基于粗糙集和支持向量机的融合算法在岩体质量评价中的应用

从数据融合角度出发,把粗糙集理论和支持向量机理论结合,用来解决隧道岩体质量评价问题。首先,应用粗糙集理论对岩体质量评价样本数据进行约简,去除冗余特征形成岩体质量影响因素与岩体质量之间简明扼要的关系数据表达形式,形成新的样本数据,然后应用支持向量机理论,对新样本数据进行学习,建立岩体质量的支持向量机评价模型。通过实际工程应用表明,该方法科学可行。      

基于支持向量机-马尔可夫链的位移时序预测

结合支持向量机和马尔可夫链,提出了一种新的位移时序预测模型--支持向量机－马尔可夫链预测模型（SVM-MC）。通过对实测位移值的学习,利用经粒子群算法优化的支持向量机对位移时间序列的宏观发展趋势进行滚动预测;在此基础上应用马尔可夫链确定位移时序的状态转移概率矩阵,通过对状态的划分、实测值与支持向量机拟合值的绝对误差及相对误差等指标的分析,实现了对预测结果的改进。将该模型应用到某工程永久船闸高边坡的位移时序预测中,结果表明,该模型具有科学可靠、预测精度高的优点,在岩土体位移时序预测中具有有一定工程应用价值。     

基于LSSVM与MCS的路基沉降可靠度分析

提出了一种计算路基沉降可靠度的新方法。基于FLAC中的修正剑桥模型,以最小二乘支持向量机为核心技术,结合蒙特卡罗法构建计算模型。由于修正剑桥模型参数较多,对模型参数进行了敏感性分析,将对沉降影响较大的参数确定为随机变量。选取训练样本对支持向量机进行训练,按照随机变量的概率分布进行抽样,馈送到最小二乘支持向量机得到相应的响应值,用Matlab编制程序完成可靠度计算,并进行了算例分析。计算结果表明,蒙特卡罗法结合支持向量机的沉降可靠度计算方法应用于公路软基沉降可靠度计算是可行的。     

基于范例推理的公路隧道拱顶变形时序支持向量机外延预测

针对公路隧道拱顶变形预测模型的普适性与外推预测的准确性,提出了基于人工智能推理的隧道工程属性（地理位置、监测位置、隧道高宽比、围岩级别和埋深）与拱顶变形时序曲线原子矩阵的相似范例检索方法,并在深入分析了获取的相似范例特征的基础上,进一步以LPG新核函数支持向量机建立先验知识的预测模型。应用该方法对通渝隧道工程K19+994断面拱顶下沉进行了预测与评估。结果表明,对于不同隧道间或同一隧道不同区段预判拱顶变形或收敛,基于范例推理能够获知良好的先验背景知识,且以此进行的支持向量机预测模型学习的回归内插（1～14步序）的平均相对误差为1.36%,而一次性外推预测15 d内的8个变形值（16～30步序）的平均相对精度为97.28%,证实了方法的可靠性     

PSO-LSSVM模型在位移反分析中的应用

提出了一种基于均匀设计原理、最小二乘支持向量机(LSSVM)和粒子群优化算法(PSO)的快速位移反分析方法。该方法利用均匀设计和有限差分法获得学习样本,再用粒子群算法搜索最优的最小二乘支持向量机模型参数。并用最小二乘支持向量机回归模型建立反演参数与监测点位移值之间的非线性映射关系,最后用粒子群算法从全局空间上搜索与实测位移最吻合的反演参数。该反演模型利用了粒子群算法高效简单、均匀设计构造高质量小样本以及最小二乘支持向量机的小样本、泛化性能好的特点。将该模型应用于龙滩水电站左岸地下厂房区岩体地应力场的反演分析中,计算结果与实测的位移值和地应力值均吻合较好,说明了该模型在岩土工程快速反演分析中具有良好的应用价值。     

福宁高速公路八尺门滑坡变形演化规律预测研究

将进化支持向量机方法用于边坡变形规律的研究,用遗传算法搜索支持向量机最优参数,避免了人为选择支持向量机参数的盲目性,提高了支持向量机的推广预测能力。利用这种方法预测边坡变形规律,并与监测到的历史数据进行对比,以便工程技术人员及时调整设计方案和施工,维护边坡的稳定性。工程实例表明,该方法具有预测精度高和实时性等特点,具有广阔的应用前景。     

