# Curve fitting tool does not respect the upper and lower limits of parameters of custom equation

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Luciano Montanelli
on 11 Aug 2022

Commented: Luciano Montanelli
on 13 Aug 2022

Hi. I hope you can help me. I have the data from measurements in vectors vel_3_Hor and tau_fr_3_Hor:

vel_3_Hor = [206.5139956

179.4945199

162.7919326

151.195134

138.3501347

130.3942364

122.4986401

106.4425864

98.45750292

89.01579654

82.19190831

70.47075771

60.70021288

49.84117539

42.22794379

32.74655746

];

tau_fr_3_Hor = [0.137735032

0.139278888

0.125791442

0.125100852

0.125945036

0.125767804

0.122046211

0.116725322

0.121744852

0.119606

0.117339514

0.115280309

0.111458901

0.111580077

0.113360071

0.11463187

];

The elements with same index in the previous vectors correspond to each other. I want to fit these points to this custom equation:

y = tau_C + (T_S - tau_C)*exp(-(x/vel_S)^delta_S) + c_vel*x

(There is a value of tau_fr_3_Hor at vel_3_Hor = 0 here, but please ignore it. tau_fr_3_Hor = 0.1208 is an average result that I got from several experiments at vel_3_Hor where I measured tau_fr_3_Hor. I cannot rely on this average for specific reasons, but still it works as an estimate).

I set this values in Curve Fitting Tool:

Then I got these results:

It just seems to be something wrong with the confidence bounds in each parameter. For instance, vel_S cannot be negative, and also should be less than 80 at first sight. Also, tau_C should be between 0.10 - 0.12.

Thanks in advance.

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John D'Errico
on 12 Aug 2022

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