PCE frequency-dependent output with FEM software

I have 7 uncertain variables in my finite element model and I’m interested in the sound transmission loss of a structure. I work between 89 Hz and 1122 Hz. I get the results of my true model thanks to a commercial software.
I’d like to know how I can obtain the frequency response of my system using the PCE metamodel with Uqlab, so that I can compare it with the frequency response given by the true model. Is there an example in Uqlab?(attached is the frequency response of my model)

Thank you for your help
Best regards


You could first try with the standard multi-output PCE, for which there is an example available (https://www.uqlab.com/pce-multiple-outputs).

If you would like to use sparse solvers like LARS, SP, OMP, etc., you will most probably need to apply a dimension reduction method for your output first, like PCA or POD (see e.g. https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/289988/eth-7964-01.pdf).

However, frequency response functions (FRFs) can be very tricky, especially if there are poles-zeros that “jump” due to the uncertain input parameters. In that case, a stochastic frequency transformation could help (also combined with PCA/POD, see https://www.sciencedirect.com/science/article/abs/pii/S0266892016301825).


Thank you for your response. I will try