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```I have the following setup:

On a grinding mill (think of a -very large 30' diameter or so- coffe-can
turned on its side and filled about 20-30% full of marbles), I have a strain
gauge in one of the bolts that holds the mill together.  Connected to the
strain gauge I have an analog signal transmitter that sends the signal off
the mill to a receiver which converts the analog value to a digital byte
value.  The byte is sent serially (2400bps) to a computer where it is
recorded.  The rotation of the mill is about 10 - 12 rpm, resulting in about
1500 data points per revolution.

Now, the tricky part...I need to analyze the data to relate the incoming
signal to the charge level of the mill (how full of "marbles" it is).  The
charge level does not change rapidly (i.e. it wont be 25% in one revolution
and 20% in the next...it takes minutes/hours to change).

Currently I have about 6 sets of data from a lab-scale version of this setup
(i.e. the mill is only a couple feet in diameter), at different charge
levels, each set has a few thousand datapoints representing several
revolutions of the mill (the lab scale mill turns much faster, about 30 rpm
or so - so there are significantly less data points per revolution).

I've been looking into using FFT's to analyze the data (especially
interesting is the amount of time it spends under high-strain - i.e. in the
strain gauge is "in the charge")...but I know little/nothing about FFTs
other than I remember some vague mention of Fourier transforms in college -
but that has been more than a decade ago.  My question(s)...does this seem
like an appropriate application of FFTs? Is there a good starting/newbie
text for doing practical applications of FFTs? So far, I've just brought the
data into Excel, used its Fourier transform, got my magnitude and phase
data, plotted magnitude against bin...but I'm still not sure what I'm
looking at.

Thanks for any tips, help

Dave Taylor
Process Engineering Resources, Inc.

```
 0
Reply David 6/27/2003 7:39:51 PM

See related articles to this posting

```"David Taylor" <nospam:dave@processeng.com> wrote in message news:<g31La.62\$On3.71014@news.uswest.net>...
> I have the following setup:
>
> On a grinding mill (think of a -very large 30' diameter or so- coffe-can
> turned on its side and filled about 20-30% full of marbles), I have a strain
> gauge in one of the bolts that holds the mill together.  Connected to the
> strain gauge I have an analog signal transmitter that sends the signal off
> the mill to a receiver which converts the analog value to a digital byte
> value.  The byte is sent serially (2400bps) to a computer where it is
> recorded.  The rotation of the mill is about 10 - 12 rpm, resulting in about
> 1500 data points per revolution.
>
> Now, the tricky part...I need to analyze the data to relate the incoming
> signal to the charge level of the mill (how full of "marbles" it is).  The
> charge level does not change rapidly (i.e. it wont be 25% in one revolution
> and 20% in the next...it takes minutes/hours to change).
>
> Currently I have about 6 sets of data from a lab-scale version of this setup
> (i.e. the mill is only a couple feet in diameter), at different charge
> levels, each set has a few thousand datapoints representing several
> revolutions of the mill (the lab scale mill turns much faster, about 30 rpm
> or so - so there are significantly less data points per revolution).
>
> I've been looking into using FFT's to analyze the data (especially
> interesting is the amount of time it spends under high-strain - i.e. in the
> strain gauge is "in the charge")...but I know little/nothing about FFTs
> other than I remember some vague mention of Fourier transforms in college -
> but that has been more than a decade ago.  My question(s)...does this seem
> like an appropriate application of FFTs?

As for using Discrete Fourier Transforms (DFTs), I think your setup
seems to be good. You have relatively high sampling rates and long
observation times, and that's good. It's usually easier to reduce these
parameters than the other way around. Which means you have some freedom
to experiment.

Assuming that the measured strain actually reflects the contents level
inside the mill, I would first record a reference data set. That is,
I would fill the mill and let it run empty (or to the lowest safe
operating level) and record the data along the way. Continuous operation
can be important, as very narrow filters will induce start-up transients
that last longer the narrower the filters are. Once you know what to
expect from the filters, you can chop the data series into shorter, more
manageable sequences. You don't want the data sequences so short that
there are only start-up and end transients.

My first attempt on analysis would be use a narrow-band low pass
filter, and see how the DC and "almost DC" parts behaved. Assuming
that the measured strain is related only to the contents level (i.e.
that the engine does not start stressing the container or structure
itself, as the grain levels reduce), I would expect to see a decrease
in the "almost DC" components as the container empties.

