基于随机有限元法的可靠性分析方法概述

基于随机有限元法的可靠性分析方法研究现状,介绍4种常用的随机有限元法:直接蒙特卡洛法、Taylor展开随机有限元法、摄动随机有限元法和Neumann展开随机有限元法,重点介绍了5种基于随机有限元法的可靠性分析方法:应力-强度积分法、功能函数积分法、可靠度指标计算法、随机抽样法和响应面法,并对可靠性研究需要开展的下一步工作进行了探讨。

基于TANA函数的非概率可靠度分析方法

建立一种基于TANA(Two-Point Adaptive Nonlinear Approximation)函数的高效稳定非概率型可靠度分析方法。首先,对随机变量采用凸集合非概率多椭球模型进行描述,在可靠度指标法框架下,采用增强混沌控制(Enhanced Chaos Control,ECC)方法,在逼近最佳设计点时,利用两点自适应非线性逼近的TANA2函数拟合强非线性的功能函数,减少了可靠度分析中功能函数的调用次数,有效提高了算法的效率及稳定性。还对不同非线性程度的功能函数进行了可靠度求解以及优化的算例验证。

缓冲包装不确定性的可靠设计与优化

针对缓冲包装防护结构的厚度不确定性问题,本文得到厚度的随机统计分布特性,并构造了缓冲包装防护结构的可靠度优化设计概率模型。探讨了传统可靠度指标方法在优化过程中出现收敛失败和数值奇异的原因,通过定义的主动集合策略对可靠度指标进行修正,提出了基于主动集合策略的可靠度优化设计方法,克服了传统可靠度指标方法方法的缺点。通过对包装系统跌落过程中的能量分析,建立了缓冲包装防护结构动态非线性本构关系的数学模型。并采用本文提出的ASS方法对概率模型进行数值求解,并通过蒙特卡罗方法(Monte-Carlo simulation,MCs)方法验证了最优解。本文的研究方法可为缓冲包装防护结构的设计提供一定的理论依据。

基于合理验算点失效相关机械系统可靠性分析及仿真

以共因失效为研究背景,根据改进的一次二阶矩原理,探讨多重联合失效概率近似计算时合理验算点的选择及其确定方法,从共因失效的内在机理出发,揭示共因载荷的分散性是引起机械系统零件间失效相关性的本质原因,并建立失效相关系数及其主要影响因素之间的近似关系。针对典型机械系统,给出系统可靠度计算的一般表达式,利用条件可靠指标法,通过不断降维实现系统可靠度求解,并给出其计算方法。在此基础上编制Matlab程序,实现机械系统可靠性分析的计算机仿真。最后,通过算例进一步验证该方法的可行性、有效性。

抗剪强度分项系数的标准差反馈标定法

基于可靠度理论的分项系数极限状态设计方法是当今岩土工程设计的一个趋势,分项系数的标定是确定设计参数的关键。岩土材料强度分项系数需反映材料参数的变异性,现有理论方法如安全系数校核法、一次二阶矩校核法、验算点校核法等理论标定方法,没有明确说明分项系数如何降低参数不确定性的影响,理论基础有待进一步完善。因此,提出岩土材料强度分项系数的标准差反馈标定法,该方法在目标可靠度的基础上,通过观察均值的调整对标准差调整的抵消作用,确定材料强度分项系数,由此确定的分项系数能充分反映强度参数的离散性。通过算例对该标定方法的实现进行了说明,并与验算点校核法进行了对比分析,指出标准差反馈标定法比验算点校核法更加合理。

概率约束评估的功能度量法及其MATLAB实现

基于可靠性的结构优化通常表述为在概率约束下最小化目标函数,其中概率约束的评定可以通过两种方法进行——传统的可靠指标法和最近被提出的功能度量法。本文简单介绍了功能度量法,明确概率功能度量的求解表述为许可可靠指标下功能函数极小值的优化问题。然后利用MATLAB强大的优化功能求解该优化模型,从而得到概率功能度量。最后给出算例,证明了可靠指标法与功能度量法在评价概率约束时的等效性,同时验证了功能度量法比可靠指标法更稳定,较少依赖于随机变量的概率分布类型。可靠指标求解的正确性都用Monte-Carlo模拟进行了验证。

基于GPR的PC连续梁桥体系可靠度分析

为解决PC连续梁桥体系可靠度分析过程中存在各失效模式下的极限状态函数不能显式表达的问题,本文提出一种基于高斯过程回归(GPR)和可靠指标矢量法的体系可靠度计算方法。该方法通过有限元分析软件得到少量训练样本,通过训练后的高斯过程回归模型逼近结构真实的极限状态函数,实现小样本条件下功能函数的显式表达,然后结合JC法和可靠指标矢量法求解桥梁体系可靠指标。本文以湖北省荆州市长湖特大桥为例验证了该方法具有较高的计算精度。

Reliability analysis for seismic stability of tunnel faces in soft rock masses based on a 3D stochastic collapse model

A new horn failure mechanism was constructed for tunnel faces in the soft rock mass by means of the logarithmic spiral curve. The seismic action was incorporated into the horn failure mechanism using the pseudo-static method. Considering the randomness of rock mass parameters and loads, a three-dimensional (3D) stochastic collapse model was established. Reliability analysis of seismic stability of tunnel faces was presented via the kinematical approach and the response surface method. The results show that, the reliability of tunnel faces is significantly affected by the supporting pressure, geological strength index, uniaxial compressive strength, rock bulk density and seismic forces. It is worth noting that, if the effect of seismic force was not considered, the stability of tunnel faces would be obviously overestimated. However, the correlation between horizontal and vertical seismic forces can be ignored under the condition of low calculation accuracy.

