Enhanced Monte Carlo using Two Scaling or Design Factors
Abstract eng: The complexity of engineering systems and their failure modes considerably limit the use of traditional methods for structural reliability analysis and advocate the application of Monte Carlo (MC) methods. A recently developed MC approach focuses on classes of safety margins parameterized by a single scaling factor λ. The idea is to estimate high system failure probabilities for λ < 1 using MC effectively with a small number of required samples. Then, weighted regression analysis is performed based on p
f (λ) = qexp{-a(λ-c)
d} to determine the target failure probability for λ = 1.
The paper's objective is to extend the current approach using two and more scaling parameters.The system failure probability using two scaling factors λ
1 and λ
2 is p
f (λ
1, λ
2) = qexp{-(b
1λ
1-b
2λ
2-c)
d} where q, b
1, b
2, c, d are unknown parameters. The developed pf (λ
1, λ
2) describes a failure probability surface that is valid for high and low failure probabilities of systems having single or multiple limit state functions. The idea is now to determine failure probabilities using MC sampling at a number of grid points (λ
1, λ
2) in the high failure domain well below the value of 1. The unknown parameters q, b
1, b
2, c, d are estimated in a weighted regression analysis on the log(p
f)-level taking the uncertainties of the MC-based point estimates into account. Low failure probabilities such as the target p
f (1, 1) are then easily available including an uncertainty band.
The effectiveness of the developed approach is illustrated on a structural frame having six limit states. The failure probability of the series system is estimated on 5 x 5 (λ
1, λ
2)-grid with 10
5 samples. The results are verified using crude MC with 108 samples.
If λ
1 and λ
2 act as design factors such as partial resistance and load factors used in design check equations, the surface p
f (λ
1, λ
2) describes the system failure probability as a function of the design factors. By inverting the new approach where λ
1 and λ
2 are estimated for a given failure probability, an effective and MC-based tool is now available for the reliability-based calibration of partial design factors.
Contributors:
Publisher:
Research Publishing, No:83 Genting Lane, #08-01, Genting Building, 349568 SINGAPORE
Conference Title:
Conference Title:
5th Asian-Pacific Symposium on Structural Reliability and its Applications
Conference Venue:
Singapore (SG)
Conference Dates:
2012-05-23 / 2012-05-25
Rights:
Text je chráněný podle autorského zákona č. 121/2000 Sb.
Record appears in:
Record created 2014-11-18, last modified 2014-11-18
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