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Natural Science Forum / Physics / Acoustics / August 2008cancelling electric motor noise and the meaning of the coherence function
I have a problem that maybe someone can help with. I have a small plastic box (about 10cm(W) by 6 cm(L) by 4cm(D) Inside the box is a small electric motor. This motor also drives a few moving parts such as gears, etc. Poking through a hole in the box is a small microphone to "listen" to the outside world. The problem is that the motor noise is picked up by the microphone, and no amount of mechanical isolation seems good enough. So I am trying to put a 2nd microphone on the inside, to pick up just the motor noise, and then use an adaptive filter to cancel the noise. But this did not work very well. Then I looked at the "coherence" function between the inside and outside mic signals and found that it was quite low. I tried moving the inside mic as close as possible to the outside mic (while still keeping it "inside"), and this helped a little, but not very much. Can anyone explain why the coherence function is so low? If have a few theories; 1) Non-linearity in the mechanical transmission of sound through the plastic 2) The motor is not a point source, but rather "spatially distributed" 3) The sound transmission is partly chaotic. Any thoughts? Bob Robert Adams <robert.adams@analog.com> wrote in news:4b2171cd-586f-443d- bf8b-b1e45ad86a32@c58g2000hsc.googlegroups.com: > I have a problem that maybe someone can help with. > [quoted text clipped - 21 lines] > > Can anyone explain why the coherence function is so low? Most likely because there are multiple signal pathways, each associated with a different frequency response function, between the inside mic and the outside mic. > If have a few theories; > [quoted text clipped - 8 lines] > > Bob > Poking through a hole in the box is a small microphone to "listen" to > the outside world. A good idea provided the box is quiet. Amplificatoin of the outside world sounds occurs at the Helholtz frequencny of the box volume combimed with the mic opening size. > The problem is that the motor noise is picked up by the microphone, > and no amount of mechanical isolation seems good enough. Indeed so. You have to either mount the microphone outside the box, or construct a cavity behind the mic opening that is totally sealed from the box volume containing the motor. The applicable helmholtz frequency is then determined by the tiny mic cavity volume and the mic opening, likely in the high kHz range. Better still, make a separate tiny mic box that is carried by the motor box. The mic has to be vibration-isolated from the cavity walls since they will carry vibrations from the motor unless the motor is isolated from the box. Tis is especially true for piezolectric mics; they are very vibration sensitive. The vibrations that need to be isolted are the those vibrations with frequencies in the passband of the mic signal amplifier. > So I am trying to put a 2nd microphone on the inside, to pick up just > the motor noise, and then use an adaptive filter to cancel the noise. That may be handy to apply to the isolated mic signal anyway since the motor noise will be "everywhere". > But this did not work very well. Then I looked at the "coherence" > function between the inside and outside mic signals and found that it > was quite low. > Can anyone explain why the coherence function is so low? The spectrum of the inside sound level is modified by the volume reaonance. That transfer function will be essentially always be frequency dependent, while the frequency transfer funtion of the inside mic space will always be frequency dependent. You can't win. > If have a few theories; > 1) Non-linearity in the mechanical transmission of sound through the > plastic It's not nonlinear in the signal processing sense. Do you mean that the transfer function is not flat? That's another meaning altogether. I wish the world would stop using "non-linear" for shaped spectra. Non-linear really means (in my world) that the output amplitude is no always a constnt times the input amplitude. A good example of non-liearity is the electric guitar players mode where they totally overdrive the amplifier so that all sorts of clipping and spurious harmponic generation arises; music to some person's ears (ugh!). So what's your meaning here? > 2) The motor is not a point source, but rather "spatially distributed" A moot point when the distances involved are a tiny fracton of a wavelength. > 3) The sound transmission is partly chaotic. "Chaotic" = Cop Out by the analysit. Angelo Campanella > > Poking through a hole in the box is a small microphone to "listen" to > > the outside world. [quoted text clipped - 65 lines] > > Angelo Campanella What I mean by non-linearity is the same as what everyone else means by non-linearity; a single-frequency input to the system produces an output with sinusoidal components at other frequencies. If this occurs then the adcaptive filter will fail. I am not using the term "non- linear" for shaped spectra. Your definition of non-linearity is necessary but not sufficient. The distances involved are not a tiny fraction of the wavelength. The motor noise is very broadband and has component all the way up to 10KHz. Chaos is not a cop-out; it is well known in the arena of noise cancellation in ducts that once the flow becomes turbulent, you can't do much to cancel it. The point of using an adaptive filter is to compensate for the frequency-dependant transfer function differences between the inside and outside mics. If the system were totally "linear" then this should work. Hence my question about non-linearity and the coherence function. Bob > What I mean by non-linearity is the same as what everyone else means > by non-linearity; a single-frequency input to the system produces an > output with sinusoidal components at other frequencies. There seems to be no chance of the mic and motor system would produce nonlinearities of that sort unless the mic and motor connections and mounts are loose or the noise levels are extremely high; above 90 dB or so, so as to cause an overdriven status. What is far more likely is that your DSP system, in digitizing any signals, is inherently nonlinear. Therefore it is the nonlinear nature of your digitizer that must be treated. Much is published and accomplished by designing digtizing steps small enough so as to cast the highr order elements out of the required information passband. It becomes an art that must be practiced. Good luck. > If this occurs > then the adcaptive filter will fail. I am not using the term "non- > linear" for shaped spectra. Your definition of non-linearity is > necessary but not sufficient. OK > The distances involved are not a tiny fraction of the wavelength. The > motor noise is very broadband and has component all the way up to > 10KHz. The acoustic wavelength at 10 kHz is about one inch, so that distances greater