随机结构动力可靠度分析的概率密度演化方法

基于随机结构动力反应分析的概率密度演化方法，提出了一类新的随机结构动力可靠度分析方法。在随机结构动力反应概率密度演化方程的基础上，对于首次超越问题，根据所给的首次超越破坏准则施加相应的吸收壁边界条件，求解具有吸收壁边界条件的概率密度演化方程并在安全域内积分．给出结构的动力可靠度。结合精细时程积分方法和具有TVD性质的差分格式，讨论了计算结构动力可靠度的数值方法。以八层框架结构为例进行了动力可靠度分析并与随机模拟分析结果进行了比较。     

随机结构在随机载荷下的动力可靠度分析

提出了综合考虑动载荷和结构参数双重随机性的动力可靠度分析方法.首先基于随机振动的首次超越破坏准则,参照随机变量功能函数模式,建立了随机结构动力可靠度功能函数;然后引入序列响应面法,对功能函数进行拟合;最后用JC法求解可靠指标.算例分析验证了本文方法具有较好的计算精度和计算效率,尤其在复杂工程结构的动力可靠度分析中有广阔的应用前景.     

多维多点地震激励下随机K8单层球面网壳的可靠度分析

大跨度空间钢结构的多维多点抗震分析已有不少研究,但针对其随机反应极值分布的研究甚少。传统的基于跨越理论的方法仅在简单的场合和很强的假定下才可得解析解;而扩散过程理论方法仅在单自由度体系等简单情形下才能使用,基于此,将近年来提出的概率密度演化法引入到多维多点激励下大跨度空间钢结构动力反应极值分布的计算中,该法构造了一个虚拟时间过程,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。为验证其效率与精度,应用此法求得了多维多点地震激励下单层球面网壳结构的可靠度与极值分布,与随机模拟结果一致,因此引入的算法具有准确、高效和通用的特点。     

随机结构复合随机振动分析的概率密度演化方法

提出了随机结构复合随机振动分析的概率密度演化方法。通过引入扩展状态向量,构造具有随机初始条件的状态方程,导出了复合随机振动反应的概率密度演化方程。结合精细时程积分方法和Lax-Wendroff差分格式对概率密度演化方程提出了数值求解方法。进行了八层层间剪切框架结构复合随机振动反应的概率密度演化分析,证明提出的方法具有计算高效、收敛性稳定与精度高的特点。研究表明随着时间的增长,复合随机振动反应概率密度曲线趋于复杂,基于正态分布假定的二阶矩分析方法可能造成可靠度分析结果的显著偏差。与仅考虑结构参数随机性和仅考虑输入随机性时的结构反应相比,复合随机振动反应概率密度曲线峰值降低、分布变宽,且随机涨落显著增强。     

基于神经网络响应面法的随机结构动力可靠度分析

在对神经网络响应面法的原理和算法进行研究的基础上，建立了基于神经网络响应面法的随机结构动力可靠度分析方法。首先，基于首次超越破坏准则，参照静力可靠度的功能函数模式，建立了随机结构的动力可靠度功能函数；然后引入响应面法，以三层BP神经网络作为拟合函数，推导了功能函数的拟合表达式；最后结合一次二阶矩方法求解可靠指标。算例分析表明了本文方法有较好的计算精度和计算效率，在复杂结构的动力可靠度分析中有较强的实用价值。     

基于模型结构振动台试验的概率密度演化方法验证

以广义概率密度演化方程为核心的概率密度演化方法可应用于一般随机动力系统的反应分析与可靠度评价。该文基于随机地震动作用下模型结构振动台试验实测数据,将试验模型典型动力响应的样本集合直接统计结果与概率密度演化分析结果进行对比,以从试验角度验证概率密度演化方法的正确性。研究结果表明,概率密度演化分析结果,无论从均值与标准差过程,还是典型时刻的概率分布上,均分别与样本统计结果吻合良好,从而证明了概率密度演化方法在随机动力系统分析中的精确性与可靠性。     

