A few suggestions based on your ques.nb notebook you attached above.

1. You use {t,0,1440} in some places, {t, 0, 1500} in others, and if I guess what your Excel data shows you have points out to 1479.55. I believe this is causing some of your warnings and errors in your NonLinearModelFit. I recommend changing everything to {t, 0, 1500}. This gets rid of some of the warnings about having to extrapolate beyond the end of your Interpolating Function.

2. Even with these changes, there are still more warnings or errors about values being outside the range of your interpolating function in NonLinearModelFit. I cannot understand your input data well enough to understand whether this is a more serious error with the equation you are trying to fit or the data you are giving it. I recommend trying to track down and understand why your interpolating function needs to give you these warnings.

3. Your excel data only has six digits of accuracy, but your PrecisionGoal -> Infinity option in your NDSolve appears like it might be invoking a different algorithm to try to satisfy your need for Infinity. I recommend eliminating that option, or perhaps using at most PrecisionGoal -> 3 because that seems to get rid of some more warnings about not being able to satisfy your demands. Even PrecisionGoal->1 is not sufficient to eliminate all the warnings.

4. If I look at your overlaid points and curve that looks like a terrible fit. Is that because the equation you have chosen doesn't match the form of the measured data? Is that because there is some error in finding the equation? I would recommend trying to find out why your red curve is not a much better fit of your data points.

5. I would have tried to plot your final fit to see how good it was. Unfortunately I have not been able to figure out enough to be able to do that from your notebook.

This is one of many disadvantages of posting the same question many places.

Please pick one thread to add to, or start a new thread if the new question is not a close follow-on to the existing one.

Moderation Team

See also (re-post)

http://community.wolfram.com/groups/-/m/t/284857?p_p_auth=XrkYA7w9

Re-posted as follow-up question in http://community.wolfram.com/groups/-/m/t/283255