Hi everyone,
I am very honor to join the community of UQLab. Recently, I came across a problem about the PCE model. I am looking forward to the answer.
I would like to obtain the first four moments of PCE model. I have noticed the relavent questions proposed by Qiang Zhang, and read the papers provided by the answers. But I cannot impliment this function yet, such as obtaining the skewness. The major problem is how to obtain the Expectation of products of three Hermite polynomials of standard normal variable. There are at least three versions of description of this problem, so I am confused which one is the easier way for implementing in UQLab?
In Sudret, B., & Der Kiureghian, A. (2000). *Stochastic finite element methods and reliability: a state-of-the-art report:
In Sudret, B., Berveiller, M., & Lemaire, M. (2006). A stochastic finite element procedure for moment and reliability analysis:
In Bruno Sudret. (2015). Polynomial chaos expansions and stochastic finite element methods:
In 2006 and 2015, the Equations of skewness is almost the same, while the range of summation may not be the same. Is the first coefficient s0 or y0 is considerd in the sum function？
By the way, the website showed in the 2006 paper, http://www.ce.berkeley.edu/haukaas/
FERUM/ferum.html , is not avaliable. Could anyone share the codes and help to achieve this function?
Thanks very much!
Best regards,
ShengWang Zhang