考虑区间和概率不确定性的机械结构优化设计

发布时间：2018-06-05 01:49

本文选题：机械结构 + 不确定性　；参考：《浙江大学》2017年硕士论文

【摘要】：实际工程中普遍存在着各种影响结构性能的不确定因素,不确定性优化设计是处理这些不确定因素并获取高性能、高稳健可靠性结构设计方案的有效途径。虽然近年来国内外不少专家学者围绕机械结构的不确定性优化设计开展了一系列研究工作,但是仍然存在许多问题有待进一步研究。一方面,现有研究在求解基于区间的结构优化设计模型时往往是通过引入罚因子、正则化因子等将区间模型转换为确定性模型,并通过加权法将多目标优化问题转化为单目标问题进行优化求解,该基于模型转换的间接求解过程比较繁琐,且不同的模型转换参数还会导致不同的求解结果;另一方面,在实际工程结构设计中概率和非概率不确定因素通常是同时存在的。因此,开展考虑区间和概率不确定性的机械结构优化设计研究,提出并实现机械结构优化设计模型的直接求解方法,对提高机械结构性能及其稳健可靠性具有重要意义。论文的主要内容如下:第一章综述了概率不确定性优化设计、非概率不确定性优化设计和概率-非概率混合不确定性优化设计的国内外研究现状,分析了现有研究中存在的问题,提出了论文的研究意义与研究内容。第二章概述了区间序关系与区间可能度等区间数学基础理论,给出了基于区间模型、概率模型和混合模型的机械结构稳健性与可靠性指标的数学描述方法,并介绍了预测机械结构性能指标的近似代理模型的构建方法以及常用的多项式响应面模型和Kriging近似模型。第三章采用区间数描述不确定因素,建立了基于区间的机械结构稳健性设计模型,提出了区间约束违反矢量的定义和基于区间约束违反矢量的优于关系准则,并结合双层嵌套的遗传算法和Kriging近似模型技术,实现了基于区间的机械结构稳健性设计模型的直接求解。最后,通过测试算例和压力机上横梁稳健设计实例验证了提出方法的有效性和相对于间接方法的优越性。第四章建立了基于区间的机械结构可靠性设计模型,给出了基于图表法的区间可靠度统一计算公式,提出了区间可靠性违反度的定义和对应的优于关系准则,完成了对可靠性设计模型的直接求解。测试算例和压力机上横梁可靠性设计实例表明,提出方法可获得比间接方法更优的结果。第五章以概率变量描述设计参数,以区间变量描述不确定因素,建立了基于概率-区间的机械结构可靠性设计模型,选择在区间变量影响下可靠度的最小值作为可靠性指标,选择多项式响应面模型作为近似代理模型,并结合遗传算法和改进的一次二阶矩法,实现了基于概率-区间的结构可靠性设计模型的求解,并通过压力机滑块机构和底座的可靠性设计实例验证了提出方法的有效性。第六章总结了论文的研究工作和主要成果,并指出了有待进一步研究的方向。
[Abstract]:There are a variety of uncertain factors affecting structural performance in practical engineering. The uncertain optimization design is an effective way to deal with these uncertain factors and to obtain high performance and high robust reliability structural design scheme. Although many experts and scholars at home and abroad have carried out a series of research work on the uncertainty optimization design of mechanical structures in recent years, there are still many problems to be further studied. On the one hand, in solving the structural optimization design model based on interval, the existing research often transforms interval model into deterministic model by introducing penalty factor and regularization factor. The multi-objective optimization problem is transformed into a single-objective problem by weighted method. The indirect solving process based on model transformation is tedious, and different model conversion parameters will lead to different results. In practical engineering structure design, both probabilistic and non-probabilistic uncertainties usually exist at the same time. Therefore, it is of great significance to improve the performance and robust reliability of mechanical structure by carrying out the research on the optimal design of mechanical structure considering interval and probability uncertainty, and putting forward and realizing the direct solution method of the optimal design model of mechanical structure. The main contents of this paper are as follows: the first chapter summarizes the research status of probabilistic uncertainty optimization design, non-probabilistic uncertainty optimization design and probabilistic non-probabilistic mixed uncertainty optimization design at home and abroad. The existing problems are analyzed, and the significance and content of the thesis are put forward. In the second chapter, the basic theory of interval mathematics such as interval order relation and interval probability degree is summarized, and the mathematical description method of mechanical structure robustness and reliability index based on interval model, probability model and mixed model is given. The construction method of approximate agent model for predicting mechanical structure performance index and polynomial response surface model and Kriging approximate model are introduced. In chapter 3, the interval number is used to describe the uncertain factors, and the robust design model of mechanical structure based on interval is established. The definition of interval constraint violation vector and the superior relation criterion based on interval constraint violation vector are proposed. Combined with double-layer nested genetic algorithm and Kriging approximate model technology, the direct solution of the robust design model of mechanical structure based on interval is realized. Finally, the effectiveness of the proposed method and the superiority of the indirect method compared with the indirect method are verified by a test example and an example of the robust design of the cross beam on the press. In chapter 4, the reliability design model of mechanical structure based on interval is established, the unified calculation formula of interval reliability based on chart method is given, and the definition of interval reliability violation degree and the corresponding superior relation criterion are put forward. The direct solution of reliability design model is completed. The test example and the reliability design example of the cross beam on the press show that the proposed method can obtain better results than the indirect method. In chapter 5, the design parameters are described by probabilistic variables, and the uncertain factors are described by interval variables. The reliability design model of mechanical structures based on probabilistic and interval-interval is established. The minimum value of reliability under the influence of interval variables is chosen as the reliability index. The polynomial response surface model is chosen as the approximate agent model and the genetic algorithm and the improved first-order second-order moment method are combined to solve the probabilistic and interval-based structural reliability design model. The effectiveness of the proposed method is verified by an example of reliability design of the slider mechanism and the base of the press. The sixth chapter summarizes the research work and main results, and points out the direction of further research.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH122

【参考文献】