than 1/8" (about 3mm) will undermine noise or signal suppression. (I usually figure that suppression is limited to 3dB at best when the canceling signal is more that 45 degrees off, or 1/8 wavelength.) > Chaos is not a cop-out; it is well known in the arena of noise > cancellation in ducts that once the flow becomes turbulent, you can't > do much to cancel it. I usually call that time-varying. Cancellation is still achievable provided the parameters can be adjusted as fast as they change. That's the time crunch propagation you face, if it exists. I would think that the motor noise will change as the load it faces changes and as the command for the motor acion is changed. These could be slow (work commands) or fast (spurious mechanical loads). > The point of using an adaptive filter is to compensate for the > frequency-dependant transfer function differences between the inside > and outside mics. If the system were totally "linear" then this should > work. Hence my question about non-linearity and the coherence > function. IMHO, saying that the inside/outside cancellation is not successful, and also that the coherence is poor, is staing the same fact twice. The coherence function being poor might be due to the physical distance from the motor to the exteerior, subject to the phase shift limit I mentioned. The location of the error sensing microphone is crucial, as is also the frequency band where that suppression signal is applied. It may be that the only motor signal that will be effective for suppression is the "whine" frequency band or the rotaton frequency band. And then again, if the motor speed and load change rapidly, the reaction rate of the adaptive filter comes in question. Designs of his nature usually become a compromise in the end, the pursuit and practice of them become more arts than sciences. Good Luck! Sincerely, Angelo Campanella > Bob > I have a problem that maybe someone can help with. > [quoted text clipped - 26 lines] > 1) Non-linearity in the mechanical transmission of sound through the > plastic I'd be surprised; a box this small is probably incapable of generating vibration velocities sufficient to drive the plastic material nonlinear, unless it's specifically designed to do so. > 2) The motor is not a point source, but rather "spatially distributed" > > 3) The sound transmission is partly chaotic. I suppose either of these is possible, but I think the low frequency noise (dimensions of the box smaller than a wavelength) would still be correlated. Are your signals correlated below a few kHz? Angelo had a good suggestion when he mentioned moving a mic outside the box or building a box within a box for the "outside" mic. If the motor noise is being coupled through a mechanical structure, you might try a vibration canceling mic. I have to admit that I have no experience with commercial units of the sort (if they exist), but I've used the concept before. If vibration canceling mics are not available, you might consider using an accelerometer on the mic housing as the second input to your adaptive filter. Hope this helps.  SignatureDave dvt at psu dot edu >> I have a problem that maybe someone can help with. >> [quoted text clipped - 49 lines] > >Hope this helps. The poster gives no details on what levels are being measured or what level are being produced and at what frequency. You always first try to reduce the noise at the source, then go from there. If this application has strict limitations and guidelines like a submarine detection device, then it may be hard to add extra space, but an extra box is a good idea, and just mounting it outside the box is a step in the right direction. greg My experience of coherence measurements in ducts, prior to installing active control, is that the coherence is high over a limited frequency range because the sound which passes the first mic also passes the second mic. A noise sauce between the two mics, such as from turbulence, will degrade the coherence. As your mics are inside and outside the box, it is possible that the outside mic is detecting external noises which the inside mic does not . Geoff Signature__________________________________ >I have a problem that maybe someone can help with. > [quoted text clipped - 34 lines] > > Bob Has anyone considered the fact that the transfer function is a mixture of airborne and structure borne sound. If the only problem were airborne then canceling will work using a microphone as a source. If a good proportion of the exterior noise is structure borne then the transfer function will be unpredictably altered by the phase change caused by structural damping and by time domain dilation effects caused by different speed of sound as structural sound speed varies with frequency unlike airborne sound. > Has anyone considered the fact that the transfer function is a mixture > of airborne and structure borne sound. If the only problem were [quoted text clipped - 4 lines] > caused by different speed of sound as structural sound speed varies > with frequency unlike airborne sound. It depends on where the microphone is placed and where the volume located in which you want sound cancelation to occur, among other things. If all that is required is to cancel airborne sound (the sum of that which arrives by air and that which arrives by radiation from nearby surfaces but traveling the its final journey segment by air into the volume to be quieted, then the simple sound cancelation scheme will work. Declaring the structureborne soundis problematic assumes that sound cancelation is required over an extended extended volume including some locations near the vibrating surface. Your problem details are needed to carry on discussion further. Angelo Campanella If the internal and external microphones receive different signals from the structure borne vibration, this will be another mechanism which degrades the coherence. To have a high coherence, essentially the same sound must travel from the first mic to the second mic. This is achievable for plane wave propagation of low frequencies in typical air-conditioning ducts, especially if a tone is the problem. Modal propagation of higher frequencies needs multiple microphones and loudspeakers in an active system. The simplest way to apply active control to a not too complex small source is to turn it into a dipole by fixing a loudspeaker close to it, fed with phase inverted sound of the source. A dipole is a less efficient radiator than a monopole and this will hold so long as the wavelength is a lot greater than the distance apart i.e. for low frequencies. Geoff Signature__________________________________ > Has anyone considered the fact that the transfer function is a mixture > of airborne and structure borne sound. If the only problem were [quoted text clipped - 4 lines] > caused by different speed of sound as structural sound speed varies > with frequency unlike airborne sound. |
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