外文翻译-机械结构的可靠性优化设计.doc

英文原文Optimize the reliability of mechanical structure designIt is now generally recognized that structural and mechanical problems are nondeterministic and, consequently, engineering optimum design must cope with un-certainties，Reliability technology provides tools for formal assessment and analysis of such uncertainties，Thus, the combination of reliability-based design procedure sand optimization promises to provide a practical optimum design solution, i，e，, a de-sign having an optimum balance between cost and risk， However, reliabilty-based structural optimization programs have not enjoyed the name popularity as their deterministic counterparts， Some reasons for this are suggested， First, reliability analysis can be complicated even for simple systems， There are various methods for handling the uncertainty in similar situations (e，g，, first order second moment methods, full distribution methods)， Lacking a single method, individuals are likely to adopt separate strategies for handling the uncertainty in their particular problems， This suggests the possibility of different reliability predictions in similar structural design situations， Then, there are diverging opinions on many basic issues, from the very definition of reliability-based optimization, including the definition of the optimum solution, the objective function and the constraints, to its application in structural design practice， There is a need to formally consider these itess in the merger of present structural optimization research with reliability-based design philosophy。In general, an optimization problem can be stated as follows,Minimizesubject to the constraintswhere X is an-dimensional vector called the design vector， f(X) is called the objective function and, k(X) and i(X) are, respectively, the inequality and equality constraints， The number of variables n and the number of constraints， L need not be related in any way， Thus, L could be less than, equal to or greater than n in a given mathematical programming problem， In some problems, the value of L might be zero which means there are no constraints on the problem， Such type of problems are called unconstrained optimization problems， Those problems for which L is not equal to zero are known as constrained optimization problems。 Traditionally the designer assumes the loading on an element and the strength of that element to be a single valued characteristic or design value， Perhaps it is equal to some maximum (or minimum) anticipated or nominal value， Safety is assured by introducing a factor of safety, greater than one, usually applied as a reduction factor to strength。Probabilistic design is propose: as an alternative to the conventional approach with the promise of producing better engineered systems， each factor in the design process can be defined and treated as a random variable， Using method-ology from probabilistic theory, the designer defines the appropriate limit state and computes the probability of failure P of the element， The basic design requirement is that，where p f is the maximum allowable probability of failure。Advantages of adopting the probabilistic design approach are well documented (Wu, 1984)， Basically the arguments for probabilistic design center around the fact that, relative to the conventional approach, a) risk is a more meaningful index of structural performance, and b) a reliability approach to design of a sys-tom can tend to produce an optimum design by ensuring a uniform risk in all components。 Optimization, which may be considered a component of operations research, is the process of obtaining the best result by finding conditions that produce the maximum or minimum value of a function， Table 1，1 illustrates area of operations research。 Mathematical programming techniques, also known as optimization methods, are useful in finding the minimum (or maximum) of a function of several variables under a prescribed set of constraints， Rao (1979) presented a definition and description of some of the various methods of mathematical programming， Stochas-tic process techniques can be used to analyze problems which are described by a set of random variables， Statistical methods enable one to analyze the experimental data and build empirical models to obtain the most accurate representations of physical behavior。 Origins of optimization theory can be traced to the days of Newton, La-grange and Cauchy in the 1800x， The application of differential calculus to optimization was possible because of the contributions of Newton and Leibnitz， The foundations of calculus of variations were laid by Bernoulli, Euler, Lagrange and Weirstrass， The method of optimization for constrained problems, which involves the addition of unknown multipliers became known by the name its inventor, La-grange， Cauchy presented the first application of the steepest descent method to solve minimization problems。