What is the Definition for "Adjustment Results" in a Fitting Element?

[[Ch...]]

I've constructed several "Section" elements on my nominal CAD geometry, cutting through various radiused faces (a single patch), using planes that I know are normal to the surface of the CAD model.

On each of these sections, I've used the "Construct -> Circle -> Auto Circle (Nominal)" dialog to create nominal circles.  On each of these nominal circles, I've applied the Measuring Principle "Fitting Element".  This creates the fitted circles on the Actual mesh.

When I do this, I can see in the "Properties" for each actual fitted circle, a number of "Adjustment Result" entries.  Among these are the type of element ("Construct Fitting Circle"), the number of points used to construct that element, Min, Max, sigma, and something called "Residual".

 I'm especially interested in the "Residual" value.  I have no idea what that means or how it is determined.

I'm guessing that Min and Max are pretty self-evident --- the minimum deviation (inside the circle?) of any point from the fitted circle; the maximum deviation is the maximum deviation of any point (outside the circle?) from the fitted circle.

But please explain what "Residual" means in this case.

Also, one last item on Fitted Circles:  are ALL the points associated with the created section ALWAYS used?  Are fliers ever ignored?  If so, how would the user be made aware of this?

[[Be...]]

The Residual value is the average absolute distance from each point to the fitted geometry and is therefore a measure how far the geometry fits the used points. Keep in mind: This is not the value we minimize with a Gausssian approach. For Gaussian we minimize the sum over all squared deviations. Therefore the sigma value and the residual value are differing in general.

Regarding 'Are ALL the points associated with the created section ALWAYS used': This depends on your settings during the fitting command. You can apply a simple filter to detect outliers with a sigma approach, but you can also specify to use always 'All points' . If you specify a sigma factor we do the fitting twice. First we consider all points, calculate a sigma and in a second run we neglect points which have a bigger distance to the first internal result than the specified factor multiplied with the calculated sigma.

Keep in mind: This detects usually only outlier if a lot of points would lead to a good fitting result with a small calculated sigma. If you have a lot of noise in your data the algorithm usually consider nearly all points because the first calculated sigma is quite high in respect to your data.

Regards

[[Ti...]]

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I was wondering what Residual was and I searched for it and found this post.

I read an article discussing the merits of minimizing squared distances vs non-squared. There were opinions that the squared approach was outdated b/c for some reason a long time ago it was easier to do the squared approach b/c it was less computer intensive...seems counterintuitive to me. Squaring stuff seems harder to me.  I always looked at the squared approach as you are placing more importance on larger deviations and not something I want to do all the time.

Would I be correct in assuming that the residual is similar to the non-squared deviation, while the sigma value is the squared deviation?

 

 

Edited September 25, 2022

[[Be...]]

Hi Tim,

yes, your understanding is correct. But keep in mind: We usually don't optimize for the non-squared-deviation, the 'Residual' is only a different interpretation of the fitted result!

Regards,

Bernd

 

[[Be...]]

One further remark:

Regarding which approach is better I found a nice short summary in the internet: https://www.kaggle.com/code/residentmario/l1-norms-versus-l2-norms/notebook
As you can see there is no easy answer! Furthermore a lot of standards (e.g. GD&T, ...) defines to use a Gaussian  (L2 norm) or Chebyshev  (min max norm) fitting.

 

[[Ti...]]

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  Great link, thanks for sharing....no need to reply as I prefer you spend your time carefully, but the article does state that doing absolute values is more costly....that was what I mentioned confused me, I don't see how simply doing an absolute value is more costly than squaring all values.  I just don't understand that....apparently a while back with limited computer power they say it was easier to square vs taking the absolute value...makes no sense to me 🙂