Using temperature and pressure data to estimate antoine coefficients for glycerol

I am trying to estimate the antoine coefficients using the nlinfit function form the statistics toolbox, I am getting some errors when trying to run this code, could somebody please help me get this to work and estimate the antoine coefficients i would really appreciate it.

antoine = @(T,p) (log10(p) - A + B/(T+C));

beta0 = [3.93737,1411.531,-200.566];

beta = [A,B,C];

beta = nlinfit(T,p,antoine,beta0);

Error using nlinfit (line 213)

Error evaluating model function '@(T,p)(log10(p)-A+B/(T+C))'.

Error in Temperatureconversion (line 55)

beta = nlinfit(T,p,antoine,beta0);

Caused by:

Error using /

Matrix dimensions must agree.

Answer 1

[Star Strider]

Since both variable are present in the objective function equation, nlinfit (or lsqcurvefit) are not really good choices for this.

A regular optimization function (such as fminsearch) would work best. (There are other optionis, however everyone has fminsearch.)

% % % DATA MATRIX MAPPING — T = Tp(:,1),  p = Tp(:,2)
Tp = [270:10:320; rand(1,6)].';                             % Data Matrix
% % % ANTOINE FUNCTION MAPPING — b(1) = A,  b(2) = B,  b(3) = C
antoine = @(b,Tp) (log10(Tp(:,2)) - b(1) + b(2)/(Tp(:,1)+b(3)));
beta0 = [3.93737,1411.531,-200.566];
[beta,fv] = fminsearch(@(b)norm(antoine(b,Tp)), beta0);
fprintf('A =\t%10.4f\nB =\t%10.4f\nC =\t%10.4f\nfv =\t%10.4f',[beta,fv])

A =	   -0.3592
B =	 5207.9099
C =	 5645.6692
fv =	    2.1267

Having the actual data would produce the best results, however the created data demonstrate that the approach works.

.

[Tom Goodland]

Hi thanks for the help i appreciate it,

I have temperature and pressure data, 23 values for both temperature and pressure. Would this method still be the best way to estimate the antoine coefficients?

The question is 'calculate the coefficients for the Antoine equation as given in Equation (1) for glycerol' Equation 1 is the Antoine Equation.

Also, what is fv?

[Star Strider]

My pleasure.

It would be necessary to put the temperature and pressure data in the ‘Tp’ matrix in the order I have them here. (Note: They are column vectors.) The rest of the code then runs without further changes.

The ‘fv’ value is the final value of the function when fminsearch converges on a solution. Here, it is the value of ‘antoine’ using the provided data and estimated parameters at convergence.

.

[Star Strider]

No, ‘Tp’ is just what I named the matrix, since the first column is temperature and the second column is pressure. A matrix by any other name would work as well, providing all references to it were changed in the code as well.

[Tom Goodland]

Hi, how should I put the data in the Tp matrix, should it be Tp = [ T;p] both in column vector form?

Thanks

[Star Strider]

Using the (:) notation that forces column vector orientation, it should be —

Tp = [T(:) p(:)]

Inm the documentation for colon,: see Index Matrix Rows and Columns for a discussion on that convention.

.

[Tom Goodland]

Thanks for the help, I plugged my data in and got different coefficient values. It also says fv = 0.0000>> is this allright?

[Star Strider]

Yes!

The optimisation routines vary the parameters of a function to search for the minimum value of the function. A function value of 0 at convergence is about as good as it’s possible to get!

[Torsten]

Unbelievable !

Maybe only three (T,p) data were supplied. :-)

[Star Strider]

The data could be very accurate so that the function provides a reasonably good fit, since in my physical chemistry labs as an undergraduate our values were often quite good and gave a good fit to the functions with little error (I suspect the function value is 0 within approximation error, so not exactly 0) or the data could be synthetic with a bit of noise added.

[Torsten]

in my physical chemistry labs as an undergraduate our values were often quite good and gave a good fit to the functions with little error

Lucky you !

[Star Strider]

We were just compulsive! All of us were doing out best to get into med school, so every little bit helped.

Answer 2

[Torsten]

antoine = @(b,T) 10.^( b(1) + b(2)./(T+b(3)));
beta0 = [3.93737,1411.531,-200.566];
beta = nlinfit(T,p,antoine,beta0)

[Tom Goodland]

Hi thanks for the answer I appreciate it, I ran this and it came up with the following errors: idk where the high line numbers are coming from my code ends at line 30.

Error using nlinfit>checkFunVals (line 649)

The function you provided as the MODELFUN input has returned Inf or NaN values.

Error in nlinfit>LMfit (line 596)

if funValCheck && ~isfinite(sse), checkFunVals(r); end

Error in nlinfit (line 284)

[beta,J,~,cause,fullr] = LMfit(X,yw, modelw,beta,options,verbose,maxiter);

Error in Temperatureconversion (line 30)

beta = nlinfit(T,p,antoine,beta0);

[Torsten]

Then use a different vector for beta0.

[Tom Goodland]

different values or make it a column vector?

[Torsten]

nlinfit starts to evaluate antoine with beta0.

To see what happens, try

vec = antoine(beta0,T)

before you call nlinfit.

Take care that all elements in "vec" are real numbers (no infinity or NaN) by varying beta0.

[Tom Goodland]

Thanks for the help