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Modelling uncertainties in limit state functions
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DOI：10.1016/j.ijar.2011.09.001.png)
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In this paper uncertainties in limit state functions g as arising in engineering problems are modelled by adding additional parameters and by introducing parameterized probability density functions which describe the uncertainties of these new additional parameters and of the basic variables of g. This will lead to a function p(f) (a, b) for the probability of failure depending on parameters a and b corresponding to the two parameterized density functions. Further the parameters a and b are assumed to be uncertain. Using intervals, sets or random sets to model their uncertainty results in upper probabilities (p) over bar (f) of failure. In this context we also discuss different notions of independence such as strong independence, epistemic irrelevance and random set independence and present a simple engineering example. (C) 2011 Elsevier Inc. All rights reserved.
Keyword:
Probability of failure
Limit state functions
Parameterized probability measures
Random set independence
Epistemic irrelevance
Strong independence
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