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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\(\varvec{{\mu }^{Y}_{1}}\)\(\varvec{{\mu }^{Y}_{2}}\)\(\varvec{{\mu }^{{Y}}_{3}}\)\(\varvec{{\Delta }\beta }\)\(\varvec{mean(P_{f} )_{PGD}}\)\(\varvec{mean(P_{f})_{analytic}}\)
03.141.77\(-\)1.283.837.16 \(\cdot 10^{-5}\)1.19 \(\cdot 10^{-6}\)
13.722.37\(-\)1.660.921.18 \(\cdot 10^{-6}\)1.19 \(\cdot 10^{-6}\)
23.692.47\(-\)1.689.76 \(\cdot 10^{-2}\)1.18 \(\cdot 10^{-6}\)1.19 \(\cdot 10^{-6}\)