Progress and advancements of coal mine gas control and management for safe mining in China. J Ind Saf 2024; 1(1):100005.

[10] Chen J, Huang HQ, Rui YC, Pu YY, Zhang S, Li Z, Wang WZ. Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach. Int J Min Sci Technol 2024; 34 (7):943-56.

[11] Ma K, Sun XY, Tang CA, Yuan FZ, Wang SJ, Chen T. Floor water inrush analysis based on mechanical failure characters and microseismic monitoring. Tunn Undergr Space Technol 2021; 108:103698.

[12] Li B, Wang EY, Shang Z, Li ZH, Li BL, Liu XF, Wang H, Niu Y, Wu Q, Song Y. Deep learning approach to coal and gas outburst recognition employing modified AE and EMR signal from empirical mode decomposition and time-frequency analysis. J Nat Gas Sci Eng 2021; 90:103942.

[13] Li B, Wang EY, Shang Z, Liu XF, Li ZH, Li BL, Wang H, Niu Y, Song Y. Optimize the early warning time of coal and gas outburst by multi-source information fusion method during the tunneling process. Process Saf Environ Prot 2021; 149:839-49.

[14] Li B, Wang EY, Shang Z, Liu XF, Li ZH, Dong J. Deep learning and heterogeneous signal fusion approach to precursor feature recognition and early warning of coal and gas outburst. Process Saf Environ Prot 2023; 178:995-1008.

[15] Chen J, Gui Z, Rui YC, Zhao XS, Pan XK, Wang QF, Pu YY, Li Z,Liu MY. A dual attention-based deep learning model for lithology identification while drilling. J Rock Mech Geotech Eng 2025.

[16] Rui YC, Chen J, Du JS, Peng X, Zhou ZL, Zhu C. Optimizing microseismic sensor networks in underground space using Cramér-Rao lower bound and improved genetic encoding. Undergr Space 2025; 23:307-26.

[17] Rui YC, Chen J, Chen JK, Qiu JD, Zhou ZL, Wang WZ, Fan JY. A robust triaxial localization method of AE source using refraction path. Int J Min Sci Technol 2024; 34(4):521-30.

[18] Guo YL, Liu HB, Zhou X, Chen J, Guo LW. Research on coal and gas outburst risk warning based on multiple algorithm fusion. Appl Sci 2023; 13 (22):12283.

[19] Wang C, Wei LK, Hu HY, Wang JR, Jiang MF. Early warning method for coal and gas outburst prediction based on indexes of deep learning model and statistical model. Front Earth Sci 2022; 10:811978.

[20] Liang YP, Zheng MH, Li QG, Mao SR, Li XY, Li JB, Zhou JJ. A review on prediction and early warning methods of coal and gas outburst. J China Coal Soc 2023; 48 (8):2976-94. in Chinese.

[21] Hu Zhao XS, QT, Ning XL. Research on comprehensive early-warning technology of coal and gas outburst. Procedia Eng 2011; 26:2376-82.

[22] Zhao ZG, Tan YL. Study of premonitory time series prediction of coal and gas outbursts based on chaos theory. Rock Soil Mech 2009; 30(7):2186-90. in Chinese.

[23] Shi SL, Song Y, He LW, Zhu CQ. Research on determination of chaotic characteristics of gas gush based on time series in excavation working face of coal mine. J China Coal Soc 2006; 31(6):701-5. in Chinese.

[24] Cheng J, Bai JY, Qian JS, Li SY. Short-term forecasting method of coalmine gas concentration based on chaotic time series. J China Univ Min Technol 2008; 37 (2):231-5. in Chinese.

[25] Lu J, Zhang JY, Niu GD, Wang Q, Zhao YP. Study on fractal characters of gas concentration time series. Microcomput Inf 2010; 26:213-5.

[26] Zhuo RS, Zhao PX, Li SG, Lin HF, Liu H, Kong XG, Jin SK, Wang Z, Jin Q. Effects of coal thickness on the fractal dimension of gas migration channels: Laboratory and field study of a gassy coal mine. Nat Resour Res 2024; 33 (3):1193-208.

[27] Gao WG. The research on the method of predicting and warning of gas emission of working face. Master’s dissertation. Henan: Henan Polytechnic University; 2015.p.76.

[28] Chen J, Chen JK, Rui YC, Pu YY. Joint inversion of AE/MS sources and velocity with full measurements and residual estimation. Rock Mech Rock Eng 2024; 57 (9):7371-86.

[29] Zhang S, Rui YC, Zhou ZL, Cai X, Cui HZ. The influence of Vickers hardness and brittleness on particle size distribution during ball milling: A multifractal approach. Rock Mech Rock Eng 2025; 58(6):6973-92.

[30] Shamsi E, Ali Ahmadi-Pajouh M, Seifi AT. Higuchi fractal dimension: An efficient approach to detection of brain entrainment to theta binaural beats. Biomed Signal Process Contr 2021; 68:102580.

[31] Katz MJ. Fractals and the analysis of waveforms. Comput Biol Med 1988; 18 (3):145-56.

[32] Sevcik C. A procedure to estimate the fractal dimension of waveforms. Chaos Soliton Fract 2010; 5:5266.

[33] Gómez C, Mediavilla Á, Hornero R, Abásolo D, Fernández A. Use of the Higuchi’s fractal dimension for the analysis of MEG recordings from Alzheimer’s disease patients. Med Eng Phys 2009; 31(3):306-13.

[34] Esteller R, Vachtsevanos G, Echauz J, Litt B. A comparison of waveform fractal dimension algorithms. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 2001; 48(2):177-83.

[35] Cao K. Extraction of acoustic, electrical and gas characteristics information and comprehensive early warning application for coal and gas outburst in Fa’er coal mine. Master’s dissertation. Xuzhou: China University of Mining and Technology; 2020.p.18.

[36] Shu ZR, Chan PW, Li QS, He YC, Yan BW, Li L, Lu C, Zhang L, Yang HL. Characterization of vertical wind velocity variability based on fractal dimension analysis. J Wind Eng Ind Aerodyn 2021; 213:104608.

[37] Wang HB, Hao ZX, Niu CH. Theory and application of nonlinear system model for gas emission. Met Mine 2006; 4:59-61. in Chinese.

[38] Wang HB. The fractal prediction theory and application of coal and gas outburst. Doctoral dissertation. Shanxi: Taiyuan University of Technology; 2009. p.130-2.

[39] Jin FY. Research on coal and gas outburst prediction based on fractal chaos theory. Master’s dissertation. Anhui: Anhui University of Science and Technology; 2006. p.43-4.

[40] Zhang XL, Chen SC, Xue J, Wang N, Xiao Y, Chen QQ, Hong YS, Zhou Y, Teng HF, Hu BF, Zhou ZQ, Ji WJ, Huang YF, Gou YX, Richer-de-Forges AC, Arrouays D, Shi Z. Improving model parsimony and accuracy by modified greedy feature selection in digital soil mapping. Geoderma 2023; 432:116383.

[41] Pappas I, Mikalef P, Giannakos M, Pavlou P. Value co-creation and trust in social commerce:An fsQCA approach. In:Proceedings of the 25th European Conference on Information Systems. Guimaraes: University of Minho; 2017. p. 2153-68.