# How to analyse periodic data obtained from a vibration experiment?

I have data from a vibration experiment on a structure. This data was obtained by attaching an accelerometer to a FFT analyser, which records the data at a high sampling rate (typically in kHz range) and can also perform real-time FFT of the recorded data.

The image above shows the recorded signal below and the FFT above. The FFT shows all the dominant frequencies in the original signals.

What more patterns/ important data points can I discern from this data, that might have utility ?

For example, one being, the RMS value of the signal. What else ?

Also, the recorded data here as a mat file, which can be loaded in matlab, the data in a variable called Track1.

The physics of the problem: The data is collected from a shake table, a rigid platform, that oscillates back and forth, so the sharp edges in the original signal periodically, representing the point of return.

• Are you doing modal analysis or what? This seems like more of a mech engineering question. Aug 7 '15 at 12:32
• The most obvious thing to think about is the lack of response at about 5 Hz.
– WhatRoughBeast
Aug 7 '15 at 12:42
• @ChintanPathak Since the analyzed phenomenon is not related to electronics you would have better chances to have meaningful answers on another site of SE network (Engineering.SE or maybe DSP.SE). Here we are mostly experts in electronics, so the significance of that data in a mechanical context could well be misunderstood here. Aug 10 '15 at 12:52
• Is this a commercial shake table? Or one you've built yourself? If I understand correctly, you gave it some input and expected a sine output, but got something different, is that it? If so, you might start with looking at the cross-correlation and coherence between your input signal and your output Aug 10 '15 at 15:16
• I'm not a civil engineer but if it is a (semi)complex structure I would have though the output would be a range of frequencies even if the input is a single frequency. I would also filter high and possibly low frequencies. I'm assuming here that the frequencies between about 5-25 Hz are of interest and the low (~2 Hz) frequencies are just your driver. Aug 10 '15 at 15:34

This certainly isn't an answer, but more of a guidance on how to approach the problem.

The analysis that you choose to do depends entirely on why you are collecting the data in the first place.

For example, the structure may have been designed and constructed to behave a certain way, and you are collecting data to determine whether it is behaving to spec. You may be trying to track changes over time. You may be collecting data under a protocol to determine under what types of stimuli your structure will fail. You may be tracking data over time to determine when your part needs repair. Each scenario, and dozens of others I can't even dream about, will determine how you need to analyze the data.

The bottom line is that when you do an experiment, you need to understand what question you will be asking of the data generated -- or the best use of your time is probably not to do the experiment in the first place.

As for a direct answer, I suggest dividing your data by \$\pi\$, which is as meaningful as any other suggestion sans some clue about why you are collecting the data.

• :) :) Exactly, but arent data scientists trying to see patterns, where none are visible on first glance. And, while I might be asking all the questions you just mentioned above, I am trying to learn techniques to analyse continuously varying high-frequency data in matlab etc. This is more about exploring the range of answers, and then posing questions. Aug 9 '15 at 14:24

I suggest a statistical approach, looking for any characteristics of the data values that are significant. The characteristics seem to be: absolute value time direction rate of change

From these you can establish other characteristics, such as period, frequency, repeat ability or variation, etc.

Other information that is available to you but not evident in the data would be things like, at what time did the structure collapse (if it did), what was the growth rate of cracks in the structure, did the structure change color, size, shape or other features during the vibration?

Statistical testing of the data displayed above plus other captured data may reveal significant points or relationships.

• Suppose I only had this data. (This data is for the vibrating table, and not of any structure. Done in an attempt to characterize the table), could you explain a little more about what you mean by "Absolute value time direction rate of change" and how that can be done ? Aug 9 '15 at 14:25
• The post removed commas which I'm sorry, made the post difficult to read. I meant that your data includes the acceleration value. The time at which the measurement was made. The direction of movement. The rate of change in velocity. Then you can calculate the period (shown in the lower display) the frequency (shown in the upper display) and since you have several repetitions of the movement, you can calculate the repeat-ability of the measurements. From all these, you can calculate position, velocity and acceleration, then test for significance between any of those values.
– Legendsk
Aug 9 '15 at 16:44

Yes. It is important to know what your goal is in analyzing vibration data. You mentioned monitoring a structure but then mention RMS. Structural vibration and rotating vibration are two very different things. There are also many reasons for studying vibration responses and properties, I.e. Condition monitoring, fault detection, tolerances, resonance frequencies etc. I understand you are trying to learn, but you do need some context for what you are trying to learn. And I'm not reading that in your question description.

• RMS here means, 'Root Mean Squared' and I understand that open-ended questions are usually discouraged on SE, I was trying to think of applications for the collected data. Jan 24 '16 at 6:20
• Yes, I guess I'm just not sure what you're asking. I'd like to help if I can though. I am a Vibration Engineer at a Nuclear Facility and specialize in Rotating Machinery.
– JBP
Jan 25 '16 at 17:03