基于代理模型的多样性可竞争结构优化设计

发布时间：2018-05-12 07:12

  本文选题：多样性 + 可竞争性　； 参考：《大连理工大学》2016年博士论文

【摘要】：随着结构优化方法在众多领域的应用,需要求解的问题越来越复杂,设计者需要考虑的因素也越来越多。在建立优化问题的数学模型时,我们将应该关注的结构性能列入约束或目标中,但是,由于各方面的原因,结构的另一些性能并没有包括在我们的数学模型中。我们将当前已考虑的、包含在优化模型中的性能定义为关注性能；将当前未考虑的、没有包括在优化模型中、但很可能也很重要的性能定义为潜在性能。结构优化得到的最优设计的关注性能或者达到最优或者满足了约束,但往往牺牲了潜在性能。此外,结构设计中采用的模型和算法可能不够精确,也可能会使得通过常用的优化列式得到的唯一一个优化设计不能被采用。所以,我们希望在设计初期获得多个不同的设计,它们都满足已经有明确要求的关注性能,彼此具有多样性,在性能上具有可竞争性,因此当设计工作进一步深入,它们之中有的设计就可能满足那些潜在性能的要求。本文研究基于代理模型的多样性可竞争结构优化设计,在这里,两个设计彼此具有多样性是指它们在设计空间具有一定距离,因此可能具有不同的潜在性能；两个设计具有可竞争性是指它们的目标函数值很接近,而且和全局最优解相比也较优。本文主要揭示在结构优化设计中进行多样性可竞争设计(Diverse Competitive Design, DCD)的意义,提出DCD优化设计的数学列式及其对偶形式DDCD(Dual Diverse Competitive Design),研究多样性可竞争设计的KKT(Karush-Kuhn-Tucker)最优化必要条件并讨论满足KKT条件的优化设计的特征,给出基于代理模型求解多样性可竞争优化设计的算法,并把多样性可竞争设计优化方法运用在预折纹吸能管的设计中。本文的主要研究内容包括：1)以拓扑优化和尺寸优化中的两个典型例题为例,揭示求解单个最优解的常用优化列式的缺点,说明进行DCD设计的需求并提出DCD优化列式。本文以桥梁设计为例进行拓扑和尺寸优化设计,通过DCD设计得到两个解,与通过常用拓扑优化方法得到的最优解进行比较,结果说明通过DCD获得的设计有可能满足施工、美观、地形及规范规定的更多需求,并且可能还具有其他较好的潜在性能。以十杆桁架的尺寸优化问题为例,在单一工况下通过DCD设计得到静定结构与超静定结构两个设计,讨论了它们具有的不同潜在性能。2)提出了对于含有n个设计变量的问题寻找k个多样性可竞争设计的优化列式,对该列式的目标函数和距离约束进行了深入讨论,研究了待求设计的数量、设计间的距离与其潜在性能同时失效的概率的联系,为采用设计间的几何距离度量多样性的方法提供一定的依据。3)对于分析问题计算量很大的工程优化问题,为了控制模拟仿真的次数以减小计算代价,采用基于代理模型的优化算法求解多样性可竞争设计。对于优化过程中Kriging代理模型的修改,提出了一种基于几何全局搜索的加点准则—-MSG(Multi-start Local Search With Geometrical Exploration),通过几个数值算例与基于不确定性全局搜索的加点准则EGO(Efficient Global Optimization)进行比较,讨论了它们的适用范围及该算法中距离下限的取值建议。提出并比较在n维和kn维设计空间中构造代理模型并采用EGO或MSG加点准则的四种算法,给出最好的求解策略。4)提出DCD优化列式的对偶形式—-DDCD(Dual Diverse Competitive Design)对偶优化列式,讨论DCD与DDCD优化列式的KKT最优化必要条件及其优化解的特征。为了不遗漏全局最优解,本文提出可以依次得到多样性可竞争设计的贪婪算法并讨论了DCD算法与贪婪算法各自的特点；给出基于代理模型的改进算法,在寻找DCD与DDCD设计的同时可以获得全局最优解。此外,本文研究了这两个优化列式的适用对象,比较了它们的收敛速度及设计域特点。5)把DCD算法运用在预折纹吸能管的优化设计中,目标函数考虑了比吸能和峰值载荷这两个性能指标,分别求解得到两个、三个和四个DCD设计。通过将优化设计在轴向撞击和30°角斜撞时获得的构型与性能在设计空间与象空间中进行分析讨论,阐明了基于代理模型的多样性可竞争设计在工程结构优化设计中的意义。
[Abstract]:With the application of structural optimization in many fields, the problems needed to be solved are becoming more and more complex and the designers need more and more factors to consider. In establishing the mathematical model of the optimization problem, we will be concerned about the structural performance in the constraints or objectives, but, for all reasons, the other performance of the structure is not It is included in our mathematical model. We define the performance that is currently considered in the optimization model to focus on performance; it is not included in the optimization model, but it is probably also very important to define the performance as potential performance. The constraints are met, but the potential performance is often sacrificed. Furthermore, the models and algorithms used in structural design may not be accurate enough, and the only optimal design that is obtained through the commonly used optimized columns can not be adopted. So, we hope to get several different designs at the early stage of the design, all of which are already satisfied. The performance of the required concerns is diverse and competitive in performance, so when the design work goes further, some of the designs in them may meet the requirements of potential performance. This paper studies the diversity and competitive structure optimization based on the proxy model. Here, the diversity of the two designs refers to each other. They have a certain distance in the design space, so they may have different potential properties; the two designs are competitive is that their target function values are very close, and they are better than the global optimal solutions. This paper mainly reveals the diversity and competitive design (Diverse Competitive Design, DCD) in the structural optimization design. The mathematical column of DCD optimization design and its dual form DDCD (Dual Diverse Competitive Design) are proposed to study the necessary conditions of KKT (Karush-Kuhn-Tucker) optimization for diversity and competitive design and to discuss the characteristics of optimal design satisfying KKT conditions, and an algorithm based on proxy model to solve diversity