考虑多重失效机制的结构体系可靠度分析

经典的体系可靠度分析仅涉及构件的抗弯失效,而未考虑可能发生的抗剪失效和抗扭失效等其他失效机制。为此,文中对经典的体系可靠度进一步拓展,提出考虑多重失效机制的体系可靠度问题,进而在概率密度演化理论的框架中,针对静定结构和超静定结构,分别引入等价极值事件和吸收边界条件,导出等价极值变量的密度变换解和考虑吸收边界条件的广义目标量的密度变换解。由于密度变换解的特殊形式,引入δ序列逼近的思想,获得各类密度变换解的δ序列逼近算法。最后,通过多个算例验证文中建议算法的合理性和有效性,同时指出抗剪失效机制对失效概率的贡献并不总是可以忽略,需慎重对待。     

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。     

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.     

考虑堆石料软化的坝坡随机地震动力稳定分析

地震尤其强震作用下,土石坝筑坝堆石料会逐渐呈现出软化特性,影响坝坡安全。为有效评估堆石料软化对坝坡稳定性的影响,结合地震动随机性,考虑不同地震强度水平,提出了基于等价极值分布和广义概率密度演化方法的坝坡安全概率分析方法,并基于坝坡稳定最小安全系数、安全系数超限累积时间、累积滑移量3个物理量,对242 m高的面板堆石坝进行随机动力响应分析和概率可靠度分析。结果表明:地震作用过程中,随着地震强度的增加,考虑软化与不考虑软化的计算结果差别逐渐增大,因为地震作用下,堆石料软化特性逐渐显现;同时,在地震激励下,堆石料软化是一个渐进过程。因此,考虑坝坡堆石料软化,对高土石坝抗震性能分析具有重要的意义。此外,单纯从最小安全系数角度考察土石坝坡稳定性,是不合理的,需要结合安全系数超限累积时间和累积滑移量,全面评估坝坡的安全性。提出的随机概率分析方法,可以对土石坝坡的可靠度给出较为准确的评价。     

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.     

基于微分等价递归算法的桥梁体系耐久性可靠度动态评估

结构耐久性可靠度评估应以体系为对象,并且要体现结构性能的自身特征及动态时变特性。基于贝叶斯动态更新技术,以混凝土碳化深度为随机变量,利用体现结构个性特征的实桥检测信息对传统静态碳化模型进行修正。以可靠度指标为评价标准,引入能计入构件间相关性的微分等价递归算法,并将其嵌入到贝叶斯动态更新框架中,构造出体系碳化耐久性动态评估模型和计算流程,形成了复杂体系碳化耐久性动态可靠度计算方法,采用MATLAB平台开发了计算程序。利用碳化试验模拟实桥检测数据,对钢筋混凝土拱桥进行了体系动态耐久性评估,发现模型更新后拱圈和立柱的碳化耐久性可靠度比更新前有所增大,而桥面板则有所降低,体系耐久性可靠度低于构件可靠度。     

可靠度分析中的荷载问题

阐述了结构可靠度分析的基本原理 ,重点分析了高层、高耸建筑结构抗风动力可靠性计算与结构的静力可靠度分析之间的本质区别。指出在动力响应分析中 ,最大的荷载效应与最大的荷载之间没有完全的对应关系。分析表明 ,在结构的抗风动力可靠度分析中是否可以采用设计基准期最大荷载取决于给出的限值水平 ,但一般采用年最大风荷载进行可靠度分析均可以得到较可靠的结论     

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.     

非线性体系动力可靠性分析的等效Duffing体系法

等效线性化法是非线性结构体系的随机反应分析最常用的方法,但使用等效线性化法给出的反应结果进行结构动力可靠性分析会带来很大的误差。将一般非线性体系通过均方最小误差原则等效为Duffing非线性体系来进行结构动力可靠性分析。Duffing非线性体系可以通过FPK方程求得其稳态精确解析解,所以使用该等效非线性法进行结构动力可靠性分析不仅计算上方便可行而且精度较高。算例分析表明了等效非线性法分析结果可靠,且比等效线性化法的计算精度有明显提高。     

Comparison of response surface and neural network with other methods for structural reliability analysis

The evaluation of the failure probability and safety levels of structural systems is of extreme importance in structural design, mainly when the variables are eminently random. Some examples of random variables on real structures are material properties, loads and member dimensions. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. Many researchers studied structural reliability problems and nowadays there are several approaches for these problems. Two recent approaches, the Response Surface (RS) and the Artificial Neural Network (ANN) techniques, have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparison are carried out using the well known First Order Reliability Method (FORM), Direct Monte Carlo Simulation and Monte Carlo Simulation with Adaptive Importance Sampling technique with approximated and exact limit state functions. Problems with simple limit state functions (LSF) and closed form solutions of the failure probability are solved in order to highlight the advantages and shortcomings using these techniques. Some remarks are outlined regarding the fact that RS and ANN techniques have presented equivalent precision levels. It is observed that in problems where the computational cost of structural evaluations (looking for the failure probability and safety levels) is high, these two techniques may turn feasible the evaluation of the structural reliability through simulation techniques.     

