PCE with correlated inputs

UQ with UQLab Community Q&A and How To
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1

Hi everyone,

Can we build a PCE model with correlated inputs?

Thanks,

Hongzhou

2

Dear Hongzhou

Yes it is possible. The usual practice is to use an isoprobabilistic transform first, so as to transform the correlated input vector into, e.g., a standard normal vector (Rosenblatt or Nataf transform, depending on the copula of the joint vector), then use a polynomial chaos expansion (PCE) based on these transformed variables. This was originally introduced in [1]. This is the way it is handled in UQLab.

Recent papers construct orthonormal polynomial bases w.r.t the joint PDF of the input vector numerically [2], but this is not available in UQLab.

Best regards
Bruno

[1] Blatman, G. and Sudret, B. (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Prob. Eng. Mech., vol. 25 (2), pp. 183–197.
[2] Jakeman, J.D., Franzelin, F., Narayan, A., Eldred, M. and Pflüger, D. (2019) Polynomial chaos expansions for dependent random variables, Comput. Methods Appl. Mech. Engrg., vol. 351, pp. 643–666.

2 Likes
3

Dear Professor Sudret,

This is really useful! Thank you very much.

Best,

Hongzhou