Journal Article10.1061/(ASCE)0733-9399(1991)117:12(2904)
Efficient algorithm for second-order reliability analysis
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TL;DR: In this article, the principal curvatures of the limit-state surface at the design point are used to construct a paraboloid approximation of the surface, which is then used to compute a second-order estimate of the failure probability.
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Abstract: In the second‐order reliability method the principal curvatures of the limit‐state surface at the design point are used to construct a paraboloid approximation of the surface, which is then used to compute a second‐order estimate of the failure probability. The principal curvatures are the eigenvalues of the Hessian of the surface. In this paper an efficient algorithm is developed to determine the principal curvatures without computing the Hessian. The curvatures are computed in an iterative manner using the gradient of the limit‐state function, and are obtained in the decreasing order of their absolute magnitudes, which is also the order of their importance in reliability analysis. The computation can be terminated when the last curvature obtained is sufficiently small. The method is efficient for problems with large numbers of random variables, especially when an efficient algorithm for computing the gradient is available. Several numerical examples, including a finite‐element application involving 99 r...
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Assessing small failure probabilities by combined subset simulation and Support Vector Machines
TL;DR: A new approach for estimating small failure probabilities by considering subset simulation proposed by S.-K.
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•Posted Content
Metamodel-based importance sampling for structural reliability analysis
TL;DR: A kriging surrogate of the performance function is proposed to use as a means to build a quasi-optimal importance sampling density and proves efficient up to 100 random variables.
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References
Exact and Invariant Second-Moment Code Format
A. M. Hasofer,Niels C. Lind +1 more
TL;DR: In this article, a fundamental analysis of the meaning of second-moment reliability in multivariate problems is presented, and the format described is entirely derived from one basic assumption concerning the measurement of reliability.
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Structural reliability under combined random load sequences
Rüdiger Rackwitz,Bernd Flessler +1 more
TL;DR: In this paper, an algorithm for the calculation of structural reliability under combined loading is formulated, in which loads or any other actions upon structures are modelled as independent random sequences and the relevant limit state criterion is pointwise approximated by a tangent hyperplane.
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