本文選題：多源不確定性 + 概率可靠性�。� 參考：《西北工業(yè)大學》2014年博士論文

【摘要】：不確定性普遍存在于機械(結構)系統(tǒng)當中，其不確定性來源是多方面的，包括客觀不確定性和主觀不確定性。單一的數學模型不足以對機械系統(tǒng)中的不確定性進行準確而全面的描述。因此開展多源不確定性結構可靠性分析及優(yōu)化設計方法研究有著重要的理論和現實意義。本文從概率模型、模糊模型、非概率模型等多個角度對結構可靠性設計問題進行研究，建立了一些適用于復雜工程問題的結構可靠性分析方法，在此基礎上開展了結構可靠性優(yōu)化設計和穩(wěn)健優(yōu)化設計方法研究，其主要內容如下： 1.基于概率可靠性模型，研究基于有限元仿真的復雜結構可靠性分析方法。以導彈吊掛結構為研究對象，，基于PCL(Patran Command Language)實現了結構有限元分析參數化。將有限元仿真與可靠性設計理論相結合，開發(fā)了基于有限元仿真分析的導彈吊掛結構可靠性分析軟件平臺。 2.基于模糊理論，研究了疲勞失效和共振失效下的模糊可靠性分析問題。采用隸屬函數來描述結構疲勞失效的漸變過程，開展了模糊失效狀態(tài)下的隨機結構廣義疲勞壽命可靠性分析。以三角型隸屬函數來描述結構的模糊共振失效區(qū)，建立了三角型隸屬函數下的結構廣義共振可靠性分析模型�；诜纸舛ɡ硖岢隽甩怂浇丶陆Y構廣義共振可靠性求解方法。 3.基于凸集模型，針對工程實際中大量存在的“未知但有界”參數的結構可靠性分析問題，建立了一種基于空間填充設計的非概率可靠性分析方法。該方法從非概率可靠性定義出發(fā)，以獲得不確定性影響下結構功能函數的上下界為目標，基于改進的優(yōu)化拉丁超立方抽樣方法，使更多抽樣點移向變量的邊界，以達到以較少的樣本點填充變量的不確定性空間并快速確定功能函數上下界的目的。該方法簡單實用，適用于復雜工程結構及系統(tǒng)的非概率可靠性分析。 4.建立了一種基于重要抽樣思想的結構非概率可靠性指標求解方法。從非概率可靠性指標的物理意義出發(fā)，將非概率可靠性指標求解問題轉化為在標準化區(qū)間變量的擴展空間中以無窮范數度量的極限狀態(tài)面上到坐標原點的最短距離問題。在此基礎上，利用空間填充設計思想，在變量的擴展空間中找到結構失效域內距離極限狀態(tài)面最近的點，然后在該設計點附近再進行重要抽樣，最后通過尋優(yōu)判據得到結構的非概率可靠性指標。 5.建立了區(qū)間、橢球、超橢球三種不確定性變量描述下的結構非概率可靠性分析統(tǒng)一模型。將均勻設計方法引入結構的非概率可靠性分析，該方法克服了傳統(tǒng)隨機抽樣空間填充能力差的缺點，能夠將樣本均勻填充于結構的不確定性空間，因此大幅度的提升了分析的精度和抽樣效率。在此基礎上本文將該方法與ANSYS有限元軟件相結合，提出了一種適用于復雜工程問題的結構非概率可靠性及參數靈敏度分析方法。 6.研究了不確定性結構的優(yōu)化設計方法及其在工程中的應用。在工程應用方面，建立了基于Matlab優(yōu)化模塊的結構可靠性優(yōu)化設計技術框架，實現了基于Isight的6σ穩(wěn)健優(yōu)化設計和基于ANSYS概率設計模塊的結構Taguchi穩(wěn)健優(yōu)化設計。在理論研究方面，采用均勻設計方法實現設計空間的均勻填充，基于加點準則建立了具有更好近似精度的Kriging模型，在此基礎上基于雙Monte Carlo方法，提出了考慮變量和代理模型雙重不確定下的結構穩(wěn)健優(yōu)化設計方法。
[Abstract]:Uncertainty generally exists in mechanical (structural) systems, and its uncertainty sources are multifaceted, including objective uncertainty and subjective uncertainty. A single mathematical model is not sufficient to describe the uncertainty in the mechanical system accurately and comprehensively. Therefore, the reliability analysis and optimization design of multi source uncertain structures are carried out. The method research has important theoretical and practical significance. This paper studies the structural reliability design problem from the probability model, the fuzzy model, the non probability model and so on, and establishes some structural reliability analysis methods suitable for the complex engineering problems. On this basis, the structural reliability optimization design and the robust optimization design are carried out. The main contents of the study are as follows:
1. based on the probability reliability model, the method of complex structural reliability analysis based on finite element simulation is studied. Based on PCL (Patran Command Language), the parameterization of structural finite element analysis is realized. The finite element simulation and reliability design theory are combined to develop the guidance based on the finite element simulation analysis. The software platform for the reliability analysis of the projectile hanger structure.
2. based on the fuzzy theory, the fuzzy reliability analysis of fatigue failure and resonance failure is studied. The membership function is used to describe the gradual process of structural fatigue failure. The reliability analysis of the generalized fatigue life of the random structure under the fuzzy failure state is carried out. The fuzzy resonance failure area of the structure is described by a triangular membership function. The structural generalized resonance reliability analysis model under the trigonometric membership function is established. Based on the decomposition theorem, a method for solving the reliability of structural generalized resonance under the lambda horizontal cut set is proposed.
