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Re: reverse engineering of acoustic sources
I have tackled this inversion as a 3D design problem to generate the
geometry for bells with harmonic overtones and other tunings.
We used gradient projection shape optimization methods to iteratively
alter a finite element model toward the desired overtone frequencies. As
you would expect from the earlier conversations there were multiple
solutions to the geometry of many of the bell tunings.
The optimisation package 'Reshape' we were using is limited to linear
FEM problems, although I believe that the optimisation algorithms in
Ansys could be used for non-linear FEM problems. However optimisation in
Ansys lacks the spatial resolution possible in Reshape.
You can see and hear the bells at www.ausbell.com and see my article in
JASA 114(1), 505-511
ps Hi Jim
>>> Georg Essl <gessl@CS.PRINCETON.EDU> 02/01/04 6:07 AM >>>
I do agree that inverse problems are hard. Though I would argue that
inverse spectral problem of the linear wave equation is much easier than
the same for the articulatory tract, which is clearly not a as simple a
On Sat, 31 Jan 2004, Pierre Divenyi wrote:
> Date: Sat, 31 Jan 2004 10:43:50 -0800
> From: Pierre Divenyi <firstname.lastname@example.org>
> To: Georg Essl <gessl@CS.Princeton.EDU>, AUDITORY@LISTS.MCGILL.CA
> Subject: Re: reverse engineering of acoustic sources
> Pardon my bringing in a negative view, but I have serious doubts that
> unique solution to any specific wave can be found. Although I have
> delved into the mathematics of it, I only know of the problem in
> where the acoustic-to-articulatory inversion has been extensively
> investigated, only to come up with the answer that solutions require
> restrictive initial and boundary values and functions. I can't imagine
> the acoustic-to-musical instrument problem should be any easier to
> But correct me if I am wrong.
> Pierre Divenyi
> At 01:13 PM 1/31/2004 -0500, Georg Essl wrote:
> >Hi Jim,
> > I think it's probably fair to say that the pure mathematicians who
> >on this don't necessarily have typical real-world acoustical
> >mind. The formalisms tend to isolate one problem and tend to try to
> >dent there. So 2-D structures (membranes) and 3-D (rooms) cases are
> >usually treated separately.
> >As for excitations, these are usually not featured prominently,
> >they are definitely there implicitly at least. I'd say in the papers
> >I've read very often harmonic drivers (force-sustained) are assumed,
> >not necessarily. It helps to bring the wave equation into reduced
> >Helmholtz form, which is convenient. It's a spatial problem only
> >than a temporal and spatial problem that way. In other formalisms,
> >dynamic response in general usually with respect to the geometry of
> >situation is considered in which case asymptotic arguments pop up
> >by lack of a better method). Asymptotic in this setting means that an
> >approximate form is assumed whose error shrinks with some parameter
> >becoming large, e.g. typically for high frequencies. Of course if the
> >situations could be treated directly, one would.
> >But despite all the simplications and reductions, the story isn't
> >(and not fully understood), which is I guess the point I wanted to
> >with respect to the paragraph of the SciAm article.
> >- Georg
> >On Sat, 31 Jan 2004, beauchamp james w wrote:
> > > Date: Sat, 31 Jan 2004 09:38:22 -0600 (CST)
> > > From: beauchamp james w <email@example.com>
> > > To: gessl@CS.Princeton.EDU
> > > Cc: firstname.lastname@example.org
> > > Subject: Re: reverse engineering of acoustic sources
> > >
> > > Dear Georg,
> > >
> > > Thank you for your wonderful response to my question.
> > >
> > > I wonder if any of the mathematical solutions to this problem take
> > > into account directivity and room responses and whether they work
> > > for forced sustained vibrations (e.g., clarinet) as opposed to
> > > free vibrations (e.g., a drum).
> > >
> > > Jim Beauchamp
> > >