工程结构可靠性分析的高阶矩法研究

提出了工程结构可靠性分析的高阶矩方法。主要是基于数值逼近原理，以切比雪夫正交函数族{Tk(x)}做基，利用功能函数的高阶矩信息，通过计算功能函数概率密度函数的逼近表达式，然后根据工程结构可靠性的一般表达式来计算结构的失效概率，进行可靠性分析。通过经典分布函数的数值检验和结构构件失效概率的计算结果比较，表明了该方法在理论上的正确性和工程中的实用性。     

代数双曲空间中拟Legendre基的应用

鉴于Legendre基等正交基在代数多项式空间中的广泛应用,论文在深入研究代数双曲空间的拟Legendre基性质的基础上,给出了其在反函数逼近和等距曲线逼近上的应用。利用多项式和双曲函数的混合多项式序列来逼近反函数,并通过实例证明给出方法的有效性;对基曲线的法矢曲线进行逼近,构造H-Bézier曲线的等距曲线的最佳逼近,这种方法直接求得逼近曲线的控制顶点,计算简单,截断误差小。     

二维联合概率密度函数构造方法及结构并联系统可靠度分析

该文目的在于研究二维联合概率密度函数构造方法对结构系统可靠度的影响规律。首先简要介绍了2种构造联合分布函数的近似方法:基于Pearson相关系数的近似方法P和基于Spearman相关系数的近似方法S。提出了基于直接积分方法的并联系统失效概率计算方法。算例结果表明2种近似方法计算的系统失效概率误差取决于系统失效概率的大小、功能函数的形式以及功能函数间相关程度。系统失效概率越小,近似方法计算的系统失效概率误差越大。当系统失效概率小于10?3量级时,近似方法计算的系统失效概率误差较大,工程应用中应该引起足够的重视。功能函数间负相关时近似方法的误差明显大于功能函数间正相关时的误差。此外,系统失效概率误差并不是随着功能函数间相关性的增加而单调增加。     

基于Copula函数的并联结构系统可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。     

联合分布函数构造的Copula函数方法及结构可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构可靠度的影响还缺少系统地研究。为此,提出了基于Copula函数的变量联合概率分布函数构造方法,并分析了不同Copula函数类型对结构可靠度的影响规律。首先,简要介绍了基于Copula函数的变量联合分布函数构造方法。其次,提出了构件失效概率计算的直接积分方法。最后以构件可靠度问题为例研究了Copula函数的类型对结构可靠度的影响规律。结果表明:不完备概率信息条件下构件可靠度是不唯一的,表征变量间相关性的Copula函数类型对构件可靠度具有明显的影响,不同Copula函数计算的构件失效概率存在明显的差别,这种差别随构件可靠指标的增大(或失效概率的减小)而增大。Copula函数尾部相关性对结构可靠度具有重要的影响。当功能函数的失效区域位于Copula函数尾部时,计算的失效概率明显比没有尾部相关性的Copula函数的失效概率大。基于功能函数的均值和标准差计算的可靠指标不能反映Copula函数的类型对结构可靠度的影响,而基于功能函数实际分布求得的失效概率则可以有效反映不同Copula函数对结构可靠度的影响。     

风速风向联合分布对结构风致疲劳寿命可靠性的影响

在进行结构风振疲劳寿命可靠性分析时,需要先求得建筑结构所在位置处的风速风向联合分布函数。本文首先对建筑结构附近两个气象站的气象资料进行统计分析,得到建筑结构位置处两个不同的风速风向联合分布函数,然后分析了不同的风速风向联合分布函数对一实际结构系统风振疲劳主要失效模式以及结构系统风振疲劳失效概率的影响。本文分析表明：用不同的风速风向联合分布函数计算风振疲劳寿命时会得到不同数目的主要失效模式,并且对结构系统的风振疲劳失效概率影响较大。     

基于失效概率积分和马尔可夫链模拟的可靠性灵敏度分析

可靠性灵敏度可以被表达为失效概率对基本随机变量分布参数的偏导数的形式,利用失效概率为基本变量的联合概率密度函数在失效域上的积分表达式,并且利用马尔可夫链能够高效模拟感兴趣区域样本的性质,一种针对单个失效模式和系统多个失效模式的可靠性灵敏度分析方法被提出。由于可靠性参数灵敏度可以表达为一个与联合概率密度函数相关的函数在失效域中的数学期望的形式,所提方法采用马尔可夫链来高效模拟失效域中的样本,进而采用样本均值替代总体均值的方法来得到可靠性灵敏度的估计值。与已有的基于Monte-Carlo模拟的可靠性灵敏度分析方法相比,所提方法在保证计算精度的基础上计算效率有显著提高,尤其是针对小失效概率的可靠性灵敏度分析问题。该算例充分说明了所提方法的合理可行性。     

