Confidence ellipsoids for static response of trusses with load and structural uncertainties
Confidence ellipsoids for static response of trusses with load and structural uncertainties
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DOI：
10.1016/j.cma.2006.04.007
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发表时间：
2006-12
影响因子：
7.2
通讯作者：
Y. Kanno;I. Takewaki
中科院分区：
文献类型：
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作者：
Y. Kanno;I. Takewaki
本文提出了一种半定松弛技术，用于计算包含不确定桁架静力响应集的最小定界椭球。假设杆件刚度参数和外力参数都是不确定但有界的。通过使用二次嵌入技术的不确定性和S-过程的组合，我们制定了一个半定规划（SDP）的问题，它提供了一个外部近似的最小边界椭球。我们的方法具有多项式的计算复杂性的问题的大小，如果SDP问题是使用原始-对偶邻域点法求解。在几种不确定情况下，计算了各种桁架的最小边界椭球。
This paper presents a semidefinite relaxation technique for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain truss. We assume that the parameters both of member stiffnesses and external forces are uncertain but bounded. By using a combination of the quadratic embedding technique of the uncertainty and the S-procedure, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. Our approach has polynomial computational complexity of the problem size, if the SDP problem presented is solved by using the primal-dual interior-point method. The minimum bounding ellipsoids are computed for various trusses under several uncertain circumstances.