本文選題：多學(xué)科設(shè)計(jì)優(yōu)化 + 近似模型　； 參考：《華中科技大學(xué)》2012年博士論文

【摘要】：工程產(chǎn)品的設(shè)計(jì)優(yōu)化涵蓋眾多學(xué)科、涉及多種因素,而且各個(gè)學(xué)科、因素之間相互作用、相互耦合,使得工程產(chǎn)品的設(shè)計(jì)優(yōu)化過(guò)程異常復(fù)雜,難以獲得滿足產(chǎn)品整體性能最佳的設(shè)計(jì)方案。多學(xué)科設(shè)計(jì)優(yōu)化(MDO)正是針對(duì)這一問(wèn)題而形成的一種系統(tǒng)綜合設(shè)計(jì)優(yōu)化的方法論,其通過(guò)充分探索和利用各學(xué)科間相互耦合所產(chǎn)生的協(xié)同效應(yīng),來(lái)獲取工程產(chǎn)品整體性能最優(yōu)的設(shè)計(jì)方案。受各學(xué)科仿真需要花費(fèi)龐大計(jì)算量、學(xué)科間信息交互耦合等因素的影響,計(jì)算復(fù)雜性和組織復(fù)雜性成為了MDO的兩大難點(diǎn)。近似模型是一種在滿足設(shè)計(jì)精度的前提條件下,對(duì)復(fù)雜、隱式或未知的函數(shù)關(guān)系進(jìn)行簡(jiǎn)化替代的方法,能夠極大地降低工程產(chǎn)品設(shè)計(jì)優(yōu)化中龐大的計(jì)算量；求解策略是一種對(duì)復(fù)雜系統(tǒng)進(jìn)行協(xié)調(diào)解耦的計(jì)算框架,能夠有效地降低工程產(chǎn)品設(shè)計(jì)優(yōu)化中組織的復(fù)雜性。當(dāng)前,近似模型和求解策略已經(jīng)成為MDO領(lǐng)域中兩大研究熱點(diǎn)。 本文從降低工程產(chǎn)品多學(xué)科設(shè)計(jì)優(yōu)化中計(jì)算復(fù)雜性和組織復(fù)雜性兩方面入手,對(duì)近似模型和求解策略進(jìn)行了詳細(xì)研究：在近似模型方面,提出了基于基因表達(dá)式編程(GEP)的近似模型構(gòu)建方法,并將其與MDO中常見(jiàn)近似模型的性能進(jìn)行了對(duì)比；在求解策略方面,提出了基于Kriging的廣義協(xié)同優(yōu)化求解策略,針對(duì)多目標(biāo)MDO問(wèn)題,進(jìn)一步提出了基于GEP和Nash均衡的多目標(biāo)求解策略；并結(jié)合小水線面雙體船船型參數(shù)設(shè)計(jì)優(yōu)化實(shí)例對(duì)本文所提出的方法進(jìn)行了驗(yàn)證,取得了很好的應(yīng)用效果。 首先,給出了MDO問(wèn)題的數(shù)學(xué)描述,對(duì)MDO中近似模型與求解策略的相關(guān)概念和術(shù)語(yǔ)進(jìn)行了定義,在此基礎(chǔ)上,提出了近似模型與求解策略的研究框架。 其次,提出了基于GEP的近似模型構(gòu)建方法并總結(jié)了GEP近似模型與MDO中三種常見(jiàn)近似模型的優(yōu)缺點(diǎn)和適用范圍。采用GEP智能進(jìn)化算法對(duì)工程產(chǎn)品多學(xué)科設(shè)計(jì)優(yōu)化中輸入設(shè)計(jì)變量和輸出觀測(cè)響應(yīng)之間復(fù)雜、隱式或未知的函數(shù)關(guān)系進(jìn)行近似替代,在避免高強(qiáng)度仿真、降低計(jì)算量的同時(shí),能為設(shè)計(jì)人員提供簡(jiǎn)潔、直觀的顯式函數(shù)表達(dá)式,有助于他們獲得設(shè)計(jì)變量變化對(duì)未知觀測(cè)響應(yīng)的影響程度,進(jìn)行靈敏度分析。在考慮大、小兩種樣本規(guī)模的情況下,從預(yù)測(cè)精度、魯棒性、透明度和計(jì)算效率四個(gè)方面將GEP近似模型與MDO中三種常見(jiàn)近似模型(即響應(yīng)面、Kriging和徑向基函數(shù)模型)進(jìn)行了全面而詳盡的比較,總結(jié)了四種近似模型的優(yōu)缺點(diǎn)和適用范圍,為工程產(chǎn)品設(shè)計(jì)人員對(duì)近似模型的選用提供指導(dǎo)和參考。 然后,提出了基于Kriging的廣義協(xié)同優(yōu)化求解策略。該求解策略消除了原有協(xié)同優(yōu)化求解策略中系統(tǒng)級(jí)設(shè)計(jì)變量和對(duì)應(yīng)子系統(tǒng)級(jí)局部變量之間的不一致性以及耦合變量取值范圍差異所帶來(lái)的不一致性。此外,基于Kriging的廣義協(xié)同優(yōu)化求解策略利用Kriging模型對(duì)子系統(tǒng)級(jí)優(yōu)化目標(biāo)(即系統(tǒng)級(jí)廣義一致性約束)和子系統(tǒng)分析模型進(jìn)行近似替代,消除了原有一致性約束形式的非光滑、不連續(xù)特性,同時(shí)降低了子系統(tǒng)分析的計(jì)算量和計(jì)算時(shí)間,提高了工程產(chǎn)品設(shè)計(jì)優(yōu)化的求解效率。 接著,提出了基于GEP和Nash均衡的多目標(biāo)求解策略。利用GEP近似模型構(gòu)建各個(gè)博弈參與者(或子系統(tǒng))的理性反應(yīng)集(RRS),通過(guò)計(jì)算所有參與者RRS的交集來(lái)獲得Nash均衡解,極大地降低了計(jì)算量,提高了求解工程產(chǎn)品多目標(biāo)MDO問(wèn)題的效率。 隨后,將本文所提出的方法應(yīng)用于小水線面雙體船船型參數(shù)的設(shè)計(jì)優(yōu)化,進(jìn)行應(yīng)用驗(yàn)證。結(jié)果表明,本文所提出的方法能夠極大地降低工程產(chǎn)品多學(xué)科設(shè)計(jì)優(yōu)化中計(jì)算和組織的復(fù)雜性,從而有效地支持工程產(chǎn)品的設(shè)計(jì)優(yōu)化。 最后,對(duì)本文的研究工作進(jìn)行了總結(jié),并指出了今后的研究方向。
[Abstract]:The design optimization of engineering products covers a wide range of disciplines , involving many factors , and the interaction between various disciplines and factors . The design optimization process of engineering products is very complex and it is difficult to obtain the optimal design scheme to meet the overall performance of the product . The multi - disciplinary design optimization ( MDO ) is the two major difficulties of MDO .
The solution strategy is a computational framework for the coordination decoupling of complex systems , which can effectively reduce the complexity of organization in engineering product design optimization . At present , approximate model and solution strategy have become two hot topics in MDO field .
