Diffuser Video Simulations Shred Sound To Death—optimized sound diffusers—for thesis.
(Scroll Down to Download the Free Report on Diffuser Design + DIY Diffuser Blueprints)
Hey guys,
Since so many of you are into sound diffusers, I thought I’d share these videos with you.
You get to see diffusers shredding the hell out of sound waves.
First, let's see what happens to a sound wave when it hits a wall of spikes [Updated]:
Horrifying. Now, onto the proper diffuser videos! The videos below are from my thesis on acoustic diffuser design. I designed them using simulated natural selection (evolutionary optimization) combined with a physical modeling method called finite difference time domain (what you see in the simulation). Basically just a fancy trial and error algorithm.
These next two simulations show fractal diffusers, which were generated from the stepped diffusers I optimized.
Nice! I'm looking forward to your posting a follow up with the "blue prints". I currently require some 1D diffusers and I have a local CNC house in mind that could machine this from structural foam.
You know, I actually had DIYers in mind when optimizing these diffusers. Two of my constraints for the stepped diffusers, were that they need to be modular and simple to manufacture by DIYers.
Then, I created fractals from the optimized forms.
The fractal versions (which are shown in the videos) are more complex to make.
. . . But if you have a CNC they should be no problem for you!
Anyway, if you're in a rush and you don't want to wait for the drawings, the numbers needed to make them are in chapters 7-8 of the thesis.
I've made two attempts on your site to forward you my email address to obtain a copy of your thesis. I'm not certain that it is working properly as I received no feedback suggesting that it was accepted.
My second question involves periodicity of your diffuser design. When using multiple periods of QRDs and PRDs it is good practice to insert "inverse" versions of your diffuser as per the barker sequence. The CAD models of your diffuser show 5 identical periods and no inverse units. What is the deal with that?
I'll look into the email issue right away. Which button did you try submitting it with? Was it a "Download the Thesis" button on the page, or was it the "Get on the List" button in the right hand sidebar?
Your second question is a great question!
You see, I optimized the designs in an aperiodic array, modulated using the sequence {1 0 1 1 0}. But, one of the designs converged to be symmetrical, so it's periodic. In that case, the best solution found by the algorithm (optimization combined with a phyisal model) was a symmetrical design.
The other one is not symmetrical, and is therefore aperiodic (because it's modulated with the sequence 1 0 1 1 0). The aperiodic design offers better performance, but is more complex in shape and deeper in profile.
Does that answer your question?
Thanks so much for your interest and for notifying me of the signup issue!
Last edited by Arqen; 22nd July 2012 at 02:28 AM..
Reason: Clarity
Oh, I should clarify that I was optimizing for depth, not simply performance.
The low profile, symmetrical design was optimized to have good performance, while being super low profile.
The asymmetrical design achieved better performance, but with a deeper depth.
So, there are multiple solutions to the optimization problem. The goal was to find solutions that provide an awesome balance between performance and depth!
My first thought was it looks like bundles of dowel rods piled up! Which then made me think...
Presumably if you made up each bundle with the right selection of dowel sizes you could come up with something covering a range of frequencies. You wouldn't know precisely what was happening but it would be a quick and cheap 'pseudo fractal' (= its got lots of small bumps on the big bumps!)diffuser.
Thanks tim really great stuff. Will your upcoming DIY plans include he fractal as well as the simpler diffusor?
You know, I've been debating whether or not to actually include the drawings for the fractal diffuser. Simply because, so far as I know, RPG holds a patent on the concept of a fractal diffuser (e.g., the Diffractal consists of nested QRD diffusers).
If they don't mind, I'll post the plans for the fractal versions as well.
One reason I optimized small stepped diffusers, was because I really wanted to turn them into fractals. Could not resist ! Fractal stepped diffusers just made so much sense to me, and I'm quite happy with the results.
My first thought was it looks like bundles of dowel rods piled up! Which then made me think...
