【作者】 李晓龙；

【导师】 王复明；

【作者基本信息】 郑州大学 ， 水工结构工程， 2009， 博士

【摘要】 基于支持向量机(SVM)的位移反分析是较新出现的一种岩土工程参数反演方法,它用训练得到的支持向量机模型代替数值模型实现岩体力学参数与位移间的复杂映射关系,大大提高了反演计算效率。与早期反分析中较多采用的神经网络方法相比,支持向量机在理论基础和求解算法方面都具有明显优势,日益受到岩土工程研究人员的重视。本文围绕目前反分析方法存在的一些问题,首先从提高建模效率和模型计算精度的角度对地下工程数值建模方法进行探讨,然后从影响支持向量机泛化性能的主要因素,即支持向量机模型参数、支持向量机类型以及核函数形式三个方面对基于支持向量机的岩体力学参数反演方法展开系统研究,并应用于工程实践,主要内容概括如下:(1)探讨了基于自然单元法的地下工程数值建模方法。为克服在处理地下工程无限域或半无限域问题时需要人为确定边界条件而带来计算误差的问题,引入无限元模拟无穷远处边界条件,与自然元相结合形成耦合分析方法,通过算例分析表明,耦合方法能够提高计算精度,降低对分析区域选取范围的要求,进而减少计算工作量;同时实现了基于自然元与无限元耦合方法的粘弹性分析,拓展了自然单元法在岩土工程中的适用范围。(2)为克服传统参数选取方法存在的不足,研究了基于粒子群算法的支持向量机模型参数优化方法。为提高算法搜索能力,对标准粒子群算法适应值比较方式和粒子运动方式做出修改,使粒子移动更具有导向性和灵活性,同时为避免算法早熟采用同时考虑时间和粒子群聚集程度影响的动态自适应惯性权重,在此基础上提出一种改进粒子群算法;算例分析表明,与传统参数选择方法相比,采用该方法明显提高了参数搜索效率和相应支持向量机模型的预测精度。(3)研究了基于最小二乘支持向量机(LS-SVM)的岩体力学参数反演方法。针对标准型支持向量机计算复杂度大的缺点,将最小二乘支持向量机代替标准型支持向量机,与改进粒子群算法相结合,用于围岩参数反演;同时为克服常规算法得到的最小二乘支持向量机的解丧失稀疏性的缺点,采用基于二次Renyi熵的增量迭代式回归算法训练最小二乘支持向量机模型;通过反演算例表明,将最小二乘支持向量机应用于岩体力学参数反演是可行的,与标准型支持向量机相比,采用最小二乘支持向量机能够有效提高反演计算效率。(4)探讨了核函数形式对反演结果的影响。目前普遍采用的径向基核函数(RBF)由于缺乏平移正交性,使得相应支持向量机模型的逼近能力受到限制,间接影响参数辨识精度,为此引入小波和尺度函数作为LS-SVM的核函数用于岩体力学参数反演;并针对常规尺度函数局部性不足的缺点,根据相关理论构造出一种具有良好紧支性和光滑性的尺度核函数;算例分析表明,核函数的逼近性能对参数识别精度有较大影响,在满足容许精度要求的前提下,采用逼近能力强的核函数可以减少所需样本数量,从而降低计算量。(5)以前面的工作为基础,结合王坑高速公路隧道项目,开展工程应用研究。在考虑爆破开挖影响的基础上,采用自然元与无限元耦合方法构建了模拟隧道施工过程的三维仿真模型;通过正交数值试验和影响度分析确定待反演参数,以实测变形为依据,用紧支尺度核最小二乘支持向量机反演岩体力学参数,通过对各测点实测变形序列与计算变形序列的灰色关联度分析检验了反演结果的合理性,最后利用反演参数对后续开挖断面的围岩变形实施预测并取得了较好的效果。更多还原

【Abstract】 The displacement back analysis based on support vector machine (SVM) is a newly appeared parameters identification method of geotechnical engineering, which realizes the complex mapping relationship between mechanical parameters and deformations of rock mass using SVM model determined by a few learning examples instead of numerical model and improves inversion efficiency. Compared with artificial neural network (ANN), which is earlier used for back analysis, the SVM bears more excellent characteristics both in basic theory and solution method, so it has been paid increasingly more attention by researchers in geotechnical engineering.In allusion to the disadvantages of present back analysis method, the numerical modeling method of underground engineering is discussed first in detailed, and then the method of rock mechanical parameter identification based on SVM is studied systematically from three aspects, parameters optimization of SVM, type of SVM, and the kernel function form, which are crucial factors affecting the generation ability of SVM, finally the research results was applied to real project. The major contents are as follows:(1) The numerical modeling method of underground engineering based on natural element method (NEM) was discussed. Aimed at the defect that the errors was inevitably caused by selecting a certain finite region and setting the boundary conditions subjectively when treating infinite or half infinite domain problem in geotechnical engineering, the infinite element method(IEM) was introduced to simulate the boundary conditions at infinitely distant place, thus the coupling analysis method of NEM and IEM was provided. Through an example, the correctness of the computation method was proved. The results show that the coupling method improves the calculation precision and reduces the requirement for calculation range; meanwhile, visco-elastic analysis based on the coupling method is successfully implemented, which extends the application scope of NEM in geotechnical engineering.(2) In order to overcome the shortcomings of conventional parameter selection methods, the parameter selection method based on particle swarm optimization (PSO) is addressed. By modifying the comparison mode of fitness value and the motion mode of individual particle of conventional PSO, and designing an auto-adaptive dynamic inertia weight which considers both the time and clustering degree of particles, an improved particle swarm optimization (IPSO) is proposed. Numerical results showed that, compared with traditional parameter selection methods, the new method obviously increases the parameter searching efficiency and the predictive precision of corresponding SVM.(3) The surrounding rock parameters identification method based on least squares support vector machine (LS-SVM) is studied. By substituting LS-SVM for standard SVM, and combined with the improved particle swarm optimization (IPSO), a novel displacement back analysis method is provided. To ensure the sparsity of support vectors of LS-SVM, an iterative regression algorithm based on quadratic Renyi entropy and incremental learning algorithm is chosen to solve the LS-SVM model. Through examples of back analysis, the feasibility and effectiveness of applying LS-SVM to parameters inversion of rock mass is demonstrated, and the results show that, compared with standard SVM, inversion efficiency is greatly improved using LS-SVM.(4) The influence of kernel function form on inversion results is discussed. Due to the lack of orthogonality by translation, the RBF kernel function, which is generally used for back analysis at present, restricts the generalization performance of corresponding SVM and impairs inversion precision indirectly. In view of this, the wavelet function and scaling function were used as kernel function for parameter inversion. In addition, aiming at the deficiency of locality of conventional scaling function, a new compact support scaling kernel function with good smoothness was constructed according to the related theory. The results of an inversion example showed that the approximation ability of kernel function has serious influence on parameter identification precision, and when the admissible accuracy is satisfied, less training examples is needed if using kernel function with better approximation ability, which means less computation cost.(5) Based on above work, application study on back analysis was performed in Wangkeng expressway tunnel project. Using the coupling method of NEM and IEM, the 3D numerical model simulating tunnel construction was build, and the influence of excavation damage zone was considered. Through influence degree analysis, the parameters that would be identified were determined. Then the compact support scaling kernel LS-SVM was used for mechanical parameters inversion of surrounding rock. The space displacement sequence grey correction analysis indicated that the inversion results were credible. Finally, based on the identified parameters, the deformations of surrounding rock caused by subsequent excavation were successfully predicted.更多还原