随机结构动力可靠度分析的极值概率密度方法

提出了随机结构动力可靠度分析的极值概率密度方法。基于概率密度演化的基本思想,构造一个虚拟随机过程,使得随机结构动力反应的极值为该虚拟随机过程的截口随机变量。进而．采用概率密度演化方法,建立概率密度演化方程并求解给出随机结构动力反应的极值分布。在安全域内积分即可给出结构动力可靠度,当安全界限为随机变量时,采用这一方法几乎不增加额外的工作量,与随机模拟结果的比较表明,本文建议方法具有良好的精度和效率。     

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...     

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.     

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...     

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。     

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。     

Evaluating the effect of land development on sediment transport using a probability density function

An important problem in sedimentation analysis is the development of a channel section that preserves, as best as possible, the current sedimentation regime even though the flood frequency tendencies have been altered due to land development within the catchment. In order to accomplish this task, a methodology is needed that estimates sediment transport capacity for various channel configurations. Such a procedure is described which allows the computation of the total sediment transport capacity for each of several T-year return frequency runoff hydrographs. This information is used to obtain an approximate probability distribution for the total sediment transport capacity, and the mean and standard deviation of this distribution are computed.Comparing the results for the catchment in its present state with a future developed state, using a selection of new channel parameters, indicates how to improve the channel to control changes in sedimentation due to development. The analysis procedure provides a basis for estimating a new channel configuration such that the new flow conditions retain, as best as possible, the existing condition sedimentation effects, and hence retain the natural sediment supply and transport trends even though runoff flow rates have changed due to land development within the catchment.The results of Wilson Creek are typical of the several sites examined, see Table 3 below. The T=2, T=5, T=25, and T=100 year values for total sediment transport capacity, in kilotons, are 6.9, 39.4, 61.3, and 96.7 with a mean of 17.1 and standard deviation of 19.3. After development with no change in the channel the respective values increase to: 17.9, 84.6, 128.1, and 258.0 with a mean of 39.1 and standard deviation of 44.3. A new channel can be constructed which will reduce these sediment transport capacity values, after development, to 5.2, 41.0, 62.0, and 124.8 with a mean of 17.4 and standard deviation of 22.0.     

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.     

工程结构地震破坏概率矩阵分析

本文提出了一种计算工程结构地震坡坏概率矩阵的方法，建立了地震地面运动模型和结构分析模型，对结构进行了随机地震反应分析，并获得了结构随机分应的统计量，进而采用双参数的结构破坏模型，给出了教育处结构地震破坏概率的表达式，利用此方法计算了一座按8度要求设计的钢筋混凝土框架型，给出了计算结构地震坡坏概率的表达式，利用此方法计算了一座按8度要求的钢筋混凝土框架结构的地震破坏概率矩阵，本文提出了方法可以在确定抗震设防标准和进行震害预测时采用。     

索杆张力结构的动力特性和非线性地震响应分析

索杆张力结构是以拉索和压杆为基本单元构成的自平衡体系,并通过预应力提供结构刚度的一类新型空间结构。通过修正的拉格朗日方程推导了索杆张力结构的增量运动方程,且采用Ne—wmark常平均加速度法求解方程,在每个时间步内应用了修正的牛顿拉斐逊法。应用此方法对索杆张力柱面网壳的自振特性及其在地震作用下的非线性动力响应进行了数值模拟分析。     

