Abstract Progressive collapse (the spread of a relatively minor local damage through a chain of failures to the collapse of a significant portion of a structure) constitutes an important mode of system failure. A robust structure is able to locally confine the effects of a relatively minor initial damage. As a technical term, robustness has different connotations in different fields; a variety of robustness measures, phenomenological in nature, are also available in the structural engineering literature. The measure of structural robustness against progressive collapse must ideally be a monotonic function of a suitable damage measure, must help identify and prioritize critically important initial damages, and must be able to rank different structures in terms of their susceptibility to progressive collapse under similar loading and initial damages. It must also take all uncertainties into account. Starting with relative entropy between the joint distributions of safety margins and the generalized Birnbaum/Barlow-Proschan-Iyer component importance measure, we propose a new robustness index for binary, coherent structural systems that is bounded by zero and one; zero signifying certain collapse given the initial damage and one signifying the structure’s complete indifference to the given initial damage. The methodology is demonstrated on an indeterminate planar truss structure. The initial damage considered is the failure of any one given member. Element strengths and the load are taken to be random. Progressive collapse being a sequence driven event, an enumerative scheme is adopted for reliability analyses of the intact and damaged structures. The relations between robustness index, importance measure, element reliability and correlation between intact and damage safety margins are investigated; comparison of the proposed index with existing robustness measures is undertaken.

中文翻译：

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基于可靠性的相干系统结构稳健性度量

摘要 渐进式倒塌（相对较小的局部损坏通过一系列故障扩散到结构的重要部分倒塌）构成了系统故障的一种重要模式。坚固的结构能够局部限制相对较小的初始损坏的影响。作为一个技术术语，健壮性在不同领域有不同的含义；结构工程文献中也提供了各种稳健性措施，本质上是现象学。理想情况下，针对连续倒塌的结构坚固性的度量必须是合适的损坏度量的单调函数，必须有助于识别和优先考虑极其重要的初始损坏，并且必须能够根据在相似载荷下对连续倒塌的敏感性对不同结构进行排序初始损害。它还必须考虑到所有的不确定性。从安全裕度的联合分布与广义 Birnbaum/Barlow-Proschan-Iyer 分量重要性度量之间的相对熵开始，我们为以零和一为界的二元相干结构系统提出了一个新的稳健性指数；零表示在给定初始损坏的情况下一定会倒塌，而 1 表示结构对给定的初始损坏完全无所谓。该方法在不确定的平面桁架结构上进行了演示。最初考虑的损害是任何一个给定成员的失败。单元强度和载荷被认为是随机的。连续倒塌是一个序列驱动事件，采用枚举方案对完整和损坏结构进行可靠性分析。稳健性指数之间的关系，研究了重要度量、元件可靠性以及完整和损坏安全裕度之间的相关性；将拟议指数与现有稳健性措施进行比较。