DOC-外文翻译--基于钢-混凝土粘接组合梁可靠度优化设计的概率和非概率不确定性-其他专业

DOC-外文翻译--基于钢-混凝土粘接组合梁可靠度优化设计的概率和非概率不确定性-其他专业
1 英文原文
Reliability-based design optimization of adhesive bonded
steel-Cconcret composite beams with probabilistic and
non-probabilistic uncertainties
ABSTRACT: It is meaningful to account for various uncertainties in the optimization design of the adhesive bonded steel-cconcrete composite beam.Based on the definition of the mixed reliability index for structural safety evaluation with probabilistic and non-probabilistic uncertainties,the reliability-based optimization incorporating such mixed reliability constraints are mathematically formulated as a nested problem.The
performance measure approach is employed to improve the convergence and the stability in solving the inner-loop.Moreover,the double-loop optimization problem is transformed into a series of approximate deterministic problems by incorporating the sequential approximate programming and the iteration scheme,which greatly reduces the burdensome computation workloads in seeking the optimal design. The validity of the
proposed formulation as well as the efficiency of the presented numerical techniques is demonstrated by a mathematical
example.Finally,reliability-based optimization designs of a single span
adhesive bonded steel-cconcrete composite beam with different loading cases are achieved throug integrating the present systematic method,the finite element analysis and the optimization package.
1. Introduction
The steel-cconcrete composite beam,which integrates the high tensile strength of steel and the high compressive strength of concrete,has been widely used in multi-storey buildings and bridges all over the world.At the beginning of the 1960s,an efficient
[1,2]adhesive bonding techniquewas introduced to connect the Concrete slab and the steel girder by an adhesive joint,not by the conventional metallic shear connectors.This so-called adhesive bonded steel-concrete composite beam is considered to be a very prospective alternate structure because it has the advantages of relieving stress concentration,avoiding site welding,and using the prefabricated concrete slab.Recently,an umber of studies on the experimental tests and numerical simulation of adhesive bonded
[3-5]steel-concrete composite beams have been presented in literatures.
With the ever increasing computational power,the past two decades have seen a
rapid development of structural optimization in both theories and engineering applications.In particular,the non-deterministic optimal design of steel or concrete beams incorporating stochastic uncertainties has been intensively studied by using the
[6,7]reliability-based design optimization (RBDO) method .Based on
the classical
probability theory,this conventional RBDO method describes uncertainties in structural systems as stochastic variables or random fields with certain probability distribution and thus provides an effective tool for determining the best design solution while explicitly
[8]considering the unavoidable effects of parameter variations.As
the most mature
non-deterministic design approach,the RBDO has been successfully
used in many
[9,10]real-life engineering applications.However,the primary
challenge to apply the
conventional RBDO in practical applications is the availability of
the precise statistical characteristics,which are crucial for a successful probabilistic reliability analysis and
design.Unfortunately,these accurate data usually cannot be obtained in some practical applications where only a limited number of samples are available.
[11,12]The early treatment for insufficient uncertainties is to construction a closest uniform probabilistic distribution by using the principle of maximum entropy.In
[13,14] 1990s,Elishakoffexplored that a small error in constructing the probabilistic density function for input uncertainties may lead to misleading assessment of the probabilistic reliability in particular
cases.This conclusion illuminates that using the traditional
probabilistic approach to deal with those problems involving in complete the information might be inconvincible. Consequently, an alternative category,namely the
[15]non-probabilistic approach,has been rapid developed for describing uncertainty with
incomplete statistical information by a fuzzy set or a convexset. In the fuzzy set
[16,17]method ,the fuzzy failure probability of structures is assessed based on membership
[18-20],function representation of the observed/measured inputs.In the convex set method
all possible values of the uncertainties are bounded within a hyper-box or hyper-ellipsoid without assuming any inner probability distributions.Non-probabilistic models have been regarded as attractive supplements to the traditional probabilistic model in the reliability design of structural engineering.The interested readers are referred to research papers
[21][23]bye.g. Moens and Vandepitte ,Moller and Beer [22],Elishakoff and Ohsaki.
In a practical engineering problem of adhesive bonded steel-concrete composite beams,the uncertain scatter of structural parameters about their expected values is unavoidable.For example,the applied loads may
fluctuate dramatically during its service life-cycle,and the parameters defining the structure,such as geometrical dimensions and material properties,are also subject to inaccuracies or
deviations.Among these concerned uncertainties,some can be characterized with precise-enough probability distributions,while others need to be treated as bounded ones due to a lack of sufficient sample data.A
typical example of such bounded uncertainties is the load magnitude and the geometrical dimensions of a manufactured product,the variation ranges of which are controlled by specified tolerance bounds.
From as early as 1993,attempts have been made to assess and analyze the structural safety in the presence of both stochastic variables and uncertain-but-bounded variables
[24]by Elishakoff and Colombi . Recently ,many numerical
methods,including the
[25] [26]multi-point approximation technique,the iterative rescaling method,the probability
[27] [28]bounds (p-box) approach,and the interval truncation method,have been proposed
