Goodness of fit between test and reference data

[hummad]

Hi,

I have experimental data that i obtained from a uniaxial test, load vs. extension. I have also created a FEA model and simulated this test which gave me another set of load vs. extension data. I wanted to perform some sort of goodness of fit test to have a quantitative value that could be used to describe how similar the two curves were. I have tried obtaining the R2 value using the coefficient of determinates but the value is far larger than 1 for some of the samples where the curves are completely off set, and when using the pearsons coefficient of correlation method i get R2 values that are .98 for samples were the curves are completely off set. Is there any reason that I am getting such strange values. Is there a better way of going about comparing two data sets?

File Attachment:
I have attached a excel file with one of my samples
The curve for the fea results was completely offset from the actual data
the R2 value obtained using the cofficient of determinate was -15.94
and the R2 value using the pearson's coefficient of correlation was 0.96

 

[Dave442]

Hi Hummad,

As far as I recall, the Pearson product-moment correlation coefficient describes the strength of the assumed linear dependence between two random variables. If you use the Pearson coefficient to calculate the assumed linear dependence between your experimental load and your FEA load [which you can calculate in excel using the function PEARSON(DATASET A,DATASET B)] you get a value of 0.98.

This value of 0.98 is telling you that there is a very strong positive linear dependence between your experimental load and your FEA load. Or in other words, as your experimental load increases, your FEA load increases in an almost perfectly linear manner. If you plot the experimental load against the FEA load in a scatter plot you will see that this makes perfect sense.

I am not sure exactly how you would measure the goodness of fit of two different curves. Maybe you could calculate the absolute difference between the experimental load and the FEA load at a fixed number (or all) of the displacements and then average these values?

Or maybe you will find a more elegant solution online.

Best of luck,
Dave

 

[burningDiesel]

both methods are not good to check if your data sets are the same
the reason pearson's R2 value is close to one is because there is an almost linear relationship between your experiment & FEA (it's the R2 of a trendline of experiment vs FEA).

Just use sum of squares or something similar.