外文翻譯--基于鋼-混凝土粘接組合梁可靠度優(yōu)化設(shè)計(jì)的概率和非概率不確定性

1、<p><b>　　1 英文原文</b></p><p>　　Reliability-based design optimization of adhesive bonded steel-Cconcret composite beams with probabilistic and non-probabilistic uncertainties</p><p&g

2、t;　　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 s

3、afety evaluation with probabilistic and non-probabilistic uncertainties,the reliability-based optimization incorporating such mixed reliability constraints are mathematically formulated as a nested problem.The</p>

4、<p>　　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 determ

5、inistic 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 for

6、mulation as well as the efficiency of the presented numerical techniques</p><p>　　Introduction</p><p>　　The steel-cconcrete composite beam,which integrates the high tensile strength of steel and

7、 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 adhesive bonding technique[1,2]was introduced to connect

8、 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 b</p><p>　　With th

9、e 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 stee

10、l or concrete beams incorporating stochastic uncertainties has been intensively studied by using the reliability-based design optimization (RBDO) method [6,7].Based on the classical probability theory,this conventional R

11、BDO method describes uncertainties in structural syst</p><p>　　The early treatment [11,12] for insufficient uncertainties is to construction a closest uniform probabilistic distribution by using the principl

12、e of maximum entropy.In 1990s,Elishakoff [13,14] explored that a small error in constructing the probabilistic density function for input uncertainties may lead to misleading assessment of the probabilistic reliability i

13、n particular cases.This conclusion illuminates that using the traditional probabilistic approach to deal with those problems involving i</p><p>　　In a practical engineering problem of adhesive bonded steel-c

14、oncrete 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

15、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 &

16、lt;/p><p>　　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 by Elishakoff and Colombi [

17、24]. Recently ,many numerical methods,including the multi-point approximation technique[25],the iterative rescaling method [26],the probability bounds (p-box) approach [27],and the interval truncation method [28],have be

18、en proposed for estimating the lower and upper bounds of failure probability of st</p><p>　　As the literature survey shows,the existing studies mainly focus on solving the combination of random/interval vari

19、ables. 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 st

20、ructural parameters and the impossibility of the acquisition of sufficient uncertainty information,problems of structural optimization must be solved in the presence</p><p>　　In this paper,using the mathemat

21、ical definition of structural reliability index based on probability and convexsetmixed model [33],a nested optimization formulation with constraints on such mixed reliability indices for the adhesive bonded steel-concre

22、te composite beam is first presented.For improving the convergence and the stability insolving sub-optimization problems,the performance measure approach (PMA) [34] is skillfully employed. Then,the sequential approximate

23、 programming approach embedd</p><p>　　RBDO of adhesive bonded steel-concrete composite beams</p><p>　　Description of probabilistic and non-probabilistic uncertainties</p><p>　　In pr

24、actice engineering,the uncertain parameters involved in the design problem can be classified into probabilistic uncertainties (denoted by X= { X1,X2，…，Xm } T）and non-probabilistic uncertainties (denoted by Y= { Y1,Y2，…，Y

25、m } T）according to their available input samples.It is desirable to select the best suitable models to respectively describe these different types of uncertainties. </p><p>　　Undoubtedly,the probabilistic un

26、certainties X can be modelled as stochastic variables with certain distribution characteristics,which are expressedas</p><p>　　where fx（x）is the joint probability density function. X= { X1,X2，…，Xm } T）repres

27、ents the realization of the variables X. In the classical probabilistic framework[36],the structural reliability is given as</p><p>　　where Pr [·] denotes the probability, g（X） is a limit-state function

28、 and g（X）≥0 defines the safety events.</p><p>　　For the non-probabilistic uncertainties ，the bounds or ranges of parameter variation,compared with precise probability density function,are more easily obtaine

29、d with the limited measurement results,e.g.the least data envelop set or the manufacturing tolerance specifications.In such circumstances,a multiellipsoid convex model [37] is competent for the non-probabilistic uncertai

30、nty description.Following this frequently used convex model,all the non-probabilistic parameters are divided into groups </p><p>　　where is the nominal value vector of the i-th group uncertainties ， is the

31、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, ng is the

32、total number of groups of the non-probabilistic uncertainties Y. Supposing ni is the number of uncer- tainties in the i-th group,there is </p><p>　　For an illustrative purpose,three specific multi-ellipsoid

33、 cases for a problem with three non-probabilistic parameters,which are divided into three groups </p><p>　　,twogroups and one group respectively,are schematicall shown in Fig. 1(a)-(c). .As illustrated in

34、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-elli

35、psoid 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 interva</p><p>　　2.2. Definition o

36、f the structural mixed reliability index</p><p>　　For the assessment of the structural reliability combining probabilistic and non-probabilistic uncertainties,it is convenient to transform the original non-n

