OpenWave #6 : Getting vertical displacement working

Post #5 outlined the steps used to go from vertical acceleration to vertical displacement and how the results were completely off. The reason why each of the displacement graphs at the end of the post look so totally different just by changing the integral reset points is because of a negative offset to the velocity signal. This causes huge problems when you go to integrate the signal. Lets take a look at the vertical acceleration signal again:

Z-axis acceleration signal

You may notice that there is a negative offset of somewhere around -0.15 in the acceleration signal.  This offset was noticed and removed before the first integration to go from acceleration to velocity. The issue occurred at the second integration stage, going from velocity to displacement. It turns out the velocity signal also had a small offset present that went unnoticed and caused all of the issues outlined in post #5.

Lets take a look at an example graph with which does not offset correct the velocity signal before integrating to get displacement:

The blue vertical lines indicate the seperate chunks of data, with everything being split based on the minima of the acceleration signal. You may notice that the velocity signal has a slight positive bias. When this signal is integrated to get the bottom graph of displacement, the displacement starts at zero but does not return to zero as you would expect as the rotating arm is rotating in a circle.

Now lets take a look at the graphs when you do offset correct before each integration step:

Displacement with offset correction of acceleration and velocity

This plot finally makes some sense, and to make things better, the average displacement for the 5 chunks of data is 41.7cm. This measurement has an error of 4.25 %. The results from offset correcting are very encouraging but more testing needs to be done to verify that this isn’t just a case of confirmation bias.  A more comprehensive experiment is planned involving multiple wave heights. Extra mounting holes have been drilled into the rotating arm at a radius of 20cm, 40cm and 60cm. Measurements will be taken with the sensor at the three different radii and compared to the actual values in the next blog post.

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