what is the best method to fit a curve to strain-stress data?

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Dear Matlab experits,
Is there any preference towards any method (Matlab function) to fit a curve into strain-stress data? Is polyfit is reliable enough?
Thank you..

Accepted Answer

John D'Errico
John D'Errico on 21 Jul 2019
Edited: John D'Errico on 21 Jul 2019
NO polynomial will ever fit that curve (at least, not fit it well.) NONE. PERIOD.
x = data_mathwork(:,1);
>> y = data_mathwork(:,2);
>> plot(x,y,'.')
Think about it. The function is clearly asymptotically linear above a certain point, but highly nonlinear below that point. Below that point, it appears to have a singularity.
How many polynomials can you think of that have those properties? (None.)
If you want to fit a model to that data, then you will need to choose one that has reasonable properties. It ain't gonna be a polynomial.
Were I to try to find a model, I would first exchange x and y, fitting the first variable as a function of the second. That eliminates the singularity. All curve fitting tools have problems with that.
If I do so, and then fit the result with a spline, I get this:
Which suggests the upper part is not truly asymptotically linear, but close. If I look at the first derivative, it is indeed trailing off.
I'd just use an intelligently fit least squares spline as the simplest thing you could do.
Abdulaziz Abutunis
Abdulaziz Abutunis on 22 Jul 2019
Thank you John I will try it, though I have tried several methods incluing using statistcal smothing such as moving avrage and moving median windows. All works however, there is always so nosy segment which is the one in the elastic region where I need to fit a linear segment. So since I have alot of curves, what i did was to scan for the best R^2 in that region then extrapolated it then shif it then use a subroutin form the file extchane that catch the intersection between the shifted line and the smoothed curve data. I wich I would find a some magical tool that will reliably smooth the data then every thing will be easy to work out.
Thank you again and apreciate your suggestion

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