多源不确定性结构可靠性分析及优化设计

发布时间：2018-04-26 06:12

本文选题：多源不确定性 + 概率可靠性　；参考：《西北工业大学》2014年博士论文

【摘要】：不确定性普遍存在于机械(结构)系统当中，其不确定性来源是多方面的，包括客观不确定性和主观不确定性。单一的数学模型不足以对机械系统中的不确定性进行准确而全面的描述。因此开展多源不确定性结构可靠性分析及优化设计方法研究有着重要的理论和现实意义。本文从概率模型、模糊模型、非概率模型等多个角度对结构可靠性设计问题进行研究，建立了一些适用于复杂工程问题的结构可靠性分析方法，在此基础上开展了结构可靠性优化设计和稳健优化设计方法研究，其主要内容如下： 1.基于概率可靠性模型，研究基于有限元仿真的复杂结构可靠性分析方法。以导弹吊挂结构为研究对象，，基于PCL(Patran Command Language)实现了结构有限元分析参数化。将有限元仿真与可靠性设计理论相结合，开发了基于有限元仿真分析的导弹吊挂结构可靠性分析软件平台。 2.基于模糊理论，研究了疲劳失效和共振失效下的模糊可靠性分析问题。采用隶属函数来描述结构疲劳失效的渐变过程，开展了模糊失效状态下的随机结构广义疲劳寿命可靠性分析。以三角型隶属函数来描述结构的模糊共振失效区，建立了三角型隶属函数下的结构广义共振可靠性分析模型。基于分解定理提出了λ水平截集下结构广义共振可靠性求解方法。 3.基于凸集模型，针对工程实际中大量存在的“未知但有界”参数的结构可靠性分析问题，建立了一种基于空间填充设计的非概率可靠性分析方法。该方法从非概率可靠性定义出发，以获得不确定性影响下结构功能函数的上下界为目标，基于改进的优化拉丁超立方抽样方法，使更多抽样点移向变量的边界，以达到以较少的样本点填充变量的不确定性空间并快速确定功能函数上下界的目的。该方法简单实用，适用于复杂工程结构及系统的非概率可靠性分析。 4.建立了一种基于重要抽样思想的结构非概率可靠性指标求解方法。从非概率可靠性指标的物理意义出发，将非概率可靠性指标求解问题转化为在标准化区间变量的扩展空间中以无穷范数度量的极限状态面上到坐标原点的最短距离问题。在此基础上，利用空间填充设计思想，在变量的扩展空间中找到结构失效域内距离极限状态面最近的点，然后在该设计点附近再进行重要抽样，最后通过寻优判据得到结构的非概率可靠性指标。 5.建立了区间、椭球、超椭球三种不确定性变量描述下的结构非概率可靠性分析统一模型。将均匀设计方法引入结构的非概率可靠性分析，该方法克服了传统随机抽样空间填充能力差的缺点，能够将样本均匀填充于结构的不确定性空间，因此大幅度的提升了分析的精度和抽样效率。在此基础上本文将该方法与ANSYS有限元软件相结合，提出了一种适用于复杂工程问题的结构非概率可靠性及参数灵敏度分析方法。 6.研究了不确定性结构的优化设计方法及其在工程中的应用。在工程应用方面，建立了基于Matlab优化模块的结构可靠性优化设计技术框架，实现了基于Isight的6σ稳健优化设计和基于ANSYS概率设计模块的结构Taguchi稳健优化设计。在理论研究方面，采用均匀设计方法实现设计空间的均匀填充，基于加点准则建立了具有更好近似精度的Kriging模型，在此基础上基于双Monte Carlo方法，提出了考虑变量和代理模型双重不确定下的结构稳健优化设计方法。
[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.

【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TB114.3

【参考文献】