Has anybody programmed the mcKL expansion?

  • #1
Summary:
I have read the article in which this methodology is described, but I cannot understand what is going on. I need help to program it.
Hello everyone. I am trying to implement the mcKL expansion proposed in this article using Matlab and two vectors of correlated data of size 1000*50, meaning 50 realizations of two random processes measured 1000 times. As the article says, if two stochastic processes are correlated, one cannot just use two Karhunen-Loève expansions but must use one of the two special cases proposed in the article.

I am very confused by the mcKl. I can understand equation 26 of the paper; however, once I arrive at equations 27 to 30, I see Kkmij and Cij(s,t) defined as functions to each other. I have no idea how to calculate them analytically and much less using Matlab.

Has anybody programmed this before? What are the dimensions of Kkmij? And the ones of Cij(s,t)? What is the set of uncorrelated random variables eta? Can I use pca to obtain the elements of equation 26?

As you can see, I don’t understand this kind of special Karhunen-Loève expansion at all, so if someone could offer me sone guidance on how to perform this I would be extremely thankful.



Best regards.
Confused engineer.
 
Last edited:

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