In spite of these early contributions, very little progress was made until the middle of the twentieth Gentry, when high-speed digital computers made the implementation of optimization procedures possible and stimulate, d further research on new methods， Spectacular advances followed, producing a m;sssive literature on optimization techniques， This advancement also resulted in the emergence of several well-defined new areas in optimization theory。It is interesting to note that major developments in the area of numerical methods of unconstrained optimization have been made in the TTnited Kingdom only in the 1960x， The development of the simplex method by Dantzig (1947) for linear programming and the annunciation of the principle of optimality by Bellman (195?) for dynamic programming problems paved the wa，; f= development of the methods of constrained optimization， The work by Kuhn and Tucker (1951) on necessary and xuflicient conditions for the optimal xolution of programming problems laid foundations for later research in nonlinear programming, the optimization area of this thesis。Although no single technique has been found to be universally applicable for nonlinear programming, the works by Cacrol (1961)and Fiacco and McCormic (1968) suggested practical solutions by employing well-known techniques of uncon xtrained optimization， Geometric programming was developed by Dufhn, Zener and Peterson (1960)， Gomory (1963) pioneered work in integer programming, which is at this time an exciting and rapidly developing area of optimization research， Many real-world applications can be cast in this category of problem， Dantzig (1955) and Charnel and Cooper (1959) developed stochastic programming techniques and solved problems by assuming design parameters to be independent and normally distributed。Techniques of nonlinear programming, employed in this study, can be categorized 1， one-dimensional minimization method2， unconstrained multivariable minimization A， gradient based method B， nongradient based method3， constrained multivariable minimization A， gradient based method B，gradient based method The gradient based methods require function and derivative evaluations while the non gradient based methods require function evaluations only， In general, one would expect the gradient methods to be more effecti;re, due to the added information provided， However, if analytical derivatives are available, the question of whether a search technique should be used at all is presented， If numerical derivative approximations are utilized, the efficiency of the gradient based methods should be approximately the same as that of nongradient based methods， Gradient based methods incorporating numerical derivatives would be expected to present some numerical problems in the vicinity of the optimum, i，e，, approximations to slopes would become small， Fig， 1，1 shows the $ow chart of general iterative scheme of optimization (Rao, 1979)， No claim is made that some methods are better than any others， A method works well on one problem may perform very poorly on another problem of the same general type， Only after much experience using all the methods can one judge which method would be better for a particular problem (Kuester snd Mize, 1973). First attempts to apply probabilistic and statistical concepts in structural analysis date back to the beginning of this century， However, the subject aid not receive much attention until after the World War II， In October 1945, a historic paper written by A， M， Freudenthal entitled The Safety of Structures appeared in the proceedings of the American Society of Civil Engineers， The publicationof this paper marked the genesis of structural reliability in the U，S，A， Professor F:eudenthal continued for many years to be in the forefront of structural reliability and risk analysis， During the 1960s there was rapid growth of academic interest in struc-total reliability theory， Classical theory became well developed and widely known through a few influential publications such as that of Freudenthal, Garrelts, and Shi-nouzuka (1966), Pugsley (1966), Kececioglu and Cormier (1964), Ferry-Borges and Castenheta (1971, and Haugen (1968)， However, professional acceptance was low for several reasons， Probabilistic design seemed cumbersome, the theory, particularly system analysis, seemed mathematically intractible， Little data were available, and modeling error was an issue which needed to be addressed，But there were early efforts to circumvent these limitations， Turkstra(l070) Yrnted