本文關(guān)鍵詞：高效魯棒優(yōu)化和多學(xué)科優(yōu)化及其在公差設(shè)計中的應(yīng)用

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【摘要】：現(xiàn)今工程系統(tǒng)越來越復(fù)雜。復(fù)雜工程系統(tǒng)的設(shè)計優(yōu)化中面臨的第一個挑戰(zhàn)是存在于參數(shù)和設(shè)計變量中的不確定性。參數(shù)不確定性在設(shè)計優(yōu)化中扮演著重要角色,它很可能導(dǎo)致原本可行的最優(yōu)解成為不可行解,從而嚴(yán)重影響系統(tǒng)性能,因此非常有必要開發(fā)高效的魯棒優(yōu)化(Robust Optimization)算法,從而求解對不確定性的變化不敏感的最優(yōu)解。工程系統(tǒng)設(shè)計優(yōu)化面對的另一個挑戰(zhàn)是,一個復(fù)雜工程系統(tǒng)往往涉及多個交叉學(xué)科,而這些學(xué)科之間有一些共同的全局設(shè)計變量,各系統(tǒng)之間也往往存在相互耦合關(guān)系。此類優(yōu)化問題需要保證共享變量在各個相關(guān)子系統(tǒng)中的一致性,因此涉及眾多優(yōu)化子問題,從而導(dǎo)致問題復(fù)雜度和求解負(fù)擔(dān)急劇增加。因此有必要開發(fā)高效的多學(xué)科優(yōu)化(Multi-disciplinary Optimization)算法求解這些全局變量和耦合變量,以便應(yīng)用于實際工程問題上。以上兩種涉及優(yōu)化問題都存在多層優(yōu)化(或嵌套優(yōu)化)結(jié)構(gòu)導(dǎo)致的計算效率低的問題,如魯棒優(yōu)化中解決魯棒約束條件的內(nèi)層問題及多學(xué)科優(yōu)化中各學(xué)科之間一致性的多層優(yōu)化問題,因此本文重點解決高效的魯棒優(yōu)化算法和多學(xué)科優(yōu)化算法的開發(fā)問題。作為汽車的核心部件,發(fā)動機(jī)是一個典型的復(fù)雜非線性多學(xué)科系統(tǒng)。發(fā)動機(jī)關(guān)鍵零部件尺寸的不確定性(以公差形式體現(xiàn))對系統(tǒng)成本和性能都有重要影響,因此其公差設(shè)計成為一大關(guān)鍵問題。傳統(tǒng)的公差設(shè)計是基于設(shè)計者的經(jīng)驗,極少考慮到優(yōu)化或者在整個系統(tǒng)層面進(jìn)行公差設(shè)計。而且,很少研究從不同部件的自主設(shè)計和系統(tǒng)層面的綜合設(shè)計對零部件進(jìn)行公差設(shè)計。本文提出對多發(fā)動機(jī)公差進(jìn)行魯棒優(yōu)化和多學(xué)科優(yōu)化設(shè)計。本文首先提出解決單學(xué)科魯棒優(yōu)化問題的算法,這些問題的目標(biāo)函數(shù)和約束條件的參數(shù)和設(shè)計變量中都可能存在不確定性,這些不確定性以區(qū)間形式體現(xiàn);其次本文提出高效的多學(xué)科優(yōu)化算法。本文共有四方面研究內(nèi)容。研究內(nèi)容一提出了一種基于二次序列規(guī)劃算法(Sequential Quadratic Programming)的魯棒優(yōu)化算法(SQP-RO),該算法可以有效解決存在區(qū)間不確定性的連續(xù)可導(dǎo)的高度非線性優(yōu)化問題,但仍然是具有內(nèi)外兩層優(yōu)化的結(jié)構(gòu)�；赟QP-RO,研究內(nèi)容二提出了一種單層優(yōu)化結(jié)構(gòu)的魯棒優(yōu)化算法(A-SQP-RO),基于提出的烏托邦點的概念,算法效率更高。研究內(nèi)容三提出了順序多目標(biāo)優(yōu)化算法和多學(xué)科優(yōu)化算法,此算法賦予每個子系統(tǒng)充分的優(yōu)化自主權(quán)對局部變量、全局變量和耦合變量進(jìn)行優(yōu)化,基于得到的全局和耦合變量的信息,系統(tǒng)層處理后分配給每個子系統(tǒng)進(jìn)行順序的優(yōu)化�；谝陨咸岢龅乃惴�,在研究內(nèi)容四中,本文提出了發(fā)動機(jī)多學(xué)科公差優(yōu)化問題并求解。以上提出的方法利用相當(dāng)數(shù)量的數(shù)值算例和工程算例進(jìn)行了驗證,以展示所提出方法的可行性和有效性。驗證結(jié)果表明,與確定型最優(yōu)問題算法SQP相比,提出的魯棒優(yōu)化算法可以相對較少的計算量有效解決魯棒優(yōu)化問題。所提出的順序多目標(biāo)和多學(xué)科算法可以得到可觀的帕雷托前沿而只需更少的計算量。發(fā)動機(jī)多學(xué)科公差設(shè)計將關(guān)鍵尺寸適當(dāng)壓縮,非關(guān)鍵尺寸適當(dāng)放松,從而在提高系統(tǒng)性能的同時降低制造成本。
【關(guān)鍵詞】：
【學(xué)位授予單位】：上海交通大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TK432
【目錄】：

