| Minimization of deviations from multiple curve fits. [message #35229] |
Mon, 26 May 2003 14:59  |
aaron_forster
Messages: 1
Registered: May 2003
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Junior Member |
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Hello Group,
I am utilizing IDL to analyze data obtained from adhesion tests. For
those interested, the tests are used to determine the work of adhesion
and system modulus. I measure contact area, load, and displacement
during the test. I currently use Craig Markwardt's MPFIT program to
fit two different non-linear equations to the experimental data. The
first equation (EQ1) expresses contact area as a function of load,
with the work of adhesion, system modulus, and indenter radius as
fitting parameters. The second equation (EQ2) expresses displacement
as a function of load and contact area, with the system modulus and
indenter radius as fitting parameters. It has been suggested by
others (Chin P. et al., J. Adhesion, 1997, 64 p. 145-160) that I can
increase the precision by analyzing the fit deviations from each curve
fit together. In other words, I need to minimize the function:
omega^2=sum {[EQ1_fit - EQ1i] + [EQ2_fit - EQ2i]^2}
where sum is the sum from i=1 to N of my data (EQ1, EQ2) and my fit
(EQ1_fit, EQ2_fit)
I hope the above equation is clear to everyone. Anyway, my
understanding of the regression programs I have seen in IDL is that
they will fit an equation and measure success of fit by minimizing
chi-sqr. My question is how do I both minimize chi-sqr for each
equation AND minimize omega^2, such that the fitting parameters I
obtain at the end of the day will provide satisfactory fits for EQ1
and EQ2. I hope this post is clearly written, but I am an IDL newbie
and I may have left relevant information out. If you would like to
hear more, please email me at aaron_forster@yahoo.com with questions.
Thank you in advance for all of your help. I greatly appreciate it.
Sincerely,
Aaron Forster
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