高效求解结构体系可靠度的新方法

传统的结构体系可靠度分析方法主要依赖于结构失效路径的分枝和约界技术,难以识别主要失效模式且结构体系失效概率计算工作量巨大。为了提高结构体系可靠度计算效率,以β-约界法和联合失效概率分枝约界法为基础,提出了一种快速求解结构体系可靠度分析方法。首先利用结构分析原理,推导出结构单元的安全余量函数并求出其对应的失效概率,拆除失效概率最大值对应的杆件并施以虚拟力形成新的结构,然后再对新的结构重新分析。循环上述步骤,直至结构形成机构为止,并利用构件的失效概率计算结构体系可靠度。算例对比研究表明,该方法计算过程简单、计算精度较高,可以获得结构的失效路径,适合于大型结构的体系可靠度计算。     

Ductile structural system reliability analysis using adaptive importance sampling

This paper presents a hybrid technique for efficient system reliability estimation of large ductile framed structures. The proposed procedure starts with a simple enumeration scheme, but quickly changes to an adaptive importance sampling scheme to make the process more efficient and easier to implement. The method solves the problem of including the effect of multiple failure sequences in an importance sampling scheme, for the system reliability estimation of large structures. The enumeration method is used to identify the first complete failure sequence. This failure sequence defines the initial failure domain for starting the adaptive sampling process. A weighted multi-modal sampling density is used to account for the contribution of different regions in the sampling domain to the system failure probability. As the simulation progresses, the failure domain is gradually modified to include the effect of other significant failure sequences and arrive at an accurate estimate of the system failure probability.     

Evaluation of multivariate normal integrals for general systems by sequential compounding

System reliability analysis often requires efficient and accurate evaluation of a multivariate normal integral. Despite recent advances in system reliability analysis methods, it is still a challenging task especially when the definition of the system event is complex; the system has a large number of components; and/or the component events have significant statistical dependence. This paper presents a new method developed for evaluating multivariate normal integrals defined for general system events including series, parallel, cut-set and link-set systems. The method compounds two components coupled by union or intersection sequentially until the system becomes a single compound event. Efficient numerical procedures are developed for obtaining the reliability index of the new compound event, and the correlation coefficients between the compound event and the remaining component events, at each step of the sequential compounding. The accuracy and efficiency of the proposed method, and its applicability to various types and sizes of multivariate normal integrals are demonstrated by numerical examples.     

Generation of dominant modes and reliability analysis of frames

The paper presents a technique for reliability analysis of frames using the stiffness matrix method of linear elastic and piecewise linear elastic-plastic structural analysis and the first order second moment reliability method. It involves automatic generation of stochastically dominant mechanisms (modes) and their safety margin equations and calculation of bounds on the system reliability. Based on the computational experiments, logical strategies are proposed for selection of plastic hinges and branching of failure paths to identify stochastically dominant mechanisms. The proposed method is illustrated with numerical examples. The results show very good agreement with the results of other research workers. The proposed method of generating stochastically dominant modes is simple and fairly efficient and less computer-time consuming.     

A PDEM-based perspective to engineering reliability: From structures to lifeline networks

Research of reliability of engineering structures has experienced a developing history for more than 90 years. However, the problem of how to resolve the global reliability of structural systems still remains open, especially the problem of the combinatorial explosion and the challenge of correlation between failure modes. Benefiting from the research of probability density evolution theory in recent years, the physics-based system reliability researches open a new way for bypassing this dilemma. The present paper introduces the theoretical foundation of probability density evolution method in view of a broad background, whereby a probability density evolution equation for probability dissipative system is deduced. In conjunction of physical equations and structural failure criteria, a general engineering reliability analysis frame is then presented. For illustrative purposes, several cases are studied which prove the value of the proposed engineering reliability analysis method.     

不完备概率信息条件下边坡可靠度分析方法

不完备概率信息条件下边坡可靠度估计是一个富有挑战性的问题。基于Copula函数提出了不完备概率信息条件下边坡可靠度分析方法。首先,简要介绍了基于Copula函数的岩土体抗剪强度参数联合概率分布函数构造方法。其次,定义了边坡稳定分析的名义安全系数,提出了边坡失效概率波动范围分析方法。最后以无限边坡稳定可靠度问题为例证明了所提方法的有效性。结果表明：不完备概率信息条件下边坡失效概率是不唯一的。抗剪强度参数间Copula函数类型对边坡失效概率具有明显的影响,这种影响直接导致了不完备概率信息条件下边坡失效概率的波动范围较大。边坡失效概率波动范围随名义安全系数的增大或失效概率的减小而增大。所提3种方法能够有效地缩小边坡失效概率的波动范围,提高了边坡失效概率的估计精度,从而为不完备概率信息条件下边坡可靠度分析提供了一条有效的途径。     

On multinormal integrals by Importance Sampling for parallel system reliability

The ability to compute multinormal integrals to any required accuracy is a key issue for an efficient computation of failure probabilities, particular important in context with system reliability analysis. Hence in this paper, an accurate Importance Sampling procedure to compute multinormal integrals in high dimensions is presented. The novel method allows to sample exclusively in the failure domain which substantially increases the efficiency of the Importance Sampling procedure. The proposed approach is extended for slightly non-linear limit state functions which typically result from non-Gaussian distributed input variables and linear limit state functions of the response in linear structural analysis.The suggested procedure is easy to implement, accurate and convenient for practical applications.     