In this paper , the approximate model and the solution strategy are discussed in detail from the aspects of computational complexity and organizational complexity in the optimization of multi - disciplinary design of engineering products . In the approximate model , the approximate model construction method based on GEP is proposed and compared with the performance of common approximate models in MDO ;
In the aspect of solving strategy , a generalized cooperative optimization solution strategy based on Kriging is proposed , aiming at the multi - objective MDO problem , a multi - objective solution strategy based on GEP and Nash equilibrium is further proposed .
Combined with the design optimization example of the ship type parameter of the small water - line surface , the method proposed in this paper is verified , and the good application effect is obtained .
Firstly , the mathematical description of MDO problem is given , and the concept and terminology of approximate model and solution strategy in MDO are defined . On this basis , the research framework of approximate model and solution strategy is proposed .
Secondly , the advantage and disadvantage and application range of three common approximate models in the GEP approximation model and MDO are presented . By using the GEP intelligent evolutionary algorithm , the complex , implicit or unknown function relation between the input design variables and the output observation responses in the multi - disciplinary design optimization of engineering products is approximated . In the case of large and small sample sizes , three common approximate models ( i.e . , response surface , Kriging and radial basis function models ) in the design variables are compared .
In addition , based on Kriging ' s generalized collaborative optimization solution strategy , the system - level optimization objective ( i.e . , the system - level generalized consistency constraint ) and the sub - system analysis model are replaced by Kriging model , which eliminates the non - smooth and discontinuous characteristics of the original consistency constraint form , reduces the calculation amount and calculation time of the sub - system analysis , and improves the solving efficiency of the engineering product design optimization .
Then , a multi - objective solution strategy based on GEP and Nash equilibrium is proposed . The rational reaction set ( RRS ) of each game participant ( or subsystem ) is constructed by using the GEP approximation model , and the Nash equilibrium solution is obtained by calculating the intersection of all participants RRS , which greatly reduces the calculation amount and improves the efficiency of solving the multi - target MDO problem of the engineering product .
Then , the method proposed in this paper is applied to the design optimization of the ship - type parameters of the small water - plane double hull ship , and the application verification is carried out . The results show that the method proposed in this paper can greatly reduce the complexity of calculation and organization in the multi - disciplinary design optimization of engineering products , thus effectively supporting the design optimization of engineering products .
Finally , the research work of this paper is summarized , and the future research direction is pointed out .

【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類號(hào)】：G642;O242.1

【引證文獻(xiàn)】

相關(guān)期刊論文 前1條

1 朱國(guó)俊;郭鵬程;羅興，

本文編號(hào)：1734048