and competitive optimization design is given. The diversity competitive design optimization method is applied to the design of the pre corrugated energy absorption tube. The main contents of this paper include: 1) taking two typical examples in topology optimization and size optimization as examples, the shortcomings of the commonly used optimal columns for solving the single optimal solution are revealed, and the requirements of the DCD design are explained and the DCD optimization column is put forward. The bridge design is taken as an example to optimize the design of topology and size. Two solutions are obtained by DCD design. The results are compared with the optimal solutions obtained by the common topology optimization method. The results show that the design obtained through DCD may meet the requirements of construction, beauty, terrain and specifications, and may also have other better potential. Performance. Taking the size optimization of ten bar truss as an example, two designs of static and statically indeterminate structures are designed by DCD under a single working condition, and the different potential properties.2 are discussed. The optimized column for the design of K diversity for the problem containing N design variables is proposed, and the target letter of this column is made. The number and distance constraints are discussed in depth. The relation between the number of design, the distance between the design and the probability of simultaneous failure of the potential performance is studied. It provides a certain basis for the method of measuring the diversity of the geometric distance between the design and the.3) for the engineering optimization problem with great calculation of the problem, in order to control the simulation simulation In order to reduce the computational cost, the optimization algorithm based on agent model is used to solve the diversity and competitive design. For the modification of the Kriging agent model in the optimization process, a point criterion based on the global search of geometry - -MSG (Multi-start Local Search With Geometrical Exploration) is proposed, and several numerical examples and bases are used. In comparison with the point criterion EGO (Efficient Global Optimization) for uncertain global search, the scope of their application and the value of the range lower limit in the algorithm are discussed. Four algorithms are proposed and compared in the design space of n-dimensional and kn dimensions, and the best solutions are given by using EGO or MSG addition criteria. 4) put forward the dual form of DCD optimization column, -DDCD (Dual Diverse Competitive Design) dual optimization column, and discuss the necessary condition of KKT optimization of DCD and DDCD optimization column and the characteristics of its optimal solution. In order to not miss the global optimal solution, this paper proposes a greedy algorithm with diversity and competitive design in turn and discusses the DCD algorithm. With the characteristics of the greedy algorithm, an improved algorithm based on the agent model is given, and the global optimal solution can be obtained while looking for the design of DCD and DDCD. In addition, this paper studies the applicable objects of the two optimized columns, compares their convergence speed and the design domain characteristics.5), and applies the DCD algorithm to the optimization design of the prepattern energy absorption tube. In the objective function, two performance indexes are considered, two, three and four DCD designs are considered respectively. The configuration and performance of the optimized design in the axial and 30 angle oblique collisions are analyzed and discussed in the design space and the image space, and the diversity of the agent model is demonstrated to be competitive. The significance of the design in the optimization design of the engineering structure.

【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB12
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本文编号：1877641