Integration formulas to evaluate functions of random variables

Structural reliability analysis often involves extensive integration of a function of multiple basic variables. Special techniques can be used to reduce this numerical effort. This paper develops integration formulas for computing the statistical parameters of a function of a random vector, in particular calculation of the first few moments. The formula is a numerical procedure using selected weights and points to estimate integrals. The points and weights are predetermined in the independent standard normal variable space. The sample points in basic variable space are then obtained by various transformations. The formulas were developed for the basic variables with various probability information known. The procedure is convenient to implement, and allows for a direct use of the available deterministic computer programs.     

An effective approximation to evaluate multinormal integrals

In structural system reliability theory, the evaluation of multivariate normal distributions is an important problem. Numerical integration of multinormal distributions with high accuracy and efficiency is known to be impractical when the number of distribution dimensions is large, typically greater than five. The paper presents a practical and effective approach to approximate a multinormal integral by a product of one-dimensional normal integrals, which are easy to evaluate. Examples considered in the paper illustrate a remarkable accuracy of the approximation in comparison with exact integration. Unlike a first-order multinormal approximation widely used in the literature, this method does not involve any iterative linearization, minimization or integration. Computational simplicity with high accuracy is the major advantage of the proposed method, which also highlights its potential for estimating reliability of structural systems.     

改进的微分等价递归算法

微分等价递归算法计算简单,在体系可靠度计算中有着广泛的应用。但是传统的微分等价递归算法精度低,并且利用数值差分来求解等价失效模式,计算量大。本文推出了等价线性失效模式的解析表达式,提高了等价模式的精度,并大大降低了计算量;在此基础上,分析了传统微分等价递归算法利用等价线性失效模式代替两个失效模式交集产生误差的原因,提出了改进的微分等价递归算法,从而大幅度地提高了计算精度,为微分等价递归算法在实际工程中的应用奠定了良好基础。     

New light on first- and second-order reliability methods

The classical first- and second order reliability methods as applied to complex systems are reviewed. They are justified and improved by new concepts of asymptotic analysis. Various asymptotically exact formulae are presented for the probability of simple failure domains and unions and intersections of such failure domains occuring in the reliability analysis of structural or other technical systems. Essentially, the computations are reduced to a problem of non-linear multi-constraint optimization and some simple algebraic manipulations. Two examples are presented which also show the effect of various simplifications.     

Reliability of an engineering system under a strong earthquake with application to offshore platforms

This paper presents a method developed for the performance evaluation of an engineering system during a strong earthquake. The seismic reliability of the system is evaluated by considering the different possible failure modes, and seismic reliability of the components of the system. The method is applied to the oil production system at the Statfjord Field in the North Sea. The objective of the analysis is to document the reliability of oil production from the field in the event of an exceptionally large earthquake, and to investigate the effect of spatial variation of earthquake loading parameters on the computed system reliability. It is shown that, with a realistic model of the spatial variation of earthquake motion, there is very little correlation between the earthquake loading parameters at different platform locations. The main consequence of this lack of correlation is that the computed failure probability of the oil production system under the design earthquake is about one order of magnitude smaller than the probability of failure of individual platforms at the Statfjord Field.     

具有中介状态的工程系统的可靠性分析

提出了其单元具有"安全-中介-失效"工作模式的各种系统的可靠性分析方法.这时,系统及其单元均具有安全、中介、失效三种工作状态.可靠性分析的结果是求出系统的安全概率PR、中介概率PM和失效概率PF.它们联合起来构成可靠性向量[PR,PM,PF].在分析中还考虑了系统各单元间失效相关性问题.     

系统可靠性的连续分析方法

将概率计算、递推公式和数值分析相结合的结构连续变更方法用于刚架结构的可靠性分析,实现了结构内力和极限状态函数的连续生成,计算了结构总体失效概率。简化了繁琐的总刚运算,避免了结构重分析,为结构退化为机构提供了新的判断依据。加快了系统失效模式的搜索速度,并进一步提高了结构系统的可靠性分析时效,为结构系统可靠性分析理论的发展提供了新思路。     

A normal probability integral and some applications

The integral of a two-dimensional normal distribution over a wedge-shaped domain has many application in reliability analysis. A simple approximation suitable for many technical applications, and several more accurate representations by fitted polynomials and by tables are given. Application is illustrated for system reliability analysis; disaggregations of failure according to human error, random error or “act of God”; estimation of errors in the normal tail approximation; and fast probability integration of piecewise normal distributions.     

