Re: Estimation of curvature based on noisy data
- From: RRogers <rerogers@xxxxxxxxxxxxxx>
- Date: Wed, 9 Jul 2008 05:12:09 -0700 (PDT)
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?
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).
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.
Ray
.
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