Orthogonal expansion of Gaussian wind velocity field and PDEM-based vibration analysis of wind-excited structures

An effective procedure for simulation of random wind velocity field by the orthogonal expansion method is proposed in this paper. The procedure starts with decomposing the fluctuating wind velocity field into a product of a stochastic process and a random field, which represent the time property and the spatial correlation property of wind velocity fluctuations, respectively. By an innovative orthogonal expansion technology, the stochastic process for wind velocity fluctuations may be represented as a finite sum of deterministic time functions with corresponding uncorrelated random coefficients. Similarly, the random field can be expressed as a combination form with only a few random variables by the Karhunen-Loeve decomposition. This approach actually simulates the wind velocity field with stochastic functions other than methods such as spectral representation and proper orthogonal decomposition. In the second part of the paper, the probability density evolution method (PDEM) is employed to predict the stochastic dynamic response of structures subjected to wind excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic responses of structures. The solution of this equation will give rise to instantaneous probability density function of the responses. Finally, the accuracy and effectiveness of the approach in representing the random wind velocity field and PDEM-based dynamic response of wind-excited building are investigated.     

Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.     

考虑桨叶旋转效应的海上风力发电高塔系统随机风振响应与动力可靠度分析

研究了考虑桨叶旋转效应的海上风力发电高塔系统随机动力响应与风振可靠度分析.在风场模拟中,桨叶风荷载需要考虑旋转效应的影响.因此,对塔体风荷载,直接采用基于物理机制的随机Fourier谱,而对桨叶风荷载,则采用考虑桨叶旋转机制的随机Fourier谱概念.在此基础上,结合概率密度演化理论,对海上风力发电高塔系统进行了随机动力响应分析以及基于塔顶位移响应的风振动力可靠度分析.结果表明,上述方法能够有效地进行此类结构的随机动力响应及可靠度分析.     

Stochastic analysis of fatigue of concrete bridges

A novel method is proposed in this work for the assessment of the remaining fatigue life and fatigue reliability of concrete bridges subjected to random loads. The fatigue reliability of a bridge is a function of the fatigue damage accumulation; a stochastic fatigue damage model (SFDM) with physical mechanism is introduced for deriving the fatigue damage process. In order to implement the probabilistic analysis, based on the probability density evolution method (PDEM), the generalised density evolution equation (GDEE) for the remaining fatigue life is developed. Finally, a prestressed concrete continuous beam bridge located in China is illustrated. The random fatigue load acting on the bridge is modelled as the compound Poisson process, and the simulation of the random load uses the stochastic harmonic function (SHF) method. To simplify the reliability analysis, an equivalent constant-amplitude (ECA) load process is introduced based on energy equivalence. By employing SFDM, the finite element analysis of the bridge under the fatigue loading is performed. Then, the fatigue damage accumulation process of the bridge under the fatigue loading is obtained. Through solving the probability density evolution equation for the remaining fatigue life, the probability density functions (PDFs) of the remaining fatigue life evolving with time is obtained. The fatigue reliability is then calculated by integrating the PDF of the corresponding remaining life.     

考虑参数随机性的高层建筑风振舒适度的非线性黏滞阻尼器优化布设

以顶层加速度作为概率特征量，建立目标函数，分别采用基于随机等效线性化系统的频域方法和基于概率密度演化理论的非线性系统时域方法，进行了考虑结构参数随机性的高层建筑风振舒适度控制的黏滞阻尼器优化布设研究。结果表明：在总黏滞阻尼器系数相同的条件下，以顶层加速度标准差和失效概率为目标函数的黏滞阻尼器优化布设方案，在确定性激励作用下均能显著降低结构的风振响应，且相对于未优化的阻尼器均匀满布方案更经济、更有效。以加速度标准差为目标函数的传统阻尼器优化布设本质上是确定性分析方法，对结构可靠度的提高作用有限，而以加速度失效概率为目标函数的阻尼器优化布设，以结构响应的概率密度函数为优化对象，能显著地提高结构的可靠度，有利于改善高层建筑结构的风振舒适度性能。     

