风力发电高塔系统风致随机动力响应分析

介绍了一种高精度且高效的随机动力系统分析方法-广义概率密度演化方法.基于广义概率密度演化方法,结合随机脉动风场物理模型和“桨叶-机舱-塔体-基础”一体化有限元模型,分别对1.25 MW风力发电高钢塔和钢筋混凝土风力发电高塔进行了风致随机动力响应分析,并将分析结果同确定性动力响应分析结果进行比较.研究表明,随机性对风力发电高塔系统结构风致动力响应分析的影响非常显著.     

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。     

随机结构动力反应的极值分布

提出了求解随机结构动力反应极值分布的概率密度演化方法。基于随机结构动力反应概率密度演化分析的基本思想，可构造一个与随机结构动力反应极值有关的具有“虚拟时间参数”的随机过程及其导数过程，导出了一维概率密度演化方程。结合结构动力反应的时程分析方法与有限差分方法，可求解该随机过程的一维概率密度函数。当虚拟时间参数为1时，即得到随机结构动力反应的极值分布。这一方法可用来求解一般的随机抽样和随机过程的极值分布。与随机抽样极大值分布的理论结果比较表明，本文建议方法具有良好的精度。在此基础上，分析了八层框架结构随机动力反应极值分布的若干特征。     

近海风力发电高塔波浪随机动力响应分析

基于拟层流风波生成机制建立的随机Fourier海浪模型,采用概率密度演化理论研究了近海风力发电高塔在随机波浪作用下的动力响应问题,给出了结构响应概率密度函数的时间演化过程、概率密度等值线图及其均值和标准差.其中随机波浪力由线性波浪理论和M0rison公式计算.结果表明,概率密度演化方法可以获得结构波浪动力响应的时变概率密度函数和等概率密度响应轨迹.据此计算的均值及标准差与Monte Carlo计算结果吻合较好.     

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。     

动力可靠度约束下基于概率测度变换-全局收敛移动渐近线法的结构优化设计EI北大核心CSCD

基于动力可靠度的结构优化是实现随机动力系统优化设计的重要途径。针对设计变量为系统中部分随机变量分布均值的情形,提出了一种基于动力可靠度的结构优化设计方法。在该方法中,通过概率密度演化理论实现了结构动力可靠度的高效分析。在此基础上,结合概率测度变换,可以在不增加任何确定性结构分析的前提下,实现动力可靠度对设计变量的灵敏度分析。进而,通过将上述概率密度演化-测度变换方法嵌入全局收敛移动渐近线法,实现了基于动力可靠度的结构优化设计问题的高效求解。数值算例的结果表明,所提方法可以显著降低结构分析次数,具有较高的效率与稳健性。     

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。     

结构随机地震反应与可靠度的概率密度演化分析研究进展

结构随机动力反应与可靠度分析对保障工程结构在灾害性动力作用下的安全性至关重要。数十年来,国内外学者进行了大量的研究,取得了丰硕的成果,但在多自由度非线性系统随机动力反应与可靠度分析方面遇到了巨大的困难。概率密度演化理论提供了全新的处理方法。该文在评述已有研究方法的基础上,着重讨论了概率密度演化理论及其在结构随机地震反应与整体可靠性分析应用方面的新进展。     

疲劳强度-寿命关系的概率密度演化方法

基于疲劳强度随加载循环次数增加不断劣化的物理事实,采用Euler描述推导出疲劳强度与随机参数联合概率密度函数满足的演化方程。采用数值求解方法,给出疲劳强度-寿命概率密度曲面（probability density S-N）,并可据此计算给定存活率的p-S-N曲线。基于疲劳试验结果的算例分析表明,疲劳强度-寿命概率密度曲面、Monte Carlo模拟及具有给定分位数参数的S-N关系三者计算的p-S-N曲线吻合良好。疲劳强度-寿命概率密度演化方法可不依赖分布假定给出S-N关系的完备概率描述。     

基于概率密度演化法的隔震结构随机地震响应与可靠度分析EI北大核心CSCD

采用简化的两质点隔震结构模型研究随机地震激励下结构设计参数随机性对结构位移响应与可靠度的影响。隔震层和上部结构分别采用Bouc-Wen模型和刚度退化的Bouc-Wen模型来模拟,结合概率密度演化方法和基于极值分布的可靠度理论,求解不同场地条件、阻尼比、周期比与屈重比下隔震层与上部结构的层间位移响应信息与整体可靠度,并对设计参数进行优化。研究结果表明:概率密度演化方法能够有效评估隔震结构的抗震性能;通过对设计参数的适当取值,能使隔震层与上部结构位移响应均最小,从而提高隔震结构整体可靠度。     

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.     

