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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\(\varvec{{\mu }^{Y}_{1}}\)\(\varvec{{\mu }^{Y}_{2}}\)\(\varvec{{\mu }^{Y}_{3}}\)\(\varvec{{\Delta }\beta }\)\(\varvec{mean(P_{f} )_{PGD}}\)\(\varvec{mean(P_{f})_{FE}}\)
03.17\(-2.75\)\(-0.12\)4.21.33 \(\cdot 10^{-5}\)9.13 \(\cdot 10^{-6}\)
13.22\(-2.79\)\(-0.17\)8.1 \(\cdot 10^{-2}\)9.05 \(\cdot 10^{-6}\)9.13 \(\cdot 10^{-6}\)
23.25\(-2.79\)\(-0.15\)3.86 \(\cdot 10^{-2}\)9.06 \(\cdot 10^{-6}\)9.13 \(\cdot 10^{-6}\)