000004556 001__ 4556
000004556 005__ 20141118192706.0
000004556 0177_ $$2doi$$a10.3850/978-981-07-2219-7_P297

000004556 0247_ $$210.3850/978-981-07-2219-7_P297
$$adoi
000004556 04107 $$aeng
000004556 046__ $$k2012-05-23
000004556 100__ $$aDann, Markus R.
000004556 24500 $$aEnhanced Monte Carlo using Two Scaling or Design Factors

000004556 24630 $$n5.$$pProceedings of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications
000004556 260__ $$bResearch Publishing, No:83 Genting Lane, #08-01, Genting Building, 349568 SINGAPORE
000004556 506__ $$arestricted
000004556 520__ $$2eng$$aThe 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<sub>f</sub> (λ) = qexp{-a(λ-c)<sup>d</sup>} 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<sub>1</sub> and λ<sub>2</sub> is p<sub>f</sub> (λ<sub>1</sub>, λ<sub>2</sub>) = qexp{-(b<sub>1</sub>λ<sub>1</sub>-b<sub>2</sub>λ<sub>2</sub>-c)<sup>d</sup>} where q, b<sub>1</sub>, b<sub>2</sub>, c, d are unknown parameters. The developed pf (λ<sub>1</sub>, λ<sub>2</sub>) 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<sub>1</sub>, λ<sub>2</sub>) in the high failure domain well below the value of 1. The unknown parameters q, b<sub>1</sub>, b<sub>2</sub>, c, d are estimated in a weighted regression analysis on the log(p<sub>f</sub>)-level taking the uncertainties of the MC-based point estimates into account. Low failure probabilities such as the target p<sub>f</sub> (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<sub>1</sub>, λ<sub>2</sub>)-grid with 10<sup>5</sup> samples. The results are verified using crude MC with 108 samples. 
 If λ<sub>1</sub> and λ<sub>2</sub> act as design factors such as partial resistance and load factors used in design check equations, the surface p<sub>f</sub> (λ<sub>1</sub>, λ<sub>2</sub>) describes the system failure probability as a function of the design factors. By inverting the new approach where λ<sub>1</sub> and λ<sub>2</sub> 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.

000004556 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000004556 653__ $$aSystem reliability, Calibration of design factors, Monte carlo simulation.

000004556 7112_ $$a5th Asian-Pacific Symposium on Structural Reliability and its Applications$$cSingapore (SG)$$d2012-05-23 / 2012-05-25$$gAPSSRA2012
000004556 720__ $$aDann, Markus R.$$iMaes, Marc A.$$iNaess, Arvid
000004556 8560_ $$ffischerc@itam.cas.cz
000004556 8564_ $$s267059$$uhttps://invenio.itam.cas.cz/record/4556/files/P297.pdf$$yOriginal version of the author's contribution as presented on CD, .
000004556 962__ $$r4180
000004556 980__ $$aPAPER