基于概率密度演化的渡槽结构抗震分析

应用随机过程的正交展开方法,将地震动加速度过程展开为标准正交基函数与标准正交随机变量的线性组合形式。在此基础上采用随机函数的思想,将正交展开式中的标准正交随机变量表达为基本随机变量的函数形式,从而实现用一个基本随机变量来表达原地震动过程的目的。结合地震动过程的正交展开 随机函数模型与概率密度演化方法,对某大型渡槽结构进行随机地震反应分析与抗震可靠度计算;重点研究空槽和三槽有水等四种工况下渡槽结构控制点位移以及控制截面内力的随机地震反应与可靠度,进而获得渡槽结构控制点和控制截面的地震反应概率信息。     

基于概率密度演化的基础隔震结构随机响应分析

针对抗震结构和基础隔震结构,应用概率密度演化方法对其进行多遇地震作用下的线性随机响应分析。通过引入工程地震动物理随机函数模型,采用数论选点法对多维外荷载随机变量进行离散代表点的生成并求得其赋得概率,利用离散代表点合成地震动加速度时程样本作为输入结构的随机激励,对于每条地震波,相当于对结构进行确定性动力反应分析。在求得结构响应及其相关导数后,应用TVD差分格式求解广义概率密度演化方程即可得到所求响应的时变概率密度及其演化。结果表明：基础隔震结构在随机地震作用下相比抗震结构具有良好的减震性能,隔震层的设置能够减小结构位移响应的标准差,减少了结构响应的离散型;概率密度演化方法不仅能够给出结构响应的二阶统计矩,还能全面地反映结构响应的时变概率信息,位移响应的概率密度函数分布不服从正态分布或其他常用分布,且随着时间演化。     

随机地震作用下特高压换流站阀厅非线性动力可靠度研究

通过模态分析研究了抗震设防烈度为8度（0.3g）的混合结构与全钢结构两种阀厅结构方案的动力特性,基于地震动的地震学模型与概率密度演化法分析了全钢阀厅的非线性随机动力可靠度,根据阀厅角柱柱顶位移响应得到了全钢阀厅动力影响的概率密度曲面及典型时刻的概率密度曲线。研究结果表明:阀塔对结构整体刚度影响较小,工程中可采用无阀模型进行简化计算;高烈度设防地区,推荐采用结构布置相对规则的钢结构方案;随机动力分析相比于确定性分析更能反应地震作用下阀厅动力响应的客观规律;阀厅钢结构方案在罕遇地震作用下可靠度较高,结构安全可靠。     

全非平稳地震作用的结构随机反应与可靠度分析

在平稳地震动过程的Clough-Penzien功率谱基础上,采用林家浩非均匀调制函数建立全非平稳地震动过程的演变功率谱。根据我国现行的《建筑抗震设计规范》进行全非平稳地震动演变功率谱的参数识别研究。应用非平稳随机过程模拟的谱表示-随机函数方法,生成建筑结构抗震设计所用地震动的代表性样本集合。通过代表性样本集合的二阶统计值及地震反应谱与目标值的拟合比较,验证本文方法的有效性。最后结合概率密度演化方法,进行以层间位移角为控制准则的结构随机地震反应分析与抗震可靠度计算。     

随机地震作用下隧道结构抗震可靠度研究

地震引起的地面运动是非常复杂的随机过程,具有时间和频率非平稳的特性。用确定性方法对隧道结构抗震性能的评价未能考虑地震动的随机性。本文提出采用概率密度演化法计算隧道结构在随机地震作用下变形响应的概率分布,并引入变形指标计算其在随机地震作用下的可靠度以评估抗震性能。首先根据概率守恒原理的随机事件描述建立概率密度演化方程;其次,根据相应的初始条件与边界条件,采用总变差不增(TVD)格式的有限差分方法求解方程;最后求和得到隧道结构变形指标的概率分布并依据指标限值给出可靠度。结果表明,在随机地震作用下,隧道结构变形响应的概率分布与地震动强度随时间变化规律一致。采用不同变形指标计算得到的可靠度存在差异,直径变形率对应的结构可靠度为0.752 1,隧道倾斜角对应的结构可靠度为0.875 0。     

基于非平稳随机地震动模型的重力坝抗震可靠度分析

基于正交展开的非平稳随机地震动模型,并考虑混凝土材料的非线性和坝体与库水之间的流固耦合,对印度Koyna重力坝进行有限元分析,得到坝顶水平位移和坝颈拉应力,结合概率密度演化方法和等价极值事件的思想,获得丰富的概率信息。这为坝体结构的随机地震反应分析和可靠度研究提供新的途径。     

随机结构动力矩阵的线性表示与线性截断

随机结构地震反应分析是地震工程研究在九十年代的热点课题之一。文中论述了随机结构分析中动力矩阵的线性表示与线性截断方式。本文，提出了虚拟结构方法，为随机结构动力矩阵的形成打开了方便之门。     