预测套管损坏的新方法研究

套损预报是石油工程中的一大技术难题,在充分考虑套管损坏影响因素多,机理复杂的前提下,提出了基于支持向量机的套损预报方法。通过对历年套管状况及其影响因素的学习,建立了支持向量机套损预报模型,运用所建立的模型对套管状况进行预报。结果表明:该方法计算效率高,结果可靠,实现了油水井正常生产过程中对套管状况进行动态判断,具有广泛的应用前景和工程价值。     

岩爆分类的支持向量机方法

针对岩爆分类问题,提出了基于支持向量机的分类方法。通过对影响岩爆因素的分析,运用支持向量机理论建立岩爆类别的支持向量机模型。结果表明,基于支持向量机的岩爆分类方法具有较高的准确率,该方法是科学可行的,具有广泛的应用前景。     

基于SVM的溶洞顶板安全厚度智能预测模型

以某岩溶隧道为背景,采用二维弹塑性有限元方法对隧道开挖进行数值模拟计算,分析了隧道底部溶洞顶板安全厚度的影响因素,用支持向量机方法得出了能综合体现各影响因素的溶洞顶板安全厚度预测模型,并和多元线性回归得到的预测模型进行对比。计算结果表明,支持向量机预测模型较之多元线性回归模型,不但具有方便快捷的优点,而且具有更高的预测精度。     

基于粒子群算法优化小波支持向量机的岩土力学参数反演

常用的确定岩土力学参数的方法有原位测试和室内试验两种,但都存在一定的局限性,参数选择的合理与否,对设计计算及数值模拟分析结果的有效性影响很大。支持向量机法在理论基础和求解算法方面都具有明显优势,为确保岩土力学参数取值的合理性,采用支持向量机法对岩土力学参数进行反演。先通过小波分析理论构造出支持向量机的核函数,再用粒子群算法(PSO)分别优化Morlet小波、Mexico小波和RBF函数的支持向量机模型参数,通过小波支持向量机模型建立反演参数与沉降值间的非线性映射关系。根据正交试验和均匀试验对需反演的岩土力学参数进行设计,结合有限元软件进行计算分析,得到学习样本和测试样本。分别采用Morlet小波、Mexico小波和RBF函数得出的预测结果和原始数据进行对比分析,发现采用Morlet小波核函数预测效果更佳。使用Morlet小波核函数预测的参数输入到Midas模型中计算建筑物最终沉降量,比较计算值与实际监测值,其相对误差不超过8.1%。研究结果表明,该方法在岩土工程参数的反演中具有良好的应用价值,对今后岩土力学参数的确定及校核提供了一种新方法。     

Slope reliability analysis using a support vector machine

The first-order second-moment method (FOSM) reliability analysis is commonly used for slope stability analysis. It requires the values and partial derivatives of the performance function with respect to the random variables for the design. Such calculations can be cumbersome when the performance functions are implicit. Implicit performance functions are normally encountered when the slope is geologically complicated and the limit equilibrium method (LEM) is used for the stability analysis.

To address this issue, this paper presents a support vector machine (SVM)-based reliability analysis method which combines the SVM with the FOSM. This method employs the SVM method to approximate the implicit performance functions, thus arriving at SVM-based explicit performance functions. The SVM method uses a small set of the actual values of the performance functions obtained via the LEM for complicated slope engineering. Using the SVM model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis using the FOSM. Examples are given to illustrate the proposed SVM-based slope reliability analysis. The results show that the proposed approach is applicable to slope reliability analysis which involves implicit performance functions.     

