Extended and Generalized Fragility Functions
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 144, Issue 9
Abstract
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.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 9 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jul 16, 2017
Accepted: Jan 18, 2018
Published online: Jul 4, 2018
Published in print: Sep 1, 2018
Discussion open until: Dec 4, 2018
ASCE Technical Topics:
- Arbitration
- Business management
- Deterioration
- Dispute resolution
- Engineering fundamentals
- Legal affairs
- Markov process
- Materials characterization
- Materials engineering
- Mathematics
- Measurement (by type)
- Methodology (by type)
- Numerical methods
- Practice and Profession
- Probability
- Statistics
- Stochastic processes
- Time dependence
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