Reliability analysis of earth slopes using hybrid chaotic particle swarm optimization

A numerical procedure for reliability analysis of earth slope based on advanced first-order second-moment method is presented,while soil properties and pore water pressure may be considered as random variables.The factor of safety and performance function is formulated utilizing a new approach of the Morgenstern and Price method.To evaluate the minimum reliability index defined by Hasofer and Lind and corresponding critical probabilistic slip surface,a hybrid algorithm combining chaotic particle swarm optimization and harmony search algorithm called CPSOHS is presented.The comparison of the results of the presented method,standard particle swarm optimization,and selected other methods employed in previous studies demonstrates the superior successful functioning of the new method by evaluating lower values of reliability index and factor of safety.Moreover,the presented procedure is applied for sensitivity analysis and the obtained results show the influence of soil strength parameters and probability distribution types of random variables on the reliability index of slopes.

Optimization design of piles subjected to horizontal loads based on reliability theory

Based on reliability theory,a general method for the optimization design of piles subjected to horizontal loads is presented.This method takes into consideration various uncertainties caused by pile installation,variability of geotechnical materials from one location to another,and so on.It also deals with behavior and side constraints specified by standard specifications for piles.To more accurately solve the optimization design model,the first order reliability method is employed.The results from the numerical example indicate that the target reliability index has significant influence on design parameters.In addition,the optimization weight increases with the target reliability index.Especially when the target reliability index is relatively large,the target reliability index has significant influence on design weight of piles.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstem-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine （SVM） was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c andfon reliability index of slopes was taken into discussion and the changing trend was observed.

Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism

Based on nonlinear failure criterion,a three-dimensional failure mechanism of the possible collapse of deep tunnel is presented with limit analysis theory.Support pressure is taken into consideration in the virtual work equation performed under the upper bound theorem.It is necessary to point out that the properties of surrounding rock mass plays a vital role in the shape of collapsing rock mass.The first order reliability method and Monte Carlo simulation method are then employed to analyze the stability of presented mechanism.Different rock parameters are considered random variables to value the corresponding reliability index with an increasing applied support pressure.The reliability indexes calculated by two methods are in good agreement.Sensitivity analysis was performed and the influence of coefficient variation of rock parameters was discussed.It is shown that the tensile strength plays a much more important role in reliability index than dimensionless parameter,and that small changes occurring in the coefficient of variation would make great influence of reliability index.Thus,significant attention should be paid to the properties of surrounding rock mass and the applied support pressure to maintain the stability of tunnel can be determined for a given reliability index.

Resistance Partial Factor and Reliability of Cast Ball-and-Socket Support Joint

Considering the uncertainty of material performance, geometric characteristic and analysis method, the analysis of statistical parameters of the resistance of cast ball-and-socket support joints and the reliability analysis are carried out by JC method （improved first-order second-moment method） based on the relevant experimental data. Results show that the resistance partial factor of the joint increases with the increase of the reliability index. The resis- tance partial factors are suggested corresponding to the reliability index under different load combinations. Moreover, the suggested resistance partial factor is adopted in reliability design, and it is found that the reliability index of the joint is larger than the target reliability index. The optimal load combination is the one in which live load plays an im- portant control role. Finally, based on the suggested resistance partial factors, the reliability analysis of cast bail-and- socket support ioints of a proiect is conducted.

Research on Risk Assessment of City Natural Disaster based on Neural Network

Aiming at the selection of fuzzy AHP and fuzzy DH methods in the previous studies, this paper evaluate the qualitative index system using expert questionnaire, the self-learning BP neural network model to construct the index of system, and complete the establishment of model, in order to avoid the serious subjectivity, and using statistical and measurement methods test the reliability index, analyze the validity of the evaluation index system and completeness. Finally, the paper validate the practicability of the model.

Finite element reliability analysis of slope stability

The method of nonlinear finite element reliability analysis (FERA) of slope stability using the technique of slip surface stress analysis (SSA) is studied. The limit state function that can consider the direction of slip surface is given, and the formula-tions of FERA based on incremental tangent stiffness method and modified Aitken accelerating algorithm are developed. The limited step length iteration method (LSLIM) is adopted to calculate the reliability index. The nonlinear FERA code using the SSA technique is developed and the main flow chart is illustrated. Numerical examples are used to demonstrate the efficiency and robustness of this method. It is found that the accelerating convergence algorithm proposed in this study proves to be very efficient for it can reduce the iteration number greatly, and LSLIM is also efficient for it can assure the convergence of the iteration of the reliability index.