麻 凯, 李 鹏, 刘巧伶. 基于Epsilon算法的不确定性结构二阶区间优化方法[J]. 工程力学, 2013, 30(1): 99-104. DOI: 10.6052/j.issn.1000-4750.2011.07.0449
引用本文: 麻 凯, 李 鹏, 刘巧伶. 基于Epsilon算法的不确定性结构二阶区间优化方法[J]. 工程力学, 2013, 30(1): 99-104. DOI: 10.6052/j.issn.1000-4750.2011.07.0449
MA Kai, LI Peng, LIU Qiao-ling. A SECOND INTERVAL OPTIMIZATION METHOD ON UNCERTAINTY STRUCTURE BASED ON EPSILON METHOD[J]. Engineering Mechanics, 2013, 30(1): 99-104. DOI: 10.6052/j.issn.1000-4750.2011.07.0449
Citation: MA Kai, LI Peng, LIU Qiao-ling. A SECOND INTERVAL OPTIMIZATION METHOD ON UNCERTAINTY STRUCTURE BASED ON EPSILON METHOD[J]. Engineering Mechanics, 2013, 30(1): 99-104. DOI: 10.6052/j.issn.1000-4750.2011.07.0449

基于Epsilon算法的不确定性结构二阶区间优化方法

A SECOND INTERVAL OPTIMIZATION METHOD ON UNCERTAINTY STRUCTURE BASED ON EPSILON METHOD

  • 摘要: 该文提出一种求解不确定性结构模态的二阶区间优化算法,首先应用拉格朗日乘子法将带有约束条件的模态优化问题转化为非约束优化,再用区间扩展的二阶泰勒展开式近似表述不确定性结构的模态区间函数。由于其二阶常数项(海森矩阵)的计算十分繁琐,这里采用DFP方法(Davidon and Fletcher-Powell method)近似迭代计算该常数项,同时计算满足约束条件和优化目标的结构参数和参数不确定性区间。在结构重分析中采用Epsilon算法,从而在保证计算精度的同时节省了计算时间。通过算例计算进一步证明该方法对于板壳加筋不确定结构的优化是有效的。

     

    Abstract: This paper presents an interval modal optimization method on uncertain structures. At first, this paper present an optimization with constraint conditions would be transformed into an optimization without constraint conditions by the Lagrange multiplier method, then an interval second Taylor expand function would be build to approximately describe the modal interval of the uncertainty structure with interval parameters. In the interval expression, the second constant term, Hessian matrix, is hardly computed by a common method normally. Therefore, The DFP method would be used to approximatively iterate it. At last, the wanted structural parameters and their interval can be computed by the interval function. During the iteration, the Epsilon method would be used to achieve the result more rapidly and accurately. The optimization method was used in an example of a plate-shell with stiffeners, which prove this method is a useful interval optimization.

     

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