本文選題：多樣性 + 可競(jìng)爭(zhēng)性��； 參考：《大連理工大學(xué)》2016年博士論文

【摘要】：隨著結(jié)構(gòu)優(yōu)化方法在眾多領(lǐng)域的應(yīng)用,需要求解的問題越來越復(fù)雜,設(shè)計(jì)者需要考慮的因素也越來越多。在建立優(yōu)化問題的數(shù)學(xué)模型時(shí),我們將應(yīng)該關(guān)注的結(jié)構(gòu)性能列入約束或目標(biāo)中,但是,由于各方面的原因,結(jié)構(gòu)的另一些性能并沒有包括在我們的數(shù)學(xué)模型中。我們將當(dāng)前已考慮的、包含在優(yōu)化模型中的性能定義為關(guān)注性能；將當(dāng)前未考慮的、沒有包括在優(yōu)化模型中、但很可能也很重要的性能定義為潛在性能。結(jié)構(gòu)優(yōu)化得到的最優(yōu)設(shè)計(jì)的關(guān)注性能或者達(dá)到最優(yōu)或者滿足了約束,但往往犧牲了潛在性能。此外,結(jié)構(gòu)設(shè)計(jì)中采用的模型和算法可能不夠精確,也可能會(huì)使得通過常用的優(yōu)化列式得到的唯一一個(gè)優(yōu)化設(shè)計(jì)不能被采用。所以,我們希望在設(shè)計(jì)初期獲得多個(gè)不同的設(shè)計(jì),它們都滿足已經(jīng)有明確要求的關(guān)注性能,彼此具有多樣性,在性能上具有可競(jìng)爭(zhēng)性,因此當(dāng)設(shè)計(jì)工作進(jìn)一步深入,它們之中有的設(shè)計(jì)就可能滿足那些潛在性能的要求。本文研究基于代理模型的多樣性可競(jìng)爭(zhēng)結(jié)構(gòu)優(yōu)化設(shè)計(jì),在這里,兩個(gè)設(shè)計(jì)彼此具有多樣性是指它們?cè)谠O(shè)計(jì)空間具有一定距離,因此可能具有不同的潛在性能；兩個(gè)設(shè)計(jì)具有可競(jìng)爭(zhēng)性是指它們的目標(biāo)函數(shù)值很接近,而且和全局最優(yōu)解相比也較優(yōu)。本文主要揭示在結(jié)構(gòu)優(yōu)化設(shè)計(jì)中進(jìn)行多樣性可競(jìng)爭(zhēng)設(shè)計(jì)(Diverse Competitive Design, DCD)的意義,提出DCD優(yōu)化設(shè)計(jì)的數(shù)學(xué)列式及其對(duì)偶形式DDCD(Dual Diverse Competitive Design),研究多樣性可競(jìng)爭(zhēng)設(shè)計(jì)的KKT(Karush-Kuhn-Tucker)最優(yōu)化必要條件并討論滿足KKT條件的優(yōu)化設(shè)計(jì)的特征,給出基于代理模型求解多樣性可競(jìng)爭(zhēng)優(yōu)化設(shè)計(jì)的算法,并把多樣性可競(jìng)爭(zhēng)設(shè)計(jì)優(yōu)化方法運(yùn)用在預(yù)折紋吸能管的設(shè)計(jì)中。本文的主要研究?jī)?nèi)容包括：1)以拓?fù)鋬?yōu)化和尺寸優(yōu)化中的兩個(gè)典型例題為例,揭示求解單個(gè)最優(yōu)解的常用優(yōu)化列式的缺點(diǎn),說明進(jìn)行DCD設(shè)計(jì)的需求并提出DCD優(yōu)化列式。本文以橋梁設(shè)計(jì)為例進(jìn)行拓?fù)浜统叽鐑?yōu)化設(shè)計(jì),通過DCD設(shè)計(jì)得到兩個(gè)解,與通過常用拓?fù)鋬?yōu)化方法得到的最優(yōu)解進(jìn)行比較,結(jié)果說明通過DCD獲得的設(shè)計(jì)有可能滿足施工、美觀、地形及規(guī)范規(guī)定的更多需求,并且可能還具有其他較好的潛在性能。以十桿桁架的尺寸優(yōu)化問題為例,在單一工況下通過DCD設(shè)計(jì)得到靜定結(jié)構(gòu)與超靜定結(jié)構(gòu)兩個(gè)設(shè)計(jì),討論了它們具有的不同潛在性能。2)提出了對(duì)于含有n個(gè)設(shè)計(jì)變量的問題尋找k個(gè)多樣性可競(jìng)爭(zhēng)設(shè)計(jì)的優(yōu)化列式,對(duì)該列式的目標(biāo)函數(shù)和距離約束進(jìn)行了深入討論,研究了待求設(shè)計(jì)的數(shù)量、設(shè)計(jì)間的距離與其潛在性能同時(shí)失效的概率的聯(lián)系,為采用設(shè)計(jì)間的幾何距離度量多樣性的方法提供一定的依據(jù)。3)對(duì)于分析問題計(jì)算量很大的工程優(yōu)化問題,為了控制模擬仿真的次數(shù)以減小計(jì)算代價(jià),采用基于代理模型的優(yōu)化算法求解多樣性可競(jìng)爭(zhēng)設(shè)計(jì)。對(duì)于優(yōu)化過程中Kriging代理模型的修改,提出了一種基于幾何全局搜索的加點(diǎn)準(zhǔn)則—-MSG(Multi-start Local Search With Geometrical Exploration),通過幾個(gè)數(shù)值算例與基于不確定性全局搜索的加點(diǎn)準(zhǔn)則EGO(Efficient Global Optimization)進(jìn)行比較,討論了它們的適用范圍及該算法中距離下限的取值建議。提出并比較在n維和kn維設(shè)計(jì)空間中構(gòu)造代理模型并采用EGO或MSG加點(diǎn)準(zhǔn)則的四種算法,給出最好的求解策略。4)提出DCD優(yōu)化列式的對(duì)偶形式—-DDCD(Dual Diverse Competitive Design)對(duì)偶優(yōu)化列式,討論DCD與DDCD優(yōu)化列式的KKT最優(yōu)化必要條件及其優(yōu)化解的特征。為了不遺漏全局最優(yōu)解,本文提出可以依次得到多樣性可競(jìng)爭(zhēng)設(shè)計(jì)的貪婪算法并討論了DCD算法與貪婪算法各自的特點(diǎn)；給出基于代理模型的改進(jìn)算法,在尋找DCD與DDCD設(shè)計(jì)的同時(shí)可以獲得全局最優(yōu)解。此外,本文研究了這兩個(gè)優(yōu)化列式的適用對(duì)象,比較了它們的收斂速度及設(shè)計(jì)域特點(diǎn)。5)把DCD算法運(yùn)用在預(yù)折紋吸能管的優(yōu)化設(shè)計(jì)中,目標(biāo)函數(shù)考慮了比吸能和峰值載荷這兩個(gè)性能指標(biāo),分別求解得到兩個(gè)、三個(gè)和四個(gè)DCD設(shè)計(jì)。通過將優(yōu)化設(shè)計(jì)在軸向撞擊和30°角斜撞時(shí)獲得的構(gòu)型與性能在設(shè)計(jì)空間與象空間中進(jìn)行分析討論,闡明了基于代理模型的多樣性可競(jìng)爭(zhēng)設(shè)計(jì)在工程結(jié)構(gòu)優(yōu)化設(shè)計(jì)中的意義。
[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.

【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TB12
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本文編號(hào)：1877641