> Is there a good starting/newbie
> text for doing practical applications of FFTs? So far, I've just brought the
> data into Excel, used its Fourier transform, got my magnitude and phase
> data, plotted magnitude against bin...but I'm still not sure what I'm
> looking at.

I don't know it first hand, but I have seen several people recommend
Rick Lyons' "Understanding Digital Signal Processing".

Rune

> Thanks for any tips, help
>
>
> Dave Taylor
> Process Engineering Resources, Inc.
```
 0
Reply allnor 6/28/2003 12:38:43 PM

```Rune Allnor wrote:
> David Taylor wrote:
.....
> > Is there a good starting/newbie
> > text for doing practical applications of FFTs? So far, I've just brought
the
> > data into Excel, used its Fourier transform, got my magnitude and phase
> > data, plotted magnitude against bin...but I'm still not sure what I'm
> > looking at.
>
> I don't know it first hand, but I have seen several people recommend
> Rick Lyons' "Understanding Digital Signal Processing".

You can also try http://www.dspguide.com, which is pretty hands-on. Just
ignore the lousy cover-photo on the opening page!

Andor.

```
 0
Reply Andor 6/28/2003 9:00:00 PM

```Andor wrote:
> Rune Allnor wrote:
>
>>David Taylor wrote:
>
> ....
>
>>>Is there a good starting/newbie
>>>text for doing practical applications of FFTs? So far, I've just brought
>
> the
>
>>>data into Excel, used its Fourier transform, got my magnitude and phase
>>>data, plotted magnitude against bin...but I'm still not sure what I'm
>>>looking at.
>>
>>I don't know it first hand, but I have seen several people recommend
>>Rick Lyons' "Understanding Digital Signal Processing".
>
>
> You can also try http://www.dspguide.com, which is pretty hands-on. Just
> ignore the lousy cover-photo on the opening page!
>
>
> Andor.

How dare you say that. The only thing customers ever see of many of us,
is our hand holding the thing we have laboured over in a publicity
photo. Please allow us some tiny measure of recognition. :-)

Regards,
Steve

```
 0
Reply Steve 6/29/2003 3:30:40 AM

```"Andor" <an2or@nospam.com> wrote in message news:<3efe00c4_2@news.tiscalinet.ch>...
> Rune Allnor wrote:
> > David Taylor wrote:
>  ....
> > > Is there a good starting/newbie
> > > text for doing practical applications of FFTs? So far, I've just brought
>  the
> > > data into Excel, used its Fourier transform, got my magnitude and phase
> > > data, plotted magnitude against bin...but I'm still not sure what I'm
> > > looking at.
> >
> > I don't know it first hand, but I have seen several people recommend
> > Rick Lyons' "Understanding Digital Signal Processing".
>
> You can also try http://www.dspguide.com, which is pretty hands-on. Just
> ignore the lousy cover-photo on the opening page!

Nah... I'd say that photo truly proves the book is hands-on...

Rune
```
 0
Reply allnor 6/29/2003 10:04:07 AM

```"Jerry Avins" <jya@ieee.org> wrote in message
news:3EFCC8D2.DAA130E6@ieee.org...
> David Taylor wrote:
>
> The best analysis technique depends on the kind of result you seek. Can
> you give more detail about that?

What we are looking for is a measurement of the total mill charge, which
includes steel grinding balls, ore and water.  Ideally we would know the
charge level and the "toe" and "shoulder" positions...i.e. the position of
the charge in the mill when it is rotating, but right now, we would be happy
just to know the total charge level.

>
> Does the weight vary with the charge in a consistent way? With the slow
> change you cite, a load cell with suitable low-pass filter might do if
> so.

The charge varies with ore feed rate and grinding ball addition rate.  Most
mills are "slug charged" meaning that they dump several tons of grinding
balls in the mill at once and let them wear down until the next slug
charge - more automated plants have a continuous slow feed of grinding
balls.  The ore is fed to the mills continuously from a conveyor belt.
Unfortunately, most mills do not have load cells - though some newer ones
do. But the charge level cannot be determined from the load cell value alone
because the total charge is made of both ore (typically about 2800 kg/m3)
and steel grinding media (7800 kg/m3) in ratios that are not known at any
given point in time, i.e. amount of ore depends on feed rate and mill
residence time and grinding media quantity is determined by the media wear
rate which is affected by ore hardness, mill speed, operating conditions,
etc etc.

