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 \(N=5000\))
\(\mathbf{N} _{\mathbf{p}}\) | \(\mathbf{p} _\mathbf{0 }\) | \(\mathbf{N} _\mathbf{total }\) | \(\frac{|\overline{{\varvec{P}}_{\varvec{f}}}-{\varvec{P}}_{{\varvec{f}}_{\varvec{ref}}}|}{{{\varvec{P}}}_{{\varvec{f}}_{\varvec{ref}}}}\) | \(\mathbf{std} (\mathbf{P }_\mathbf{f })\) | \({\overline{\sqrt{(\varvec{Var}({\varvec{P}}_\mathbf{f })}}}\) |
|---|---|---|---|---|---|
5 | 0.1 | 5039.8 | 0.45 | 5.93 \(\cdot 10^{-7}\) | 1.25 \(\cdot 10^{-7}\) |
10 | 0.1 | 5071 | 1.8 \(\cdot 10^{-2}\) | 2.25 \(\cdot 10^{-7}\) | 1.53 \(\cdot 10^{-7}\) |
50 | 0.1 | 5332 | 7.14 \(\cdot 10^{-3}\) | 6.66 \(\cdot 10^{-8}\) | 5.67 \(\cdot 10^{-8}\) |
100 | 0.1 | 5646 | 3.25 \(\cdot 10^{-3}\) | 6.97 \(\cdot 10^{-8}\) | 6.05 \(\cdot 10^{-8}\) |
200 | 0.1 | 6276 | 4.11 \(\cdot 10^{-3}\) | 5.71 \(\cdot 10^{-8}\) | 5.36 \(\cdot 10^{-8}\) |
1000 | 0.1 | 11,020 | 5.98 \(\cdot 10^{-4}\) | 5.46 \(\cdot 10^{-8}\) | 5.02 \(\cdot 10^{-8}\) |