非平稳随机地震作用的结构整体可靠度分析

应用随机过程的正交展开-随机函数方法,建立了非平稳地震动过程的概率模型,实现了用一个基本随机变量来表达地震动过程的目的。通过选取基本随机变量的代表性离散点集,可以直接获取地震动过程的代表性样本集合。结合概率密度演化理论,进行了多自由度Duffing系统的随机地震反应分析与抗震可靠度计算。研究表明,非平稳地震动过程的概率模型与概率密度演化理论有机结合,可以实现复杂工程结构整体抗震可靠度的精确计算。     

Lifecycle operational reliability assessment of water distribution networks based on the probability density evolution method

In this study, a lifecycle operational reliability assessment framework for water distribution networks (WDNs) is proposed on the basis of the probability density evolution method (PDEM). The occurrence models of daily accidents are fitted using the maintenance data provided by a local water administration sector. For a given accident, two types of accidents (e.g., leaks and bursts) are distinguished in different occurrence probabilities and simulated in various ways. The pipe deterioration process in the lifecycle is reflected by incorporating the time-dependent pipe roughness model. Considering various randomness in the model, PDEM, a newly proposed and developed method for a stochastic system, is used to evaluate the lifecycle operational reliability of WDNs. The framework is demonstrated using an actual WDN, and the nodal reliabilities in the lifecycle are obtained. Comparisons of the operational reliabilities of all nodes calculated via the PDEM and Monte Carlo simulations prove that PDEM is an accurate and highly efficient method.     

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。     

Probability density evolution analysis of engineering structures via cubature points

The probability density evolution method (PDEM) is a new approach for stochastic dynamics whereby the dynamic response and reliability evaluation of multi-degree-of-freedom nonlinear systems could be carried out. The apparent similarity and subtle distinction between the ordinary cubature and PDEM are explored with the aid of the concept of the rank of an integral. It is demonstrated that the ordinary cubature are rank-1 integrals, whereas an rank-?? integral is involved in PDEM. This interprets the puzzling phenomenon that some cubature formulae doing well in ordinary high-dimensional integration may fail in PDEM. A criterion that the stability index does not exceed unity is then put forward. This distinguishes the cubature formulae by their applicability to higher-rank integrals and the adaptability to PDEM. Several kinds of cubature formulae are discussed and tested based on the criterion. The analysis is verified by numerical examples, demonstrating that some strategies, e.g. the quasi-symmetric point method, are preferred in different scenarios. Problems to be further studied are pointed out.     

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.     

Response and reliability analysis of a high-dimensional stochastic system

The efficiency of the probability density evolution method (PDEM) is improved in this paper by embedding the Kullback–Leibler (K–L) relative sensitivity in the response analysis of a stochastic dynamic system. The response reliability obtained and the probability density function of the response peaks are used for ranking to get a reduced set of random variables for the PDEM analysis. The need of complicated point selection technique with the high-dimensional uncertain variables is therefore alleviated. The proposed method is illustrated with the response analysis of a random crowd-structure system where the load randomness is considered. The acceleration response induced by the presence of the crowd is evaluated with the proposed method. Results obtained highlight the significant improvements in the computation efficiency of the probabilistic response analysis of a high-dimensional dynamic system.     

随机结构反应概率密度演化分析的切球选点法

发展了随机结构反应概率密度演化分析中随机参数空间的切球选点法。密度演化方法是一类直接获取随机结构动力反应概率密度函数及其演化过程的有效方法。在多个随机变量时，随机变量空间中的离散代表点选点规则直接关系到密度演化方法的精度和效率。本文构造了平面内等半径相切圆圆心分布定位的算法，以此为基础，建立了三维空间中等半径相切球球心坐标定位的计算公式。从而给出随机变量空间中的离散代表点及其赋得概率。计算表明，基于空间切球法的选点规则具有良好的精度和效率，在2个和3个随机变量情况下是较为理想的选点方法。