>
> What do you grind in your ball mill? In power plants, big ones are used
> to pulverize coal. The banks of them I remember in the Ravenswood
> (Astoria, NY) plant were driven by 50 HP motors.

What is being ground depends on the operation...typically we deal with
copper, iron and gold ores.  We are most interested in performing this
analysis on SAG mills currently (semi-autogenous grinding), which usually
have diameters of 30 - 40 feet, and motors with several thousand HP.

>
> Jerry
>
> Jetty
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������

```
 0
Reply David 6/30/2003 4:29:42 PM

```David Taylor wrote:
>
...
>
> What is being ground depends on the operation...typically we deal with
> copper, iron and gold ores.  We are most interested in performing this
> analysis on SAG mills currently (semi-autogenous grinding), which usually
> have diameters of 30 - 40 feet, and motors with several thousand HP.
>
Before the application of spectrometers to Bessemer converter plumes,
there were a few individuals with slightly deviant visual pigments who
could see when the conversion was finished, and they got high salaries.
If there's hope that the spectrum you'd get from Fourier analysis of the
mill's vibration carries useful information, then I would guess that
some mill operators can know something useful by listening to them. If
that's the case, whatever they hear can probably be quantified. Whoever
(or whatever group) succeeds will need the operators' practical knowhow,
an awareness of different ways to extract information from sampled data,
good tools, and a keen "eye". That platitude is about all I can offer.
You have a difficult and interesting problem, and I don't know enough
about it to ask reasonable questions. Good luck.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
```
 0
Reply Jerry 6/30/2003 5:11:22 PM

```Rune Allnor wrote:
>
> "Andor" <an2or@nospam.com> wrote in message news:<3efe00c4_2@news.tiscalinet.ch>...
> > Rune Allnor wrote:
> > > David Taylor wrote:
> >  ....
> > > > Is there a good starting/newbie
> > > > text for doing practical applications of FFTs? So far, I've just brought
> >  the
> > > > data into Excel, used its Fourier transform, got my magnitude and phase
> > > > data, plotted magnitude against bin...but I'm still not sure what I'm
> > > > looking at.
> > >
> > > I don't know it first hand, but I have seen several people recommend
> > > Rick Lyons' "Understanding Digital Signal Processing".
> >
> > You can also try http://www.dspguide.com, which is pretty hands-on. Just
> > ignore the lousy cover-photo on the opening page!
>
> Nah... I'd say that photo truly proves the book is hands-on...
>
> Rune

It's a good book. I got tired of reading it on line, so I bought a copy.
I like Lyons' book better, but they're different. For an engineer like
David Taylor (related to the eponym of the towing basin?), who wants to
do DSP but not break new ground, they're collectively excellent.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
```
 0
Reply Jerry 6/30/2003 5:18:46 PM

```Hi David
A couple of bits of information you didn't provde. You said previously,
that you did an FFT on your data, but you didn't say what the length of
the data window that you processed. Also the fact that you are asking the
question here implies that nothing in particular appeared to be different
between an FFT of data collected from a fully loaded drum to a lightly
loaded one. But you didn't expressly state that computing the difference
between the 2 FFT's produced nothing.
I would guess, that if the amount of load and the composition of the
material in your mill produces different frequency components in your
data, then they will be at fairly low frequencies. So you may need a much
longer time frame for your data to discern any subtle differences. Also if
the frequencies of interest have long cycles relative to your sampling
rate it may be a good idea to decimate the data. For example, if you
downsample the data by a factor of four (with the right filters its sort
of like converting your 8-bit data to 32-bit) you will get much better
resolution and S/N ratio at the frequencies that are of interest.