structural design as a problem of decision making under uncertainty and risk， Lind, Turkstra, and Wright (1965) defined the problem of rational design of a code as finding a set of best values of the load and resistance factors， Cornell (1967) suggested the use of a second moment format, and subsequently it was demonstrated that Cornells safety index requirement could be used to derive a set of safety factors on loads and resistances， This approach related reliability analysis to practically accepted methods of design The Cornell approach has been refined and employed in many structural standards，Difficulties with the second moment format were uncovered 1969 when Ditlevsen and Lind independently discovered the problem of invariance， Cornells index was not constant when certain simple problems were reformulated in a mechanically equivalent way， But the lack of invariance dilemma was overcome when Hasofer and Lind (1974) defined a generalized safety index which was invariant to mechanical formulation， This landmark paper represented a turning point in structural reliability theory， More sophisticated extensions of the Hasofer-Lind approach proposed in recent years by Rackwitz and Fiessler (1978), Chen and Lind (1982), and Wu (1984) provide accurate probability of failure estimates for complicated limit state functions，There are many modes of failure in structural systems, depending on the configuration of the system, shapes and materials of the members, the loading conditions, etc， Lz order to perform a system reliability assessment the failure modes must be defined， However, for a large system with a high degree of redundancy it is difficult in practice to determine a priori which failure modes are probabilistically significant， The following methods have been proposed to produce approximate solutions: (a) automatic generation of safety margins, (b) the p-unzipping method, and (c) branch-and-bound method (Thoft-Christensen and Murotsu, 1986)， The state of the art in sysiems structural reliability analysis is comprehended in the works vi Bennett (1983), Ang and Tang (1984), Guenard (1984), Ditlevsen (1986), Madsen, Krenk, and Lind (1986), and Thoft-Christensen and Murotsu (1986)， Butat this time there no general me hon for obtaining practical solutions to the system reliability problem。中文翻译机械结构的可靠性优化设计实际情况表明，所有的机械结构都具有很大的不确定性，因而使得机械工程学上的优化设计也具有不确定性，在不同的条件下所得到的优化结果是不一样的。可靠性设计就为这种不确定性问题提供了一个很好的比较正式的评价和分析工具。因此，这种结合了可靠性设计过程的优化设计方法就有很大实用性，也就是说，这种优化结果同时考虑到了机构的最优和最安全可靠两个设计要求。然而，基于可靠性的优化设计方法并没有得到广泛地应用。造成这种情况的原因有很多方面。首先，即使对于简单的系统，进行可靠性分析工作则是非常复杂的，对于比较相似的情况（例如采用完全分布法和主要分布法）有很多不同的方法用来处理这种不确定性。缺乏一种简单的、独立的可以相互适用的方法用来处理各种不同问题的不确定性。这就使得对于不同的但非常相似的机构设计具有不同的可靠性设计结果。还有，在关于可靠性概念的许多基本问题上面，还存在这一些分歧，这些分歧包括了关于可靠性优化的基本定义、优化结果、目标函数和约束条件已经它在结构设计中的实际应用等多个方面。总之，有必要对可靠性结构优化设计体系进行一个系统的正式的研究。一般的，一个结构优化问题可以归结为如下的数学模型：对目标函数的最小化： （11）约束条件：（1，2，K） （12）（，L） （13）其中，X是一个n维的设计变量，是目标函数，而和分别是不等式约束条件和等式约束条件。变量n的个数和约束条件L的个数与具体的应用情况有关系，不是确定不变的。因此，在一个给定的数学模型中，约束条件L的个数可能大于、等于或者小于设计变量n的个数。在一些实际问题中，约束条件L的个数为零，则表示这些问题没有约束条件，并称该类问题为无约束优化问题。而另外的一些约束条件不为零的问题则称为约束优化问题。在常规的设计中，认为外载荷是作用在零件上的固定单元上面，并且认为该单元的强度是一个单一的固定值或设计值。这个强度值可能是该类材料的预期或许用值的最大（最小）值。并且用安全系数来衡量零件的安全性，安全系数一般要大于一个推荐值。采用概率设计可以在传统的设计方法的基础上得到相对最好的设计结果，概率设计也就是这样的一种方法。在概率设计中，设计过程中的每个因素都需要定义并被当作随机变量处理。利用概率论的基本方法原理，定义一个合适的限制条件并计算此条件下单元的失效概率。并且要求，其中，是最大的许用失效概率。采用概率设计方法有许多的优点，并且在很多的书本里面都有相关的介绍和描述（Wu，1984）。而关于概率设计方法和传统设计方法的基本争论主要有以下两点：a）零件结构性能方面产生危险破坏的可能原因有很多方面。b）如果先确定一个合适的会产生危险破坏的标准，那么对一个系统的概率设计过程往往就是一个优化设计过程。优化可以被认为是一个工业研究的组成部分，主要通过利用目标函数在一定条件下的最大值或最小值条件来寻找一组最优的结果。表1，1介绍的就是工业研究的一般领域。数学处理方法，也就是所谓的优化数学模型，常用来计算一个有有限个随机变量的目标函数的在一定的约束条件下的最大（或最小）值。Rao（1979）提出了优化的定义并且记载了一些可用来计算优化数学模型的数学方法。随机过程方法就可以分析一些带有随机变量的问题。统计学方法则可以用来分析一些实验数据并建立经验模型以对物理行为进行最准确的描述。至于最早的优化方法可以追溯到17世纪时的牛顿，拉格朗日和柯西时期。由于牛顿和莱布尼茨创造了微分学，并得到了广泛的应用，使得优化过程成为可能。柏努利，欧拉，拉格朗日和魏尔斯特拉斯建立了变动的微积分学。约束优化问题的处理方法即设计到了对设计变量的增加方法也就是所谓的拉格朗日方法，这时用该种方法的创造者命名的。柯西则利用最速上升法来解决最小化问题。如果不考虑这些早期的数学家对优化过程的所做的成果，那么直到二十世纪中期对于该类问题的处理方法都没有取得明显的发展和进步。此时，高速计算机已经发明并且被用来执行优化处理过程，由此引发了对于新的优化方法近一步研究和应用。随后取得了巨大的进步，在优化方法领域产生了大量的文献著作。这种显著的进步时通过对优化理论的几个定义明确的新领域的合并所得到的。需要注意的是在二十世纪六十年代的英国已经在无约束优化领域方面取得了巨大的研究成果。丹奇克（1947）发明了单纯形法用来进行计算线性规划问题，而可以用来处理动态问题过程贝尔曼最优原则（1957）有力的促进了约束优化方法的发展。在库恩（1951）的关于在必要和充分的条件下优化问题的规划求解的论文则为非线性问题的近一步研究奠定了基础。尽管对于非线性问题，至今并没有发现一种单一的通用性的方法，但是，卡罗（1961）、费耶科和麦考密克（1968）的著作中称应用一些比较好的方法就可以得到无约束优化问题的实际解。达芬，奇纳和彼得森（1960）发明了几何规划法。戈莫里（1963）创立了整数规划法，并在当时的优化研究领域得到了巨大的发展。在实际工程应用中的很多方面都属于这个范畴。丹奇克（1955）和查纳斯和库珀（1959）发明了随机规划方法可以用来解决设计参数是相互独立和无关的线性分布问题。在本文中所用的非线性处理方法，可以归结为如下几个方面：1 一维最小化方法。2 无约束多变量最小化方法。 A 梯度法。 B 非梯度法。3 约束多变量最小化方法 A 梯度法。 B 非梯度法。梯度法需要用的目标函数的值和其微分值，而非梯度法则只需要用的目标函数的值，对目标函数是否具有微分值没有要求。一般的来说，用的函数梯度的方法效率更高，这是因为相当于增加了已知条件。然而，如果函数解析的微分解是存在并可用的，那么就可以用到目前正在使用的一维搜寻法。如果用的的是函数的引出的数值近似方法，那么梯度法和非梯度法的效率基本相当。梯度法里面可以包括了一些数值近似法，可以用来解决一些优化问题，其结果都是近似的，误