基于v-SVR和MVPSO算法的边坡位移反分析方法及其应用
摘要
针对传统粒子群算法存在搜索空间有限、容易陷入局部最优点的缺陷,通过引入迁徙算子和自适应变异算子,提出基于粒子迁徙和变异的粒子群优化(MVPSO)算法。基准测试函数结果表明,改进的MVPSO算法较传统的粒子群优化算法在收敛效率上有大幅度提高,在处理非线性、多峰值的复杂优化问题中能快速地搜索,得到全局最优解。应用改进的MVPSO算法搜索最佳的支持向量机(v-SVR)模型参数,建立岩体力学参数与岩体位移之间的非线性支持向量机模型,提高v-SVR的预测精度和推广泛化性。然后,利用v-SVR模型的外推预测替代耗时的FLAC正向计算,利用改进的MVPSO算法搜索岩体力学参数的最优组合,提出v-SVR和MVPSO相结合的边坡位移反分析方法(v-SVR-MVPSO算法),与传统的BP-GA算法和v-SVR-GA算法相比,该算法在反演精度和反演效率上均有较大幅度提高。最后,将本文发展的v-SVR-MVPSO算法应用到大岗山水电站右岸边坡岩体参数反演分析,并对边坡后续开挖位移和稳定性进行预测,取得较好的效果。
To address the problems of the limit search space and local optimization in traditional particle swarm optimization algorithm,a modified variation particle swarm optimization(MVPSO) algorithm is proposed based on particle migration and variation by introducing migration operator and adapting mutation operator.The results of the benchmark test functions show that the convergence rate of this MVPSO algorithm has significantly improved than the traditional particle swarm optimization algorithm.For the nonlinear and multimodal problems,the proposed MVPSO functions well in searching the global minimum.In order to establish a nonlinear relation between the mechanical parameters of rock mass and the displacements,the MVPSO algorithm is adopted to search for the most suitable parameters of the v-SVR model.The results show that the prediction accuracy and generalization ability of the v-SVR have been significantly increased.Then,the optimal v-SVR model is an alternative for the time-consuming FLAC calculations;and the MVPSO algorithm can be used to search for the best group of the mechanical parameters of rock mass.Consequently,a new displacement back analysis method is developed in combination of the v-SVR with the MVPSO algorithm.Compared with the traditional displacement back analysis methods,including BP-GA and the v-SVR-GA,the proposed method has its merits in inversion efficiency and accuracy.Finally,the new method is applied to the parametric back analysis of rock mass in the right-bank slope of Dagangshan hydropower station.Based on the back-analyzed parameters,the deformation and stability of the slope during subsequent construction period are analyzed.The results demonstrate that the proposed method has high accuracy and good applicability.
To address the problems of the limit search space and local optimization in traditional particle swarm optimization algorithm,a modified variation particle swarm optimization(MVPSO) algorithm is proposed based on particle migration and variation by introducing migration operator and adapting mutation operator.The results of the benchmark test functions show that the convergence rate of this MVPSO algorithm has significantly improved than the traditional particle swarm optimization algorithm.For the nonlinear and multimodal problems,the proposed MVPSO functions well in searching the global minimum.In order to establish a nonlinear relation between the mechanical parameters of rock mass and the displacements,the MVPSO algorithm is adopted to search for the most suitable parameters of the v-SVR model.The results show that the prediction accuracy and generalization ability of the v-SVR have been significantly increased.Then,the optimal v-SVR model is an alternative for the time-consuming FLAC calculations;and the MVPSO algorithm can be used to search for the best group of the mechanical parameters of rock mass.Consequently,a new displacement back analysis method is developed in combination of the v-SVR with the MVPSO algorithm.Compared with the traditional displacement back analysis methods,including BP-GA and the v-SVR-GA,the proposed method has its merits in inversion efficiency and accuracy.Finally,the new method is applied to the parametric back analysis of rock mass in the right-bank slope of Dagangshan hydropower station.Based on the back-analyzed parameters,the deformation and stability of the slope during subsequent construction period are analyzed.The results demonstrate that the proposed method has high accuracy and good applicability.
