Structural reliability analysis with probability-boxes. Hao Zhang School of Civil Engineering, University of Sydney, NSW 2006, Australia Michael Beer Institute for Risk & Uncertainty, University of Liverpool, Liverpool, UK. Reliability assessment with limited data A common scenario.
School of Civil Engineering, University of Sydney, NSW 2006, Australia
Institute for Risk & Uncertainty, University of Liverpool, Liverpool, UK
rj : a sample of iid standard uniform random variates.
When Fx( ) is unknown but bounded, interval samples can be generated
A lower and an upper bound for Pf can be estimated as
Variance of direct interval Monte Carlo
2D scatter plots: (a) random sample; (b) Good lattice point; (c) Halton sequence; (d) Faure sequence.
Fn(x) = empirical cumulative frequency function
Dnα= K-S critical value at significance level α with a sample size of n
If the knowledge of the first two moments (and the range) of the random variable is available, (one-sided or two-sided) Chebyshev inequality can be used.
If the (unknown) statistical parameter (θ ) of the distribution varies in an interval
When there are multiple candidate distribution models which cannot be distinguished by standard goodness-of-fit tests,
Fi (x) = ith candidate CDF
Limit state: roof drift < 17.78 mm
Roof drift is computed by (linear elastic) finite
10-bar truss (after Nie and Ellingwood, 2005)