钢筋混凝土框架结构体系可靠度分析

结构体系可靠度是一个40年来尚没有得到很好解决的问题,即使对于理想弹塑性体系,经典的结构体系可靠度分析也往往会遭遇两个难以克服的困难:相关失效与组合爆炸。近年来,基于概率守恒原理的随机事件描述,提出了广义密度演化方程,从而将确定性系统和随机系统分析纳入到统一的理论框架之中。基于这一进展,结合结构非线性全过程分析的位移控制算法,本文推导了结构静力非线性发展过程的概率密度演化方程。采用纤维梁柱单元进行结构非线性分析,研究钢筋混凝土框架结构的体系可靠度,并与Monte Carlo法进行对比分析。研究结果证明了概率密度演化理论对结构体系可靠度分析的适用性。     

3D reliability evaluation of tunnels under strong-motion earthquakes considering spatial randomness

This paper studied the stochastic response and reliability of the tunnel system through modelling the elastic modulus and yield stress of the surrounding soil as a random field. A 3D tunnel-soil finite element model was established and the corresponding random field was simulated by the spectral representation method. The Wenchuan earthquake was chosen as input from the bottom in the perpendicular direction to the longitudinal axis. Results show that the peak values of the internal forces of the cross sections of the tunnel are not uniformly distributed and the hoop forces and bending moments are higher under the condition that the elastic modulus and yield stress of soil are both random fields (Case II) than only the elastic modulus of the soil is considered as random field (Case I). Using PDEM (probability density evolution method), the stochastic response of the tunnel indicates that the probability density function of the response is complex with two or more peaks. The design limit and ultimate limit states of Cases I and II are evaluated in this paper in terms of the respective reliabilities, which indicated that the reliability under Case II is lower than that of Case I.     

A computational model to calculate the flow-induced pressure fluctuations on buildings

A computational model to predict the flow-induced pressure fluctuation on bluff bodies is presented. Unlike direct and large-eddy simulation, the present model employs a stochastic model to generate plausible velocity fluctuations (synthetic turbulence) that satisfy the mean turbulent quantities such as turbulent kinetic energy (k) and dissipation energy rate (ε). This model has three main components: (1) prediction of mean flow quantities by solving the 3D Navier-Stokes equations using the standard k-ε model with Kato and Launder modifications; (2) generating a synthetic turbulent velocity field using a stochastic model and finally (3) solving the Poisson equation that governs the pressure fluctuations field. Flow around the low-rise building at Texas Tech was analyzed using the developed model. Two different wind angles of attack are considered for the analysis. Results obtained using the developed model are compared with wind tunnel and field measurements. The computed rms values for pressure fluctuations show good agreement with the experimental results.     

高耸结构风振疲劳的随机裂纹扩展分析

采用随机裂纹扩展模型对高耸结构的风振疲劳问题进行分析,同时考虑平均风速的概率分布和时间相关性对裂纹扩展的影响,用ZMNL法模拟相关的平均风速时程样本,根据Monte-Carlo法得出裂纹长度的概率分布.推导出计算裂纹长度和疲劳寿命的二次矩近似法公式,用对数正态模型近似计算其概率分布.通过对一单杆输电塔的计算,证明上述方法的可行性,并对时间相关性对裂纹扩展的影响进行分析.     

高耸结构风振疲劳的随机裂纹扩展分析

采用随机裂纹扩展模型对高耸结构的风振疲劳问题进行分析,同时考虑平均风速的概率分布和时间相关性对裂纹扩展的影响,用ZMNL法模拟相关的平均风速时程样本,根据Monte-Carlo法得出裂纹长度的概率分布。推导出计算裂纹长度和疲劳寿命的二次矩近似法公式,用对数正态模型近似计算其概率分布。通过对一单杆输电塔的计算,证明上述方法的可行性,并对时间相关性对裂纹扩展的影响进行分析。     

An experimental study on the intermittent extension of flames in wind-driven fires

