# Autocorrelation of sound in liquids vs gas

This is just a curiosity and you need to bear with me as my math skills were always sub-par and so is my English academic language. My specialty is Electronics but I have always been a programmer. Years ago I was working on my diploma paper that dealt with locating leaks using auto-correlation.
Basically you have several sound sensors along a pipe which record the sound wave. If a leak appears then you get a peak in the autocorrelation function. Then you perform a 'triangulation' from two or more sound sensors and you can locate the leak pretty accurately. Anyway, my task was mostly to help a PHD student with transposing her algorithms into Matlab.

We have succeeded doing this with air but as soon as we switched to water I could not use any kind of windowing and/or transformation to get relevant peaks. At some point I just hunted blindly for some Matlab functions that would give me a relevant peak somewhere that would correlate with the distance to the leak, but failed.

I cannot to this day understand why we were not able to succeed, though I do assume that is has to do with water's turbulence. The setup was a running tap routed through metal pipes (about 10cm diameter), with about 5 very sensitive sound sensors (going to about 100kHz) placed about 3 meters apart and some taps along the way that simulate leaks. Everything was placed in a phonic-insulated basement, signals were truncated taken to stabilize against footsteps/vibrations so measurements were pretty good.

The multiple question is: what could have been done to achieve the goal or at least get closer to it? Is it really achievable (probably not in real life where you have trucks running above)?
Some variables that could influence but for which I lack the knowledge to explain: pipe diameter, water debit rate, tap/leak rate and diameter, choice of liquid, pipe material, sound spectrum and possible frequency filtering.

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Did you see the experimental setup?

I believe that a leak in a gas pipeline generally makes a whistling sound whereas leaking liquid will be very quiet. Without sound, the autocorrelation approach doesn't make sense.

To find the leak in a pipeline for liquids, one could use a marker to find the leak (e.g. add some color). Or one could seal segments of the pipe using inflatable pistons and measure the flow through them. When less flows out than you pump in, you have a leak in the segment.

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I had a water (copper pipe) leakage in my house about 20 years ago. Because that pipe was located in some wall or below floor, the plumber did some detecting first. The pipe was separated from the rest of piping and then air pressure was applied. Under this condition the likely place of the pipe was followed with a special microphone for solids. The sound to hear was as You would expect from a hole where air and water droplets "spit and sizzle" out. – Georg Aug 2 '11 at 9:30
@Georg: excelent setup, did not thought of that. #whoplisp: I did see the setup, it is like I described it - 10-15m of metal pipe about 10-15cm diameter. The issue here however is: detecting the location without having to walk up to it and measure. Think about buried water utility pipes, you can have some monitoring on some computer which will detect the leak in time and also its location. I don't know if audible range for humans is really the place to scan, this was part of my question. – brainwash Aug 2 '11 at 9:49

Without being able to see the data, I can only suggest two things that worked for me in a project about turbulence in water. The first is, if turbulence is a significant factor, it will show up in the auto-correlation function as violent oscillations getting worse and worse in the graph, basically exceeding the accuracy of the software to calculate it after a certain point. If you did not see that in the autocorrelation function, then turbulnece was not your problem.

To deal with it, we just pre-whitened the data and this got rid of that noise so we could detect the relevant peaks, up to a point and within a certain range (high enough it still got out of control, but the pre-whitening improved it).

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