I am trying to do an probabilitic analysis based on Random Fields, on a finite element model, via UQLink. My aim is to set a PCE to surrogate the model’s response to this random Field.
Consider I have one input (say Young’s modulus), and my stochastic mesh corresponding to the random field is 10x10. I have a (continuous) correlation function, which describs the dependance between two elements, based on the distance between them (say \rho (x,x')).
I create samples of my Random Field with the EOLE method, and I am able to get the model’s response for those samples.
I have then a theorical problem with the creation of a PCE.
I’d like to set a PCE with the option Experimental Data, since some samples are already computed.
As specified in the UQlab User Manual, the implementation of the inputs is required in the PCE module. I am not sure which input I should specify.
On the one hand my theorical input is the underlying distribution of the Young’s Modulus, which is only one input.
But on the other hand, the input of my model is a vector X, which has 10 \times 10 = 100 elements, which are dependant, and which have the same distribution, ie the underlying distribution of young’s modulus.
Should I specify 10x10 inputs for the PCE, and set the dependance via the copula module ? Or is the dependance not necessary to create the PCE ?
If it is the way to do it, is a Gaussian Copula able to describ correctly the random field ?
Thanks for your time.