37、ormal or dependent random variables X= { X1,X2，…，Xm } T into independent normal random ones U= { U1,U2，…，Um } T in U-space via the Rackwitz-Fiessler method [38] or the Rosenblatt method [39].</p><p>　　In t

38、he simplest case,a normal random variable X can be transformed into a standard normal random variable U by</p><p>　　where X and are the mean value and the standard deviation of</p><p>　　X, resp

39、ectively.</p><p><b>　　2 中文譯文</b></p><p>　　基于鋼-混凝土粘接組合梁可靠度優(yōu)化設(shè)計(jì)的概率和非概率不確定性</p><p><b>　　摘要</b></p><p>　　在膠粘劑粘結(jié)的鋼-混凝土組合梁的優(yōu)化設(shè)計(jì)中考慮各種不確定的因素是有很重要的意義的。根據(jù)

40、對(duì)概率和非概率不確定性評(píng)價(jià)結(jié)構(gòu)安全性的綜合可靠度指標(biāo)的定義，隨然這種可靠度優(yōu)化與綜合可靠度組合會(huì)成為一個(gè)嵌套問題。用性能測(cè)試的方法改善結(jié)構(gòu)內(nèi)循環(huán)時(shí)的收斂性和穩(wěn)定性。此外，通過整合連續(xù)近似法和迭代方案，雙循環(huán)優(yōu)化問題轉(zhuǎn)化為一系列近似確定性的問題，從而大大降低了尋求最優(yōu)設(shè)計(jì)的繁瑣的計(jì)算工作量。通過一個(gè)數(shù)學(xué)例子可以表明所建議公式的有效性和數(shù)值計(jì)算技術(shù)的效率。最后，通過整合目前的系統(tǒng)理論，有限元分析及優(yōu)化方案，實(shí)現(xiàn)了在膠接單跨鋼-混凝土組合梁可

41、靠度為基礎(chǔ)的不同工況的優(yōu)化設(shè)計(jì)</p><p><b>　　引言</b></p><p>　　在世界各地，集于高抗拉強(qiáng)度鋼和高抗壓強(qiáng)度混凝土于一體的鋼與混凝土組合梁，已廣泛用于多層建筑和橋梁。在20世紀(jì)60年代初，一個(gè)有效的粘接技術(shù)[1,2]就被介紹，用一個(gè)膠接接頭把混凝土板和鋼梁連接在一起，而不是用傳統(tǒng)的金屬剪切連接器。這種所謂的粘合劑粘鋼-混凝土組合梁被認(rèn)為是一個(gè)

42、有前景可供選擇的結(jié)構(gòu)，因?yàn)樗哂芯徑鈶?yīng)力集中的優(yōu)點(diǎn)，避免現(xiàn)場(chǎng)焊接，并采用預(yù)制混凝土板。最近，許多關(guān)于粘接鋼-混凝土組合梁在實(shí)驗(yàn)測(cè)試和數(shù)值模擬的研究在文獻(xiàn)中提出了[3-5]。</p><p>　　隨著計(jì)算能力的不斷提高，過去的二十年已經(jīng)見證了在理論和工程應(yīng)用中結(jié)構(gòu)優(yōu)化的快速發(fā)展。特別是，通過是用以可靠性的為基礎(chǔ)的設(shè)計(jì)優(yōu)化研究（RBDO）方法[6,7]，非確定性的鋼梁或混凝土梁優(yōu)化設(shè)計(jì)組合隨機(jī)不確定性已被集中的研究。

43、以古典概率理論為基礎(chǔ)，這種傳統(tǒng)可靠度優(yōu)化設(shè)計(jì)方法把結(jié)構(gòu)體系不確定性領(lǐng)域描述為隨機(jī)變量或以一定的概率分布的隨機(jī)領(lǐng)域，從而為確定最佳的設(shè)計(jì)解決方案，同時(shí)明確考慮參數(shù)變化的不可避免的影響[8]的有效工具。作為最成熟的非確定性設(shè)計(jì)方法，可靠度優(yōu)化設(shè)計(jì)已成功地應(yīng)用于許多實(shí)際工程應(yīng)用[9,10]。然而，在實(shí)際應(yīng)用中運(yùn)用傳統(tǒng)可靠度優(yōu)化設(shè)計(jì)，最主要的挑戰(zhàn)是精確的統(tǒng)計(jì)特性的可用性，這個(gè)可用性對(duì)成功的概率可靠性分析與設(shè)計(jì)來(lái)說很關(guān)鍵。不幸的是，在樣本數(shù)量有限