引文
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[19]邬凯,盛谦,梅松华,等.PSO-LSSVM模型在位移反分析中的应用[J].岩土力学,2009,30(4):1109–1114.(WU Kai,SHENGQian,MEI Songhua,et al.A model of PSO-LSSVM and its application todisplacement back analysis[J].Rock and Soil Mechanics,2009,30(4):1 109–1 114.(in Chinese))
[20]杨云浩,徐卫亚,聂卫平.基于-SVR与PSO-DE的岩层弹塑性参数反演及应用[J].中国矿业大学学报,2011,40(1):95–102.(YANGYunhao,XU Weiya,NIE Weiping.Inverse analysis of strata elasto-plastic mechanic parameters based onε-SVR and PSO-DE algorithmand its application[J].Journal of China University of Mining andTechnology,2011,40(1):95–102.(in Chinese))
[21]颜七笙,王士同.基于PSO-SVR的岩质边坡稳定性评价模型[J].计算机工程与应用,2011,47(16):235–238.(YAN Qisheng,WANGShitong.Stability evaluation model of rock mass slope based onPSO-SVR[J].Computer Engineering and Applications,2011,47(16):235–238.(in Chinese))
[22]方开泰,马长兴.正交与均匀试验设计[M].北京:科学出版社,2001:233–248.(FANG Kaitai,MA Changxing.Orthogonal andUniform test design[M].Beijing:Science Press,2001:233–248.(inChinese))
[23]梅松华,盛谦,冯夏庭.均匀设计在岩土工程中的应用[J].岩石力学与工程学报,2004,23(16):2694–2697.(MEI Songhua,SHENG Qian,FENG Xiating.Application of uniform design togeotechnical engineering[J].Chinese Journal of Rock Mechanics andEngineering,2004,23(16):2 694–2 697.(in Chinese))
[24]张振华.深切河谷岸坡开挖过程动态预警方法研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2008.(ZHANGZhenhua.Study on dynamic warnning method of bank slopes indeep-cut valley during the course of excavation[Ph.D.Thesis][D].Wuhan:Institude of Rock and Soil Mechanics,Chinese Academy ofSciences,2008.(in Chinese))
[25]漆祖芳,姜清辉,唐志丹,等.锦屏一级水电站左岸坝肩边坡施工期稳定性分析[J].岩土力学,2012,33(2):531–538.(QI Zufang,JIANG Qinghui,TANG Zhidan,et al.Stability analysis of abutmentslope at left bank of Jinping-I Hydropower Project during construction[J].Rock and Soil Mechanics,2012,33(2):531–538.(in Chinese))
[26]武汉大学.大岗山水电站右岸边坡稳定分析及加固措施研究:专题报告[R].武汉:武汉大学,2010.(Wuhan University.Special report ofstability analysis and study on reinforcement measure of the right bankslope of Dagangshan hydropower station[R].Wuhan:Wuhan University,2010.(in Chinese))
[2]杨志法,王思敬,冯良紫,等.岩土工程反分析原理及应用[M].北京:地震出版社,1992:76–83.(YANG Zhifa,WANG Sijing,FENGLiangzi,et al.The principle and application of back analysis ingeotechnical engineering[M].Beijing:Earthquake Press,1992:76–83.(in Chinese))
[3]杨林德.岩土工程问题的反演理论和工程实践[M].北京:科学出版社,1995:148–162.(YANG Linde.The inversion theory andengineering practice of geotechnical engineering[M].Beijing:SciencePress,1995:148–162.(in Chinese))
[4]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000:1–14.(FENG Xiating.Introduction to intelligent rock mechanics[M].Beijing:Science Press,2000:1–14.(in Chinese))
[5]VAPNIK V N.The nature of statistical learning theory[M].New York:Springer Verlag,1995:1–15.
[6]丁蕾,朱德权.基于BP与SVR的非线性回归之比较[J].安庆师范学院学报:自然科学版,2011,17(2):94–96.(DING Lei,ZHUDequan.Comparison of nonlinear regression based on BP and SVR[J].Joumal of Anqing Teachers College:Natural Science,2011,17(2):94–96.(in Chinese))
[7]MULI F.Vapnik-chervonenkis learning theory and its applications[J].IEEE Transactions on Neural Network,1999,10(5):985–987.
[8]ELEGBEDE C.Structural reliability assessment based on particleswarm optimization[J].Structural Safety,2005,27(10):171–186.
[9]POBINSON J,RAHMAT-SAMII Y.Particle swarm optimization inelectromagnetics[J].IEEE Transactions on Antennas and Propagation,2004,52(2):397–406.
[10]SALMAN A,AHMAD I.AI-MADANI S.Particle swarm optimizationfor task assignment problem[J].Microprocessors and Microsystems,2002,26(8):363–371.
[11]POBINSON J,RAHMAT-SAMII Y.Particle swarm optimization inelectromagnetics[J].IEEE Transactions on Antennas and Propagation,2004,52(2):397–406.
[12]KENNEDY J,EBERHERT R.Particle swarm optimization[C]//IEEEInternational Conference on Neural Networks.[S.l.]:[s.n.],1995:1 942–1 948.
