Using Fminsearch to fit two functions recursively

Hi Matlab community,

I am trying to fit this xdata and ydata with Fminsearchbnd to extract 4 parameters using the following functions (see attached document)

Function 1: psi = [(Kf + Kb)Ro' - Kb] * exp(-Kf-Kb)

Function 2: Ro'' = (psi + Kb) / (Kf + Kb)

where

psi = ydata / (2*96485*0.045*0.2e-12 / 0.0083)

Kf = Ko * exp(-alpha*((2*96485)/(8.314*298))*(xdata-Enot))

Kb = Ko * exp((1-alpha)*((2*96485)/(8.314*298))*(xdata-Enot))

Ro' is at t = 0 and Ro'' is at t + 0.00833 and are interlinked with this equation Ro' = Ro / 0.2e-12 or Ro'' = Ro / 0.2e-12.

The initial guesses for Ko, alpha, Ro and Enot are: 0.1 (range between 1e-6 to 1e5), 0.5 (range between 0.3 to 0.7), 1 (no range) and -0.26 (range from -0.35 to -0.15), respectively.

Each function should be used recursively at each xdata point and how can I incorporate the second function?

So far, I have been able to fit the first point but it is not following and the initial guesses appear to influence the outcome of the fit...

Any help would be greatly appreciated!

Thanks!

[jgg]

I'm not clear what you mean by recursively here. Is there a time dimension here?

A good idea would be to try and set this up as an optimization problem? What is your fit criterion? What are your choice variables? What are the observations?

You don't seem to have very clearly laid those out, so it's making your life difficult (and hard for use to understand).

Basically, you want to define your y and x variables, the relationship between them given the parameters, and a criterion for measuring the difference between the observed values and the predicted values.

[Philippe]

The y variable are the currents (psi, or ydata) and the x variable are the potentials (E or xdata). Both of these variables are experimentally acquired.

There is a time dimension in the problem. For the first point of xdata, ydata, the function 1 should be use with Ro' = 1 as the initial guest. Following the obtention of this result, Ro'' at t > 0 should be used from function 2 and implemented in function.

Hope this clarifies some of your questions!

[jgg]

Why not add time as another X variable, then code a single objective function which switches between the two functions?

I'm still not clear what your objective function is. You switch between these Rho functions, but how do you evaluate the fit?

[Philippe]

You are right jgg. I am not making my case very strongly here and maybe I am not seeing the link between each function very clearly... If that would not be to much to ask, would you mind going through this small blurb of text as it appears I am not summarizing my problem clearly.

The experiment I am performing involves applying a pulse waveform (tp in length) at an electrode while measuring its current (psi). The objective is to fit theory with experimental with 4 parameters, ko, alpha, Rho, and Eo. These parameters are very informative for me and the reason why I want to extract them.

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[jgg]

Okay, so as far as I understand it, you measure psi and E in those equations, although with time.

So, I think equations (6) and (7) relate the values of E to the K_f and K_b values. You can plug those into one of the other equations (3),(4),(5) to relate the E values to psi.

Basically, you want a single function which you would feed in the x-data, your potentials, then it should output a predicted psi which you can then compare to the actual y-data.

I don't really know anything about this field, so I'm not clear which equation is the right one to relate the different variables to one another.

You want a function you can write like this:

y_predictions = function(x_data,parameters);

then you can compare the fit by looking at abs(y_predictions - y_data) or something like that.

[Philippe]

That sounds pretty close to what I want to do. So far this is what I have come up with. Let me know what you think.

http://www.mathworks.com/matlabcentral/answers/uploaded_files/50434/NonLinFit.m

[jgg]

I think this is the right approach; I would suggest moving your objective function to another file and then calling it anonymously instead of defining it like that; it will make it easier to work with. But it looks like the right idea!

[Philippe]

Thanks jgg for looking into it.

Would you have any better algorithm than the fminsearch that you would recommend me ??

[jgg]

It depends on your problem; if you have a pretty good idea where your solution should be, fminsearch is probably good enough. Otherwise, you can try ga the genetic algorithm or patternsearch if you have those toolboxes. Otherwise, it's best to just test a lot of starting points.