Figure 1. BAD panels consist of a binary template over an absorptive core, upholstered with fabric

The patented BAD™ panel is now offering the architectural acoustics community a long sought after flat diffusing surface that offers both high frequency diffusion and mid/low frequency absorption. In DRV6I2, we illustrated how addition of the binary amplitude template, shown in Figure 1, reduces absorption above 1 kHz and increases absorption below 1 kHz. We showed how the sound above 1 kHz, which is not absorbed, is uniformly diffused, thus providing reflection control while maintaining ambiance. And lastly, we showed that the diffusion is fairly uniform at normal incidence from 1 kHz up to roughly 12 kHz. It should be noted that it is not possible to obtain this performance with a thin membrane or a thin resin coating on the fiberglass. The membrane must have sufficient mass and thickness.

Non-normal Incidence

What about non-normal incidence? For an observation angle of 45⁰ with respect to the surface normal, Figure 2 indicates that the BAD™ panel offers greater diffusion at non-normal incidence angles of 30⁰ and 60⁰ compared to 0⁰ normal incidence. This behavior has also been observed for reflection phase gratings. Thus BAD™ panels can be used in almost any orientation for reflection control, without excessive high frequency absorption.

Reflectivity

Figure 2. BAD™ panel Diffusion Coefficients for incidence angles of 0, 30, and 60 degrees. Random random incidence (RI) diffusion coefficients for the BAD™ panel and flat reflector

Figure 2 compares the scattered level from a purely absorptive panel (dotted) to the same panel covered with the BAD template (solid). Notice how the BAD panel reduces absorption above 1 kHz.

The optimal binary codes that are effective in forming the BAD™ panel have roughly the same number of zeros and ones, resulting in a fixed reflectivity. They are also somewhat restricted in their size. 2D MLS sequences, for example, are restricted to 2n -1, where n= 2, 4, 6, etc.

Therefore, to provide a range of reflectivities, new optimal binary sequences have to be devised. To accomplish this, we need to define a performance metric. A good diffusor provides diffraction lobes with similar scattering levels. This is achieved by a sequence with a constant power spectrum or, put another way, a delta function autocorrelation coefficient. In practice, this ideal autocorrelation coefficient is approximated by an autocorrelation coefficient with minimal side lobes. Now that we have a metric to evaluate potential sequences, one approach to finding optimal sequences is to conduct an iterative search for an appropriate sequence with two desired characteristics: (i) low autocorrelation side lobes and (ii) the appropriate reflectivity. This result can be achieved by employing a genetic algorithm. A genetic algorithm essentially mimics the process of biological evolution. A population of individuals with a given set of genes is randomly formed. In this case, the genes are simply the binary sequences indicating where hard and soft patches should be placed on the diffusor surface.

Figure 3. The upper thick solid line illustrates the frequency response of a BAD™ at an observation angle of 45⁰ for normal incidence, while the lower dotted line represents the frequency response of a 1” absorber panel without the BAD™ template

Each individual is assigned a fitness value that indicates how good it matches the criteria of appropriate reflectivity and minimum autocorrelation sidelobes. Over time new populations are produced by breeding and old individuals die. Offspring are produced by pairs of parents. An offspring has a binary sequence that is a composite of the sequences from the parents. As with conventional evolution theory, the fittest are most likely to breed and pass on their genes, and the least fit the most likely to die. Mutation is also allowed to occur in the breeding to enable sequences outside the parent population to be searched. By these principles, the fitness of successive populations improves. This process is continued until the population becomes sufficiently fit so that the sequence produced can be classified as optimum. Thus, this new genetic algorithm allows RPG to provide a range of BAD panels, with the same outward appearance, that offer optimal diffusion for a wide range of reflectivities.

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