REW Accuracy/Precision - Page 2 - Home Theater Forum and Systems - HomeTheaterShack.com

Old 02-06-11, 01:58 AM
Shackster

Join Date: Jun 2010
Location: East Bay, CA
Posts: 14
Re: REW Accuracy/Precision

I'm a scientist by profession. In recently acquiring a REL subwoofer, and with the data acquisition system that Tim helped (greatly..thanks, Tim) to set me up with, it naturally occured to me that one could use a formal system of experimentation called Design of Experiments (henceforth referred to here as DOE) to formally and reproducibly optimize the integration of the sub with the mains to provide the ideal room response.

Design of Experiments is different than the classic scientific "change one factor, leave everything else the same" (One Factor At A Time or OFAT) approach that scientists and engineers were taught in school and are still primarily using to this day (much to their detriment in many cases). While the basic concepts of DOE have been around since the 1700s, it was originally formalized by the statistician R.A. Fisher. The difference between DOE and the classic OFAT approach is that you can change multiple factors at a time, set the the factors different "levels" (effectively, high or low), and run a series of a defined pattern of experiments (even in random order), measure the response (the effect you are interested in) and the DOE will tell you which factors are most important to get the response you want, and more importantly, what, if any INTERACTIONS there are between factors.

The ability to examine interactions between factors is one of the most important aspects of DOE, because if there are interactions involved between complex set factors and their resultant responses, you will never be able to deconvolute them without DOE, or if you can, it will not usually be without pure chance or luck, or without spending a lot more time, money, and effort in trying to figure them out, and often, you will still not figure them out in terms of which of the factors have the biggest effect from a statistically valid point of view.

Given this, I set out to to perform a set of experiment to see if I could determine the optimal settings of speakers, REL sub settings and other factors, like grilles on or off, speaker toe-in, port plugs, etc. that would optimize the in-room response.

My next post will be a brief introduction to DOE, and setting up the precepts of the experiments.
scharfsj is offline

Old 02-06-11, 01:59 AM
Shackster

Join Date: Jun 2010
Location: East Bay, CA
Posts: 14
Re: REW Accuracy/Precision

Description
Design of experiments (DOE) is a powerful tool that can be used in a variety of experimental situations. DOE allows for multiple input factors to be manipulated determining their effect on a desired output (response). By manipulating multiple inputs at the same time, DOE can identify important interactions that may be missed when experimenting with one factor at a time. All possible combinations can be investigated (full factorial) or only a portion of the possible combinations (fractional factorial). Fractional factorials will not be discussed here.

When to Use DOE
Use DOE when more than one input factor is suspected of influencing an output. For example, it may be desirable to understand the effect of temperature and pressure on the strength of a glue bond.

DOE can also be used to confirm suspected input/output relationships and to develop a predictive equation suitable for performing what-if analysis.

DOE Procedure
Acquire a full understanding of the inputs and outputs being investigated. A process flow diagram or process map can be helpful. Utilize subject matter experts as necessary.

Determine the appropriate measure for the output. A variable measure is preferable. Attribute measures (pass/fail) should be avoided. Ensure the measurement system is stable and repeatable.

Create a design matrix for the factors being investigated. The design matrix will show all possible combinations of high and low levels for each input factor. These high and low levels can be generically coded as +1 and -1. For example, a 2 factor experiment will require 4 experimental runs

..........................Input A Level.......Input B Level
Experiment #1.........-1......................-1
Experiment #2........-1......................+1
Experiment #3.......+1.......................-1
Experiment #4 ......+1......................+1

Note: The required number of experimental runs can be calculated using the formula 2n where n is the number of factors.

For each input, determine the extreme but realistic high and low levels you wish to investigate. In some cases the extreme levels may be beyond what is currently in use. The extreme levels selected should be realistic, not absurd. For example:

Enter the factors and levels for the experiment into the design matrix. Perform each experiment and record the results. For example:

Factors................Input -1 Level.......Input +1 Level
Temperature........100 degrees.........200 degrees
Pressure..............50 psi.................100 psi

Calculate the effect of a factor by averaging the data collected at the low level and subtracting it from the average of the data collected at the high level. For example:

Effect of Temperature on strength:
(51 + 57)/2 - (21 + 42)/2 = 22.5 lbs

Effect of Pressure on strength:
(42 + 57)/2 - (21 + 51)/2 = 13.5 lbs

The interaction between two factors can be calculated in the same fashion. First, the design matrix must be amended to show the high and low levels of the interaction. The levels are calculated by multiplying the coded levels for the input factors acting in the interaction. For example:

..........................Input A Level............Input B Level....Interaction
Experiment #1.....-1.............................-1.................+1
Experiment #2.....-1............................+1.................-1
Experiment #3.....+1............................-1................. -1
Experiment #4.....+1...........................+1.................+1

Calculate the effect of the interaction as before.

