基于Kriging方法的结构可靠性优化设计

发布时间：2018-04-04 16:31

本文选题：结构可靠性　切入点：基于可靠性的结构优化　出处：《沈阳航空航天大学》2017年硕士论文

【摘要】：在结构可靠性分析过程中,Kriging方法是工程实践中常用方法之一。本文开展了Kriging方法的研究工作,对经典Kriging方法进行改进,并将改进的Kriging方法运用到结构可靠性优化设计中。具体研究内容和结论如下:1)改进Kriging法针对样本点选取对Kriging模型预测精度具有一定影响(即样本点过多计算效率低下;样本点过少难以保证预测精度)的问题,本文提出基于梯度投影取样的改进Kriging方法。改进方法可以充分利用梯度投影技术的优势,能够合理选取用于构建Kriging模型的样本点,可以解决极限状态函数具有单个或多个最可能失效点的问题。2)基于可靠性的结构优化本文将改进Kriging方法应用到基于可靠性的结构优化之中。算例结果表明,改进Kriging方法具有较高的计算效率和较好的计算精度,能够大幅提高基于可靠性的结构优化效率。3)结论结构可靠性分析算例结果表明,改进Kriging方法求得的最可能失效点、可靠性指标和失效概率均具有满意的精度;相比经典可靠性分析方法,改进Kriging方法所需样本点数量明显减少,具有较好的计算效率。基于可靠性的结构优化算例表明,改进Kriging方法在提高优化效率的同时,能够获得满意的优化结果,具有良好的稳健性。
[Abstract]:Kriging method is one of the commonly used methods in engineering practice in the process of structural reliability analysis.In this paper, the research work of Kriging method is carried out, the classical Kriging method is improved, and the improved Kriging method is applied to the structural reliability optimization design.The specific research contents and conclusions are as follows: (1) the improved Kriging method has a certain effect on the prediction accuracy of Kriging model in view of the selection of sample points (that is, the calculation efficiency of too many sample points is low; the prediction accuracy is difficult to be guaranteed by too few sample points).This paper presents an improved Kriging method based on gradient projection sampling.The improved method can make full use of the advantage of gradient projection technology and can reasonably select the sample points used to construct Kriging model.The problem that limit state functions have single or more most likely failure points. 2) Reliability based structural optimization this paper applies the improved Kriging method to reliability based structural optimization.The results of numerical examples show that the improved Kriging method has higher computational efficiency and better accuracy, and can greatly improve the efficiency of structural optimization based on reliability .Conclusion the example of structural reliability analysis shows that,The reliability index and the failure probability obtained by the improved Kriging method have satisfactory accuracy, and the number of sample points needed by the improved Kriging method is obviously reduced compared with the classical reliability analysis method, and the efficiency of the improved Kriging method is better than that of the classical reliability analysis method.An example of structural optimization based on reliability shows that the improved Kriging method not only improves the optimization efficiency but also obtains satisfactory optimization results and has good robustness.
【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB114.3

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