基于裂纹扩展尺寸概率密度演化法的疲劳可靠性预测方法研究

疲劳破坏是金属构件的一种主要破坏形式。该文提出一种新的疲劳可靠性预测方法—裂纹扩展尺寸概率密度演化法,该方法通过求解裂纹扩展尺寸时变概率密度函数来预测疲劳寿命可靠性。首先建立随机裂纹扩展模型,然后根据此模型建立概率密度演化方程,并运用数值方法进行求解。最后的算例证明了裂纹扩展尺寸的概率密度函数具有演化特征,新方法计算结果与蒙特卡罗法的结果符合较好。     

具有非线性功能函数的结构时变可靠度分析

基于任一时段内的结构时变可靠度可通过求解一等效的单个功能函数来获得的认识,提出了一种改进的时变可靠度计算方法。首先以简单的梁柱构件为例,分析了结构功能函数为非线性的原因。接着揭示了满足结构非线性极限状态方程的荷载解可能会存在着两个值的特殊现象。然后通过引入一假想的综合各抗力因素的变量来缩减响应面方程中的变量数目,使得响应面方程能简洁地表达出来。最后应用该思路对一承受全跨永久荷载和半跨可变荷载作用下的混凝土拱结构进行了分析,结果表明极限荷载曲线具有较高的非线性程度,且该方法具有较高的精度。     

复合随机振动系统的动力可靠度分析

建议了一类新的复合随机振动系统动力可靠度分析方法。基于复合随机振动系统反应分析的密度演化方法,根据首次超越破坏准则,对密度演化方程施加相应的边界条件,进而求解密度演化方程,在安全域内积分给出结构的动力可靠度。结合精细时程积分方法与具有TVD性质的差分格式,研究了基于密度演化方法求解结构动力可靠度问题的数值方法。以受到随机地震作用、具有随机参数的八层层间剪切型结构为例,进行了结构动力可靠度分析并与随机模拟结果进行了比较。研究表明,建议的方法具有较高的精度和效率。     

考虑混凝土材料变异性的超大型冷却塔随机屈曲承载力分析

基于屈曲本征方程的形式解推导出随机屈曲本征值满足的概率密度演化方程.取混凝土弹性模量服从正态分布及对数正态分布,分析了超大型冷却塔随机屈曲承载力的概率密度函数、均值、标准差及可靠度.结果表明:正态分布假定时随机屈曲承载力的均值与不考虑随机性的屈曲承载力十分接近,其变异性与混凝土弹性模量的变异性相似.而对数正态分布假定时,一阶屈曲本征值偏离了正态分布,均值及变异性增大,但可靠度降低.规范关于冷却塔整体稳定安全系数的规定偏于保守.     

结构二次二阶矩可靠度指标的回归分析预测算法

针对具有强非线性结构功能函数的可靠度指标计算问题,通过数值抽样及回归分析方法对改进的功能函数二阶展开形式进行了系统研究,揭示了二次二阶矩可靠度指标#x003b2;_SORM与一次二阶矩可靠度指标#x003b2;_FORM之间的关系规律。根据上述规律结合线抽样MonteCarlo法,建立了基于回归分析预测算法的可靠度分析方法。该方法通过对若干基本抽样点的回归分析,确定了#x003b2;_SORM与#x003b2;_FORM之间一般关系规律的具体表达式,从而实现了强非线性可靠度问题的高精度求解。研究表明:所建立的方法能够有效改善传统二阶可靠度算法计算过程繁琐、求解效率低下的问题;在求解精度、适用范围及算法稳定性等方面具有优势;且计算直观简便,易于为一般设计人员掌握,更适合于实际工程应用。     

An ensemble evolution numerical method for solving generalized density evolution equation

The key issue of the probability density evolution method (PDEM) is to solve a generalized density evolution equation (GDEE). Previously, the GDEE was solved in the framework of the point evolution method which is essentially a zero-order ensemble evolution method. In this paper, a first-order ensemble evolution method is proposed aiming at increasing the accuracy and robustness of the PDEM. The main idea of the proposed method is to incorporate information of standard deviation of each probability subdomain into the probability density evolution equation (PDEE) by introducing an ensemble velocity term. Compared with the point evolution method, the proposed method can truly reflect the fluctuation of a stochastic dynamic system. In order to estimate the ensemble velocity term accurately, a piecewise quadratic polynomial fitting method is also proposed. In addition, a GF-discrepancy based point selection method and a finite difference scheme that is total variation diminishing are adopted to solve the new PDEE. A single-degree-of-freedom oscillator, a Riccati equation and a 2-span 8-storey frame structure are investigated in detail to demonstrate the advantage of the proposed method over the original one.     