-jim

David Taylor wrote:
>
> "Jerry Avins" <jya@ieee.org> wrote in message
> news:3EFCC8D2.DAA130E6@ieee.org...
> > David Taylor wrote:
> >
> > The best analysis technique depends on the kind of result you seek. Can
> > you give more detail about that?
>
> What we are looking for is a measurement of the total mill charge, which
> includes steel grinding balls, ore and water.  Ideally we would know the
> charge level and the "toe" and "shoulder" positions...i.e. the position of
> the charge in the mill when it is rotating, but right now, we would be happy
> just to know the total charge level.
>
> >
> > Does the weight vary with the charge in a consistent way? With the slow
> > change you cite, a load cell with suitable low-pass filter might do if
> > so.
>
> The charge varies with ore feed rate and grinding ball addition rate.  Most
> mills are "slug charged" meaning that they dump several tons of grinding
> balls in the mill at once and let them wear down until the next slug
> charge - more automated plants have a continuous slow feed of grinding
> balls.  The ore is fed to the mills continuously from a conveyor belt.
> Unfortunately, most mills do not have load cells - though some newer ones
> do. But the charge level cannot be determined from the load cell value alone
> because the total charge is made of both ore (typically about 2800 kg/m3)
> and steel grinding media (7800 kg/m3) in ratios that are not known at any
> given point in time, i.e. amount of ore depends on feed rate and mill
> residence time and grinding media quantity is determined by the media wear
> rate which is affected by ore hardness, mill speed, operating conditions,
> etc etc.
>
> >
> > What do you grind in your ball mill? In power plants, big ones are used
> > to pulverize coal. The banks of them I remember in the Ravenswood
> > (Astoria, NY) plant were driven by 50 HP motors.
>
> What is being ground depends on the operation...typically we deal with
> copper, iron and gold ores.  We are most interested in performing this
> analysis on SAG mills currently (semi-autogenous grinding), which usually
> have diameters of 30 - 40 feet, and motors with several thousand HP.
>
> >
> > Jerry
> >
> > Jetty
> > --
> > Engineering is the art of making what you want from things you can get.
> > �����������������������������������������������������������������������

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```
 0
Reply jim 7/1/2003 11:41:33 AM

```David,

An easy thing to overlook is that the samples you get may not be
suitably bandlimited for processing. If I recall correctly, you have
about 1500 samples per revolution. In order to avoid corrupting the FFT
spectrum with aliases, you need to remove frequencies above 750 cycles
per revolution before sampling and digitizing. (Practical systems need
some margin.) For 12 RPM -- 1/5 RPS -- the cutoff needs to be as much
below below 15 Hz as you can tolerate. At lower RPMs or coarser
resolution, it needs to be lower. Many converters are AC coupled. At
these low frequencies, that can be a problem.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Jerry Avins wrote:
>
> David Taylor wrote:
> >
>   ...
> >
> > What is being ground depends on the operation...typically we deal with
> > copper, iron and gold ores.  We are most interested in performing this
> > analysis on SAG mills currently (semi-autogenous grinding), which usually
> > have diameters of 30 - 40 feet, and motors with several thousand HP.
> >
> Before the application of spectrometers to Bessemer converter plumes,
> there were a few individuals with slightly deviant visual pigments who
> could see when the conversion was finished, and they got high salaries.
> If there's hope that the spectrum you'd get from Fourier analysis of the
> mill's vibration carries useful information, then I would guess that
> some mill operators can know something useful by listening to them. If
> that's the case, whatever they hear can probably be quantified. Whoever
> (or whatever group) succeeds will need the operators' practical knowhow,
> an awareness of different ways to extract information from sampled data,
> good tools, and a keen "eye". That platitude is about all I can offer.
> You have a difficult and interesting problem, and I don't know enough
> about it to ask reasonable questions. Good luck.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������
```
 0
Reply Jerry 7/1/2003 3:05:40 PM

```On Mon, 30 Jun 2003 13:18:46 -0400, Jerry Avins <jya@ieee.org> wrote:

(snipped)
>
>It's a good book. I got tired of reading it on line, so I bought a copy.
>I like Lyons' book better, but they're different. For an engineer like
>David Taylor (related to the eponym of the towing basin?), who wants to
>do DSP but not break new ground, they're collectively excellent.
>
>Jerry

Hi Jer,
I agree with you.  My book has a little more math (for those folk
who like a little math), but Smith's book covers SOooo many topics!
Whew.  He did a good job.

I saw an advertisement for another Smith DSP book.  The new title is:
"Digital Signal Processing: A Practical Guide for Engineers and
Scientists".  (Publisher is Elsevier Science, and they're
different from whoever publisher Smith's first book.)

I wonder how different Smith's 2nd book is from his first book.

I'm workin' on a 2nd edition of my book.   WHAT A PAIN!

See Ya,
[-Rick-]

```
 0
Reply ricklyon 7/2/2003 10:52:21 PM

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