本文選題：不確定性多學(xué)科設(shè)計(jì)優(yōu)化　切入點(diǎn)：概率目標(biāo)級(jí)聯(lián)法　出處：《華中科技大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：對(duì)于不確定環(huán)境下的多學(xué)科設(shè)計(jì)優(yōu)化問(wèn)題，用確定性多學(xué)科設(shè)計(jì)優(yōu)化方法求解很難保證產(chǎn)品的可靠性和穩(wěn)健性。因此，將傳統(tǒng)的多學(xué)科設(shè)計(jì)優(yōu)化方法與不確定優(yōu)化方法相結(jié)合引起了廣大學(xué)者的關(guān)注與研究，并形成了不確定性多學(xué)科設(shè)計(jì)優(yōu)化（Uncertaintybased Multidisciplinary Design Optimization， UMDO）方法。其中，概率目標(biāo)級(jí)聯(lián)（ProbabilisticAnalytical Target Cascading，PATC）方法是一種很有潛力的UMDO方法，，它繼承了目標(biāo)級(jí)聯(lián)方法（Analytical Target Cascading，ATC）的各種特點(diǎn)，具有嚴(yán)格的收斂性。但是，在PATC中，每個(gè)子系統(tǒng)均采用傳統(tǒng)嵌套雙循環(huán)優(yōu)化策略，并且各子系統(tǒng)的一致性通過(guò)傳統(tǒng)的協(xié)調(diào)策略來(lái)保證，這使得PATC方法的不確定性優(yōu)化效率和系統(tǒng)協(xié)調(diào)效率不是很高。 為了探索更高效的PATC方法，本文對(duì)PATC方法進(jìn)行了深入研究，重點(diǎn)改進(jìn)了其不確定優(yōu)化策略和協(xié)調(diào)策略。 首先，針對(duì)PATC的不確定性優(yōu)化策略，本文研究了基于混合均值法（Hybrid MeanValue，HMV）的單層序列規(guī)劃與可靠性分析（Sequential Optimization and ReliabilityAssessment，SORA）策略，用于改進(jìn)PATC方法中的嵌套雙層循環(huán)策略，提出了HMV-PATC方法，建立了該方法的求解模型和流程，并驗(yàn)證了該方法的可行性和高效性。 其次，針對(duì)HMV-PATC的協(xié)調(diào)策略，本文分析對(duì)比了各種協(xié)調(diào)策略，分別將拉格朗日對(duì)偶方程（Lagrangian Duality Function，LDF）和二次外罰函數(shù)(Quadratic ExteriorPenalty Function，QEPF)方法作為HMV-PATC方法的協(xié)調(diào)策略，建立了LDF-HMV-PATC和QEPF-HMV-PATC的數(shù)學(xué)模型和求解流程，并應(yīng)用到一個(gè)幾何規(guī)劃問(wèn)題的求解中，結(jié)果顯示兩種方法都具有獲得最優(yōu)解的能力，并且QEPF方法的協(xié)調(diào)效率比LDF方法的效率更高。由于在QEPF中罰系數(shù)更新步長(zhǎng)的設(shè)置對(duì)結(jié)果有很大的影響，因此本文對(duì)其做了進(jìn)一步研究，在上述算例的基礎(chǔ)上，研究了其罰系數(shù)更新步長(zhǎng)與優(yōu)化效率和收斂性的關(guān)系，為罰因子更新步長(zhǎng)的選取提供了依據(jù)。 最后，將QEPF-HMV-PATC應(yīng)用到了工程實(shí)例中，采用QEPF-HMV-PATC方法實(shí)現(xiàn)了齒輪減速器的概念多學(xué)科設(shè)計(jì)優(yōu)化，獲得了理想的設(shè)計(jì)效果。
[Abstract]:For the multidisciplinary design optimization problem in uncertain environment, it is difficult to ensure the reliability and robustness of the product by using the deterministic multidisciplinary design optimization method. The combination of traditional multidisciplinary design optimization method and uncertain design optimization method has attracted the attention and research of many scholars, and formed the uncertain multidisciplinary design optimization method named Uncertainty-based Multidisciplinary Design Optimization (UMDO). Probabilistic Analytical Target cascading (UMDO) is a potential UMDO method, which inherits the characteristics of Analytical Target cascading (ATC) and has strict convergence. Each subsystem adopts the traditional nested double-loop optimization strategy, and the consistency of each subsystem is guaranteed by the traditional coordination strategy, which makes the uncertainty optimization efficiency and system coordination efficiency of PATC method not very high. In order to explore more efficient PATC method, the PATC method is deeply studied in this paper, and its uncertain optimization strategy and coordination strategy are improved. Firstly, aiming at the uncertainty optimization strategy of PATC, this paper studies the single layer sequence planning and reliability analysis based on Hybrid mean value (HMV), which is used to improve the nested double-layer cycle strategy in PATC method, and proposes the HMV-PATC method. The solution model and flow chart of the method are established, and the feasibility and efficiency of the method are verified. Secondly, aiming at the coordination strategy of HMV-PATC, this paper analyzes and compares various coordination strategies. The Lagrangian Duality function method and the Quadric ExteriorPenalty function QEPF method are used as the coordination strategies of the HMV-PATC method, respectively. The mathematical model and solution flow of LDF-HMV-PATC and QEPF-HMV-PATC are established and applied to a geometric programming problem. The results show that both methods have the ability to obtain the optimal solution. And the coordination efficiency of QEPF method is higher than that of LDF method. Because the setting of penalty coefficient update step size in QEPF has great influence on the result, this paper makes further research on it, and based on the above examples, The relationship between the updating step size of penalty coefficient and the optimization efficiency and convergence is studied, which provides the basis for the selection of the update step size of penalty factor. Finally, the QEPF-HMV-PATC is applied to the engineering example, the concept of gear reducer is optimized by QEPF-HMV-PATC method, and the ideal design effect is obtained.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TB47

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