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Table 6 Cross-section: summary of itPGDrel process is given by the averaged design point \(\varvec{\mu }_{h_{it}}\) in the normal space as well as the failure probability ranges with \(N=1600\) based on PGD and FE model (50 runs, \(p_0=0.1\), \(N_p=100\) and \(\xi =10\))

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

it

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

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

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

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

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

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

0

3.17

\(-2.75\)

\(-0.12\)

4.2

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

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

1

3.22

\(-2.79\)

\(-0.17\)

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

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

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

2

3.25

\(-2.79\)

\(-0.15\)

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

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

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