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I have two simulations of ship motion, and measured ship motion. Generally, the motion is random. I've been asked to compare the three sets of data. I was trying the goodness of fit (sum((fi-Fi)^2/Fi) where Fi is count in bins like histogram) and evaluating Fi using Chi Squared cdf to get the probability of being the different. I'm also comparing the mean and standard deviation to see if they are statistically the same. Are there other approaches to compare random data. I'd like to do something with the power spectrum, but what is the statistical comparison between two psd?

The signals are not recorded simultaneously, they represent ship motion in a similar seaway. So I think correlation and coherence don't apply.

Oh, maybe I misunderstood. You are suggesting to do corr on the PSD signals.

Edit>

I have a little trouble understanding some of the comments, so I'll expand on what I am doing. I have three sets of data, two are simulations, and one is measured. The data is ship motion, pitch, roll, heave displacements and rates. The basic question is are the two simulations similar, and use the measured data for reference. So, there are two random signals. The signals differ in duration, and also sample rate.

1) probability of same of mean and standard deviation

2) probability distribution function (histogram) of response with probability of same

4) comparison of autocorrelation of response

5) Comparison between frequency / spectral content of response

6) Quintile-quintile plot of two simulation, include slope and correlation coefficient of linear fit

I'm just starting to write up the results, but it appears that the QQ plot may be the best comparison. The frequency comparison is good to, and can potentially help guide resolution. The autocorrelation is also helpful, but I don't have experience in reading the figure.

Star Strider
on 1 Mar 2016

Edited: Star Strider
on 1 Mar 2016

You may have actually answered your own question with the power spectral density idea. Comparing them by convolving them or convolving the inverse of one with the other in the complex frequency domain (a sort of transfer function calculation) could give you the information you want. That would be my first approach.

If they have different d-c offsets (mean values), that could be enough to give them different probability density functions. Binning each of them with histfit might give you some information.

EDIT — Comparing three sets of histogram data might be more appropriate for an analysis-of-variance than chi-squared.

Image Analyst
on 1 Mar 2016

Can you take 3 signals, 2 that are similar and one that is different from those two, and use pwelch() to plot the spectrum, and attach your screenshot?

Can you take the moments (1st, 2nd, 3rd, 4th, 5th) of the spectrum and see how they change/differ?

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