An Improved Dempster–Shafer Evidence Theory Based on the Chebyshev Distance and Its Application in Rock Burst Prewarnings
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 1
Abstract
The prewarning and responses of different monitoring indices are out of sync in engineering disaster warning, and the disaster risk assessment is inaccurate based on individual response index or comparison with different indices. The traditional Dempster–Shafer (DS) evidence theory cannot readily integrate the conflicting multivariate monitoring data. In the present study, the DS evidence theory was improved by integrating various conflicting multivariate monitoring data, and the application condition, advantages, and disadvantages of those modified methods based on the DS evidence theory were investigated. An improved DS evidence theory method was proposed based on the Chebyshev distance and the zero-divisor modified evidence source method. The results indicated that the improved DS evidence theory based on the Chebyshev distance performs well in both integrating the conflicting and nonconflicting monitoring data and is superior to other improved methods in suppressing interfering evidence with good stability. The proposed improved DS evidence theory based on the Chebyshev distance is then applied to rock burst prewarning, and the prewarning model is established based on multiphysics in situ monitoring data. The probability with various risk levels is employed to assess the safety state, which can reflect the degree of rock burst. The risk of rock burst can be quantitatively predicted using this proposed method, which can provide some guidance in the prewarning of engineering disasters.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Financial support for this study is provided by the National Natural Science Foundation of China (Nos. 42272329 and 52204140) and the Natural Science Foundation of Shandong Province (No. ZR2020ME099).
References
Chen, J. J., W. Zhang, and J. H. Wang. 2017. “Data fusion analysis method for assessment on safety monitoring results of deep excavations.” J. Aerosp. Eng. 30 (2): B4015005. https://doi.org/10.1061/(asce)as.1943-5525.0000593.
Chu, X. H., J. He, H. Q. Song, Y. Qi, Y. Q. Sun, W. H. Bai, W. Li, and Q. W. Wu. 2020. “Multimodal deep learning for heterogeneous GNSS-R data fusion and ocean wind speed retrieval.” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 13 (Jun): 5971–5981. https://doi.org/10.1109/JSTARS.2020.3010879.
Coelho, B. Z., and M. Karaoulis. 2022. “Data fusion of geotechnical and geophysical data for three-dimensional subsoil schematisations.” Adv. Eng. Inf. 53 (Apr): 101671. https://doi.org/10.1016/j.aei.2022.101671.
Deng, Y., W. K. Shi, Z. F. Zhu, and Q. Liu. 2004. “Combining belief functions based on distance of evidence.” Decis. Support Syst. 38 (3): 489–493. https://doi.org/10.1016/j.dss.2004.04.015.
Dezert, T., S. Palma Lopes, Y. Fargier, L. Saussaye, and P. Côte. 2021. “Data fusion of in situ geophysical and geotechnical information for levee characterization.” Bull. Eng. Geol. Environ. 80 (6): 5181–5197. https://doi.org/10.1007/s10064-021-02225-2.
Dymova, L., and P. Sevastjanov. 2012. “The operations on intuitionistic fuzzy values in the framework of Dempster-Shafer theory.” Knowledge-Based Syst. 35 (Feb): 132–143. https://doi.org/10.1016/j.knosys.2012.04.026.
EI Faouzi, N. E., H. Leung, and A. Kurian. 2011. “Data fusion in intelligent transportation systems: Progress and challenges–A survey.” Inf. Fusion 12 (1): 4–10. https://doi.org/10.1016/j.inffus.2010.06.001.
Guo, K., and L. M. Zhang. 2021. “Multi-source information fusion for safety risk assessment in underground tunnels.” Knowledge-Based Syst. 227 (Jun): 107210. https://doi.org/10.1016/j.knosys.2021.107210.
Hall, D. L., and J. Llinas. 1997. “An introduction to multisensor data fusion.” Proc. IEEE 85 (1): 6–23. https://doi.org/10.1109/5.554205.
Jiang, L. 2022. “Artificial intelligence algorithms for multisensor information fusion based on deep learning algorithms.” In Mobile information systems. London: Hindwai. https://doi.org/10.1155/2022/3356213.
Ke, T., M. Li, L. D. Zhang, H. Lv, and X. C. Ge. 2020. “Construct a biased SVM classifier based on Chebyshev distance for PU learning.” J. Intell. Fuzzy Syst. 39 (3): 3749–3767. https://doi.org/10.3233/JIFS-192064.
Khaleghi, B., A. Khamis, F. O. Karray, and S. N. Razavi. 2013. “Multisensor data fusion: A review of the state-of-the-art.” Inf. Fusion 14 (1): 28–44. https://doi.org/10.1016/j.inffus.2011.08.001.
Leung, Y., N. N. Ji, and J. H. Ma. 2013. “An integrated information fusion approach based on the theory of evidence and group decision-making.” Inf. Fusion 14 (4): 410–422. https://doi.org/10.1016/j.inffus.2012.08.002.
