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Table 4 1D truss: summary of itPGDrel process is given by the averaged design point \(\varvec{\mu }_{h_{it}}\) in the normal space, the difference in the distance \(\Delta \beta \) as well as the failure probability with \(N=1600\) based on PGD and FE model (50 runs, \(p_0=0.1\), \(N_p=100\), \(\xi =10\))

From: Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema

it

\(\varvec{{\mu }^{Y}_{1}}\)

\(\varvec{{\mu }^{Y}_{2}}\)

\(\varvec{{\mu }^{{Y}}_{3}}\)

\(\varvec{{\Delta }\beta }\)

\(\varvec{mean(P_{f} )_{PGD}}\)

\(\varvec{mean(P_{f})_{analytic}}\)

0

3.14

1.77

\(-\)1.28

3.83

7.16 \(\cdot 10^{-5}\)

1.19 \(\cdot 10^{-6}\)

1

3.72

2.37

\(-\)1.66

0.92

1.18 \(\cdot 10^{-6}\)

1.19 \(\cdot 10^{-6}\)

2

3.69

2.47

\(-\)1.68

9.76 \(\cdot 10^{-2}\)

1.18 \(\cdot 10^{-6}\)

1.19 \(\cdot 10^{-6}\)