Effect of the interaction on strength:
(21 + 57)/2 - (42 + 51)/2 = -7.5 lbs

The experimental data can be plotted in a 3D Bar Chart.

The effect of each factor can be plotted in a Pareto Chart.

[img]http://photos.imageevent.com/puma_cat/fujif31andf20photos/doe-tutorial2.gif[/imp]

The negative effect of the interaction is most easily seen when the pressure is set to 50 psi and Temperature is set to 100 degrees. Keeping the temperature at 200 degrees will avoid the negative effect of the interaction and help ensure a strong glue bond.
_________________

This simple-minded example above shows that there is an interaction between temperature and pressure in the strength of the glue bond. This is one feature of DOEs that is particularly useful when looking at the effect of a number of factors and their effect on the critical functional response.

Now that that is out of the way as intro, let's look at the specific experiment I had in mind in the next post.
scharfsj is offline
Old 02-06-11, 02:00 AM
Shackster

Join Date: Jun 2010
Location: East Bay, CA
Posts: 14
Re: REW Accuracy/Precision

The experiment I was trying to reproduce was the one based on the graph that
Tim linked to a while ago from resarch from JBL showing a much preferred percieved flat room reponse actually looked more like thist that perfectly flat...

With that in mind, I set out to see what I could do with my set up to emulate that via DOE.

The desired responses were to maximize 20 and 50 Hz repsonse in dB, and minimize the 150 and 500 Hz responses. These 150 and 500 Hz responses were nodes that I wanted to minimize, if possible.

The factors I used for the DOE were sub gain (as clicks up from zero), sub crossover, likewise clicks up from zero, plug or no plug in the speaker reflex port. So, four responses being measured as the result of 3 factors at two different levels (low, high as in the examples above shown).

Setting up a full-factorial DOE in JMP (a stastical package), here are the experimental matrix I ran per JMP's output for the experimental design and the measurements (as measured in dB by room Eq Wizard).

An example trace as my starting point for reference is shown; the goal hear was to maximize the 20-50Hz node to range, while smothing the 70, and minimizing the 105, 155 and 500 Hz node peaks, so as to emulate the JBL graph.

. The red is one of interest, as this is the one with the sub engaged. The brown trace is the one w/o the sub engaged.

Here is the result of analyzing the 20 Hz response of the DOE (warning: large image)

We can see from the actual by predicted plot that the R^2 and r^2 adjusted are strongly correlated at 0.97 and 0.94, respectively, indicating that our results fit our model pretty well. Also the leverage plots (the factors affecting the response (20Hz output), show that Sub gain has a large effect, and quite possibly that the interaction of sub gain and sub crossover may have an effect, as the p-value is just barely above p>-.05, which tends to suggest there may be a significant effect if we gather more data or relax our confidence level from 95% to 90%. In, fact, if we relax our alpha from 5% (the chance we are willing to accept that we are wrong) to 10%, then the Sub crossover point becomes significant. In addition, our analysis of variance with probability of F >0.0016, suggests that that this result occurred from our null hypothesis, that the model does not predict sub 20 Hz performance is very low.

The interaction profile plots also suggest that there is a likely interaction between sub XO setting and sub gain, and the plot lines are not perfectly parallel, but appear to intersect.

Looking at the Prediction Profiler from JMP, comparing Sub gain with Sub XO, we can see that the max 20 Hz response is obtained by the Sub gain at 12 clicks up, and sub set at zero clicks, and we could expect a level of 75.1875 dB.

JMP is also cool because it will show you a 3-D image of two factors at one time as they affect the desired response, in this case, 20 Hz:

These analyses show how you can utitlize DOE to predict with good confidence the response from setting the factors (crossover point and gain) to give the desired response at 20 Hz. I'll show other data later for the other target responses of 50, 155 and 500 Hz and you can see how we might be able to arrive at a set of setting that maximizes the responses we want, and minimizes the responses we don't want.

Interesting stuff to mull over....
scharfsj is offline
Old 02-06-11, 06:19 AM
REW Author

John

Join Date: Apr 2006
Location: UK
Posts: 6,308
Re: REW Accuracy/Precision

As it happens, REW's EQ optimiser uses a Simultaneous Perturbation Stochastic Approximation algorithm. On the original measurement repeatibility results, the main cause of variations between runs is low frequency noise from traffic, wind and other external factors.
JohnM is offline
Old 02-06-11, 09:38 PM
Shackster

Join Date: Jun 2010
Location: East Bay, CA
Posts: 14
Re: REW Accuracy/Precision

I just noticed this...my base room level SPL went down about 3-4 when I turned off the AC in the house.
scharfsj is offline

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