for estimating the lower and upper bounds of failure probability of structures with a combination of stochastic and interval
variables.Detailed surveys of both known and new
[29]algorithms for this safety assessment problem have also been made by Berleant etal.
[30]and Kreinovich etal..However,it is noted that a few studies have considered various
[31] uncertainties in the reliability-based design optimization problems.Duetal.extended
the conventional RBDO method to structural design problems under the combination of random and interval variables.In their study,a procedure for seeking the worst-case combination of the interval variables is embedded into the probabilistic reliability analysis.
As the literature survey shows,the existing studies mainly focus on solving the combination of random/interval variables. Basically,the interval set does not account for the dependencies among the bounded uncertainties,which can be regarded as the simplest instance of the set-value based convex model.Due to the unpredictability of structural parameters and the impossibility of the acquisition of sufficient uncertainty information,problems of structural optimization must be solved in the presence of various
[32]types of uncertainties,which remains a challenging problem in realistic systems.As a
consequence,apractical and efficient reliability-based design optimization being capable of quantifying probabilistic and non-probabilistic uncertainties,as well as associated numerical techniques,should be fully developed and adopted in the professional practice of adhesive bonded steel-concrete composite beam design.
In this paper,using the mathematical definition of structural reliability index based
[33]on probability and convexsetmixed model,a nested optimization formulation with
constraints on such mixed reliability indices for the adhesive bonded steel-concrete
composite beam is first presented.For improving the convergence and the stability
[34]insolving sub-optimization problems,the performance measure approach (PMA) is
skillfully employed. Then,the sequential approximate programming approach embedded by an iterative scheme is proposed for converting the nested problem into a serial of deterministic ones, which will greatly reduce the burdensome computation workloads in seeking the optimal design.Through comparing with the direct nested double-loop approach,the applicability and the efficiency of the proposed methods are demonstrated by aclassical mathematical example.Finally,the reliability-based optimization designs of a single span adhesive bonded steel-concrete composite beam are achieved through integrating the present systematic method,the finite element analysis program and the
[35]gradient-based design optimization package CFSQP .
2. RBDO of adhesive bonded steel-concrete composite beams
2.1. Description of probabilistic and non-probabilistic
uncertainties
In practice engineering,the uncertain parameters involved in the design problem can
Tbe classified into probabilistic uncertainties (denoted by X=
{ X,X，…，Xm } )and 12
Tnon-probabilistic uncertainties (denoted by Y= { Y,Y，…，
Ym } )according to their 12
available input samples.It is desirable to select the best suitable models to respectively describe these different types of uncertainties.
Undoubtedly,the probabilistic uncertainties X can be modelled as stochastic variables with certain distribution characteristics,which are expressedas
Twhere f(x)is the joint probability density function. X= { X,X，…，Xm } )represents x12
[36]the realization of the variables X. In the classical
probabilistic framework,the
structural reliability is given as
where Pr [?] denotes the probability, g(X) is a limit-state function and g(X)?0 defines
the safety events.
For the non-probabilistic uncertainties ，the bounds or ranges of parameter
variation,compared with precise probability density function,are more easily obtained with the limited measurement results,e.g.the least data envelop set or the manufacturing
[37]tolerance specifications.In such circumstances,a multiellipsoid convex model is
competent for the non-probabilistic uncertainty
description.Following this frequently
used convex model,all the non-probabilistic parameters are divided into groups with the rule that variations of parameters in different groups are uncorrelated.Herein,each group of uncertainties are bounded by an individual hyper-ellipsoid convex set,respectively,as
where is the nominal value vector of the i-th group uncertainties ，is the
characteristic matrix and it is a symmetric positive-definite real matrix defining the orientation and aspect ratio of the i-th ellipsoid, is a real number defining the
magnitude of the parameter variability, n is the total number of groups of the g
non-probabilistic uncertainties Y. Supposing n is the number of uncer- tainties in the i-th i
group,there is
For an illustrative purpose,three specific multi-ellipsoid cases for a problem with three non-probabilistic parameters,which are divided into three groups
,twogroups and one group
respectively,are schematicall shown in Fig. 1(a)-(c). .As
illustrated in Fig.1(a), the multi-ellipsoid set is reduced to an hyper-box(or interval set) when each group consists of only one uncertainparameter.In Fig.1(c),the single-ellipsoid set represents another special case of the multi-ellipsoid set when all the bounded uncertainties are correlated into one group.Thus,the multi-ellipsoid convex model in (4) provides a generalized framework that extends common interval sets and single-ellipsoid sets for the representation of non-probabilistic uncertainties.
2.2. Definition of the structural mixed reliability index
For the assessment of the structural reliability combining probabilistic and non-probabilistic uncertainties,it is convenient to transform the original non-normal or
Tdependent random variables X= { X,X，…，Xm } into independent normal random 12
T [38]ones U= { U,U，…，Um } in U-space via the Rackwitz-Fiessler method or the 12
[39]Rosenblatt method.
In the simplest case,a normal random variable X can be transformed into a standard normal random variable U by
where X and are the mean value and the standard deviation of X, respectively.
2 中文译文
基于钢-混凝土粘接组合梁可靠度优化设计的概率和非概率不
确定性
摘要
在胶粘剂粘结的钢混凝土组合梁的优化设计中考虑各种不确定的因素是有很- 重要的意义的。

