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Table 2 1D truss: influence of the number of samples \(N_p\) with a fixed \(p_0 = 0.1\) in the adaptive design point estimation using the analytic limit state function (50 runs with \(N=5000\))

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

\(\mathbf{N} _{\mathbf{p}}\)\(\mathbf{p} _\mathbf{0 }\)\(\mathbf{N} _\mathbf{total }\)\(\frac{|\overline{{\varvec{P}}_{\varvec{f}}}-{\varvec{P}}_{{\varvec{f}}_{\varvec{ref}}}|}{{{\varvec{P}}}_{{\varvec{f}}_{\varvec{ref}}}}\)\(\mathbf{std} (\mathbf{P }_\mathbf{f })\)\({\overline{\sqrt{(\varvec{Var}({\varvec{P}}_\mathbf{f })}}}\)
50.15039.80.455.93 \(\cdot 10^{-7}\)1.25 \(\cdot 10^{-7}\)
100.150711.8 \(\cdot 10^{-2}\)2.25 \(\cdot 10^{-7}\)1.53 \(\cdot 10^{-7}\)
500.153327.14 \(\cdot 10^{-3}\)6.66 \(\cdot 10^{-8}\)5.67 \(\cdot 10^{-8}\)
1000.156463.25 \(\cdot 10^{-3}\)6.97 \(\cdot 10^{-8}\)6.05 \(\cdot 10^{-8}\)
2000.162764.11 \(\cdot 10^{-3}\)5.71 \(\cdot 10^{-8}\)5.36 \(\cdot 10^{-8}\)
10000.111,0205.98 \(\cdot 10^{-4}\)5.46 \(\cdot 10^{-8}\)5.02 \(\cdot 10^{-8}\)
  1. The failure probability is given with respect to \(P_{f_{ref}}=1.18 \times 10^{-6}\) computed with \(N_p=1000\), \(p_0=0.1\) and \(N=25,600\) in 50 runs