3. based on the convex set model, a non probabilistic reliability analysis method based on space filling design is established to solve the problem of structural reliability analysis of "unknown but bounded" parameters in the engineering practice. This method is based on the non probabilistic reliability definition to obtain the upper and lower bounds of the structural function function under the influence of uncertainty. Based on the improved optimization Latin hypercube sampling method, more sampling points are moved to the boundary of variables to reach the uncertain space of filling variables with less sample points and to quickly determine the upper and lower bounds of functional functions. This method is simple and practical, and is applicable to the non probabilistic reliability analysis of complex engineering structures and systems.
4. a non probabilistic reliability index solution method based on the important sampling idea is established. From the physical meaning of the non probabilistic reliability index, the problem of the non probabilistic reliability index solution is transformed into the shortest distance from the limit state surface to the coordinate origin in the limit state surface of the infinite norm in the extended space of the standardized interval variable. On this basis, using the idea of space filling design, we find the nearest point of the range limit state in the structural failure domain in the extended space of the variable, and then make an important sampling near the design point. Finally, the non probabilistic reliability index of the structure is obtained by the optimization criterion.
5. the unified model of structural non probabilistic reliability analysis under the description of three uncertain variables of interval, ellipsoid and super ellipsoid is established. The uniform design method is introduced to the non probabilistic reliability analysis of the structure. The method overcomes the shortcomings of the traditional random sampling space filling ability, and can fill the uncertain space of the structure evenly. Therefore, the accuracy and the sampling efficiency of the analysis are greatly improved. On this basis, the method is combined with the ANSYS finite element software, and a method of structural non probabilistic reliability and parameter sensitivity analysis for complex engineering problems is proposed.
6. the optimization design method of uncertain structure and its application in engineering are studied. In engineering application, the technical framework of structural reliability optimization design based on Matlab optimization module is established, and the 6 Sigma robust optimization design based on Isight and the structural Taguchi robust optimization design based on ANSYS probability design block are realized. In the research, uniform design method is used to realize the uniform filling of design space. Based on the point criterion, a Kriging model with better approximate accuracy is established. Based on the double Monte Carlo method, a structural robust optimization design method with double uncertainty of variable and agent model is proposed.

【學位授予單位】：西北工業(yè)大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TB114.3

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