Solution of generalized density evolution equation via a family of <Emphasis Type="Italic">δ</Emphasis> sequences

The traditional probability density evolution equations of stochastic systems are usually in high dimensions. It is very hard to obtain the solutions. Recently the development of a family of generalized density evolution equation (GDEE) provides a new possibility of tackling nonlinear stochastic systems. In the present paper, a numerical method different from the finite difference method is developed for the solution of the GDEE. In the proposed method, the formal solution is firstly obtained through the method of characteristics. Then the solution is approximated by introducing the asymptotic sequences of the Dirac δ function combined with the smart selection of representative point sets in the random parameters space. The implementation procedure of the proposed method is elaborated. Some details of the computation including the selection of the parameters are discussed. The rationality and effectiveness of the proposed method is verified by some examples. Some features of the numerical results are observed.     

An RKPM-based formulation of the generalized probability density evolution equation for stochastic dynamic systems

In the stochastic dynamic analysis, the probability density evolution method (PDEM) provides an optional way to capture the complete probability distribution of the stochastic response of general nonlinear systems. In the PDEM, the key point is to solve the generalized probability density evolution equation (GDEE), which governs the evolution of the joint probability density function (PDF) of the response and the randomness. In this paper, a new numerical method based on the reproducing kernel particle method (RKPM) is proposed. The GDEE can be approximated through the RKPM. By some particles in the response domain, the instantaneous PDF and its partial derivative with respect to response are smoothly expressed. Then, the approximated GDEE can be discretized directly at the collocation points in the response domain. At the same time, discretization in the time domain is achieved by the difference scheme. Therefore, the RKPM-based formulation to obtain the numerical solution of GDEE is formed. The implementation procedure of the proposed method is given in detail. The accuracy and efficiency of this method are illustrated with some numerical examples. Some details of parameter analysis are also discussed.     

隔震结构损伤性能与可靠度研究

提出隔震结构的地震损伤模型,并采用概率密度演化理论分析隔震结构地震损伤指数的概率统计特征,为隔震结构性态目标的量化提供依据。考虑隔震支座的压剪相关性和拉压性能的差异,给出隔震层的损伤指数模型,再利用Park-Ang损伤指数描述上部结构的损伤状况,建立隔震体系的损伤指数模型;将隔震结构简化为双质点模型,采用Bouc-Wen模型和刚度退化的Bouc-Wen模型分别描述隔震层与上部楼层的滞变特性,建立隔震结构的状态方程,应用四阶龙格-库塔方法迭代求解求解出隔震结构的位移反应和滞变耗能,进而求解隔震结构的损伤指数;建立隔震结构损伤指数的概率密度演化方程,求解损伤指数的统计特征和概率密度函数,然后根据极值分布理论计算损伤指数超过不同性能水准的可靠度。本研究为以可靠度为理论基础的隔震结构损伤分析提供了可借鉴的方法。     

Comparison of PDEM and MCS: Accuracy and efficiency

The accuracy and efficiency of two methods for stochastic analysis, the probability density evolution method (PDEM) and the Monte Carlo simulation (MCS) method, are compared in terms of how well they reflect the physical properties of stochastic systems. The basic principle and the numerical implementation details of PDEM and MCS are revisited. The analytical solutions of generalized probability density evolution equation (GDEE) for three typical stochastic systems are given and are to be used as the basis for comparing the two methods. It is verified that, with the rational partition of the probability space, the PDEM provides a continuous and complete reflection of physical properties over the whole probability space. Meanwhile, with the help of the numerical solution of GDEE, PDEM is efficient and accurate to describe the process of the probability density evolution of stochastic systems. In contrast, the random samples in the MCS may not reflect the physical properties of a stochastic system adequately, and the local cluster of sample points may cause redundant calculation, which leads to lower computational efficiency. Through three typical numerical examples, the paper compares the accuracy and efficiency of PDEM and MCS specifically. It is shown that, as the numerical approaches for the stochastic response of a system, the PDEM could get much higher numerical accuracy than MCS with the same number of samples. To achieve the same level of calculation accuracy, MCS needs a much higher number of samples than PDEM.