I have some questions about the application of AK-MCS with PCK metamodel for calculating the probability of failure of a structural system.
I am interested in the calculation of small probability of failure. I tested a simple example and I compared the results coming from AK-MCS (PCK metamodel) with results from crude Monte Carlo analysis. For Pf more or less of 10-4 everything worked well and the analysis returned a good approximation of Pf with a good CV ( I used the convergence criteria based on Pf).
Then I changed the input to test a smaller Pf but then AK-MCS (always with PCK metamodeling) stopped because some tolerances were satisfied. The message was the following:
Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance. <stopping criteria details>
Clicking on the following message will appear:
Optimization completed: The relative first-order optimality measure, 6.220469e-05, is less than options.OptimalityTolerance = 1.000000e-04, and the relative maximum constraint violation, 0.000000e+00, is less than options.ConstraintTolerance = 1.000000e-06.
I do have some questions:
Is it possible to change this tolerance criteria to make the analysis stop when the convergence criteria of Pf is satisfied?
What is exactly this tolerance criteria telling me?
What are other methods that would be suitable to estimate really small probability of failure?
Thank you for the support!