Q2. What is the final criterion used to validate results?
The final criterion used to validate results is the size of the interval around the estimated probability of failure, calculated with the bootstrap method.
Q3. How can the criteria be calculated on each RS?
since criteria depend on SSE and number of terms in the RS, the selection can be performed with respect to SSE in order to build RS of different sizes (with one term, two terms, three terms, etc) and criteria can be calculated on each RS.
Q4. What are the main reasons why the current literature of reliability is increasing?
Within the current literature of reliability, analysis based on meta-models such as kriging, neural network or support vector machine is increasing since mechanical models are more and more complicated.
Q5. What is the criterion used to estimate the prediction error?
the criterion used to estimate the prediction error must be robust and, second, it must be minimized in order to find the best RS from sets of potential terms.
Q6. How many times can a stepwise selection be performed?
if four penalized criteria are used, stepwise selection needs repeating four times the procedure, whereas only one can be performed with forward selection.
Q7. What are the main reasons why response surfaces are still widely used in structural reliability analysis?
response surfaces (RS) are still widely used in structural reliability analysis because of their simplicity and effectiveness.
Q8. What is the simplest way to estimate the probability of failure?
A bootstrap method is used in order to estimate variations of RS predictions and an interval of the estimed probability of failure is deduced.
Q9. What is the cost of evaluating the limit state function in engineering problems?
in a lot of engineering problems, the limit state function comes from finite element discretization and is thus very expensive to evaluate.
Q10. Why is the initial size of ED fixed to n?
the initial size of ED has been arbitrary fixed to Ninit ¼ 3M, where M is the number of input variables, because it enables to potentially include all linear terms in the RS.
Q11. What is the importance level of the structure?
The importance level is epdf ¼ 0:05, criterion on region convergence is eb ¼ 0:01 and criterion which controls RS quality is set to ers ¼ 0:99.
Q12. What is the definition of the probabilistic framework?
the probabilistic framework is considered, which means that input parameters are realizations of random variables or random fields.
Q13. What is the RS among the four?
As said before, the best RS among the four, will be selected with cross-validation, i.e. the RS with the highest predictive coefficient Q2 will be chosen.
Q14. How many simulations have been done with the generalized reliability index?
As in previous example, reference value of the generalized reliability index has been estimated by Blatman and Sudret [7] with FORM followed by Importance Sampling with 500,000 simulations, and is bREF ¼ 3:51.
Q15. What is the probability interval for the b-th bootstrap sample?
The following probability interval is definedPf low ¼PðGðf̂ðXÞÿêlowÞr0ÞPf up ¼PðGðf̂ðXÞþ êupÞr0Þ:8 <:ð14ÞThis interval is the final information to validate the probability of failure estimated with RS.