A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models

Applying reliability methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess effi...

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Vydáno v:Reliability engineering & system safety Ročník 111; s. 232 - 240
Hlavní autoři: Echard, B., Gayton, N., Lemaire, M., Relun, N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Elsevier Ltd 01.03.2013
Elsevier
Témata:
Applied sciences
Computation
Computer simulation
Exact sciences and technology
Fatigue failure
Importance sampling
Kriging
Kriging metamodel
Learning
Linear inference, regression
Mathematical models
Mathematics
Operational research and scientific management
Operational research. Management science
Probability and statistics
Reliability
Reliability theory. Replacement problems
Safety
Sciences and techniques of general use
Small failure probability
Statistics
Surrogate model
Small failure probability
Surrogate model
Reliability
Kriging metamodel
Importance sampling
Monte Carlo method
Probabilistic approach
Fatigue
Modeling
Kriging
Metaanalysis
Complex method
Break up time
Aerospace
Variance reduction
Sampling methods
Mechanical structure
Safety
Time complexity
Metamodel
ISSN:0951-8320, 1879-0836
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Shrnutí:Applying reliability methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling. This new method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the method is, first, proved on two academic applications. It is then conducted for assessing the reliability of a challenging aerospace case study submitted to fatigue.
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ISSN:0951-8320
1879-0836
DOI:10.1016/j.ress.2012.10.008