Presumably if you made up each bundle with the right selection of dowel sizes you could come up with something covering a range of frequencies. You wouldn't know precisely what was happening but it would be a quick and cheap 'pseudo fractal' (= its got lots of small bumps on the big bumps!)diffuser.
Has anyone actually tried something like this?
That would work well I think! The bigger diffuser looks like it could be called a "Cactus Fractal". And bundles of dowl might give a similar Cactal look. Cylinders make excellent diffusers (the ideal diffuser is actually a massive cylinder that would render your room unusable), I imagine log cabin walls make decent diffusers if the logs are vary in size . . . and of course randomness scatters like mad.
Typically when diffusers get bigger, the performance gap between quazirandom forms and optimized forms shrinks. It's intuitive, but Peter D'Antonio (or RPG) and Trevor Cox (University of Salford) also verified this in a paper in the 90's. I believe it was called "The optimization of profiled diffusers".
So in general, the bigger the diffuser, the more random you can be.
Tim
Last edited by Arqen; 22nd July 2012 at 06:48 PM..
Reason: Clarity
Periodicity, Grating Lobes, And 3rd Order Fractals
Quote:
Originally Posted by johndykstra
How are you avoiding lobing given the repetition of the design?
Good question!
During optimization, the array of 5 diffuser modules was modulated using the aperiodic sequence {1 0 1 1 0}. If you look closely, you'll see that one of the designs (the bumpier looking one) does not have symmetrical modules, therefore when five are placed in the array {1 0 1 1 0} it acts as aperiodic modulation. This is the best performing design I found, period. But it's not as low profile as the other design.
You see, I optimized multiple designs, which design is 'optimal' will depend on the needs of the person making them.
The other design, which is periodic, is simpler and lower profile. It was the best performer the optimization algorithm found that had a depth less than 8 cm . It has a symmetrical module (by choice of the algorithm), and is therefore periodic even though it was optimized in the array {1 0 1 1 0}. According to the scattering simulations (using a finite difference time domain physical model), this low profile symmetrical module has an awesome performance-to-depth ratio, even though it's periodic.
The designs are based on simulation data. Check out the diffusion coefficients and scattered sound polar plots from the simulations (the polar plots let you visualize the grating lobes).
For the deeper, aperiodic-modulated fractal diffuser.
For the shallower, periodic fractal diffuser.
Something to note about grating lobes:
Some diffusers rely on periodicity to function optimally. For example, did you know that QRDs need to be arranged in a periodic array to produce 'optimal' scattering at their design frequency? They will still produce diffusion no matter how you arrange them, but they will only behave 'optimally' when placed in a periodic array.
This periodic assumption is built into the design equations for QRDs and other Shroeder diffusers... But, it's is not true for optimized stepped diffusers, which are designed based on a realistic physical model, not simple equations. So, you are absolutely right to be suspicious about how I'm avoiding grating lobes in the periodic design -- I tried to avoid them but the optimization algorithm wanted to keep them .
Food for thought: A low frequency fractal modulation (Creates a 3rd order fractal diffuser)
We can potentially enhance the periodic, low profile design.
We can modulate it a different way, by applying a fractal to the entire array. This, I have not simulated. But I think it would work well. Imagine, instead of having an array of 5 diffusers, we had an array of 7. And each one was mounted on the wall at a different depth, based on the step height in the optimized stepped diffuser.
In this case, we would have a 3rd order fractal based on the optimized stepped diffuser! (I believe RPG offers this option with their Diffractal series, except each fractal is based on a QRD rather than a stepped diffuser).
At least one person has had trouble downloading the free reports on Arqen.com. If you run into an issue, please let me know what browser you're using so we can adjust our code and let you in!
What Materials Would You Use For DIY Diffusers?
Also, I'm wondering, for any of you interested in DIY diffusers... what would be the most likely material you'd use for building them?
Also, what tools are available to you? Do you have access to woodworking equipment? CNC?
One of my goals was to optimize a DIY diffuser that practically anyone can build, regardless of what materials are available to them.
