Re: Estimation of curvature based on noisy data

On 10 Jul., 16:01, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
RRogers wrote:
On Jul 9, 4:12 pm, Anders <Anders.Lyckega...@xxxxxxxxx> wrote:

On 9 Jul., 14:12, RRogers <rerog...@xxxxxxxxxxxxxx> wrote:

On Jul 8, 8:16 am, Anders <Anders.Lyckega...@xxxxxxxxx> wrote:

Hi all,

I'm working on a bit postprocessing of experimental data.I'm trying to
find a robust algorithm for estimation of the curvature of a beam
based on measurements of deflections and inclination of a beam.

I have a few measurements of deflection and inclinations of a beam
along the length of it. Now I would like to find the curvature and an
estimate of the accuracy of my estimate.

Furthermore, I could possibly define some bounds for the magnitude of
curvature and a physical model for the beam, i.e. equilibrium.

I have tried fitting different polynomials to the data points using
regression analysis, but I get different results based on my choice of
polynomial.

Thus, I was hoping to find a method that defines the problem in a more
general way, and can provide an accurate estimate and an estimate of
the accuracy.

I have a feeling that estimation theory might be helpful, but I'm not
familiar with it and don't know were to start off.http://en.wikipedia.org/wiki/Estimation_theory

Any suggestions are welcome,

Best,
Anders

Do you have some kind of Model/Description in mind for the result?

Yes, I have a set of governing equations, which are differential
equations. However, some of the parameters are not known, but can be
defined within bounds based on physical arguments.

Possibly a differential equation? Polynomials work okay as long as
you stop, and specify the "weighting function"; say maximum or least
squares. This is determined by your goals and the expected nature of
the errors. Polynomials and such are typically descriptors and won't
reflect the underlying differential constraints unless they are chosen
carefully.
In other words: what are your expectations; an arbitrary description,
a description that satisfies enough mathematical conditions to be
symbolically reusable, or a physically meaningful description (my
favorite).

My expectations are that a set of requirements for the shape of the
beam can be established mostly based on physical arguments.

E.g
* The curvature should be bounded.
* The inclination should be smooth
* Equilibrium (fundamental physics) should be fulfilled.

In any case stop the detailing (order of the polynomials for instance)
once the residuals match your expected error distribution; say normal
or log normal.

That makes sense. That would give me the possiblity of evaluating the
suitability of the shape functions that I choose. I'll have to think
about that.

Best,
Anders

Can you give a reference for, or write out, the differential
equations. In the end it would be nice to have something like
"moments" as the result, and then you could rule out higher moments on
physical grounds; thus allowing a description of the noise or at least
an explicit description of the censoring/smoothing done by the model.
My problem with splines is that they provide a description that is not
physically meaningful. If you just want a description then they are
fine.

Maybe "Fuzzy Frenet Analysis" is useful for you:

http://hdebruijn.soo.dto.tudelft.nl/www/programs/delphi.htm#frans

Disclaimer: anything free comes without referee, hence without guarantee
(Sorry; I _know_ there are several errors in the accompanying documents)

Han de Bruijn

Super, I'll look into it.

Best,
Anders
.

Relevant Pages

  • Re: Estimation of curvature based on noisy data
    ... find a robust algorithm for estimation of the curvature of a beam ... based on measurements of deflections and inclination of a beam. ... what are your expectations; ... Equilibrium (fundamental physics) should be fulfilled. ...
    (sci.math.num-analysis)
  • Re: Estimation of curvature based on noisy data
    ... find a robust algorithm for estimation of the curvature of a beam ... based on measurements of deflections and inclination of a beam. ... Equilibrium (fundamental physics) should be fulfilled. ...
    (sci.math.num-analysis)
  • Re: Estimation of curvature based on noisy data
    ... find a robust algorithm for estimation of the curvature of a beam ... based on measurements of deflections and inclination of a beam. ... Equilibrium (fundamental physics) should be fulfilled. ...
    (sci.math.num-analysis)
  • Re: Estimation of curvature based on noisy data
    ... find a robust algorithm for estimation of the curvature of a beam ... based on measurements of deflections and inclination of a beam. ... I have tried fitting different polynomials to the data points using ...
    (sci.math.num-analysis)
  • Re: Estimation of curvature based on noisy data
    ...  >find a robust algorithm for estimation of the curvature of a beam ...  >based on measurements of deflections and inclination of a beam. ... We did try splines. ...
    (sci.math.num-analysis)
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