Reliability-based design optimization using kriging surrogates and subset simulation
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Cites methods from "Reliability-based design optimizati..."
...Later, this approach has been widely used in computer experiment domain [25, 10, 11, 12], sequential design of experiments [26, 27, 28] and global optimization [29]....
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...In future investigations, this approach could be applied to global optimization problems and sequential design of experiments oriented to the evaluation of quantiles or oriented to reliability analysis [27, 28, 52, 53]....
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"Reliability-based design optimizati..." refers methods in this paper
...it uniformally covers M) by means of the K -means clustering technique ( MacQueen 1967 )....
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...This population of candidates is then reduced to a smaller one that has essentially the same statistical properties (i.e. it uniformally covers M) by means of the K-means clustering technique (MacQueen, 1967)....
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"Reliability-based design optimizati..." refers background in this paper
...Kriging (Santner et al., 2003) is one particular emulator that is able to give a probabilistic response bY (x ) whose variance (spread) depends on the quantity of available knowledge....
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...Kriging (Santner et al., 2003) is one particular emulator that is able to give a probabilistic response b Y (x ) whose variance (spread) depends on the quantity of available knowledge....
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2,500 citations
"Reliability-based design optimizati..." refers methods in this paper
...In this field, the autocovariance structure is usually estimated from the data using variographic analysis (Cressie, 1993)....
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2,238 citations
"Reliability-based design optimizati..." refers background or methods in this paper
...Note that the idea is inspired from Hurtado (2004); Deheeger and Lemaire (2007); Deheeger (2008); Bourinet et al....
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...In this field, the autocovariance structure is usually estimated from the data using variographic analysis (Cressie, 1993)....
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...In this field, the autocovariance structure is usually estimated from the data using variographic analysis (Cressie, 1993). Then, provided the empirical variogram features some required properties it can be turned into an autocovariance model. However, this methodology is not well-suited to our purpose because of its user-interactivity. In computer experiments, the most widely used methodology is the MLE technique. Provided a functional set f ∈ L2 Dx , R and a stationary autocorrelation model R(•, l) are chosen, one can express the likelihood of the data with respect to the model and maximize it with respect to the sought parameters (l, β and σ(2) Y ). One can show that β and σ(2) Y can be derived analytically (using the first-order optimality conditions) and solely depends on the autocovariance parameters l that are solution of a numerically tractable global optimization problem – see e.g. Welch et al. (1992); Lophaven et al. (2002) for more details....
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...In this field, the autocovariance structure is usually estimated from the data using variographic analysis (Cressie, 1993). Then, provided the empirical variogram features some required properties it can be turned into an autocovariance model. However, this methodology is not well-suited to our purpose because of its user-interactivity. In computer experiments, the most widely used methodology is the MLE technique. Provided a functional set f ∈ L2 Dx , R and a stationary autocorrelation model R(•, l) are chosen, one can express the likelihood of the data with respect to the model and maximize it with respect to the sought parameters (l, β and σ(2) Y ). One can show that β and σ(2) Y can be derived analytically (using the first-order optimality conditions) and solely depends on the autocovariance parameters l that are solution of a numerically tractable global optimization problem – see e.g. Welch et al. (1992); Lophaven et al. (2002) for more details. This technique, implemented within the DACE toolbox by Lophaven et al. (2002), was used for the applications presented in this paper....
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...In this field, the autocovariance structure is usually estimated from the data using variographic analysis (Cressie, 1993). Then, provided the empirical variogram features some required properties it can be turned into an autocovariance model. However, this methodology is not well-suited to our purpose because of its user-interactivity. In computer experiments, the most widely used methodology is the MLE technique. Provided a functional set f ∈ L2 Dx , R and a stationary autocorrelation model R(•, l) are chosen, one can express the likelihood of the data with respect to the model and maximize it with respect to the sought parameters (l, β and σ(2) Y ). One can show that β and σ(2) Y can be derived analytically (using the first-order optimality conditions) and solely depends on the autocovariance parameters l that are solution of a numerically tractable global optimization problem – see e.g. Welch et al. (1992); Lophaven et al....
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