逐时降雨概率密度的适用函数与理论密度函数

暴雨强度公式在水文、气象、工程设计等各领域都是非常关注的问题,而常用降雨概率分布函数的适用性欠缺,理论分布函数一直处于争鸣之中。从逐时降雨概率密度函数的适用性分析入手,有利于发现普适且恰当的理论密度函数。本文从我国暴雨洪涝灾害易发区中沿30°N选取4个经纬度长方形区域(雅安附近、鄂西南、江汉平原南部、杭州湾西),并在其南、北各选一对比分区(海南岛、郑州),对6个分区内降雨资料直接采用全样本,统计逐时降雨的三类概率密度经验函数,对照这些函数的特性,从理论上分析了众多分布函数的适用性,筛选适用函数并进行拟合试验,优选出理论密度函数。研究结果表明:三参广义伽玛函数拟合误差最小,而两参广义正态函数更恰当、被首推为理论密度函数;拟合参数寻优时的目标函数综合了乘性与加性误差模型,能使拟合曲线兼顾头尾;本研究有别于极值降雨概率分布中仅采用极少部分样本的方法,采用降雨概率密度方法替代传统的年极值法,使重现期计算更准确有效,能提高暴雨强度公式的科学性,拟合的高精度与函数的普适性有望解决降雨概率分布模型统一的问题。     

平稳随机激励下随机结构非线性动力响应分析

为了在结构强震灾变过程模拟中正确反映结构参数的随机性并准确界定结构失效模式,提出一种平稳随机激励下随机结构非线性动力响应分析的简化方法.首先运用点估计法将复合非线性随机系统转化为一系列平稳随机激励下的确定性非线性结构,然后再应用成熟的等效线性化方法计算出平稳随机激励下非线性结构动力响应的各阶矩.文末进行了算例分析与验证...     

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。     

随机地震反演关键参数优选和效果分析(英文)

随机地震反演技术是将地质统计理论和地震反演相结合的反演方法,它将地震资料、测井资料和地质统计学信息融合为地下模型的后验概率分布,利用马尔科夫链蒙特卡洛(MCMC)方法对该后验概率分布采样,通过综合分析多个采样结果来研究后验概率分布的性质,进而认识地下情况。本文首先介绍了随机地震反演的原理,然后对影响随机地震反演效果的四个关键参数,即地震资料信噪比、变差函数、后验概率分布的样本个数和井网密度进行分析并给出其优化原则。资料分析表明地震资料信噪比控制地震资料和地质统计规律对反演结果的约束程度,变差函数影响反演结果的平滑程度,后验概率分布的样本个数决定样本统计特征的可靠性,而参与反演的井网密度则影响反演的不确定性。最后通过对比试验工区随机地震反演和基于模型的确定性地震反演结果,指出随机地震反演可以给出更符合地下实际情况的模型。     

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。     

Bivariate Gaussian mixture–based equivalent linearization method for stochastic seismic analysis of nonlinear structures

To address challenges in stochastic seismic analysis of nonlinear structures, this paper further develops a recently proposed Gaussian mixture–based equivalent linearization method (GM‐ELM). The GM‐ELM uses a Gaussian mixture distribution model to approximate the probabilistic distribution of a nonlinear system response. Using properties of the Gaussian mixture model, GM‐ELM can decompose the non‐Gaussian response of a nonlinear system into multiple Gaussian responses of linear single–degree of freedom oscillators. With the set of the equivalent linear systems identified by GM‐ELM, response statistics as crossing rate and first‐passage probability can be computed conveniently using theories of linear random vibration analysis. However, the original version of GM‐ELM may lead to an inaccurate estimate because of the heuristic parameters of the linear system introduced to supplement insufficient information. To overcome this limitation and define unique equivalent linear systems, this paper proposes a further developed version of GM‐ELM, which uses a mixture of bivariate Gaussian densities instead of univariate models. Moreover, to facilitate the use of elastic response spectra for estimating the mean peak responses of a nonlinear structure, a new response spectrum combination rule is proposed for GM‐ELM. Two numerical examples of hysteretic structural systems are presented in this paper to illustrate the application of the bivariate GM‐ELM to nonlinear stochastic seismic analysis. The analysis results obtained by the bivariate GM‐ELM are compared with those obtained by the univariate GM‐ELM, the conventional equivalent linearization method, the tail equivalent linearization method, and Monte Carlo simulation. The supporting source code and data are available for download at https://github.com/yisangri/GitHub‐bGM‐ELM‐code.git     

