【作者】 冯德成； 梁艳萍； 任晓丹；

【Author】 Feng De-Cheng;Liang Yan-Ping;Ren Xiaodan;Southeast University;Tongji University;

【机构】 东南大学； 同济大学；

【摘要】 随机场被广泛用于反映结构属性等的空间变异性,然而,传统的随机场生成方法仅仅适用于规则结构的空间变异性表征,如二维平面结构。对于常见的复杂流形结构,因其几何结构复杂,很难显式推导出相关函数,因此无法直接采用传统的方法来生成随机场。为了解决这一问题,本文提出了一种两阶段策略来模拟流形上的随机场。其核心思想是通过等距特征映射(Isomap)将流形映射到二维欧几里德空间,使映射后的二维欧几里德空间中点与原流形空间的测地距离保持不变。因此,相关函数可以很容易地推导出来,并可以直接使用传统方法产生随机场。为了验证该方法的有效性,将几种不同类型的流形降维到二维平面域,并使用随机谐波函数(SHF)方法生成随机场。最后,通过两种不同结构的随机有限元分析实例验证了该方法的适用性和有效性。更多还原

【Abstract】 Random fields are widely used to reflect the spatial variability of structural attributes.However,the traditional random fields generation method is only applicable to the representation of the spatial variability of regular structures,such as two-dimensional planar structures.For the common complex manifold structure,because of its complex geometry structure,it is difficult to derive the correlation function explicitly,so it can not directly use the traditional method to generate random fields.To solve this problem,a two-stage strategy is proposed to simulate random fields over manifolds.The key idea is to map manifolds to 2-d Euclidean space by Isomap,so that the geodesic distance between the mapped 2-D Euclidean space and the original manifold space remains unchanged.Therefore,correlation functions can be easily derived and random fields can be generated directly using traditional methods.In order to verify the effectiveness of this method,several manifolds of different types are reduced to two-dimensional plane domains and the random harmonic function(SHF) method is used to generate random fields.Finally,the applicability and effectiveness of the method are verified by two random finite element analysis examples of different structures.更多还原