The importance of characterizing your random inputs and their influence in your probabilistic process.

Hi everyone,

So its time for a new message in the blog about work.

I told you before that I was looking at these very cool models called Kriging models. Well, I m still looking at them, but now I have been inveting some time on the analysis if their design of experiments, or, the variables that are used to create the model that, lets say, stay on our x axis (y axis will give the output, just imagine a 2D curve).

Why is it important to look at these variables before any further progress? I have the surrogate model, I have the means to compute the results, why spend some time doing tests with these variables?

Well, maybe you don't need, but lets see why it is important.

When you run an experiment some variables affect much more the output of your experiment than the other. So, if a variable is 98% responsible for the variations in your output why should you consume your time looking at the other variables. You just do it once, you quantify these relations between variables and then in future experiments you now "whats happening". This is of particular interest in the case where you're going to repeat your experiments a lot!

But do not forget, this preliminary analysis, usually called, sensitivity analysis, needs to be very well done. Otherwise you may neglect important effects. Like coupled effects or similar.

So, you spend some more time in this and in the future you just save some time. We just need to believe that the balance will be positive. And it is very likely to be.

In cases where budget and time is a limited resource (in other words, always), this can be very interesting.

I believe and I heard it many times before from big scientists that, no additional complexity should be added to the analysis if it is not needed. Or, that "simple is beautiful".

In the case of Offshore Wind Turbine Towers there are many many variables that affect the behaviour of the turbine. As a very complex technology, its analysis is time consuming, so, characterizing well the different variables that affect the turbine is important before going on loops trying to do new things. Basically, before trying intensive research !
Even more when you work on probailistic research, quantifiying uncertainty adds a new layer of complexity and effort, so this is even more important.

To analyse the influence of the different variables there are many different techniques, Screening, Sobol, Anova, KL divergence, you can find many in the literature. Also, different techniques exist to simulate experiments, as the simple Monte Carlo or the Latin Hypercube Sampling. If variables ar correlated it gets a bit more complex, but still feasible.  You can find many of them in literature.

Well, all this just to tell you that despite looking a secndary task from your main topic, or boring in some way, sensitivity analysis are very relevant and they can be a milestone when you're doing research in terms of saving time and resource and in the end your skin. Its like that subject that you're never into during the university but suddendly when you start working you realise it is much harder than it looks and much more important.

I know I know, some of you will now say....I didn't need 95% of the university courses.... bu this one for sure you needed and for sure it was diluted in the many different courses and you probably never had it to its full extent.

I recomend some reaidng on the topic. Very interesting indeed!

See you soon!