Principal Component Analysis and Spring-Mass System Assignment

Assignment Task

A Spring-Mass Experiment is recoreded by using three cameras. We want to illustrate the application of PCA and the effects of noise on the PCA algorithms.

Download data sets from Canvas.

Do the PCA for the following four test cases and report your findings (IEEE format is requires).

1. Ideal case: Consider a small displacement of the mass in the direction and the ensuing oscillations. In this case, the entire motion is in the directions with simple harmonic motion being observed (camN.1.mat where N=1,2,3).

2. Noisy case: Repeat the ideal case experiment, but this time, introduce camera shake into the video recording. This should make it more difficult to extract the simple harmonic motion. But if the shake isn't too bad, the dynamics will still be extracted with the PCA algorithms. (camN 2.mat where N=1,2,3)

3. Horizontal displacement: In this case, the mass is released off-center so as to produce motion in the x-y plane as well as the direction. Thus there is both a pendulum motion and a simple harmonic oscillations. See what the PCA tells us about the system. (camN_3.mat where N=1,2,3)

4. Horizontal displacement and rotation: In this case, the mass is released off- center and rotates so as to produce motion in the xy plane, rotation as well as the z direction. Thus there is both a pendulum motion and a simple harmonic oscillations. See what the PCA tells us about the system. (camN_4.mat where N=1,2,3)

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