Within a research space: obtain velocity measurements (m/s-rms) in
the frequency domain using one-third octave analysis. Compare these velocities against the International Standards Organization's (ISO) vibration criteria for structures.
Performed across multiple laboratory locations, including the frame
of a Bluefors Dilution Refrigerator measurement system.
This research was conducted in 2021 for UConn's Department of Physics, and was intended by Dr. Ilya Sochnikov as a follow-up
to a 2019 paper co-authored by himself and a previous student, Jonah Cerbin:
Isolation solution for extreme environmental vibrations for quantum-enabling cryogenic setups installed on raised frames.
My research would not have been possible without Mr. Cerbin and Dr. Sochnikov's detailed investigation, nor without Dr. Sochnikov's laboratory resources.
Supplementary resources to the 2019 paper were crucial when writing and reviewing my original MATLAB code during 2021.
This module will provide a ground-up demonstration of how signal analysis is performed, starting from the raw voltage inputs of a seismic accelerometer. A review of the following are necessary -- ordered from lowest-level to highest-level:
A set of Vibration Criteria (VC) are used to evaluate the magnitude of external vibrations within a sensitive research facility.
The vibration-sensitive instrument of focus is Bluefors' LD closed-cycle Dilution Refrigerator System.
Dilution refrigerators may achieve temperatures in the milikelvin-range (mK). Here,
as quantum phenomena emerge, random movement of a system is generally unwanted. For dilution refrigerators,
significant vibrations may affect cooling cycle(s), and will inhibit any technology involved in measurement,
scanning, and imaging.
Given the obligatory low-noise conditions of these research spaces, it is adavantageous to characterize vibrations in the space,
even if one does not intend to implement any solutions to attenuate and reduce vibrations.
Signals are detected by the accelerometer's electrical components, passed through the amplifier to achieve gain, and then fed to the oscilloscope for recording. Data are exported from the oscilloscope as time-trace voltages. The accelerometer's product manual provides the rates for converting voltage (V) to acceleration (m/s2).
Accelerometers produce [voltage] measurements in the time domain, but meaningful vibration characterization occurs when one quantifies the contributions of each component frequency; this is how engineers and physicists predict and design-against unwanted resonances. Given a discrete, 1-D array of time-trace data (xk), one may transform between representations in the time- and frequency-domains using the following algorithm (and its inverse):
$$ \begin{align} X_\ell = &\sum_{k=0}^{N-1} x_k e^{-i2\pi k\ell/N}\\ x_k = \frac{1}{N} &\sum_{l=0}^{N-1} X_\ell e^{-i2\pi \ell k/N} \end{align}$$
For a deeper mathematical-approach to Fourier transforms and analysis, look into properties of unitary matrices, singular value decomposition, and the DFT matrix (Chui & Jiang, 2013, pg. 171).