一种基于可靠度分析的简化风振系数

为将风致响应分析与体系可靠性评价结合起来,提出了一种基于可靠度分析的简化风振系数。该简化风振系数通过计算出风荷载动力效应下与静风作用下结构整体最大位移或极限承载能力的比值,将动力可靠度问题转变为静力可靠度问题,方便了可靠度的求解。同时采用该简化风振系数进行分析还能给出峰值因子一个合理的取值。示例验算过程表明,该简化风振系数具有较好的效果。这为实现考虑风致响应的可靠度分析提供了一种方法。     

Sensitivity of metal frames reliability to semirigid connections parameters

The present study deals with the sensitivity of metal frames reliability to the randomness of the characteristics of both the structural members and the connections. The random variables involved are the geometrical dimensions, the mechanical properties of the constitutive materials and the applied loads.

The reliability analysis must be, in principle, defined through the probability of failure, denoted Pf, by either buckling or plastic mechanisms events. Monte Carlo simulations could be run to assess the Pf values. However, as a first step in the comprehension of the phenomena that cause the structural failure, the authors restrict their present study to the analysis of the evolution of the critical values of the applied loads. The results show that, with an adequate numerical procedure, an acceptable precision of these values may be reached for a reduced number of simulations. The multimodal failure of the structure is also demonstrated. Conclusions can be made about the attention that must be devoted to the random character of either the structural members or the connections.     

Event oriented analysis of series structural systems

The event oriented analysis of technical objects is in general accomplished by representing them as complete or incomplete systems and subsystems of events. It is argued in the article how the compound engineering systems of events can be partitioned by inclusion-exclusion expansion into individual and common cause modes. The event analysis is based on the random variable model and employs the results of operational modes and effect analysis, of the reliability analysis and of the uncertainty analysis. The system redundancy and robustness are considered as uncertainties, due to the fact that really a number of events are possible, expressed by the entropy concept in probability theory, conditioned by operational and failure modes, respectively. Relative and average uncertainty measures are introduced to facilitate uncertainty interpretations in engineering problems. It is investigated how the sensitivity analysis of reliability measures can be applied to the assessments of system uncertainties. Numerical examples presented in the article illustrate the application of event oriented system analysis to series structural systems with common cause failures. Additionally, system performance presentation and optimization with constraints, as well as potential improvements in system analysis, design and maintenance are investigated.     

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。     

Adaptive sampling — an iterative fast Monte Carlo procedure

An iterative Monte-Carlo simulation procedure for structural analysis is suggested. This proposed new approach utilizes results from simulation to adapt the importance sampling density to the specific problem. Considerable reduction of the statistical error of the estimated failure probability is achieved. Most important, problems connected with optimization procedures commonly used in structural reliability are avoided. This makes the suggested procedure especially attractive for systems reliability analyses.     

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.     

Probability analysis method using Fast Fourier transform and its application

This paper presents an efficient probability analysis method using Fast Fourier transform taking into account that (1) a probability density function and its characteristic function are a pair of Fourier transforms, and (2) the characteristic function of the sum of statistically independent random variables is given by the product of the characteristic functions of each random variable. The efficient probability analysis method is extended for the sum of correlated non-normal random variables with correlation coefficients expressed by the power of a common value. Expressing the correlated basic variables in terms of two sets of uncorrelated random variables, the characteristic function of their sum can be estimated approximately by the characteristic functions of the correlated basic variables. The probability density function of the sum is obtained using Fast Fourier transform. The accuracy and applicability of the approximation method are investigated based on the estimation error of the cumulant and using numerical examples. Applications of the proposed method to various aspects of structural reliability analysis and design are illustrated.     

Structural reliability techniques applied to plume impingement loading of the Space Station Freedom photovoltaic array

A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design due to the examined failure modes is minute. Significantly, this paper details a structural reliability analysis of a complex aerospace structure for which little statistical information is available.     

Serviceability‐based damping optimization of randomly wind‐excited high‐rise buildings

Fluid viscous dampers are proved to be effective for reducing the response of high‐rise buildings subjected to wind excitations so as to enhance structural habitability, which serves as a critical performance in serviceability design. High‐rise buildings attached with fluid viscous dampers, however, exhibit nonlinearity and even act as stiff systems in most cases of wind‐induced vibration mitigation. The traditional equivalent linearization methods employed in practices often fail to obtain an accurate solution. Equivalent linearization methods, including the energy‐dissipation equivalent linearization method and the statistical linearization technique, are first studied and validated in this paper by the backward difference formula, which was verified to be of high accuracy through the nonlinear dynamic analysis. The damping optimization for habitability control is then proceeded. Two families of serviceability criteria, the minimization of standard deviation of roof acceleration employed in traditional habitability analysis and the minimization of failure probability of roof acceleration proposed in the present study, are addressed. For the logical treatment of randomness inherent in wind excitations and its influence upon structural reliability, the probability density evolution method is employed. Numerical results reveal that the criterion of minimizing failure probability of roof acceleration has better performance in habitability enhancement.     

Reliability analysis of roof sheathing panels exposed to a hurricane wind

Light-frame wood roofs are frequently used in the US for residential and commercial construction. High wind events, such as hurricanes, may cause severe damage to these structures by breaking the roof envelope and allowing penetration of wind-driven rain. Most previous wood panel reliability studies have used static, uniform wind pressure load models and code-specified load distribution rules for analysis. This study re-estimates the reliability of roof sheathing panels exposed to a specific hurricane event using actual wind pressure data and a more refined structural analysis model. The objective is to examine the adequacy of the simplified wind load and structural analysis models used for roof panel reliability analysis. In the procedure here, panel failure behavior is modeled by individual fastener extraction from the panel as dynamic wind pressure is increased. For reliability analysis, the limit state is based on panel pull-off. The results show that the use of a refined model provides some significant differences in panel reliability found from simplified techniques.