[13]常晓林,喻胜春,马刚,等.基于粒子迁徙的粒群优化算法及其在岩土工程中的应用[J].岩土力学,2011,32(4):1077–1082.(CHANG Xiaolin,YU Shengchun,MA Gang,et al.Particle swarmoptimization based on particle migration and its application togeotechnical engineering[J].Rock and Soil Mechanics,2011,32(4):1 077–1 082.(in Chinese))
[14]SHI Y H,EBERHART R C.Experimental study of particle swarmoptimization[C]//Proceedings of SCI Conference.Orlando:[s.n.],2000,1 945–1 950.
[15]崔红梅,朱庆保.微粒群算法的参数选择及收敛性分析[J].计算机工程与应用,2007,43(23):89–91.(CUI Hongmei,ZHU Qingbao.Convergence analysis and parameter selection in particle swarmoptimization[J].Computer Engineering and Applications,2007,43(23):89–91.(in Chinese))
[16]吕振肃,侯志容.自适应变异的粒子群优化算法[J].电子学报,2004,32(3):416–420.(LU Zhensu,HOU Zhirong.Particle swarmoptimization with adaptive mutation[J].Acta Electronica Sinica,2004,32(3):416–420.(in Chinese))
[17]高岳林,任子晖.带有变异算子的自适应粒子群优化算法[J].计算机工程与应用,2007,43(25):43–47.(GAO Yuelin,REN Zihui.Adaptive particle swarm optimization algorithm with mutation operator[J].Computer Engineering and Applications,2007,43(25):43–47.(inChinese))
[18]余志雄,周创兵,陈益峰,等.基于v-SVR和GA的初始地应力场位移反分析方法研究[J].岩土力学,2007,28(1):151–162.(YUZhixiong,ZHOU Chuangbing,CHEN Yifeng,et al.Study on v-SVR andmodified GA in back analysis of initial stress fields from displacements[J].Rock and Soil Mechanics,2007,28(1):151–162.(in Chinese))
[19]邬凯,盛谦,梅松华,等.PSO-LSSVM模型在位移反分析中的应用[J].岩土力学,2009,30(4):1109–1114.(WU Kai,SHENGQian,MEI Songhua,et al.A model of PSO-LSSVM and its application todisplacement back analysis[J].Rock and Soil Mechanics,2009,30(4):1 109–1 114.(in Chinese))
[20]杨云浩,徐卫亚,聂卫平.基于-SVR与PSO-DE的岩层弹塑性参数反演及应用[J].中国矿业大学学报,2011,40(1):95–102.(YANGYunhao,XU Weiya,NIE Weiping.Inverse analysis of strata elasto-plastic mechanic parameters based onε-SVR and PSO-DE algorithmand its application[J].Journal of China University of Mining andTechnology,2011,40(1):95–102.(in Chinese))
[21]颜七笙,王士同.基于PSO-SVR的岩质边坡稳定性评价模型[J].计算机工程与应用,2011,47(16):235–238.(YAN Qisheng,WANGShitong.Stability evaluation model of rock mass slope based onPSO-SVR[J].Computer Engineering and Applications,2011,47(16):235–238.(in Chinese))
[22]方开泰,马长兴.正交与均匀试验设计[M].北京:科学出版社,2001:233–248.(FANG Kaitai,MA Changxing.Orthogonal andUniform test design[M].Beijing:Science Press,2001:233–248.(inChinese))
[23]梅松华,盛谦,冯夏庭.均匀设计在岩土工程中的应用[J].岩石力学与工程学报,2004,23(16):2694–2697.(MEI Songhua,SHENG Qian,FENG Xiating.Application of uniform design togeotechnical engineering[J].Chinese Journal of Rock Mechanics andEngineering,2004,23(16):2 694–2 697.(in Chinese))
[24]张振华.深切河谷岸坡开挖过程动态预警方法研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2008.(ZHANGZhenhua.Study on dynamic warnning method of bank slopes indeep-cut valley during the course of excavation[Ph.D.Thesis][D].Wuhan:Institude of Rock and Soil Mechanics,Chinese Academy ofSciences,2008.(in Chinese))
[25]漆祖芳,姜清辉,唐志丹,等.锦屏一级水电站左岸坝肩边坡施工期稳定性分析[J].岩土力学,2012,33(2):531–538.(QI Zufang,JIANG Qinghui,TANG Zhidan,et al.Stability analysis of abutmentslope at left bank of Jinping-I Hydropower Project during construction[J].Rock and Soil Mechanics,2012,33(2):531–538.(in Chinese))
[26]武汉大学.大岗山水电站右岸边坡稳定分析及加固措施研究:专题报告[R].武汉:武汉大学,2010.(Wuhan University.Special report ofstability analysis and study on reinforcement measure of the right bankslope of Dagangshan hydropower station[R].Wuhan:Wuhan University,2010.(in Chinese))
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