I am trying to perform a reliability analysis using PCE model. In the analysis, I can get the first two statistical moments of limit state function. However, how can I get the failure probability, the reliability index, PDF and CDF?
Thank you very much.
you can compute mean and variance of a PCE model analytically, but there is no analytical formula for the PDF and CDF of the PCE response. However, you can do Monte Carlo sampling: just propagate a huge input sample through the PCE model and look a the histogram of the output. This is computationally cheap, because the PCE is just an analytical function and very fast to evaluate.
Regarding failure probability, I am no expert in reliability analysis, but I guess you can use any of the estimation methods (FORM, SORM, subset simulation… see chapter 1.3 of the Reliability User Manual) with the PCE surrogate model instead of your original model.
I hope this helps! Let us know how you did it in the end.