I’m currently learning active PCE, So we’re trying to replicate 《An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis》. When reproduced by our own program, the sought learning sample point is not near the limit state surface, and when reproduced by UQLab toolbox, the stopping criterion mentioned in the paper is not applicable to PCE, and the convergence curve of failure probability drawn does not show the upper and lower bounds of failure probability.

Hi @Wang,

Thanks for your question.

We compute upper and lower bound of Pf only for Kriging and PC-Kriging (using the Kriging variance). For bootstrap PCE, we do not estimate bounds of Pf (if needed, you could do it using the bootstrap replicates though). As for the stopping criterion, we use the stability of Pf or Beta.

Which learning function are you using precisely and which stopping criterion are you referring to?

Cheers,

Moustapha