Do you think your algorithm could be of any use for 3d diffusers?
Good question!
Yes, but it would take a LONG time . It would take months for my computer (with an i7 2600K processor) to find a good solution to the optimization problem.
A nice alternative is use the Chinese remainder theorem to convert the 2D diffusers to 3D designs. RPG uses this technique in some of their 3D diffuser designs (and I believe they've patented it).
There are also a few mods I could do to make the algorithm more time efficient. I did not do them for my thesis because it would have taken too long to program.
You guys will be the first to know if I ever come up with optimized 3D designs!
RPG uses what Salford Uni uses, that is BEM stuff and currently FTDT stuff.. Diffusers are not my forté but PM me and I will put you in touch with someone who does that stuff if you are interested.
I still think diffusers should be wood, mdf is fine :-)
RPG uses what Salford Uni uses, that is BEM stuff and currently FTDT stuff.. Diffusers are not my forté but PM me and I will put you in touch with someone who does that stuff if you are interested.
I still think diffusers should be wood, mdf is fine :-)
Right on Andre. Sounds like you know your stuff!
[If any casual readers are confused, BEM and FDTD are modelling methods used to simulate the scattering from diffusers. The optimization algorithm relies on a simulation to grade designs, while searching for the 'optimal' design]
I presume that RPG has developed a good 3D boundary element solver that integrates with the optimization process. So they can whip up new design designs just like that. My design system uses FDTD instead, which is very useful and fun (you can view the simulation in real time, and collect detailed data from both the time domain and frequency domain)... But, FDTD is computationally much slower than BEM.
A hot research topic these days is finding "cheat codes" that speed up FDTD simulation... because FDTD is so useful. For the thesis, I used a different kind of cheat code. Instead of hacking the FDTD simulation to make it more efficient, I hacked the design problem so that I could use a large grid spacing on the FDTD mesh. The hack involved using an integer genetic algorithm, giving me the power of parallel, nonlinear search. It's an efficient optimization algorithm, with an inefficient simulation method.
I'm also prefer wood or fibreboard over synthetic materials. As a nice alternative, I've been thinking about bamboo plywood.
FYI: I created the plots in the thesis by coding up some equations in the book "Acoustic Absorbers and Diffusers" by Trevor Cox at the University of Salford and Peter D’Antonio of RPG Diffusor Systems. There is a discrepancy between those plots and the plots on my website. Please refer to the plots on my website for more accurate performance predictions.
Arqen, regarding your post 14;
If one were to DIY your diffusers one would not need more than a hammer, nails and glue plus a straight ruler with clamps at each end.
At least this goes for the base shape with 7 wells with width 60 mm each => total width 420 mm per panel. Trickier though with the fractal one on top of each base shape well, as this one requires thickness of the material of 8,57 mm = not a standard thickness in metric or imperial system => this would require a good planer to cut down the thickness of a standard wooden board. –Even if one had such a planer, one has to consider moisture in wood which make it shrink and expand depending on season, shrinkage / expansion is also not the same along the length versus the width => not good.
Suggestion / question: If the base shape had well width 70 mm instead of 60 mm = total panel width 490 mm, how would this affect the frequency range? If this is still acceptable, one could use strips of standard thickness of 10 mm MDF for both the base shape diffuser and the fractal diffuser on top of the base shape. => A lumber yard with a large table saw could easily cut up large sheets of 10 mm MDF into suitable strip widths and there would be very little scrap material. The strips could then be glued and nailed together, requiring no special tools at all, to achieve base shape and fractal shape into one piece. This cutting with a saw would cost some money of course but most certainly less than to have the fractal parts planed or milled to correct thickness of 8,57 mm x 7 = 60 mm total width = the base shape well width. (As MDF is just saw dust mixed with glue to get "an isotropic compound”, there would also be less problems with dimension changes over the seasons.)
Arqen, regarding your post 14;
If one were to DIY your diffusers one would not need more than a hammer, nails and glue plus a straight ruler with clamps at each end.