Reliability sensitivity method by line sampling

Reliability sensitivity refers to the derivative of the failure probability with respect to the distribution parameter of basic random variable. Conventionally, this requires repetitive evaluations of the failure probability for different distribution parameters, which is a direct but computationally expensive task. An efficient simulation algorithm is presented to perform reliability sensitivity analysis using the line sampling technique, which gives a good failure probability evaluation for high-dimensional problems and still presents a comparative one for low-dimensional problems. On the basis of the line sampling procedure for failure probability analysis, the concept and implementation are presented for reliability sensitivity. It is shown that the desired information about reliability sensitivity can be obtained by a very limited increase of computation effort based on the failure probability analysis by the line sampling technique. The presented reliability sensitivity algorithm is more efficient than the one based on the direct Monte Carlo technique, especially for cases where the failure probability is low and the number of random variables is large, which is illustrated by several examples. Additionally, limitations of the line sampling based reliability sensitivity method are demonstrated by a numerical example as well.     

考虑地层变异性和土体参数变异性的边坡可靠度分析

现有边坡可靠度分析大多数只考虑土体参数的固有变异性,而忽略了地层变异性的影响。为此,提出了同时考虑地层变异性和土体参数固有变异性的边坡可靠度分析方法,利用耦合马尔可夫链模拟地层分布,采用基于乔列斯基分解的中点法离散土体参数随机场,采用有限元强度折减法计算边坡安全系数,通过蒙特卡洛法模拟进行边坡可靠度分析。利用澳大利亚珀斯市钻孔资料,以边坡可靠度问题为例阐明了同时考虑地层变异性和土体参数固有变异性的重要性,研究了钻孔布置方案对边坡可靠度的影响规律,结果表明:提出的方法能够有效地反映地层变异性和土体参数固有变异性对边坡可靠度的影响。当钻孔数目较少时,模拟的边坡土体类型分布与真实边坡土体类型分布相差较大,此时忽略地层变异性将导致边坡可靠度不精确的估计结果。钻孔布置方案对边坡失效概率和安全系数有明显的影响,钻孔应尽可能多的布置在边坡关键影响区域。边坡失效概率和安全系数统计量与钻孔数目并不呈单调关系,但是随着钻孔数目的增加,边坡失效概率和安全系数统计量逐渐收敛至"精确解"。     

Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces

Slope reliability analysis considering inherent spatial variability (ISV) of soil properties is time-consuming when response surface method (RSM) is used, because of the “curse of dimensionality”. This paper proposes an effective method for identification of representative slip surfaces (RSSs) of slopes with spatially varied soils within the framework of limit equilibrium method (LEM), which utilizes an adaptive K-means clustering approach. Then, an improved slope reliability analysis based on the RSSs and RSM considering soil spatial variability, in perspective of computation efficiency, is established. The detailed implementation procedure of the proposed method is well documented, and the ability of the method in identifying RSSs and estimating reliability is investigated via three slope examples. Results show that the proposed method can automatically identify the RSSs of slope with only one evaluation of the conventional deterministic slope stability model. The RSSs are invariant with the statistics of soil properties, which allows parametric studies that are often required in slope reliability analysis to be efficiently achieved with ease. It is also found that the proposed method provides comparable values of factor of safety (FS) and probability of failure (P_f) of slopes with those obtained from direct analysis and literature.     

Seismic system reliability analysis of bridges using the multiplicative dimensional reduction method

Abstract

A combined method of finite element reliability analysis and multiplicative dimensional reduction method (M-DRM) is proposed for systems reliability analysis of practical bridge structures. The probability distribution function of a structural response is derived based on the maximum entropy principle. To illustrate the accuracy and efficiency of the proposed approach, a simply supported bridge structure is adopted and the failure probability obtained are compared with the Monte Carlo simulation method. The validated method is then applied for the system reliability analysis for a practical high-pier rigid frame railway bridge located at the seismic-prone region. The finite element model of the bridge is developed using OpenSees and the M-DRM method is used to analyse the structural system reliability under earthquake loading.     

基于n维等效方法的岩质边坡楔体稳定体系可靠度分析

 提出岩质边坡楔体稳定体系可靠度分析的n维等效方法,建立考虑多失效模式相关的楔体稳定体系可靠度分析的概率故障树模型。采用四参数b 分布来描述可靠度分析中基本随机变量的分布。最后采用n维等效方法计算楔体稳定体系可靠度,并着重分析随机变量敏感性分析的3个层次及不同层次上的可靠度对基本随机变量的敏感性。结果表明,n维等效方法计算的楔体体系失效概率均在Cornell简单上下限法的范围内,它能够有效地评价楔体体系可靠度。概率故障树模型能够清晰直观地模拟多失效模式相关的楔体体系可靠度问题,忽略失效模式间的相关性将会明显高估楔体体系失效概率。此外,黏聚力和内摩擦角之间的负相关性对边坡的可靠度具有有利的影响。随机变量敏感性分为单一极限状态方程、单一失效模式以及体系可靠度3个不同的层次,在研究随机变量敏感性时必须明确相应的分析层次。水压力和结构面产状的敏感因子较大,因此布置良好的边坡排水系统以及进行详细的地质勘测工作是提高楔体可靠度有效的方法。研究成果为边坡风险分析奠定了一定的基础。