用经验格林函数法和随机方法模拟卢龙地震的比较

在介绍用经验格林函数方法和随机方法模拟地震动的基础上,分别用这两种方法模拟了卢龙5．7级地震。模拟结果表明,用经验格林函数方法模拟地震动的结果与地震记录符合得很好。用随机方法模拟地震动在高频部分与地震动记录符合得比较好,而在中、低频部分符合得不太好。两种方法比较,经验格林函数方法模拟的结果更符合实际记录。但随机方法具有计算简单、无需小震记录的优点,因此发展随机的方法是有意义的。随机方法中中、低频部分不太符合的原因是随机方法中的很多经验关系是在美国大陆得到的。因此建议加强对中国大陆经验关系的研究,并把中国大陆的经验关系加入到随机方法中,使随机的方法成为中国大陆普适的模拟地震动的方法。     

地震荷载作用下兰州地铁隧道结构动力响应

根据《兰州轨道交通1号线一期工程地震安全性评价报告》所给出的100年超越概率63%、10%和2%的场地基岩地震加速度时程,利用有限差分软件进行地下隧道硐室的地震反应分析。在模型底部施加基岩地震动,设置监测点监测衬砌结构的弯矩、轴力及剪力随时间的变化过程,得到100年超越概率63%、10%及2%工况下的隧道结构地震响应。结果表明:隧道衬砌结构最大弯矩位于拱顶处,最大轴力位于拱顶和拱底处,最大剪力位于上侧壁或下侧壁处;隧道结构内力随着超越概率的降低而增大;以超越概率63%的结构最大内力为基准值,在超越概率10%和2%时,弯矩分别增大1.2和1.7倍,轴力分别增大1.3和1.5倍,剪力分别增大1.5和2.9倍,增幅最大。这可能预示着隧道结构在强地震动作用下会发生剪切破坏。     

Nonstationary seismic responses of structure with nonlinear stiffness subject to modulated Kanai–Tajimi excitation

A simple structure under earthquake excitation is modeled as a single‐degree‐of‐freedom system with nonlinear stiffness subject to modulated Kanai–Tajimi excitation. The nonstationary responses including the nonstationary probability densities of the system responses and the statistical moments are obtained in semi‐analytical form. By applying the stochastic averaging method based on the generalized harmonic functions, the averaged Fokker–Planck–Kolmogorov(FPK) equation governing the nonstationary probability density of the amplitude is derived. Then, the solution of the FPK equation is approximately expressed by a series expansion in terms of a set of properly selected basis functions with time‐dependent coefficients. According to the Galerkin method, the time‐dependent coefficients are solved from a set of linear first‐order differential equations. Thus, the nonstationary probability densities of the amplitude and the state responses as well as the statistic moments of the amplitude are obtained. Finally, two types of the modulating functions, i.e. constant function and exponential function, are considered to give some semi‐analytical formulae. The proposed procedures are checked against the Monte Carlo simulation. The effects of the structure natural frequency and the intensity of the excitation as well as the ground stiffness on the system responses are discussed. It should be pointed out that the proposed method is good for broadband excitation and light damping. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear stochastic seismic analysis of buried pipeline systems

In this paper, a nonlinear stochastic seismic analysis program for buried pipeline systems is developed on the basis of a probability density evolution method (PDEM). A finite element model of buried pipeline systems subjected to seismic wave propagation is established. The pipelines in this model are simulated by 2D beam elements. The soil surrounding the pipelines is simulated by nonlinear distributed springs and linear distributed springs along the axial and horizontal directions, respectively. The joints between the segmented pipes are simulated by nonlinear concentrated springs. Thereafter, by considering the basic random variables of ground motion and soil, the PDEM is employed to capture the stochastic seismic responses of pipeline systems. Meanwhile, a physically based method is employed to simulate the random ground motion field for the area where the pipeline systems are located. Finally, a numerical example is investigated to validate the proposed program.