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[33]Zheng DJ,Cheng L,Bao T F,et al.Integrated parameter inver-工程科学学报,第 41 卷,第 1 期 (3)基于 B鄄PSO鄄MSVM 概率反演方法结合了多 输出支持向量机模型多参数同时输出与贝叶斯方法 参数动态更新的特点,不但提高了反演计算效率,而 且实现了隧道多源监测数据的智能融合,概率反演 后的围岩参数值相对传统的反演方法所得确定性参 数值信息更加全面准确,为后续隧道施工安全风险 评估与可靠性分析提供了基础依据. 参 考 文 献 [1] Baecher G B, Christian J T. Reliability and Statistics in Geotechni鄄 cal Engineering. New York: John Wiley and Sons, Inc, 2003 [2] Der Kiureghian A, Ditlevsen O. Aleatory or epistemic? Does it matter? Struct Saf, 2009, 31(2): 105 [3] Langford J C, Diederichs M S. Quantifying uncertainty in Hoek鄄 Brown intact strength envelopes. Int J Rock Mech Min Sci, 2015, 74: 91 [4] Cai M F, He M C, Liu D Y. Rock Mechanics and Engineering. 2nd Ed. Beijing: Science Press, 2013 (蔡美峰, 何满潮, 刘东燕. 岩石力学与工程. 2 版. 北京: 科 学出版社, 2013) [5] Gilbert R B, Tang W H. Model uncertainty in offshore geotechni鄄 cal reliability / / Proceeding of the 27th Offshore Technology Con鄄 ference. Houston, 1995: 557 [6] Gilbert R B, Wright S G, Liedtke E. Uncertainty in back analysis of slopes: Kettleman Hills case history. J Geotech Geoenviron Eng, 1998, 124(12): 1167 [7] Zhang L L, Zhang J, Zhang L M, et al. Back analysis of slope failure with Markov chain Monte Carlo simulation. Comput Geotech, 2010, 37(7鄄8): 905 [8] Zhang L L, Zuo Z B, Ye G L, et al. Probabilistic parameter esti鄄 mation and predictive uncertainty based on field measurements for unsaturated soil slope. Comput Geotech, 2013, 48: 72 [9] Zhang J, Tang W H, Zhang L M. Efficient probabilistic back鄄 analysis of slope stability model parameters. J Geotech Geoenviron Eng, 2010, 136(1): 99 [10] Wang L, Hwang J H, Luo Z, et al. Probabilistic back analysis of slope failure———a case study in Taiwan. Comput Geotech, 2013, 51: 12 [11] Li S J, Zhao H B, Ru Z L, et al. Probabilistic back analysis based on Bayesian and multi鄄output support vector machine for a high cut rock slope. Eng Geol, 2016, 203: 178 [12] Miranda T, Dias D, Eclaircy鄄Caudron S, et al. Back analysis of geomechanical parameters by optimisation of a 3D model of an un鄄 derground structure. Tunnell Undergr Space Technol, 2011, 26 (6): 659 [13] Miro S, K觟nig M, Hartmann D, et al. A probabilistic analysis of subsoil parameters uncertainty impacts on tunnel鄄induced ground movements with a back鄄analysis study. Comput Geotech, 2015, 68: 38 [14] Haas C, Einstein H H. Updating the “Decision Aids for Tunne鄄 ling冶. J Constr Eng Manage, 2002, 128(1): 40 [15] Miranda T, Correia A G, e Sousa L R. Bayesian methodology for updating geomechanical parameters and uncertainty quantifica鄄 tion. Int J Rock Mech Min Sci, 2009, 46(7): 1144 [16] Zhang J, Tang W H, Zhang L M, et al. Characterising geotech鄄 nical model uncertainty by hybrid Markov Chain Monte Carlo sim鄄 ulation. Comput Geotech, 2012, 43: 26 [17] Peng M, Li X Y, Li D Q, et al. Slope safety evaluation by in鄄 tegrating multi鄄source monitoring information. Struct Saf, 2014, 49: 65 [18] Feng X D, Jimenez R. Bayesian prediction of elastic modulus of intact rocks using their uniaxial compressive strength. Eng Geol, 2014, 173: 32 [19] Wang Y, Cao Z J. Probabilistic characterization of Young蒺s mod鄄 ulus of soil using equivalent samples. Eng Geol, 2013, 159: 106 [20] Cao Z J, Wang Y, Li D Q. Quantification of prior knowledge in geotechnical site characterization. Eng Geol, 2016, 203: 107 [21] Wang Y, Aladejare A E. Bayesian characterization of correlation between uniaxial compressive strength and Young蒺s modulus of rock. Int J Rock Mech Min Sci, 2016, 85: 10 [22] Contreras L F, Brown E T, Ruest M. Bayesian data analysis to quantify the uncertainty of intact rock strength. J Rock Mech Geotech Eng, 2018, 10(1): 11 [23] Li D Q, Zheng D, Cao Z J, et al. Response surface methods for slope reliability analysis: Review and comparison. Eng Geol, 2016, 203: 3 [24] Lv Q, Sun H Y, Low B K. Reliability analysis of ground鄄鄄support interaction in circular tunnels using the response surface method. Int J Rock Mech Min Sci, 2011, 48(8): 1329 [25] Zhao H B, Ru Z L, Chang X, et al. Reliability analysis of tun鄄 nel using least square support vector machine. Tunnell Undergr Space Technol, 2014, 41: 14 [26] Lv Q, Chan C L, Low B K. Probabilistic evaluation of ground鄄 support interaction for deep rock excavation using artificial neural network and uniform design. Tunnell Undergr Space Technol, 2012, 32: 1 [27] Gomes H M, Awruch A M. Comparison of response surface and neural network with other methods for structural reliability analy鄄 sis. Struct Saf, 2004, 26(1): 49 [28] Li X, Li X B, Su Y H. A hybrid approach combining uniform design and support vector machine to probabilistic tunnel stability assessment. Struct Saf, 2016, 61: 22 [29] Lv Q, Xiao Z P, Ji J, et al. Moving least squares method for re鄄 liability assessment of rock tunnel excavation considering ground鄄 support interaction. Comput Geotech, 2017, 84: 88 [30] Drucker H, Burges C J C, Kaufman L, et al. Support vector re鄄 gression machines. Adv in Neural Inf Process Syst, 1996, 28 (7): 779 [31] Hurtado J E. An examination of methods for approximating im鄄 plicit limit state functions from the viewpoint of statistical learning theory. Struct Saf, 2004, 26(3): 271 [32] Tuia D, Verrelst J, Alonso L, et al. Multioutput support vector regression for remote sensing biophysical parameter estimation. IEEE Geosci Remote Sens Lett, 2011, 8(4): 804 [33] Zheng D J, Cheng L, Bao T F, et al. Integrated parameter inver鄄 ·86·