Journal ArticleDOI
AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation
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TLDR
An iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the reliability of structures in a more efficient way and is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function.About:
This article is published in Structural Safety.The article was published on 2011-03-01. It has received 1234 citations till now. The article focuses on the topics: Reliability (statistics) & Kriging.read more
Citations
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Journal ArticleDOI
A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models
TL;DR: An original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling, based on the AK-MCS algorithm, that enables the correction or validation of the FORM approximation with only a very few mechanical model computations.
Journal ArticleDOI
Metamodel-based importance sampling for structural reliability analysis
TL;DR: In this paper, the authors propose to use a Kriging surrogate for the performance function as a means to build a quasi-optimal importance sampling density, which can be applied to analytical and finite element reliability problems and proves efficient up to 100 basic random variables.
Journal ArticleDOI
LIF: A new Kriging based learning function and its application to structural reliability analysis
TL;DR: Results show that LIF and the new method proposed in this research are very efficient when dealing with nonlinear performance function, small probability, complicated limit state and engineering problems with high dimension.
Journal ArticleDOI
Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation
TL;DR: AK–SS: an active learning method combining Kriging model and SS can provide accurate solutions more efficiently, making it a promising approach for structural reliability analyses involving small failure probabilities, high-dimensional performance functions, and time-consuming simulation codes in practical engineering.
Journal ArticleDOI
Polynomial-Chaos-based Kriging
TL;DR: PC-Kriging is derived as a new non-intrusive meta-modeling approach combining PCE and Kriging, which approximates the global behavior of the computational model whereas Kriged manages the local variability of the model output.
References
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Efficient Global Optimization of Expensive Black-Box Functions
TL;DR: This paper introduces the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering and shows how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule.
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Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
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An Automatic Method for Solving Discrete Programming Problems
Ailsa H. Land,Alison G. Doig +1 more
TL;DR: In the late 1950s there was a group of teachers and research assistants at the London School of Economics interested in linear programming and its extensions, in particular Helen Makower, George Morton, Ailsa Land and Alison Doig.
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Lipschitzian optimization without the Lipschitz constant
TL;DR: In this article, the Lipschitz constant is viewed as a weighting parameter that indicates how much emphasis to place on global versus local search, which accounts for the fast convergence of the new algorithm on the test functions.
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Structural Reliability Methods
Ove Ditlevsen,H. O. Madsen +1 more
TL;DR: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometricreliability Index Generalized Reliability index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis.
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