Application Of Kriging Method To Structural Reliability Problems

By Irfan Kaymaz. 2005

722 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a881db1258cbf7819c32a081e4c5a5ac8ed12851

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In Computational Theory and Mathematics

In Mechanics of Materials

In Statistics and Probability

Citations in the corpus

Metamodel-based importance sampling for structural reliability analysis (2011, background): “…(Bucher and Bourgund, 1990; Kim and Na, 1997; Das and Zheng, 2000), support vector machines (Hurtado, 2004; Deheeger and Lemaire, 2007; Bourinet et al., 2011), francois.deheeger@gmail.com (F. Deheeger) neural networks (Papadrakakis and Lagaros, 2002) andKriging (Kaymaz, 2005; Bichon et al., 2008).”
A new adaptive response surface method for reliability analysis (2013, methodology): “This new model, called metamodel, can be of various kinds: quadratic response surfaces [21], polynomial chaos [23,6], kriging [40,27], neural network [36,13,20] or even support vector machine [25].”
Calibration and Uncertainty Analysis for Computer Simulations with Multivariate Output (2008, methodology): “Gaussian process models are increasingly being used as surrogates to expensive computer simulations for the purposes of optimization and uncertainty propagation [10,14–18].”
A new learning function for Kriging and its applications to solve reliability problems in engineering (2015, methodology): “It is called metamodel with various kinds: Quadratic Response Surfaces [14], Polynomial Chaos [15], Kriging [16,17], Neural Network [18], and Support Vector Machine [19,20], etc.”
The promise and peril of uncertainty quantification using response surface approximations (2005, background): “Over the past 30 years, response surface approximations have found increasing use in engineering design optimization studies (cf. Simpson et al. 2001) and are becoming increasingly common in engineering UQ studies as well (cf. Gomes and Awruch 2004, Romero et al. 2004, Kaymaz 2005).”
An application of the Kriging method in global sensitivity analysis with parameter uncertainty (2013, methodology): “[15], the unknown parameters b and r(2) can be estimated as: b̂ 1⁄4 ðQ T RQÞ (1)Q T R (1)Pf ð24Þ r̂(2) 1⁄4 1 NT ðP f Q b̂Þ T R (1)ðP f Q b̂Þ ð25Þ”
Recent advances and applications of surrogate models for finite element method computations: a review (2022, background): “One can find a comprehensive treatment of MLE in the context of Kriging in Kaymaz (2005).”
Support vector machine in structural reliability analysis: A review (2023, neutral): “…radial basis functions networks (RBFN) [7], polynomial chaos expansion (PCE) [8,9], multivariate adaptive regression splines (MARS) [10], Kriging method [11,12], artificial neural networks (ANN) [13,14], etc., were developed to address the computational challenge of large complex SRA problems.”