Li, B., E. Y. Wang, Z. Shang, X. F. Liu, Z. H. Li, B. L. Li, H. Wang, Y. Niu, and Y. Song. 2021a. “Optimize the early warning time of coal and gas outburst by multi-source information fusion method during the tunneling process.” Process Saf. Environ. Prot. 149 (Apr): 839–849. https://doi.org/10.1016/j.psep.2021.03.029.
Li, B. C., B. Wang, J. Wei, Z. B. Qian, and Y. Q. Huang. 2002. “An efficient combination rule of evidence theory.” [In Chinese.] J. Data Acquis. Process. 17 (1): 33–36. https://doi.org/10.1117/12.441655.
Li, S. C., C. Liu, Z. Q. Zhou, L. P. Li, S. S. Shi, and Y. C. Yuan. 2021b. “Multi-sources information fusion analysis of water inrush disaster in tunnels based on improved theory of evidence.” Tunnelling Underground Space Technol. 113 (Jan): 103948. https://doi.org/10.1016/j.tust.2021.103948.
Li, X. L. 2014. Study on comprehensive warning of rock burst in Qianqiu Coal Mine. [In Chinese.] Xuzhou, China: China Univ. of Mining and Technology.
Liu, X. L., G. M. Chen, F. X. Li, and Q. Zhang. 2012. “Research on conflict evidence combination based on compatibility distance.” [In Chinese.] Appl. Res. Comput. 29 (12): 4527–4529. https://doi.org/10.3969/j.issn.1001-3695.2012.12.032.
Ma, T. H., C. A. Tang, S. B. Tang, L. Kuang, Q. Yu, D. Q. Kong, and X. Zhu. 2018. “Rockburst mechanism and prediction based on microseismic monitoring.” Int. J. Rock Mech. Min. Sci. 110 (Apr): 177–188. https://doi.org/10.1016/j.ijrmms.2018.07.016.
Murphy, C. K. 2000. “Combining belief functions when evidence conflicts.” Decis. Support Syst. 29 (1): 1–9. https://doi.org/10.1016/S0167-9236(99)00084-6.
Pan, Y., L. M. Zhang, Z. W. Li, and L. Y. Ding. 2019. “Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D–S evidence theory.” IEEE Transact. Fuzzy Syst. 28 (9): 2063–2077. https://doi.org/10.1109/TFUZZ.2019.2929024.
Rassafi, A. A., S. S. Ganji, and H. Pourkhani. 2017. “Road safety assessment under uncertainty using a multi attribute decision analysis based on Dempster–Shafer theory.” KSCE J. Civ. Eng. 22 (8): 3137–3152. https://doi.org/10.1007/s12205-017-1854-5.
Ren, X. G., C. W. Li, X. J. Ma, F. X. Chen, and H. Y. Wang. 2021. “Design of multi-information fusion based intelligent electrical fire detection system for green buildings.” Sustainability 13 (6): 3405. https://doi.org/10.3390/su13063405.
Shafer, G. 2016. “A mathematical theory of evidence turns 40.” Int. J. Approx. Reason. 79 (Jun): 7–25. https://doi.org/10.1016/j.ijar.2016.07.009.
Sinha, P., M. Ilunga, and T. Tobgyel. 2023. “Harmonic response analysis of seismic excitations on tunnel linings.” GeoStruct. Innov. 1 (1): 1–16. https://doi.org/10.56578/gsi010101.
Sun, Q., X. Q. Ye, and W. Gu. 2000. “A new combination rules of evidence theory.” [In Chinese.] Acta Electron. Sin. 28 (8): 117.
Sun, S., L. Liang, M. Li, and X. Li. 2019. “Bridge performance evaluation via dynamic fingerprints and data fusion.” J. Perform. Constr. Facil. 33 (2): 04019004. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001256.
Tai, L., X. Zhang, H. Zhen, J. R. Chen, and H. Wu. 2023. “Asymmetrical deformation mechanisms in layered inclined surrounding rock of roadways.” GeoStruct. Innov. 1 (1): 17–31. https://doi.org/10.56578/gsi010102.
Wang, H. F., X. Y. Deng, W. Jiang, and J. Geng. 2021a. “A new belief divergence measure for Dempster–Shafer theory based on belief and plausibility function and its application in multi-source data fusion.” Eng. Appl. Artif. Intell. 97 (Mar): 104030. https://doi.org/10.1016/j.engappai.2020.104030.
Wang, S., L. P. Li, S. Cheng, J. Y. Yang, H. Jin, S. Gao, and T. Wen. 2021b. “Study on an improved real-time monitoring and fusion prewarning method for water inrush in tunnels.” Tunnelling Underground Space Technol. 112 (Aug): 103884. https://doi.org/10.1016/j.tust.2021.103884.