Experiments were conducted to study the intermittent extension of flames from wind-driven line fires using stationary burners. These fires are thought to share similar features with propagating wildland fires, where forward pulsations of flame have been observed to quickly ignite material far ahead of the mean flame front. However, stationary burners offer the ability to study the movement of the flame and its heating processes in greater detail than a spreading fire. In these stationary experiments, propane gas was used as a fuel with different burner sizes, 25–30 cm wide and 5–25 cm long in the direction of the flow. A specially-built wind tunnel was used to provide a well-characterized laminar flow for the experimental area. The free-stream flow velocity, measured by a hot-wire anemometer, ranged in the experiments from 0.2 to 2.7 m/s. The shape of the flame was measured using a high-speed video camera mounted perpendicular to the apparatus. A method was developed to track the extension of the flame close to the surface, simulating flame contact with unburnt fuel downstream of the fire. This extension length was then measured frame by frame and frequencies of flame presence/absence determined as a function of downstream distance. The location of maximum pulsation frequency, x_max, for each burner/wind configuration, was obtained using a level-crossing approach (essentially the variable-interval time-average (VITA) method). Further study indicates that x_max can be well estimated using mean flame properties. Probability distributions describing the location of the flame over time also showed that, the probability the flame extends far beyond the mean flame front is sensitive to increasing ambient winds and fire size.     

Time-domain dynamic drift optimisation of tall buildings subject to stochastic wind excitation

Wind-resistant design of tall buildings has been traditionally treated using the equivalent static load approach. In order to account for the uncertainties in random wind excitation, it is necessary to develop a comprehensive and reliable dynamic optimisation technique in the time domain. The optimal lateral stiffness design problem of wind-excited tall buildings consists of (1) identifying the critical dynamic drift response in the time domain and (2) searching for the optimal distribution of element stiffness of the building subject to multiple drift design constraints. The critical time-history drift constraints of a wind-excited building are first treated by the worst-case formulation and then explicitly expressed in terms of element sizing variables using the principle of virtual work. The extreme value distribution and the Gaussian assumption are employed to formulate and simplify the probabilistic drift constraints, which are explicitly considered in the dynamic optimisation problem. The system reliability associated with the interstory drift is estimated approximately by the bound approach to ensure that the most cost-efficient solution also attains an acceptable reliability level. A full-scale 45-story building example under wind tunnel derived time history wind loading is presented to illustrate the effectiveness and practicality of the reliability-based dynamic optimisation technique.     

Wind-induced fatigue of structures under neutral and non-neutral atmospheric conditions

The authors of this paper have carried out a wide research project aimed at determining the wind-induced fatigue of structures, hypothesising the wind field as neutrally stratified, as it is typical of evaluations addressed to ultimate loading conditions. As wind-induced fatigue is sensitive to moderate wind velocities, for which stable or unstable atmospheric conditions can occur, this paper extends the procedures previously established to non-neutral thermal stratifications. The mean wind velocity profile and the cross-power spectral density functions of the atmospheric turbulence are expressed in terms of the Monin–Obukhov length. The occurrence of stable, unstable and neutral conditions is taken into account by means of the joint probability distribution of the mean wind velocity and direction and of the Monin–Obukhov length. The effects of non-neutral stratifications on the structural response and on the mean fatigue life are preliminary discussed with reference to an example concerning a steel chimney.     

Feasible method,utilizing density changes,for estimating in situ dynamic strength and deformation properties of sand samples

Laboratory tests and design reliability are directly controlled by sample quality. The frozen sampling (FS) method is useful for dynamic strength and deformation tests of undisturbed clean sand. However, it is very expensive and requires considerable equipment. The sample quality of Toyoura sands obtained from 48 mm and 75 mm samplers are scrutinized based on void ratio, dynamic strength and deformation properties through model and cyclic undrained triaxial tests. A conventional method for estimating in-situ dynamic strength and deformation properties of sand samples utilizing density changes is examined and the applicability of the proposed method is discussed for the samples obtained from Niigata sand deposits.The main conclusions obtained from this study are summarized as follows:(1) A conventional method for estimating in-situ void ratio (e₀), D_r, stress ratio (R_L20) in a 20 cyclic time frame and the initial modulus of rigidity (G₀) of sand samples utilizing density changes is proposed.(2) The in-situ R_L20 and G₀ estimated from the proposed method for sand samples from tube samplers were similar to those of frozen sampling and the in-situ modulus of initial rigidity was calculated from the secondary wave velocity for Niigata sand deposits.Therefore, dynamic strength and deformation properties changes, caused by sampling, can be modified appropriately to an in-situ condition by this proposed method.     

