结构系统稳健优化设计的新方法研究及应用

发布时间：2018-05-10 21:44

本文选题：结构稳健优化设计 + 信息熵　；参考：《电子科技大学》2015年硕士论文

【摘要】：结构稳健优化设计的核心就是寻找最佳设计方案以确保约束条件和输出性能在外部不确定性影响下均具有足够的稳健性,以输出性能均值和标准差加权和作为目标函数,在满足约束条件情况下,寻求最佳优化设计结果。该项先进技术在设计阶段就考虑实际工程中广泛存在的不确定性因素,并最大程度地降低这些因素对工程结构性能的影响,从而提升结构性能。因此在机械设计、航空航天、土木工程、振动控制和加工制造等诸多领域得到了极为广泛的应用。但是,传统的结构稳健优化设计依赖于设计者对权值的选择,不同的权重可以导致截然不同的设计方案,限制了该技术的工程推广应用。针对这一问题,本论文提出不依赖于权重选择的新稳健优化设计模型,并采用全新的高效求解方法以兼顾高计算精度和高求解速度,并最终实现所提方法在印刷电路板稳健优化设计中的应用。具体研究内容如下:(1)以标准差作为输出性能稳健性度量指标。本论文提出以性能均值和性能标准差乘积为目标函数,以约束可靠度大于设计可靠度为约束条件的新型稳健优化设计模型。并引入稀疏网格法这种高效、高精度的方法来实现对该问题的快速求解。数值算例和工程算例验证所提方法的可行性及高效性。(2)以信息熵作为输出性能稳健性度量指标。本论文提出以性能均值和性能熵乘积为目标函数,以约束可靠度大于设计可靠度为约束条件的新型稳健优化设计模型。以核密度估计法确定输出性能的信息熵,并结合线性拟合技术确定性能熵与设计变量之间的近似直接函数关系式,引入稀疏网格法实现对该问题的快速求解。工程算例验证了所提方法的可行性及高效性。(3)以某印刷电路板的有限元分析模型为对象,以一阶模态最大振幅的均值和标准差乘积为目标函数构建稳健优化设计模型。对优化前后印刷电路板模型分别进行了模态分析和随机振动分析,有限元分析结果验证了所提稳健模型的有效性和可行性。
[Abstract]:The core of structural robust optimization design is to find the best design scheme to ensure that the constraint conditions and the output performance are robust enough under the influence of external uncertainty. The weighted sum of the mean and standard deviation of the output performance is taken as the objective function. In the case of satisfying the constraint conditions, the optimal design results are sought. In the design stage, the advanced technology takes into account the uncertainty factors widely existing in the actual engineering, and minimizes the influence of these factors on the structural performance of the engineering, thus improving the structural performance. Therefore, it has been widely used in many fields such as mechanical design, aerospace, civil engineering, vibration control and manufacturing. However, the traditional structural robust optimization design depends on the designer's choice of weights. Different weights can lead to different design schemes, which limits the engineering application of this technology. To solve this problem, a new robust optimal design model is proposed, which does not depend on weight selection, and a new and efficient solution method is adopted to give consideration to high calculation accuracy and high speed. Finally, the application of the proposed method in the robust optimization design of printed circuit board is realized. The main contents are as follows: (1) the standard deviation is used as a measure of output performance robustness. In this paper, a new robust optimal design model is proposed, in which the mean performance and the product of performance standard deviation are taken as objective functions and the constraint reliability is greater than the design reliability. The sparse mesh method is introduced to solve the problem quickly. Numerical examples and engineering examples verify the feasibility and efficiency of the proposed method. In this paper, a new robust optimal design model is proposed, in which the mean value of performance and the product of performance entropy are taken as objective functions, and the constraint condition is that the constraint reliability is greater than the design reliability. The information entropy of the output performance is determined by the kernel density estimation method and the approximate direct function relationship between the performance entropy and the design variables is determined by the linear fitting technique. The sparse mesh method is introduced to solve the problem quickly. The engineering example verifies the feasibility and high efficiency of the proposed method. The finite element analysis model of a printed circuit board is taken as an object, and the mean value and standard deviation product of the maximum amplitude of the first mode are taken as objective functions to construct a robust optimal design model. The modal analysis and random vibration analysis of printed circuit board model before and after optimization are carried out respectively. The results of finite element analysis verify the validity and feasibility of the proposed robust model.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN41

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