Skip to main content

Table 3 1D truss: influence of the adaptive parameters \(N_p\) and \(p_0\) using the same relation (\(N_p \cdot p_0 = 10\)) 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

\(\varvec{N_{p}}\)\(\varvec{p}_{\mathbf{0}}\)\(\varvec{N}_{\mathbf{total}}\)\({\frac{|\overline{\mathbf{P}_\mathbf{f }}-\mathbf{P }_{\mathbf{f }_\mathbf{ref }}|}{\mathbf{P }_{\mathbf{f}_\mathbf{ref }}}}\)\(\mathbf{std (\mathbf{P }_\mathbf{f })}\)\({\overline{\sqrt{(\mathbf{V} \mathbf{ar} (\mathbf{P }_\mathbf{f })}}}\)
500.254642.34\(\cdot 10^{-3}\)5.93\(\cdot 10^{-8}\)6.04\(\cdot 10^{-8}\)
1000.156463.25\(\cdot 10^{-3}\)6.97\(\cdot 10^{-8}\)6.05\(\cdot 10^{-8}\)
2005\(\cdot 10^{-2}\)60007.56\(\cdot 10^{-3}\)5.84\(\cdot 10^{-8}\)5.63\(\cdot 10^{-8}\)
10001\(\cdot 10^{-2}\)80002.79\(\cdot 10^{-3}\)4.61\(\cdot 10^{-8}\)5.26\(\cdot 10^{-8}\)
  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