Permanent deformations of rigid-plastic structures subject to random dynamic loads

The probabilistic analysis of the inelastic displacement response for simple rigid-plastic structures subject to dynamic loads is considered.The paper presents a method able to approximate the probability density function of the residual displacement at any time $\text{t}$. The procedure is based on the filtered Poisson process theory. This model aims to idealize the input stochastic process (i.e. the loading function) and to describe the output process (i.e. the residual displacement). The extension to elastic-perfectly plastic structures is immediate. Finally a numerical example is developed in order to show the computational aspects of the method.     

Probability density evolution analysis of stochastic nonlinear structure under non-stationary ground motions

In the present paper, a framework of dimension-reduction modeling method is developed for a dual stochastic dynamic structural system of spectrum-compatible non-stationary stochastic ground motion processes and stochastic structures. With the aid of the proposed method, the random variables used to describe the stochastic characteristics of the non-stationary ground motion processes and the structural parameters are respectively represented by the one-elementary-random-variable functions, contributing to an entire stochastic dynamic structural system readily described by merely two elementary random variables. Owing to the fact that the number of the elementary random variables needed is extremely small, the set of the representative points associated with the elementary random variables can thus be selected by the widely-used number theoretical method, and then the probability density evolution method can be conveniently combined to conduct the dynamic response analysis and dynamic reliability evaluation of nonlinear stochastic structures. In the numerical examples, the probability density evolution analysis of an eight-storey reinforced concrete frame structure with random parameters subjected to spectrum-compatible non-stationary stochastic ground motion processes is investigated as a case study. Numerical results fully demonstrated the effectiveness and robustness of the proposed method.     

A new method to calculate wind profile parameters of the wind tunnel boundary layer

This paper introduces a new method to process wind profile data of simulated atmospheric boundary layer flows in the wind tunnel so as to obtain the two important wind profile parameters—the surface roughness length z₀ and the friction velocity u_*. Instead of using the wind speed profile, the turbulent intensity profile of the turbulent surface layer, which is measured with a single probe hot-wire anemometer, is used to calculate the surface roughness length z₀. Then, the calculated surface roughness length z₀ is substituted into the mean wind speed profile of the constant flux layer to calculate friction velocity u_*. From our results this method is better than the simple regression method using the wind speed profile, which has been widely used.     

考虑轨道不平顺全概率分布的车桥随机分析方法

轨道不平顺是车桥耦合系统最主要的激励之一,其高维的随机性导致车桥耦合确定性计算模型不能精确反映实际系统动力响应的离散性。为了完整地反映实际线路中的轨道不平顺信息,文章建立一种适用于车桥耦合随机系统分析的轨道不平顺随机场模型,模型在包含了轨道谱概率、幅值、波长、相位等信息的基础之上,尽可能地减少了参数数量,通过与实测数据对比,该模型的有效性得以验证。此外,将该轨道不平顺随机场模型作为三维车 线 桥耦合时变计算模型的激励源,引入概率密度演化方法,对该耦合系统动力指标的统计特性及动力可靠度进行分析。结果表明,该轨道不平顺随机分析模型产生的空间序列较好地表征了平稳随机过程的谱表达;概率密度演化方法相对于蒙特卡洛方法有着更高的计算效率;不同的动力指标有着不同的均值、均方差、可靠度特征。     

Wind structure in a rural atmospheric boundary layer near the ground

This paper describes mean velocity, turbulence intensity, Reynolds stresses and co-spectra measured during field experiments. The data were obtained using orthogonal arrays of propeller anemometers mounted on a 20 m tower. Data were recorded only when the wind speed was ～ 10 m s^?1 or higher, and the boundary layer was therefore assumed to be neutrally stable.Values of ?_uw (0) calculated both by the eddy correlation technique and from the velocity profile were found to agree well, and also to agree well with values suggested in the literature review of Counihan [1].     

脉动风速互随机Fourier谱函数

为了在随机Fourier谱中考虑风场的空间相关性,首先在经验物理关系的意义上定义了互随机Fourier谱,其表达式由两个随机过程的随机Fourier谱和一个可以反映风场空间相关性的随机相干函数组成;然后,利用现场实测风速资料,研究并建立了实际风场的随机相干函数的经验物理模型;最后,基于假设检验理论,确定了互随机Fourier谱函数中基本随机参数及其概率密度信息。实例表明,建立的互随机Fourier谱函数可以在概率的意义上很好地表征实际风场的空间相关性。