结构-声强耦合腔振声响应预报研究

针对结构-声强耦合腔在边界激励下的响应预报问题，提出了一种基于能量原理的耦合系统响应计算方法。该方法从能量原理出发得到结构-声耦合腔拉格朗日函数形式的动力学方程，根据Rayleigh-Ritz法选择Legendre多项式级数分别将结构位移函数和声场声压函数展开，代入动力学方程并求解得到耦合腔的结构振动和声场声压响应。由于Legendre多项式满足L~2内积正交性，简化了方程中高重积分项，计算效率大大提升。以充水矩形腔为例，通过与已有研究、有限元结果对比验证了该方法的正确性。并分析了结构边界条件，背腔深度对系统响应的影响，结果表明：结构边界由强约束过渡到弱约束和背腔深度的减小都会导致响应峰值频率向低频偏移，同时背腔深度的减小还会导致由结构传递至声场的能量增加。     

联合分布函数蒙特卡罗模拟及结构可靠度分析

针对复杂极限状态方程可靠度计算问题,提出了基于理论联合分布函数以及2 种近似联合分布函数的结构失效概率蒙特卡罗模拟方法,并给出了计算流程图.采用2 个算例证明了所提方法的有效性.结果表明:所提的失效概率模拟方法的计算精度很高,尤其适用于复杂极限状态方程的可靠度计算问题.2 种联合分布函数近似构造方法得到的失效概率精度相当,近似方法与精确方法结果的差异随失效概率的减小而增大,而且随着变量间相关性的增加而增加.当失效概率小于10-3时,近似方法的失效概率误差较大.     

考虑状态模糊性时广义失效概率计算的矩方法

针对失效状态和安全状态具有模糊性的广义可靠性分析问题,提出了一种广义失效概率计算的矩方法。所提方法首先将广义失效概率的积分区域依据功能函数的取值离散化,在离散化的积分区域中,极限状态函数对模糊失效域的隶属函数近似保持为常数,从而将模糊可靠性问题转化为一般的随机可靠性问题,进而可以利用近似的矩方法求得广义失效概率。该文给出了所提方法的实现步骤和原理,算例结果表明所提方法对于中低维问题具有很高的精度和效率。     

基于概率密度演化理论的结构抗震可靠性分析

运用随机过程的正交展开方法,将地震动加速度过程表示为由10个左右的独立随机变量所调制的确定性函数的线性组合形式。结合概率密度演化方法和等价极值事件的基本思想,研究了非线性结构的抗震可靠度分析问题。以具有滞回特性的非线性结构为例,对某一多自由度的剪切型框架结构进行了抗震可靠性分析。结果表明：按照复杂失效准则计算的结构抗震可靠度较之结构各层抗震可靠度均低。这一研究为基于概率密度函数的、精细化的抗震可靠度计算提供了新的途径。     

A semi-analytical simulation method for reliability assessments of structural systems

A semi-analytical simulation method is proposed in this paper to assess system reliability of structures. Monte Carlo simulation with variance-reduction techniques, systematic and antithetic sampling, is employed to obtain the samples of the structural resistance in this method. Variance-reduction techniques make it possible to sufficiently simulate the structural resistance with less runs of structural analysis. When resistance samples and its moments determined, exponential polynomial method (EPM) is used to fit the probability density function of the structural resistance. EPM can provide the approximate distribution and statistical characteristic of the structural resistance and then the first-order second-moment method can be carried out to calculate the structural failure probability. Numerical examples are provided for a structural component and two ductile frames, which illustrate the method proposed facilitates the evaluation of system reliability in assessments of structural safety.     

小样本岩土参数概率分布的正交多项式推断方法

实际工程中的岩土参数往往是小样本情况,利用经典概率分布（如正态分布、对数正态分布、贝塔分布、威布尔分布等）推断其最优概率类型时,存在样本分布区间不匹配、限定范围选择和单峰值概率分布函数无法反映参数随机波动性等三个未解决的基本问题。为此,选取了五种不同取值区间,利用10组小样本岩土参数的实测样本,以勒让德多项式和第二类切比雪夫多项式对岩土参数的概率分布函数进行推断,利用K-S检验法对所得的概率分布函数进行检验。通过区间取值匹配、拟合检验值和累积概率值的比较,提出了以3σ原则为基础,同时考虑偏度进行调整的积分区间确定标准。研究结果表明:以有限比较法原理确定最优概率分布的阶数,所得最优概率分布能够反映小样本数据的随机波动;而且正交多项式推断方法所得概率分布函数的检验值均小于传统分布的检验值,说明所得分布更加符合岩土参数的实际情况。     

Hybrid perturbation-Galerkin methods for structural reliability analysis

A major challenge in the reliability analysis of complex structures is to determine the response function or surface from which the limit state function can be established and hence the failure probability of the structure can be predicted. The intention of this paper is to propose a new class of hybrid perturbation-Galerkin methods to determine the response function (surface) of the structure. The proposed methods, mainly including single-variable and double-variable approximations, are based on a combination of the perturbation technique and Bubnov–Galerkin projection, where various orders of summation terms of power polynomial expansions are used as the Galerkin trial functions or basis vectors. A series of examples is provided to demonstrate the accuracy and efficiency of the proposed method by comparison with various existing methods. It is found from the numerical examples that with a significantly lower computational effort with respect to the existing reliability methods, very accurate results can be obtained by the proposed methods.     