根据对概率和非概率不确定性评价结构安全性的综合可靠度指标的定义，随然这种可靠度优化与综合可靠度组合会成为一个嵌套问题。

用性能测试的方法改善结构内循环时的收敛性和稳定性。

此外，通过整合连续近似法和迭代方案，双循环优化问题转化为一系列近似确定性的问题，从而大大降低了寻求最优设计的繁琐的计算工作量。

通过一个数学例子可以表明所建议公式的有效性和数值计算技术的效率。

最后，通过整合目前的系统理论，有限元分析及优化方案，实现了在胶接单跨钢混凝土组合梁可靠度为基础的不同工况的优化设计- 、引言1
在世界各地，集于高抗拉强度钢和高抗压强度混凝土于一体的钢与混凝土组合
[1,2]梁，已广泛用于多层建筑和桥梁。

在世纪年代初，一个有效的粘接技术2060
就被介绍，用一个胶接接头把混凝土板和钢梁连接在一起，而不是用传统的金属剪切连接器。

这种所谓的粘合剂粘钢混凝土组合梁被认为是一个有前景可供选择的结-
构，因为它具有缓解应力集中的优点，避免现场焊接，并采用预制混凝土板。

最近，
[3-5]许多关于粘接钢混凝土组合梁在实验测试和数值模拟的研究在文献中提出了。

-
随着计算能力的不断提高，过去的二十年已经见证了在理论和工程应用中结构优化的快速发展。

特别是，通过是用以可靠性的为基础的设计优化研究()RBDO [6,7]方法，非确定性的钢梁或混凝土梁优化设计组合随机不确定性已被集中的研究。

以古典概率理论为基础，这种传统可靠度优化设计方法把结构体系不确定性领域描述为随机变量或以一定的概率分布的随机领域，从而为确定最佳的设计解决方案，同时明确考虑参数变化的不可避免的影响的有效工具。

作为最成熟的非确定性设[8]
[9,10]计方法，可靠度优化设计已成功地应用于许多实际工程应用。

然而，在实际应用中运用传统可靠度优化设计，最主要的挑战是精确的统计特性的可用性，这个可用性对成功的概率可靠性分析与设计来说很关键。

不幸的是，在样本数量有限的实际应用中，这些精确的数据通常不能获得。

[11,12]对不确定性的不足，早期的方法是利用最大熵原理，建立一个最接近统一
[13,14]的概率分布。

在世纪年代，研究表明在构建一个输入不确定
2090Elishakoff
性的概率密度函数的小错误可能导致在特定情况下概率可靠性误导性的评估。

这一结论阐明，使用传统的概率方法处理包括不完整信息的这些问题，可能无法使人信
[15]服。

因此，另一类，即非概率方法，通过模糊集或凸集来描述不完全的统计信息
[16,17]的不确定性得到了飞速发展。

在模糊集方法中，结构的模糊失效概率是以所观
[18-20]察到的测量输入的子函数表示来做评估的。

在凸集方法中，所有的具有不确/
定性的可能值是有界内的超框或超椭球界里，而不承担任何内部的概率分布。

非概率模型已被视为传统的结构工程可靠性设计的概率模型有吸引力的补充。

有兴趣的读者可参考的研究论文
[21] [22][23]例如和和和Moens Vandepitte, Möller Beer, Elishakoff Ohsaki .
在一个粘接钢混凝土组合梁的实际工程问题中，关于结构参数预期值的不确定-
性分散是不可避免的。

例如，在其使用寿命周期，应用负载可能大幅波动，并且参数定义的结构，如几何尺寸和材料特性，也会有错误或偏差。

在这些方面的不确定性，有些可以精确表征概率分布，而其它需要作为由于缺乏足够的样本数据来处理。

一个有界不确定性的典型例子是负荷的大小和一个制作构件的几何尺寸，其变化范围是由指定的误差范围控制。

从早在年，和曾尝试进行评估和分析这两个随机变1993ElishakoffColombi
[24][25]量存在的结构安全和不确定但是有界的变量。

最近，包括多点逼近技术，重
[26][27][28]新调整迭代法，概率边界(型盒)的方法，区间截断法的许多数值方法p
[29]已提出估计与随机变量组合及区间结构失效概率的下限和上限。

