how to retrieve 3 parameters by fitting data into a model

I have a data set of surface impedance of a material. I need to retrieve 3 parameters from a model by fitting this data into it. I have no previous experience in Matlab. can i get any suggestions and explanations on how to go about it?

Answer 1

[Ameer Hamza]

See fit(): https://www.mathworks.com/help/releases/R2020a/curvefit/fit.html from curve fitting toolbox and https://www.mathworks.com/help/releases/R2020a/optim/ug/lsqcurvefit.html from optimization toolbox. For a specific suggestion, share the equation of your mathematical model.

[Sareesh Haridas]

please look at this equation sheet.

[Ameer Hamza]

These equations look quite complicated. You need to write these in MATLAB format before trying to estimate the parameters.

[Sareesh Haridas]

x = 0.001; %porosity

s = 001; % mean pore size

y = 0.001;% standard deviation

w = 127; % frequency (input from data sheet)

theta1 = (1/3);

theta2 = exp((-1/2)*((y*log2)^2))/sqrt(2); %theta values

theta3 = theta1/theta2;

rhozero = 1.225; %ambient density of air

alpha = exp(4*(y*log2)^2); %tortosity

eta = 1.81e-5; %dynamic viscosity of air

sigma = (((8*eta*alpha)/((s^2)*x)))* (exp(6*(y*log2)^2)); %bulk flow resistivity

epsilonp = sqrt((-(w*rhozero*alpha)i)/(x*sigma));

fp = (1+ (theta3*epsilonp)+(theta1*epsilonp))/(1+(theta3*epsilonp));

%substituting to main equation part 1

pw = ((rhozero*alpha)/(x))*((1+(epsilonp)^-2)*fp); %p omega

gamma = 1.4; %specific heat ratio

thetab = exp((3/2)*((y*log2)^2));

thetac = theta1/thetab;

sigma1 = (((8*eta*alpha)/((s^2)*x)))* (exp(-6*(y*log2)^2));

npr = 0.71; %prandtl number of air

epsilonc = sqrt((-(w*rhozero*npr*alpha)i)/(x*sigma1));

fc = (1+(thetac*epsilonc)+(theta1*epsilonc))/(1+(thetac*epsilonc));

po = 1.013e5; %ambient atmospheric pressure

cw = (x/(gamma*po))*(gamma-((gamma-1)/(1+((epsilonc)^-2)*fc); %c omega

%equations

zb = sqrt(pw/cw);

kb = (w* sqrt(pw*cw));

h = 50; % thickness of sample

czero = 343; %speed of sound m/s

%main equation

z = (zb * coth((-(kb*h)i)/(rhozero * czero)));

x0 = [x,s,y];

m = fminsearch(z,x0);

i want to use fminsearch on function z to retrieve the paramters porosity, mean pore size and standard deviation. i have given them initial values. could you check if the syntax for fminsearch is correct?

[Ameer Hamza]

You need to write an objective function to use fminsearch. What is your equation?

[Sareesh Haridas]

z = (zb * coth((-(kb*h)i)/(rhozero * czero)))

this is my equation.

[Ameer Hamza]

You need to write a separate function that takes the value of x, s, and y as input and output the value of z. Just take your code and encapsulate it into a function.

[Sareesh Haridas]

so i need to expand this equation just in terms of x,s and y as input? just defining them like i did at the start of the coding won't work?

[Ameer Hamza]

No. You need to write a separate function. fminsearch needs a function handle. You just need to write the function in which value of x, s and y are not pre-defined. The function takes these values as input and returns the value of 'z'.

[Sareesh Haridas]

i have a set of data for z which i got from experimients. i need a tool that will run these equations and iterate values for x,s and y until i get the closest value of z. is this possible using fminsearch?

ie the tool should give me the closest theoretical z to experimental z and the respectives values of x,s and y at that point.

[Ameer Hamza]

In that case, you will need to use lsqcurvefit() instead of fminsearch. In any case, you need to write it into a function of the variables you are trying to estimate. Something like this

function z = myModel(z,s,z)
    % you code to calculate z
    z = .. % value of z
end

[Sareesh Haridas]

okay thank you very much. i will try it out and get back to you