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# Help with 1/3-Octave, averaging, summing please

Genius

I'm having issues with Test.Lab in the area of averaging dB values, specifically when using 1/3-octaves and averaging the data from multiple microphones.  I have been copying a lot of data over to Excel, to attempt to find what I'm doing incorrectly.

Background: we use ISO-3744 to record five microphone positions and then calculate A-Weighted, Sound Power. I don't have V17A installed yet, so I do the actual Lwa calculation using a spreadsheet.

Since ISO-3744 has the A-weighting table shown in 1/3-octaves, I typically follow this procedure:

1. Record the five mics

2. Display in un-weighted, 1/3-octaves, in dB

3. Copy the data to Excel

4. Average the data from the five mics

5. Apply the A-Weighting to the Average

6. Sum the individual octave values to obtain a single number - Overall SPL(dB(A))

7. Calculate the Sound Power (Lwa)

FIGURE 1: Snip from ISO-3744 showing A-Weighting and Summing 1/3-Octave Values

Note that in Figure 1, the ISO standard shows the A-Weighting and summation of the Octaves occurring simultaneously.  I get the same results whether I do them simultaneously, as shown in Figure 1, or separate them into two functions; first A-Weighting each octave, and then summing the octaves.

Now, according to the Test.Lab HELP, averaging in dB is the same as linear averaging?  I question this, since I have always written relatively long equations in Excel, to 'un-decibel' the individual points, average them, and then 're-decibel' the resultant.

FIGURE 2: Snip from Test.Lab HELP - showing dB averaging

Now, let me grab some screen shots in Excel and Test.Lab to show the, albeit minor, differences:

I'm just focusing on the 1/3-octave at 50Hz to keep things simple, but the same problem occurs at every frequency band.

Here are five data points in Pascals, with the average calculated in Excel:

FIGURE 3: Example #1 from Excel - copying data from Test.Lab in Un-Weighted Pascals

Now, if I grab the data from Test.Lab in decibels, and perform the same calculations, I get this:

FIGURE 4: Example #2 from Excel - copying data from Test.Lab in Un-Weighted Decibels

Now, in Excel Example 2, I'm using Post Processing - Average of Functions - Linear Average of dB Values, to calculate the average of the five microphones in each of the 1/3-Octave bands (that's the column labeled 'LMS Ave (dB)').  The LMS Average and my Excel calculated average match, but they do not match the first example!

Then, I go back to my initial thoughts about accurately averaging decibels (by un-decibeling, averaging, and re-decibeling), and I get this:

Figure 5: Example 3 from Excel - data from Test.Lab in Un-Weighted dB, but converting to Pa before averaging

The good news is that the third Excel example matches the first, as expected, but the bad news is it doesn't match the average given to me by Test.Lab (or when directly averaging dB values in Excel).

Now, let me add some coinciding Figures taken from Test.Lab:

FIGURE 6: 1/3-Octave plot of pressures, in Pascals, with cursor showing values at 50Hz band.

In Figure 6, all of the data points (mics 1-5) match those in Excel Example 1, but the calculated average from the Post-Processing does not match.

FIGURE 7: 1/3-Octave plot of pressures, in dB, with cursor showing values at 50Hz band.

In Figure 7, all of the data points at 50Hz match Excel Example #2, including the LMS Average in dB, calculated from Post-Processing.  The Excel average of those five data points (36.649 dB), in dB, does not match the LMS Average.

FIGURE 8: 1/3-Octave plot of pressures, in dB(A), with cursor showing values at 50Hz band.

And finally, showing the A-Weighted plot of the same exact data.  Again, the A-Weighted LMS Average does not match the Excel calculated A-Weighted Average.  I'm expecting that value to be 6.449 dB(A) at 50Hz.

Here are my Excel Calculations:

FIGURE 9: Refers back to Excel Example #1 - Linear Average of Pascals, and converting to dB.

FIGURE 10: Refers back to Excel Example #2 and #3 - Showing the un-decibel, average, and re-decibel, and then the Linear Average of dBs.

FIGURE 11: This is the equation used to sum all 1/3-Octave values, between 50Hz and 10kHz (A-Weighting not shown)

OR -

FIGURE 12: Summation of 1/3-octave values, with application of A-Weighting, as shown in Figure 1, above

If anyone can see where I'm going wrong in the above equations/examples, please let me know.  I know the difference is minor, but it becomes larger when I'm dealing with more octave bands, or more microphones.

Thanks,

Shelly

7 REPLIES 7

# Re: Help with 1/3-Octave, averaging, summing please

Siemens Phenom

Hello Shelly,

Unfortunately this is beyond the scope of what we normally see on this community forum.  Could you reach out to your local customer services team so that they can create an incident report (IR) to log your questions and then reply back.

Thank you.