• 摘要7-8
• Abstract8-10
• Acknowledgement10-15
• Nomenclature15-20
• Chapter 1 Introduction20-30
• 1.1 Motivation and Objective21-24
• 1.2 Research Thrusts24-27
• 1.2.1 Research Thrust 1: Robust Optimization Based on Sequential QuadraticProgramming25
• 1.2.2 Research Thrust 2: Advanced single-loop RO Algorithm25-26
• 1.2.3 Research Thrust 3: Sequential MOO and MDO Methods26
• 1.2.4 Research Thrust 4: Tolerance Design Optimization for Internal CombustionEngines26-27
• 1.3 Assumptions27
• 1.4 Organization of Dissertation27-30
• Chapter 2 Definitions and Terminologies30-44
• 2.1 Introduction30
• 2.2 Problem Definitions30-35
• 2.2.1 Robust Optimization (RO)31-34
• 2.2.2 Multi-disciplinary Design Optimization (MDO)34-35
• 2.2.3 Multi-objective Optimization (MOO)35
• 2.3 Sequential Quadratic Programming35-37
• 2.4 Matrix decomposition method for QPs subject to box constraints37-38
• 2.5 Design of Experiment (Do E)38-39
• 2.6 Gaussian Process (GP) Modeling39-44
• Chapter 3 Robust Optimization Based on Sequential Quadratic Programming44-76
• 3.1 Introduction44-48
• 3.2 Sequential Quadratic Programming Approach for Robust Optimization48-61
• 3.2.1 Approach to solve the objective robustness index49-54
• 3.2.2 Approach to solve the constraint robustness index54-55
• 3.2.3 SQP for Robust Optimization (SQP-RO)55-59
• 3.2.4 Computational efficiency of SQP-RO59-61
• 3.3 Test Examples and Comparison Results61-74
• 3.3.1 Nonlinear numerical example 162-64
• 3.3.2 Additional numerical examples64-67
• 3.3.3 Two-bar truss67-69
• 3.3.4 Speed Reducer69-71
• 3.3.5 Compression Spring71-74
• 3.4 Conclusion74-76
• Chapter 4 Advanced Robust Optimization Algorithm with a Single-looped Structure76-106
• 4.1 Introduction76-79
• 4.2 Utopian Solution to QPs Subject to Box Constraints79-86
• 4.2.1 Convex maximization (or concave minimization) problem81-83
• 4.2.2 Concave maximization (or convex minimization) problem83-84
• 4.2.3 Indefinite problem84-86
• 4.3 Advanced Sequential Quadratic Programming Approach for Robust Optimization(A-SQP-RO)86-96
• 4.3.1 Approach to Solve the Objective Robustness Index86-89
• 4.3.2 Approach to Solve the Constraint Robustness Index89-92
• 4.3.3 Advanced SQP for Robust Optimization (A-SQP-RO)92-94
• 4.3.4 Discussion of A-SQP-RO94-96
• 4.4 Test Examples and Comparison of Results96-103
• 4.4.1 Nonlinear Numerical Example 196-100
• 4.4.2 Additional Numerical Examples100-101
• 4.4.3 Two-bar Truss101-102
• 4.4.4 Speed Reducer102-103
• 4.5 Conclusion103-106
• Chapter 5 A New Sequential Multi-Disciplinary Optimization Method Based on A NovelSequential Multi-Objective Optimization Approach106-140
• 5.1 Introduction106-110
• 5.2 Background110-111
• 5.2.1 Definition for the monotonicity of a function along a certain direction110-111
• 5.2.2 Definition for the data sets111
• 5.3 S-MOO and S-MDO Methodologies111-127
• 5.3.1 Illustrative observations112-118
• 5.3.2 A novel Sequential MOO approach118-119
• 5.3.3 Handling of coupling variables and generation of data set Y119-120
• 5.3.4 A novel sequential MDO approach120-123
• 5.3.5 Steps of S-MOO and S-MDO123-125
• 5.3.6 Discussion of the proposed method125-127
• 5.4 Examples and Comparison of Results127-139
• 5.4.1 Test examples for S-MOO127-134
• 5.4.2 Test examples for S-MDO134-139
• 5.5 Conclusion139-140
• Chapter 6 Multi-disciplinary Tolerance Design Optimization for Gas Engines140-168
• 6.1 Introduction140-146
• 6.2 Robust tolerance optimization of compression ratio for a typical gas engine146-149
• 6.3 Gaussian process modeling for a typical gas engine149-162
• 6.3.1 Gaussian process modeling for performances vs. compression ratio149-157
• 6.3.2 Gaussian process modeling for friction loss vs. tolerance157-162
• 6.4 Multi-disciplinary tolerance design optimization problem162-166
• 6.5 Conclusion166-168
• Chapter 7 Conclusions and Future Work168-176
• 7.1 Concluding Remarks168-172
• 7.1.1 Robust Optimization Based on Sequential Quadratic Programming169
• 7.1.2 Advanced Robust Optimization Algorithm of a Single-looped Structure169-170
• 7.1.3 A sequential MDO approach based on a novel sequential MOO approach .. 1517.1.4 Application of proposed approaches for engineering examples170-172
• 7.2 Main contributions172-173
• 7.3 Future research directions173-176
• 7.3.1 Representing uncertainty with additional statistical information173
• 7.3.2 Problems with discrete variables and discontinuous or non-differentiablefunctions as well as black box problems173-174
• 7.3.3 Algorithms development for robust MDO problems174-176
• Bibliography176-184
• Publications184

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