44、的實(shí)際應(yīng)用中，這些精確的數(shù)據(jù)通常不能獲得。</p><p>　　對(duì)不確定性的不足，早期的方法是利用最大熵原理[11,12]，建立一個(gè)最接近統(tǒng)一的概率分布。在20世紀(jì)90年代，Elishakoff[13,14]研究表明在構(gòu)建一個(gè)輸入不確定性的概率密度函數(shù)的小錯(cuò)誤可能導(dǎo)致在特定情況下概率可靠性誤導(dǎo)性的評(píng)估。這一結(jié)論闡明，使用傳統(tǒng)的概率方法處理包括不完整信息的這些問題，可能無(wú)法使人信服。因此，另一類，即非概率方法[15

45、]，通過模糊集或凸集來(lái)描述不完全的統(tǒng)計(jì)信息的不確定性得到了飛速發(fā)展。在模糊集方法中[16,17]，結(jié)構(gòu)的模糊失效概率是以所觀察到的/測(cè)量輸入的子函數(shù)表示來(lái)做評(píng)估的。在凸集方法中[18-20]，所有的具有不確定性的可能值是有界內(nèi)的超框或超橢球界里，而不承擔(dān)任何內(nèi)部的概率分布。非概率模型已被視為傳統(tǒng)的結(jié)構(gòu)工程可靠性設(shè)計(jì)的概率模型有吸引力的補(bǔ)充。有興趣的讀者可參考的研究論文例如Moens 和 Vandepitte [21], Mö

46、ller 和 Beer [22], Elishakoff和 Ohsaki [23].</p><p>　　在一個(gè)粘接鋼-混凝土組合梁的實(shí)際工程問題中，關(guān)于結(jié)構(gòu)參數(shù)預(yù)期值的不確定性分散是不可避免的。例如，在其使用壽命周期，應(yīng)用負(fù)載可能大幅波動(dòng)，并且參數(shù)定義的結(jié)構(gòu)，如幾何尺寸和材料特性，也會(huì)有錯(cuò)誤或偏差。在這些方面的不確定性，有些可以精確表征概率分布，而其它需要作為由于缺乏足夠的樣本數(shù)據(jù)來(lái)處理。一個(gè)有界不確定性的典型

47、例子是負(fù)荷的大小和一個(gè)制作構(gòu)件的幾何尺寸，其變化范圍是由指定的誤差范圍控制。</p><p>　　從早在1993年，Elishakoff和Colombi曾嘗試進(jìn)行評(píng)估和分析這兩個(gè)隨機(jī)變量存在的結(jié)構(gòu)安全和不確定但是有界的變量[24]。最近，包括多點(diǎn)逼近技術(shù)[25]，重新調(diào)整迭代法[26]，概率邊界（p型盒）的方法[27]，區(qū)間截?cái)喾╗28]的許多數(shù)值方法已提出估計(jì)與隨機(jī)變量組合及區(qū)間結(jié)構(gòu)失效概率的下限和上限。Ber

48、leant al.[29]和Kreinovich al.[30] 對(duì)這個(gè)問題的已知安全性評(píng)價(jià)和新算法的具體細(xì)節(jié)已經(jīng)做了調(diào)查。然而，人們注意到，一些研究考慮了可靠性為基礎(chǔ)的設(shè)計(jì)優(yōu)化問題的各種不確定性。Du et al. [31] 在組合結(jié)構(gòu)設(shè)計(jì)問題里，擴(kuò)展了傳統(tǒng)RBDO方法下的隨機(jī)變量和區(qū)間變量。在他們的研究，為尋求區(qū)間最差情況相結(jié)合的過程變量嵌入到概率可靠性分析。</p><p>　　正如文獻(xiàn)調(diào)查顯示，現(xiàn)有的研究

49、主要集中在解決隨機(jī)/區(qū)間變量的組合。基本上，設(shè)置間隔并沒有考慮為邊界不確定性之間的相關(guān)性，這可以被看作是設(shè)定值的凸模型把最簡(jiǎn)單的實(shí)例。由于結(jié)構(gòu)參數(shù)的不可預(yù)測(cè)性和不確定性信息的獲取不是足夠，結(jié)構(gòu)優(yōu)化問題必須在各類不確定因素中解決，仍然是一個(gè)在現(xiàn)實(shí)系統(tǒng)中存在的具有挑戰(zhàn)性的問題[32]。因此，對(duì)專業(yè)實(shí)踐的粘合的鋼與混凝土組合梁，一個(gè)以實(shí)用高效的可靠性為基礎(chǔ)的設(shè)計(jì)優(yōu)化可以被量化為概率和非概率不確定性，以及相關(guān)的數(shù)值方法，設(shè)計(jì)應(yīng)充分發(fā)展和采用。&

