Enforcing a particular curve to fit the data points

Hi, I am trying to fit some data points so that the trend is first any polynomial function and then it becomes a plateau. In the figure below I am ok with the first part of the fitting but I am trying to get a plateau approximately from the crossed symbol to the end. Of course the point from where the curve will be a plateau needs to be determined by the function and not by me.

So far I tried the code below to fit:

figure

ft = fittype('f*x^5+e*x^4+d*x^3+b*x^2+c*x+a');

SS = fit(CMOD(1:end-1)',dEpsilonDtMean(1:end,1),ft,'StartPoint',[0,0,0,0,0,0],'Robust','Bisquare')

plot(SS,CMOD(1:end-1),dEpsilonDtMean(1:end,1))

[the cyclist]

Can you help us understand what you are trying to accomplish here? It is confusing to me.

Usually, when fitting data, you have some kind of functional form (often based upon an underlying theoretical model), and you want to find the parameters that result in the best fit to that function.

But that doesn't seem to be the case for you, because you are just throwing a 5th-order polynomial at it.

But then, you seem to want to get rid of the part of the fit that is actually doing pretty well (beyond 0.1), by making this plateau.

So, it is really unclear to me what you are trying to do. What is the purpose of this fit?

[Mohammod Minhajur Rahman]

The blue dots are raw data that ideally should have a plateau beyond 0.06 (just eye estimation), but it can never be achived practically, so I need to find the point from where the polynomial curve becomes a plateau. From the beginning, the first portion of these data should be fitted by a polynomial (not necessarily 5th order) and there should be a point (let's say 0.06) beyond which it should be a plateau. Basically, I need to find the point where the derivative of the fitting function becomes zero, and beyond that I can enforce a plateau manually. Of course I can not pick that point on eye estimation.

[the cyclist]

The first step is to define -- just in words, not in code -- where the plateau begins.

I understand that you want the MATLAB code to figure out where the plateau begins; but code cannot figure it out if you cannot describe it.

So, when I look at the data -- how do I know I have reached the plateau region?

Also, just out of curiosity, why do you think a polynomial is the appropriate choice in the pre-plateau region? Why not, say, an oscillatory function that damps out exponentially?

Answer 1

[Image Analyst]

What if you just made the y values constant after the x value of 0.6

index = find(x >= 0.06, 1, 'first');
CMOD(index:end) = 0.5; % Or whatever value you want the plateau to have.
plot(x, CMOD, 'b-')

[Mohammod Minhajur Rahman]

Sorry, my bad, I edited the post now: Of course the point from where the curve will be a plateau needs to be determined by the function and not by me. So, bascically I am trying to find the point where the derivative of the polynomial will be zero for the first time, and beyond that point I can make all the y values similar to have a plateau till end.