Analysis of Shockwaves on Liquid Surfaces, pt II

I continue examining several analyses of recordings collected from liquid surfaces using my laser microphone array. This test compares the results of the first experiment with those of a distinct but similar dataset.

This test explores the second dataset, which was derived from the same configuration of measurement points as test 1. The goal of this test is to compare the previous results to the results of the same set of analyses on a different dataset. The forcing function, not the steady-state, should be the primary differentiating factor between the two signals, so the eigenvalues should be reasonably matched.

trial one:
"drop 1"
channels: 4
order: 20
winsize: 152000

The 80 resulting eigenvalues (blue) are plotted against those of the previous dataset (red) here:
drop_1_trial_1

The eigensystem can be downloaded here, as a .txt file.

The clusters of eigenvalues are very well matched. Even in the lower frequency bands, where there appears to be a larger variance among values, there exist a few near matches.

trial two:
"drop 1"
channels: 4
order: 10
winsize: 152000

The 40 resulting eigenvalues (blue) are plotted against those of the previous dataset (red) here:
drop_1_trial_2

The eigensystem can be downloaded here, as a .txt file.

The clusters are still well matched. The lower frequency bands are less so, however there are still a couple of "direct hits."

The next trial examines the later half of the time series, in an attempt to hone in on the steady state.

trial three:
"drop 1"
channels: 4
order: 10
winsize: 76100

The 40 resulting eigenvalues (blue) are plotted against those of the previous dataset (red) here:
drop_1_trial_3"

The eigensystem can be downloaded here, as a .txt file.

The clusters are still well matched, and the lower frequencies show an even greater degree of similarity. This suggests that the transient state might contribute to the low frequency error.

For completeness' sake, we will examine two of four channels to be sure the eigenvalues are still evenly spread across frequency bands.

trial four:
"drop 1"
channels: 2
order: 10
winsize: 76100

The 20 resulting eigenvalues (blue) are plotted against those of the previous dataset (red) here:
drop_1_trial_4"

The eigensystem can be downloaded here, as a .txt file.

This suggests that the channels are not by and large spread across the available bandwidth, but arranged in clusters. A notable example in this case is the cluster immediately above the 0 hz cluster. The second eigenvalue in this cluster must have been shifted down to 0 hz.

It will be helpful to assess the ability of this decomposition to afford a regression, in the hopes of estimating the forcing function. It will also be helpful to examine the eigenvectors of both datasets, to estimate the initial conditions of each.

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