This paper discusses the concepts of auto‐ and cross‐interdependence in interval field finite element analysis. In classic interval analysis, independent intervals are used to construct hyper‐rectangular input spaces that correspond to the bounded uncertainty that is present on some model parameters. This is a direct result from the inability of modeling interdependence. Such assumption of complete independence might prove in some cases to be highly over‐conservative. A first example is the modeling of spatial uncertainty, where the interdependence is governed by allowable spatial gradients of field realizations. Secondly, interdependence can also occur in case uncertainty in several structural quantities has the same root cause (eg, the manufacturing process). Recent work by the authors introduced concepts for modeling dependence between intervals in a spatial and multivariate context. However, it is unclear how an analyst has to deal with multiple quantities that have a spatial uncertainty component and are furthermore interdependent. This paper presents an approach to link multiple interval fields using recently introduced convex hull pair constructions and inverse distance weighting interpolation. Two case studies to illustrate the new methodology are included, proving the flexibility of the methodology in the modeling of auto‐ and cross‐interdependence between multiple interval scalars and/or interval fields.

中文翻译：

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区间场有限元分析中的自相关和交叉相关

本文讨论了区间场有限元分析中自相关和交叉相关的概念。在经典区间分析中，独立区间用于构造与某些模型参数上存在的有界不确定性相对应的超矩形输入空间。这是无法建模相互依赖性的直接结果。在某些情况下，这种完全独立的假设可能被证明过于保守。第一个示例是空间不确定性的建模，其中相互依赖性由现场实现的允许空间梯度控制。其次，如果几个结构量的不确定性具有相同的根本原因（例如，制造过程），也会发生相互依赖性。作者最近的工作介绍了用于对空间和多元上下文中的区间之间的依赖性进行建模的概念。但是，尚不清楚分析师如何处理具有空间不确定性成分且相互依赖的多个量。本文提出了一种使用最近引入的凸包对构造和反距离权重插值来链接多个间隔场的方法。其中包括两个案例研究，以说明新方法，证明了该方法在建模多个间隔标量和/或间隔字段之间的自相关和交叉依赖方面的灵活性。本文提出了一种使用最近引入的凸包对构造和反距离权重插值来链接多个间隔场的方法。其中包括两个案例研究，以说明新方法，证明了该方法在建模多个间隔标量和/或间隔字段之间的自相关和交叉依赖方面的灵活性。本文提出了一种使用最近引入的凸包对构造和反距离权重插值来链接多个间隔场的方法。其中包括两个案例研究，以说明新方法，证明了该方法在建模多个间隔标量和/或间隔字段之间的自相关和交叉依赖方面的灵活性。