Wen, Z. J., P. F. Jiang, Z. Q. Song, Y. J. Jiang, J. H. Wen, and S. L. Jing. 2023. “Structural model and capacity determination of underground reservoir in goaf: A case study of Shendong mining area in China.” Geomech. Geophys. Geo-Energy Geo-Resour. 9 (1): 143. https://doi.org/10.1007/s40948-023-00677-2.
Wu, R. T., and M. R. Jahanshahi. 2020. “Data fusion approaches for structural health monitoring and system identification: Past, present, and future.” Struct. Health Monit. 19 (2): 552–586. https://doi.org/10.1177/1475921718798769.
Wu, S. L., S. Yang, and X. D. Du. 2021. “A model for evaluation of surrounding rock stability based on DS evidence theory and error-eliminating theory.” Bull. Eng. Geol. Environ. 80 (3): 2237–2248. https://doi.org/10.1007/s10064-020-02060-x.
Wu, X. G., J. C. Duan, L. M. Zhang, and S. M. AbouRizk. 2018. “A hybrid information fusion approach to safety risk perception using sensor data under uncertainty.” Stochastic Environ. Res. Risk Assess. 32 (1): 105–122. https://doi.org/10.1007/s00477-017-1389-9.
Xiao, F. Y. 2019. “Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy.” Inf. Fusion 46 (Mar): 23–32. https://doi.org/10.1016/j.inffus.2018.04.003.
Yager, R. R. 1987. “On the Dempster-Shafer framework and new combination rules.” Inf. Sci. 41 (2): 93–137. https://doi.org/10.1016/0020-0255(87)90007-7.
Yang, J. B., and D. L. Xu. 2002. “On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty.” IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 32 (3): 289–304. https://doi.org/10.1109/TSMCA.2002.802746.
Ye, F., J. Chen, and Y. Li. 2017. “Improvement of DS evidence theory for multi-sensor conflicting information.” Symmetry 9 (5): 69. https://doi.org/10.3390/sym9050069.
Yu, Q., D. Zhao, Y. Xia, S. Jin, J. Zheng, Q. Meng, C. Mu, and J. Zhao. 2022. “Multivariate early warning method for rockburst monitoring based on microseismic activity characteristics.” Front. Earth Sci. 10 (Feb): 837333. https://doi.org/10.3389/feart.2022.837333.
Zhang, G. K., F. Gao, Z. Wang, and S. L. Yue. 2021a. “Quantifying the progressive fracture damage of granite rocks by stress–strain, acoustic emission, and active ultrasonic methods.” J. Mater. Civ. Eng. 33 (12): 04021353. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003962.
Zhang, L. M., W. W. Cao, Z. Y. Liu, Y. Cong, and Z. Q. Wang. 2022. “Crack propagation characteristics during progressive failure of circular tunnels and the early warning thereof based on multi-sensor data fusion.” Geomech. Geophys. Geo-Energy Geo-Resour. 8 (5): 172. https://doi.org/10.1007/s40948-022-00482-3.
Zhang, L. M., Y. Cong, F. Z. Meng, Z. Q. Wang, P. Zhang, and S. Gao. 2021b. “Energy evolution analysis and failure criteria for rock under different stress paths.” Acta Geotech. 16 (2): 569–580. https://doi.org/10.1007/s11440-020-01028-1.
Zhang, L. M., D. Zhang, Z. Q. Wang, Y. Cong, and X. S. Wang. 2023. “Constructing a three-dimensional creep model for rocks and soils based on memory-dependent derivatives: A theoretical and experimental study.” Comput. Geotech. 159 (Apr): 105366. https://doi.org/10.1016/j.compgeo.2023.105366.
Zhang, P., Z. P. Meng, K. Zhang, and S. Jiang. 2020. “Impact of coal ranks and confining pressures on coal strength, permeability and acoustic emission.” Int. J. Geomech. 20 (8): 04020135. https://doi.org/10.1061/(asce)gm.1943-5622.0001752.
Zhang, S. R., T. Liu, and C. Wang. 2021c. “Multi-source data fusion method for structural safety assessment of water diversion structures.” J. Hydroinf. 23 (2): 249–266. https://doi.org/10.2166/hydro.2021.154.
Zhou, H., Y. H. Zhao, Q. Shen, L. Yang, and H. B. Cai. 2020. “Risk assessment and management via multi-source information fusion for undersea tunnel construction.” Autom. Constr. 111 (May): 103050. https://doi.org/10.1016/j.autcon.2019.103050.
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 1 • March 2024
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© 2023 American Society of Civil Engineers.
History
Received: Jul 30, 2023
Accepted: Oct 10, 2023
Published online: Dec 6, 2023
Published in print: Mar 1, 2024
Discussion open until: May 6, 2024
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