Let's say I am trying to validate a model. I have a signal from measurement and a signal from the simulation of the model. Simulation was done with the same initial and boundary conditions as measurement.

Now I want to compare two signals (e.g. temperatures of one modeled component). I want to have a number (or more than one) to quantify similarities in signals. The signals can be shifted in y-axis, have slightly different behaviours and can possibly have some delay in x-axis (time).

So far I tried some simply criterias like comparing max, min, first, last values and evaluating maximum differences in absolute value. Also I tested fitting percentage of fitting simulation signal into the neighbourhood of measured signal with given range.

I would like to have something more sophisticated. I tried Pearson correlation, but all coefficient are above 90% since the signals represent the same things.

I am looking for any ideas what statistical criteria or algorithms could be applied on this issue.

  • $\begingroup$ Welcome to SE.SP! Interesting question. Before anyone can really answer, I'd suggest adding what you're trying to use the model for. The best measures of validation are when the model does what you want it to do.. Apart from this being a temperature measurement, you haven't said much else about what you're using the numbers for. What's important about it? $\endgroup$
    – Peter K.
    May 26 at 13:59
  • $\begingroup$ One very good measure is the Mean Square Error (MSE). $\endgroup$ May 26 at 17:17


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