# Re: Help with 1/3-Octave, averaging, summing please

Genius

Done.

I will post back if I hear back from GTAC support, or if I can figure this out myself.

PS: Since I initially posted the thread, I thought maybe the fact that I'm looking at the data in Amplitude, as opposed to Real, could have been the issue, but when rescaling the Y-Axis to Real in Figure 6 above, the data doesn't change.

# Re: Help with 1/3-Octave, averaging, summing please

Genius

I'm just writing a quick update - this was submitted to GTAC support, and they were able to get back to me immediately with a proposed solution.  The problem is, since that has occurred, I haven't had time to apply their solution to my problem and my data set(s).

.

You know those times when you're overwhelmed with work?  That's what happened immediately after contacting this forum, and then GTAC support.

.

I will update this forum about how well the solution worked, when applied to my data, once I have had time to apply the solution.  I apologize for the delay.

# Re: Help with 1/3-Octave, averaging, summing please

Experimenter

I'm hoping you get to the bottom of this, because I'm having a similar issue

I have an excel macro that copys AutoPower curves from LMS Test.Lab to excel, and then uses them (the AutoPower Sound Pressure Levels) to calculate 1/3rd Octave levels.

Basically my macro does an average of the sound pressure levels. For example, for the 125Hz 1/3rd octave, I'll get all the soud pressure levels of the AutoPower from 88Hz up to 177Hz and logarithmically average them, but the results I get from excel differ up to 1,5 dB from the 1/3rd Octave levels calculated directly inside Test.Lab by putting the Autopower on an "Octave" Picture.

# Re: Help with 1/3-Octave, averaging, summing please

Siemens Phenom

Hello,

The level in an octave band is the RMS level and not the average.  As a first step I would put the autopower curve in a front back display and use the Double X cursor calculations to calculate the average and the RMS across the octave band and compare that to the same value in the octave display.  Once that is understood, then try it in Excel.

See the following articles on RMS and Overall Level.  The RMS level needs some care to be calculate.  First it needs to be energy corrected so if your data is amplitude corrected in Excel you must remove the amplitude correction by its correction factor which is window depeneded.  Then apply the energy correction.  The RMS then sums the squared values (if the data is in linear format) and takes half the first and last values (except at 0Hz).  Then takes the square root.  For more information see:

https://community.plm.automation.siemens.com/t5/Testing-Knowledge-Base/Root-Mean-Square-RMS-and-Over...

https://community.plm.automation.siemens.com/t5/Testing-Forum/RMS-Calculation/m-p/382342#M157

https://community.plm.automation.siemens.com/t5/Testing-Forum/RMS-Calculation-for-Sound-Power-Spectr...

Lastly, the octave calculation will depend on what octave method is specified under Tools, Options, General in Test.Lab and the frequencies used for the octave band limits.  See the picture below showing the RMS calculation for the 250 Hz octave band.

Note that the RMS level across the 250 Hz octave band in the Front Back display exactly matches the 250 Hz octave band value of 55.82 dB(A).

Octave bands as specified in Acoustic Quantities.pdf in the Test.Lab theory documents installed with Test.Lab.  Based on the default octave calculation, the 125 Hz third octave band is from 112.2018 - 141.2538 Hz and not the 88-177 Hz you are using.

# Re: Help with 1/3-Octave, averaging, summing please

Genius

Leon,

After contacting GTAC Support, I received an answer from Hong.  Please see a copy of his email message below.

I haven't had time to work through Hong's method yet.  I also see that Kevin submitted a response below, and I haven't tested his method either, but after reading through, it makes sense.

I do plan on working through both suggestions when I have a few hours to work with them and the hoards of data I have collected (or when another request comes up to perform identical testing).  I will report back after that.

Thank you for the Kudos!

Message from Hong at GTAC Support:

When you average dB value, I don't you should use linear avage. In Test.Lab->data calculator->

when performing an avaerge there are four ways, linear, energy, logarithmic and peak hold. please see screen shot below:

In an 1/3 octave display you can hold Ctrl + right click choose Overall level Options...

go to Views please check Show overall level values that's the same as your excel calculated sum.

# Re: Help with 1/3-Octave, averaging, summing please

Experimenter

Thanks for the answers Shelly and Kevin!

With the information posted here I've now managed to get results exactly the same as Test.Lab and found my errors:

First: The equation I was using to calculate the octave's sound pressure levels, that I got from some book, was the wrong approach  :

Second: I had assume incorrectly that, since my Autopower resolution was at 1Hz, that the software would use the closest integer value of the frequency limits of the octave. For example, at the 1/1 Octave of 125Hz it would get the sound pressure level for 89Hz for the lower limit, and that it did not interpolate for getting the sound pressure level of 89,1251Hz, which complicates the calculation in excel a bit, but it's managable.

-Leon