基于不同参数的基础隔震结构非线性概率密度演化

为了研究不同设计参数条件下基础隔震结构非线性响应的概率密度演化特征,采用两质点模型来模拟基础隔震结构,隔震层与上部结构分别采用Bouc-Wen模型与刚度退化的Bouc-Wen模型来描述其非线性特征,运用概率密度演化理论,进行隔震结构非线性随机地震响应的概率密度演化分析。采用基于物理的随机地震动模型生成人工地震动,提出基础隔震结构非线性随机地震响应的概率密度演化分析的基本步骤。通过改变基础隔震结构的设计参数,同时考虑激励的随机性,研究基础隔震结构非线性随机地震响应的概率密度演化规律。结果表明,基础隔震结构的阻尼比、周期比和屈重比取合理范围,能使隔震结构上部和下部的位移可控。     

多高层建筑结构层间位移和层剪力的动力可靠度计算

在虚拟激励法的基础上推导了多高层建筑结构剪切层模型在地震作用下层间相对位移和层地震剪力的自功率谱密度函数的解析表达,通过数值积分获得层间相对位移和层地震剪力的各阶谱矩和标准差,基于随机动力响应过程跨越安全界限次数为泊松过程和两态马尔可夫过程的假设,计算了层间相对位移和层地震剪力的动力可靠度,并用Matlab语言编制了动力可靠度的计算程序.算例表明该方法是高效的和有效的.     

随机结构动力可靠度估计算法的对比分析

对比分析了随机结构动力可靠度计算的三种估计算法.渐进展开法是基于Laplace算法对概率积分进行渐进估计的,此法通过计算最大被积分式值对应点,并将其代入概率积分的渐进估计表达式求解失效概率.由于概率积分的主要贡献来自于最大被积分式值对应点的周围,因此本文的重要抽样法假定重要抽样函数的最大似然值等于最大被积分式值对应点值.极值分布-泰勒展开法首先通过结构随机参数的极值分布函数给出失效概率的表达式,随后利用泰勒展开法对失效概率进行估计,其中采用中心差分法对极值分布函数的梯度进行估算.最后应用三种算法和Monte Carlo法对受高斯白噪声激励作用的单自由度随机结构进行了计算,结果表明三种方法不但运算简便,而且对比Monte Carlo法计算效率有显著提高.     

Extreme value distribution and reliability of nonlinear stochastic structures

A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.     

动态随机有限元法

本提出分析了不确定性结构随机动力响应的一种新的数据方法－－动态随机有限元法。经的特点是引入反映结构振动特征的动态形函数,中引出了相应的计算列式。算例表明,本方法的计算效率及数值精度均优于一般的随机有了限元法,具有应用前景。     

模糊检测数据下服役钢筋混凝土桥梁的动态可靠度评估

针对服役桥梁的可靠性评估中无法基于不完备、缺陷的检测数据准确获得变量统计特征的问题,提出了模糊检测数据下既有钢筋混凝土桥梁的动态可靠性分析方法。以氯盐腐蚀下引起钢筋截面积减弱,导致结构承载能力和可靠性能降低为主线,采用隶属函数来描述缺陷信息,通过等概率原理将模糊变量转化成当量随机变量,进而基于任意概率密度函数的Monte Carlo抽样方法,分析了一座实桥的动态可靠指标变化情况。结果表明：模糊检测数据的均值对钢筋截面减弱影响较大,其中保护层厚度均值对其影响最为显著,这同样表现在对可靠指标的影响中;变量模糊幅度的影响较小,在确定隶属函数的过程中,更应注重隶属函数的均值。     

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.     

Probability density evolution method for seismic liquefaction performance analysis of earth dam

To investigate the seismic liquefaction performance of earth dams under earthquake loading, we present a new methodology for evaluating the seismic response of earth dams based on a performance‐based approach and a stochastic vibration method. This study assesses an earthfill dam located in a high‐intensity seismic region of eastern China. The seismic design levels and corresponding performance indexes are selected according to performance‐based criteria and dam seismic codes. Then, nonlinear constitutive models are used to derive an array of deterministic seismic responses of the earth dam by dynamic time series analysis based on a finite element model. Based on these responses, the stochastic seismic responses and dynamic reliability of the earth dam are obtained using the probability density evolution method. Finally, the seismic performance of the earth dam is assessed by the performance‐based and reliability criteria. Our results demonstrate the accuracy of the seismic response analysis of earth dams using the random vibration method. This new method of dynamic performance analysis of earth dams demonstrates that performance‐based criteria and reliability evaluation can provide more objective indices for decision‐making rather than using deterministic seismic acceleration time series as is the current normal practice. Copyright © 2016 John Wiley & Sons, Ltd.     

RESPONSE ANALYSIS FOR FUZZY STOCHASTIC DYNAMICAL SYSTEMS WITH MULTIPLE DEGREES OF FREEDOM

Most real-life structural/mechanical systems have complex geometrical and material properties and operate under complex fuzzy environmental conditions. These systems are certainly subjected to fuzzy random excitations induced by the environment. For an analytical treatment of such a system subjected to fuzzy random excitations, it becomes necessary to establish the general theory of dynamic response of a system to fuzzy random excitations. In this paper, we extend the work published in Reference [1], and discuss the case of Multi-Degree-of-Freedom (MDF) fuzzy stochastic dynamical systems. The theory of the response, fuzzy mean response and fuzzy covariance response of multi-degree-of-freedom system to fuzzy random excitations in the time domain and frequency domain is put forward. Two cases to determine the fuzzy response statistics of the fuzzy stochastic dynamical system with multiple degrees of freedom are discussed. Two examples are considered in order to demonstrate the rationality and validity of the theory. © 1997 by John Wiley & Sons, Ltd.