岩土工程可靠度分析的神经网络四阶矩法

针对岩土工程的功能函数强非线性且难以显式表达的特点,提出了基于人工神经网络的四阶矩法,充分利用了基本随机变量的统计信息。首先利用神经网络对结构的隐式功能函数进行拟合,求得基本随机变量在均值点处的功能函数值及其偏导数,然后利用泰勒级数展开的方法由基本随机变量的前四阶矩求得功能函数的前四阶矩,并借助于Pearson系统获得功能函数的更高阶矩。在此基础上,通过最大熵原理确定以功能函数各阶矩为约束的功能函数的概率密度函数,最后由一次积分得到结构的失效概率。通过数值算例和工程实例不同方法的对比分析,表明基于神经网络的结构可靠度分析四阶矩方法是可行的,有效的,能够满足岩土工程可靠度分析的要求。     

边坡可靠度分析的支持向量机法

提出了基于支持向量机（SVM）的边坡可靠度分析新算法。该方法采用均匀设计确定样本点,通过一定数量的确定性计算来训练SVM,拟合边坡的功能函数;采用一阶可靠度方法（FORM）和迭代算法优化SVM模型,获得可靠度指标和验算点信息;在SVM模型基础上进一步通过二阶可靠度方法（SORM）和蒙特卡罗模拟（MCS）计算边坡的失稳概率。以两个典型边坡为例,通过与其他方法比较,证明了该方法的准确性和高效性。结果表明：提出的在标准正态空间（U空间）中取样并构建SVM,在原始空间（X空间）中计算功能函数的算法,有效地解决了具有相关非正态分布变量的可靠度分析问题,并且可很容易扩展到SORM的计算。算例结果证明,该方法的精度高于FORM;而效率优于MCS。分析过程中,边坡安全系数计算和可靠度分析相互独立。因此,该方法既适用于具有显式功能函数的简单问题,也适用于需要软件计算安全系数的实际边坡问题。     

岩土工程可靠度分析的改进四阶矩方法

岩土工程可靠度分析中,功能函数往往呈隐式且具有强非线性性质,而目前最为实用的矩方法,如JC法、二次二阶矩法,主要适用于显式功能函数情形。为此,将高效的统计矩估计方法和可靠度分析的高阶矩法相结合,提出了一种岩土工程可靠度分析的改进四阶矩方法。首先,通过引入变量的独立化变换和线性变换将功能函数转换为参考变量的函数,并结合多变量函数的单变量降维近似方法和参考变量计算节点与权系数的确定方法,建立了功能函数前四阶矩的高效点估计法。然后,将上述统计矩与立方正态变换假设相结合,提出了易于实现的岩土工程可靠度分析的改进四阶矩方法。最后,由数学算例验证了统计矩估计方法的效率和精度,并通过经典的岩土工程算例验证了建议的改进四阶矩方法具有高效率、高精度且操作简单等特点。     

Probabilistic analysis of tunnel displacements based on correlative recognition of rock mass parameters

Displacement is vital in the evaluations of tunnel excavation processes,as well as in determining the postexcavation stability of surrounding rock masses.The prediction of tunnel displacement is a complex problem because of the uncertainties of rock mass properties.Meanwhile,the variation and the correlation relationship of geotechnical material properties have been gradually recognized by researchers in recent years.In this paper,a novel probabilistic method is proposed to estimate the uncertainties of rock mass properties and tunnel displacement,which integrated multivariate distribution function and a relevance vector machine(RVM).The multivariate distribution function is used to establish the probability model of related random variables.RVM is coupled with the numerical simulation methods to construct the nonlinear relationship between tunnel displacements and rock mass parameters,which avoided a large number of numerical simulations.Also,the residual rock mass parameters are taken into account to reflect the brittleness of deeply buried rock mass.Then,based on the proposed method,the uncertainty of displacement in a deep tunnel of CJPL-II laboratory are analyzed and compared with the in-situ measurements.It is found that the predicted tunnel displacements by the RVM model closely match with the measured ones.The correlations of parameters have significant impacts on the uncertainty results.The uncertainty of tunnel displacement decreases while the reliability of the tunnel increases with the increases of the negative correlations among rock mass parameters.When compared to the deterministic method,the proposed approach is more rational and scientific,and also conformed to rock engineering practices.     

Slope reliability analysis by updated support vector machine and Monte Carlo simulation

This paper presents a new methodology for slope reliability analysis by integrating the technologies of updated support vector machine (SVM) and Monte Carlo simulation (MCS). MCS is a powerful tool that may be used to solve a broad range of reliability problems and has therefore become widely used in slope reliability analysis. However, MCS often involves a great number of slope stability analysis computations, a process that requires excessive time consumption. The updated SVM is introduced in order to build the relationship between factor of safety and random variables of slope, contributing to reducing a large number of normal computing tasks and enlarging the problem scale and sample size of MCS. In the algorithm of the updated SVM, the particle swarm optimization method is adopted in order to seek the optimal SVM parameters, enhancing the performance of SVM for solving complex problems in slope stability analysis. Finally, the integrating method is applied to a classic slope for addressing the problem of reliability analysis. The results of this study indicate that the new methodology is capable of obtaining positive results that are consistent with the results of classic solutions; therefore, the methodology is proven to be a powerful and effective tool in slope reliability analysis.     

Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Rock mechanical parameters and their uncertainties are critical to rock stability analysis, engineering design, and safe construction in rock mechanics and engineering. The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass, but this does not consider the uncertainty. This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data, then integrating the monitored data, prior knowledge of geotechnical parameters,and a mechanical model of a rock tunnel using Markov chain Monte Carlo(MCMC) simulation. The proposed approach is illustrated by a circular tunnel with an analytical solution, which was then applied to an experimental tunnel in Goupitan Hydropower Station, China. The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables. The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements. It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically. Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data. Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering.     

基坑土钉支护可靠性分析优化算法

针对基坑工程中岩土参数存在随机性和变异性的特点,基于响应面重构法、遗传算法和禁忌搜索方法研究了土钉墙边坡可靠性分析方法。考虑土钉的加固作用,建立了适用于土钉墙边坡任意形状滑面安全系数计算的改进Morgenstern-Price法。基于响应面原理,将改进Morgenstern-Price法取代传统响应面法中的有限单元法来随机抽样构造响应面函数,建立了一种近似的土钉墙边坡可靠度计算方法。以土体的抗剪强度指标 、 为随机变量,提出了一种能同时确定土钉墙边坡最小可靠度指标 及相应最危险滑面的全局优化计算方法--土钉墙可靠性分析自适应禁忌搜索遗传算法（ATSGA）。结合算例,分别以土钉墙边坡的最小可靠度指标和最小中值安全系数为目标函数,采用ATSGA法搜索其相应的最危险滑动面,结果表明,二者相差较大。     

Probabilistic analysis of underground rock excavations using response surface method and SORM

Probabilistic analysis of underground rock excavations is performed using response surface method and SORM, in which the quadratic polynomial with cross terms is used to approximate the implicit limit state surface at the design point. The response surface is found using an iterative algorithm and the probability of failure is evaluated using the first-order and the second-order reliability method (FORM/SORM). Independent standard normal variables in U-space are chosen as basic random variables and transformed into correlated non-normal variables in the original space of random variables for constructing the response surface. The proposed method is first illustrated for a circular tunnel with analytical solutions considering Mohr–Coulomb (M–C) and Hoek–Brown (H–B) yield criteria separately. The failure probability with respect to the plastic zone criterion and the tunnel convergence criterion are estimated from FORM/SORM and compared to those obtained from Monte Carlo Simulations. The results show that the support pressure has great influence on the failure probability of the two failure modes. For the M–C model, the hypothesis of uncorrelated friction angle and cohesion will generate higher non-performance probability in comparison to the case of negatively correlated shear strength parameters. Reliability analyses involving non-normal distributions are also investigated. Finally, an example of a horseshoe-shaped highway tunnel is presented to illustrate the feasibility and validity of the proposed method for practical applications where numerical procedures are needed to calculate the performance function values.     

Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables

This paper proposes a stochastic response surface method for reliability analysis involving correlated non-normal random variables, in which the Nataf transformation is adopted to effectively transform the correlated non-normal variables into independent standard normal variables. Transformations of random variables that are often used in reliability analyses in terms of standard normal variables are summarized. The closed-form expressions for fourth to sixth order Hermite polynomial chaos expansions involving any number of random variables are formulated. The proposed method will substantially extend the application of stochastic response surface method for reliability problems. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed stochastic response surface method. The results indicate that the proposed stochastic response surface method can evaluate the reliability of rock slope stability involving correlated non-normal variables accurately and efficiently. Its accuracy is shown to be higher than that for the first-order reliability method, and it is much more efficient than direct Monte-Carlo simulation. The results also show that the number of collocation points selected should ensure that the Hermite polynomial matrix has a full rank so that different order SRSMs can produce a robust estimation of probability of failure for a specified performance function. Generally, the accuracy of SRSM increases as the order of SRSM increases.