Re: Estimation of curvature based on noisy data
- From: Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx>
- Date: Tue, 08 Jul 2008 16:22:52 +0200
Peter Spellucci wrote:
In article <9287e0fe-96e7-4379-ad63-279a04653c01@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Anders <Anders.Lyckegaard@xxxxxxxxx> writes:
>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
>
using polynomials is not a good idea for this task since these will exhibit a strong oscillatory behaviour especially for higher degrees. for your task a smoothing spline with a variable number of nodes (and using estimates of the variance of the noise) might be usable, however, since you also have inclination data you cannot use existing software off the shelf
which allows (x,y=deflection) data only. but the basic principle of derivation of such a spline applies: minimizing a weighted sum of the integral of the square of curvature and the least squares sum of deviation of model data from measured data.
hth
peter
Splines, yes. The simplest ones are quadratic. Here are some basics:
http://hdebruijn.soo.dto.tudelft.nl/www/programs/delphi.htm#knuth
Han de Bruijn
.
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