Extended and Generalized Fragility Functions
Extended and Generalized Fragility Functions
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DOI：
10.1061/(asce)em.1943-7889.0001478
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发表时间：
2018-09-01
影响因子：
3.3
通讯作者：
Papakonstantinou, K. G.
中科院分区：
文献类型：
--
作者：
Andriotis, C. P.;Papakonstantinou, K. G.
脆弱性函数表示系统超过某些损伤状态的概率，给出了表征记录或模拟数据序列的一些适当的措施。本文分为两个主要部分，在其最大的通用性，占两个（1）多变量强度措施与多个损伤状态和（2）纵向损伤状态的时间依赖性的脆弱性函数。没有采用共同方差的限制性假设，以避免不适当的函数交叉，第一部分介绍了这里被称为扩展脆弱性函数。如图所示，对于不同状态的强度测量可能属于的指数族的任何任意分布，包括强度测量的对数尺度中通常使用的正态分布，softmax函数最好地支持这些。在第二部分中，广义脆弱性函数的情况下，需要捕捉多个系统状态转换。为此，依赖马尔可夫和隐马尔可夫模型，因为它们能够描绘纵向数据的依赖性，并揭示内在的恶化趋势多个连续的事件。数值结果，连同基本的实施细节，统计特性，和实用的建议。
Fragility functions indicate the probability of a system exceeding certain damage states given some appropriate measures that characterize recorded or simulated data series. Presented in two main parts, this paper develops fragility functions in their utmost generality, accounting for both (1)multivariate intensity measures with multiple damage states and (2)longitudinal damage state dependencies in time. Without adopting the limiting assumption of common variance to avoid improper function crossings, the first part presents what is here compactly termed as extended fragility functions. As shown, these are best supported by the softmax function for any arbitrary distribution of the exponential family to which the intensity measures of different states may belong, including the typically used normal distribution in the logarithmic scale of intensity measures. In the second part, generalized fragility functions are introduced for cases where multiple system state transitions need to be captured. To that end, dependent Markov and hidden Markov models are employed because they are able to portray longitudinal data dependencies and reveal intrinsic deterioration trends for multiple sequential events. Numerical results are presented, together with underlying implementation details, statistical properties, and practical suggestions.