50、lt;/p><p>　　本文利用結(jié)構(gòu)基于概率可靠性指標(biāo)的數(shù)學(xué)定義和凸集的混合模型[33]，本文利用結(jié)構(gòu)基于概率可靠性指標(biāo)的數(shù)學(xué)定義和凸集的混合模型[33]，在這樣一個(gè)粘合的鋼-混凝土組合梁的混合的可靠性指標(biāo)約束嵌套優(yōu)化可以表述首先提出。為了提高收斂和解決次優(yōu)化問題的穩(wěn)定性，性能測(cè)量方法（PMA）[34]巧妙地得以應(yīng)用。然后，通過一個(gè)反復(fù)的方案連續(xù)的近似規(guī)劃方法的嵌入，提出將一個(gè)嵌套的問題轉(zhuǎn)換為一系列確定性的問題，這將

51、大大減少在尋求最佳設(shè)計(jì)的繁瑣的計(jì)算工作負(fù)荷。通過與直接嵌套的雙回路方法的嵌套相比，所提出的方法的適用性和效率證明了一個(gè)經(jīng)典的數(shù)學(xué)例子。最后，一個(gè)單跨鋼-混凝土疊合梁可靠性為基礎(chǔ)的優(yōu)化可以設(shè)計(jì)是通過整合現(xiàn)有的系統(tǒng)方法，有限元分析程序和基于梯度設(shè)計(jì)優(yōu)化軟件包CFSQP[35] 實(shí)現(xiàn)。</p><p>　　粘接鋼-混凝土組合梁可靠度優(yōu)化設(shè)計(jì)</p><p>　　2.1.概率和非概率不確定性的描述

52、</p><p>　　在實(shí)際工程，根據(jù)自己可用的輸入樣本，在設(shè)計(jì)問題所涉及的不確定參數(shù)可分為概率不確定性（記的X={x1和x2，…，Xm的} T）和非概率不確定性（記為Y={ Y1，Y2，…，Yn} T）。選擇最適合的模型來(lái)分別描述這些不同類型的不確定性是可取的。</p><p>　　毫無(wú)疑問，X可以被視為具有一定的分布隨機(jī)變量的特點(diǎn)，可把模型的概率不確定性表示為</p>&

53、lt;p>　　其中fx（x）是聯(lián)合概率密度函數(shù)。x={x1和x2，… ，XM} T代表的變量X的實(shí)現(xiàn)。在古典概率框架[36]中，結(jié)構(gòu)可靠性給出</p><p>　　其中Pr[·]表示概率，g（x）是一種極限狀態(tài)函數(shù)且g（x）≥0定義為安全事件。</p><p>　　對(duì)于非概率不確定性，界限或參數(shù)的變化范圍，與精確的概率密度函數(shù)相比較，更容易獲得有限的測(cè)量結(jié)果，例如最少的數(shù)據(jù)

54、集或封套的制造公差規(guī)格。在這種情況下，對(duì)于非概率不確定性，一個(gè)多橢球凸模型[37]是可以表述的。按照這一經(jīng)常使用的凸模型，所有的非概率參數(shù)按照在不同的組中參數(shù)的變化是不相關(guān)的來(lái)劃分。這樣，每個(gè)組的不確定性由個(gè)別超橢球凸集來(lái)分界，分別為</p><p>　　其中是第i個(gè)向量組的不確定性的名義數(shù)值向量，是特征矩陣，它是一個(gè)界定第i個(gè)橢球取向和高寬比的對(duì)稱正定實(shí)矩陣，是一個(gè)定義實(shí)數(shù)參數(shù)的變化幅度，是對(duì)非概率不確定性的總

55、數(shù)。假定是第i組的不確定性，則有：。</p><p>　　對(duì)于介紹用途，三個(gè)具體多橢球案例有三個(gè)非概率參數(shù)，問題可以分成三組，兩組和一組分別示意如圖1(a)-(c)。如圖1(a)所示，多橢球集減少到一個(gè)超框（或區(qū)間設(shè)置）時(shí)，每個(gè)組只有一個(gè)不確定參數(shù)組成。在圖1(c) 單橢球集表示的是另一個(gè)特殊的多橢球集情況時(shí)，所有的有界不確定性被相關(guān)的分為一組。</p><p>　　因此，多橢球凸模型（4

56、）提供一個(gè)通用的框架，擴(kuò)展了非概率不確定性代表的共同區(qū)間集，即單套橢球。</p><p>　　2.2.混合結(jié)構(gòu)可靠性指標(biāo)的定義</p><p>　　對(duì)于結(jié)構(gòu)可靠性評(píng)估相結(jié)合的概率和非概率不確定性，在U-空間通過Rackwitz- Fiessler方法[38]或羅森布萊特方法[39]，可以很方便地改變?cè)瓉?lái)的非正?；蛳嚓P(guān)隨機(jī)變量為獨(dú)立的正態(tài)隨機(jī)。</p><p>　　在