和Berleant al.
[30]对这个问题的已知安全性评价和新算法的具体细节已经做了调Kreinovich al.
查。

然而，人们注意到，一些研究考虑了可靠性为基础的设计优化问题的各种不确
[31] 定性。

在组合结构设计问题里，扩展了传统方法下的随机变量Du et al. RBDO
和区间变量。

在他们的研究，为寻求区间最差情况相结合的过程变量嵌入到概率可靠性分析。

正如文献调查显示，现有的研究主要集中在解决随机区间变量的组合。

基本上，/
设置间隔并没有考虑为边界不确定性之间的相关性，这可以被看作是设定值的凸模型把最简单的实例。

由于结构参数的不可预测性和不确定性信息的获取不是足够，结构优化问题必须在各类不确定因素中解决，仍然是一个在现实系统中存在的具有
[32]挑战性的问题。

因此，对专业实践的粘合的钢与混凝土组合梁，一个以实用高效的可靠性为基础的设计优化可以被量化为概率和非概率不确定性，以及相关的数值方法，设计应充分发展和采用。

[33]本文利用结构基于概率可靠性指标的数学定义和凸集的混合模型，本文利用
[33]结构基于概率可靠性指标的数学定义和凸集的混合模型，在这样一个粘合的钢-
混凝土组合梁的混合的可靠性指标约束嵌套优化可以表述首先提出。

为了提高收敛
[34]和解决次优化问题的稳定性，性能测量方法()巧妙地得以应用。

然后，PMA
通过一个反复的方案连续的近似规划方法的嵌入，提出将一个嵌套的问题转换为一系列确定性的问题，这将大大减少在寻求最佳设计的繁琐的计算工作负荷。

通过与直接嵌套的双回路方法的嵌套相比，所提出的方法的适用性和效率证明了一个经典的数学例子。

最后，一个单跨钢混凝土叠合梁可靠性为基础的优化可以设计是通过-
[35]整合现有的系统方法，有限元分析程序和基于梯度设计优化软件包实CFSQP 现。

、粘接钢混凝土组合梁可靠度优化设计2 -
述概率和非概率不确定性的描2.1.
在实际工程，根据自己可用的输入样本，在设计问题所涉及的不确定参数可分为概率不确定性(记的和，…，的)和非概率不确定性(记为，X={x1x2Xm}
TY={ Y1，…，)。

选择最适合的模型来分别描述这些不同类型的不确定性是可取的。

Y2Yn} T
毫无疑问，可以被视为具有一定的分布随机变量的特点，可把模型的概率不X 确定性表示为
其中()是联合概率密度函数。

和，…，代表的变量的fxxx={x1x2 XM} TX
[36]实现。

在古典概率框架中，结构可靠性给出
其中?表示概率，()是一种极限状态函数且()?定义为安全事Pr[]gxgx0件。

对于非概率不确定性，界限或参数的变化范围，与精确的概率密度函数相比较，更容易获得有限的测量结果，例如最少的数据集或封套的制造公差规格。

[37]在这种情况下，对于非概率不确定性，一个多椭球凸模型是可以表述的。

按照这一经常使用的凸模型，所有的非概率参数按照在不同的组中参数的变化是不相关的来划分。

这样，每个组的不确定性由个别超椭球凸集来分界，分别为
其中是第个向量组的不确定性的名义数值向量，是特征矩阵，它是i
一个界定第个椭球取向和高宽比的对称正定实矩阵，是一个定义实数参数的变i
化幅度，是对非概率不确定性的总数。

假定是第组的不确定性，则有i:。

对于介绍用途，三个具体多椭球案例有三个非概率参数，问题可以分成三组两组和一组，
分别示意如图。

如图所示，多椭球集减少到1(a)-(c)1(a)
一个超框(或区间设置)时，每个组只有一个不确定参数组成。

在图单椭球1(c) 集表示的是另一个特殊的多椭球集情况时，所有的有界不确定性被相关的分为一组。

因此，多椭球凸模型()提供一个通用的框架，扩展了非概率不确定性代表4
的共同区间集，即单套椭球。

混合结构可靠性指标的定义2.2.
对于结构可靠性评估相结合的概率和非概率不确定性，在空间通过U-
方法或罗森布莱特方法，可以很方便地改变原来的非正Rackwitz-
Fiessler[38][39]
常或相关随机变量为独立的正态随机。

在一个简单的例子里，一个正常的随机变量通过下式可以转化为一个标准正X 态随机变量U
其中和分别为的平均值和标准差。

X。