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。     

基于概率密度演化的隔震结构随机地震响应

本文考虑地震动的随机性,运用概率密度演化方法对基础隔震结构的随机响应进行研究.上部结构与隔震层分别采用刚度退化的Bouc-Wen模型与Bouc-Wen模型,建立隔震结构的概率密度演化方程,直接应用四阶龙格-库塔方法迭代求解隔震结构的非线性的响应,得出隔震结构在8度罕遇地震下每层的位移概率.结果显示隔震结构较非隔震结构上部结构的位移大大地减小了,上部结构具有足够的安全性.结构整个概率密度演化过程显示了隔震结构的响应信息,概率密度演化方法能够有效评估隔震结构的抗震性能.     

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...     

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.     

基于小波分析的结构动力可靠度估计

利用小波分析估计的地震动局部谱,采用虚拟激励法求得了线笥结构非平衡随机响应,结合基于首超破坏准则的几种动力可靠度表达式,对结构的动力可靠度进行了讨论,并与平稳响应的情况进行了比较。     

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。     

石结构抗震可靠度的分析与应用

在文献［１］的基础上进一步探讨了石结构体系抗震动力反应分析的计算方法，给出了场地地震条件下结构在使用期间内抗震可靠度的应用实例。定量分析的结果表明，严格地控制结构高度、层数和砂浆强度等级等指标，是提高多层石结构抗震能力的有效措施。     

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。     

随机结构分析的扩阶系统方法(Ⅱ)——结构动力分析

本文论述随机结构系统在确定性时程激励下的分析方法。文中提供的扩阶系统动力方程的一般公式,适用于同时具有随机质量、随机阻尼、随机刚度参数的多自由度动力系统。文中并对此扩阶动力方程建议了基于线性加速度假定的递归聚缩算法。     

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.     

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.     

计算结构首次穿越时间概率密度函数的新方法

本文在M adsen等提出的积分方程方法基础上,采用单点FORM方法计算结构首次穿越问题中的条件穿越率、联合穿越率及首次穿越时间概率密度。提出的新方法计算简单,结果精确,适于进行脆性结构的首次穿越破坏分析。     

地震台站台基噪声功率谱概率密度函数Matlab实现

选取2015年四川数字测震台网中筠连和华蓥山地震台记录的垂直分向连续波形数据,利用Matlab软件,计算地震台站台基噪声功率谱概率密度函数,分析地震台站环境噪声特征。结果表明,台站环境噪声功率谱密度概率密度分布对地震事件波形（体波、面波）、人为噪声（台站周围人为活动、车辆及机器噪声等高频干扰）、系统瞬变（数据丢失、地震计小故障）以及仪器标定信号等反映较好。使用台基噪声功率谱概率密度函数方法,有利于监测地震台站数据记录,提高观测数据质量。     

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes.In the method,a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique,which transforms a correlated random vector into a vector of standard uncorrelated random variables,is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartl...     

随机动力系统最优控制准则研究

根据线性二次最优控制理论,给出了系统随机最优控制的控制律一般形式。从目标控制量的物理意义出发,提出了基于系统概率密度演化分析的最优控制准则,建立了递阶层次的演化过程控制准则类。以线性单自由度体系随机地震反应最优控制为例,分析了各控制准则类的权矩阵参数优化结果,并根据最优控制律进行了系统随机最优控制研究。结果表明,本文提出的系统随机最优控制的控制律确定方法可以对系统性态进行有效的控制。     

Identification of contaminant point source in surface waters based on backward location probability density function method

A backward location probability density function (BL-PDF) method capable of identifying location of point sources in surface waters is presented in this paper. The relation of forward location probability density function (FL-PDF) and backward location probability density, based on adjoint analysis, is validated using depth-averaged free-surface flow and mass transport models and several surface water test cases. The solutions of the backward location PDF transport equation agreed well to the forward location PDF computed using the pollutant concentration at the monitoring points. Using this relation and the distribution of the concentration detected at the monitoring points, an effective point source identification method is established. The numerical error of the backward location PDF simulation is found to be sensitive to the irregularity of the computational meshes, diffusivity, and velocity gradients. The performance of identification method is evaluated regarding the random error and number of observed values. In addition to hypothetical cases, a real case was studied to identify the source location where a dye tracer was instantaneously injected into a stream. The study indicated the proposed source identification method is effective, robust, and quite efficient in surface waters; the number of advection–diffusion equations needed to solve is equal to the number of observations.