At least this goes for the base shape with 7 wells with width 60 mm each => total width 420 mm per panel. Trickier though with the fractal one on top of each base shape well, as this one requires thickness of the material of 8,57 mm = not a standard thickness in metric or imperial system => this would require a good planer to cut down the thickness of a standard wooden board. –Even if one had such a planer, one has to consider moisture in wood which make it shrink and expand depending on season, shrinkage / expansion is also not the same along the length versus the width => not good.
Suggestion / question: If the base shape had well width 70 mm instead of 60 mm = total panel width 490 mm, how would this affect the frequency range? If this is still acceptable, one could use strips of standard thickness of 10 mm MDF for both the base shape diffuser and the fractal diffuser on top of the base shape. => A lumber yard with a large table saw could easily cut up large sheets of 10 mm MDF into suitable strip widths and there would be very little scrap material. The strips could then be glued and nailed together, requiring no special tools at all, to achieve base shape and fractal shape into one piece. This cutting with a saw would cost some money of course but most certainly less than to have the fractal parts planed or milled to correct thickness of 8,57 mm x 7 = 60 mm total width = the base shape well width. (As MDF is just saw dust mixed with glue to get "an isotropic compound”, there would also be less problems with dimension changes over the seasons.)
Great question!
Increasing the width will decrease the maximum frequency where diffusion occurs. I would not worry about this if you're building the fractal version. If you're just building the stepped diffuser and it's inconvenient to use the exact dimensions, I think it's acceptable to vary them a bit...
But I make no guarantees! Bear in mind that since these are stepped diffusers, it's difficult to predict how a slight mod will change the performance (QRDs, on the other hand, have simple equations you can use to predict their performance).
I'm glad you think the diffuser designs are dirt simple. That was my goal . Thanks for checking out the report!
Well, I will not be building any of them. Not because they are of no interest but because there is no wall area left for further treatment.
If I were to DIY any though, I would use the thickness of a common standard sheet as "base" for the whole device, ie 10 mm or 3/8", starting with the fractal. Not the other way around which makes the device more labour intensive.
Fractal: 7 cells => 7 x 10 mm = 70 mm total width ( or 7x3/8" = 2 5/8")
=> 70 mm or 2 5/8" should be the width of each well for the base shape diffusor. Multiply the "base" with the numbers in your document to get correct depth of each well. Correct? Or should there be a fraction involved, 70 vs 60 mm, to stay close to your simulated result figures?
This would cut down labour and only one dimension and material needed be used and cut up with a saw into certain widths and lengths. (It will be heavy though, if made in MDF)
Yes, I think your approach would save manufacturing effort. Ideally, I think, one would multiply the depth of each well (i.e. the height of each step) by the scale factor 7/6. To keep the proportions the same.
However, it would probably be insignificant for the 2nd level of the fractal, so you could simply multiply the height of the base shape (the first level of the fractal) by 7/6, and build the fractal cells as you mentioned.
Even if you don't do any scaling of the depths I think it will perform just fine. But I can't know for sure, because the proportions will be different... therefore, the sound waves will be scattered differently.
I'm not sure that was the greatest answer to your question. But does that make sense?
For aesthetic reasons and to hide any nails or screws from sight, a DIY project should start with the fractal parts towards the room. Then build the diffuser backwards towards the room walls.
(Your / this concept has parts reminding a bit of details in Boggys “MyRoom Acoustics” document MyRoom Acoustics )
Nice stuff! Interesting also to see the almost semicircular shape in one of the optimizations. Almost like a stepped poly of sorts.
Subscribed.
__________________
:: Christian Borg
"It's the sound itself that's important and the ability to work with it, not where it comes from. They [musicians] are manipulators of sound, not purists." - Bob Moog
Hey, thank you all. I was hoping to get feedback from people who take diffusers seriously, from a practical point of view. It's no use designing something if the people who might use them end up hating them!
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! Fractal stepped diffusers just made so much sense to me, and I'm quite happy with the results.