Wave propagation in multilayered piezoelectric spherical plates

This paper proposes an improvement of the Legendre polynomial series method to solve the harmonic wave propagation in multilayered piezoelectric spherical plates, which are used in point-focusing transducers. The conventional Legendre polynomial method can deal with the multilayered structures only when the material properties of two adjacent layers do not change significantly and cannot obtain correctly normal stress and normal electric displacement shapes unlike the proposed improved orthogonal polynomial approach which overcomes these drawbacks. Detailed formulations are given to highlight its differences from the conventional Legendre polynomial approach. Through the comparisons of numerical results given by an exact solution (obtained from the reverberation-ray matrix method), and by the conventional polynomial approach and the improved polynomial approach, the validity of the proposed approach is illustrated. The influences of the radius-to-thickness ratio on dispersion curves, stress and electric displacement distributions are discussed. It is found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: radius-to-thickness ratio, wave speed, and position of the component material.     

一种新的体系可靠度的近似计算方法

提出了一种新的体系可靠度的近似计算方法。首先将一个线性失效模式在另一线性失效模式失效前提下的条件失效模式近似为一个等价的线性失效模式,然后利用条件概率的基本原理并结合所推导的等价失效模式的理论表达式,提出了一种并联体系可靠度的近似计算方法,从而将求解一组失效模式交集失效概率的复杂问题转化为求解一组线性等价失效模式失效概率乘积的简单问题。由于串联体系以及串并联混合体系均可表示为一系列失效模式交集的线性组合,因此方法可以很方便地应用于串联体系以及串并联混合体系的体系可靠度计算。此算法计算过程简单、计算量小、计算精度高,适合于大型结构体系的体系可靠度计算。     

A multi-mode failure boundary exploration and exploitation framework using adaptive kriging model for system reliability assessment

Various adaptive reliability analysis methods based on surrogate models have recently been developed. A multi-mode failure boundary exploration and exploitation framework (MFBEEF) was proposed for system reliability assessment using the adaptive kriging model based on sample space partitioning to reduce computational cost and use the characteristics of the failure boundary in multiple failure mode systems. The efficiency of the adaptive construction of kriging model can be improved by using the characteristics of the center sample of the small space to represent the characteristics of all samples in the small space. This method proposes a failure boundary exploration and exploitation strategy and a convergence criterion based on the maximum failure probability error for a system with multiple failure modes to adaptively approximate the failure boundary of a system with multiple failure modes. A multiple-failure-mode learning function was used to identify the optimal training sample to gradually update the kriging model during the failure boundary exploration and exploitation stages. In addition, a complex failure boundary-oriented adaptive hybrid importance sampling method was developed to improve the applicability of the MFBEEF method to small failure probability assessments. Finally, the MFBEEF method was proven to be effective using five system reliability analysis examples: a series system, a parallel system, a series–parallel hybrid system, a multi-dimensional series system with multiple failure modes, and an engineering problem with multiple implicit performance functions.     

基于节点冲切破坏的板柱结构连续倒塌可靠性分析

从结构体系可靠度的角度认识钢筋混凝土板柱结构的抗连续倒塌性能,用Monte-Carlo连续成组抽样方法对以节点冲切破坏为主的板柱结构连续倒塌进行可靠度分析。在建立板柱节点功能函数的基础上,推演了抗冲切承载力分布及荷载基本变量分布和荷载效应组合的方法。通过计算初始条件下任意一个板柱节点失效的概率和一个节点失效条件下其他节点失效的条件概率,分析了不同位置板柱节点在抗连续倒塌中的重要性以及板柱结构的抗连续倒塌鲁棒性指标。结果表明:底层中柱节点冲切失效最容易引起其他节点的连续性破坏及倒塌,按我国规范设定了柱顶贯通受压钢筋的板柱结构鲁棒性指标比较高。     

A New Adaptive Response Surface Model for Reliability Analysis of 2.5D C/SiC Composite Turbine Blade

In order to calculate the failure probability of complex structures such as a 2.5D/SiC composites turbine blade and improve the structure safety, a new adaptive model of Response Surface (RS) analysis has been developed in this paper, which can improve the computational efficiency of structural failure problem while ensure the accuracy. The Gaussian Process Regression (GPR) theory was used to establish the RS and reconstruct the performance function of structure. And, an Adaptive Latin hypercube Sampling (ALHS) strategy was adopted in the process of establishing and correcting the RS. Finally the Direct Simulation Monte Carlo(DSMC)was utilized to calculate the failure probability of the performance function replacing the complex structure. Two numerical examples were calculated to validate the accuracy and computational efficiency of the proposed method. Additionally the finite element stress analysis results of 2.5D C/SiC composite turbine blade were used to structural reliability analysis by the proposed method. The approach in this paper provides a new way to evaluate the risk of the complex structures.     

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.