Nonlinear least-squares data fit

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MOHAMED ABDULAZIM 2020-8-14

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/579642-nonlinear-least-squares-data-fit

评论： Star Strider 2020-8-19

all data for fitting.xlsx

I am trying to make a data fit for the data attached to this post,Nu=f(Re,Theta,Beta).I use lsqnonlin(fun,x0) function for this purpose.I have created a script file for this fitting,but everytime I try to run the script,the program always shows error messages.So,what is the problem with this script.

clc
clear all
% Create an anonymous function that describes the expected relationship
% between X and Y
f=@(c,x) c(1).*(x(:,1).^c(2)).*(x(:,2).^c(3)).*(x(:,3).^c(4))./x(:,4)-1;
% data set 
% Specify x variables from data file,Re,Theta and Beta columns.
x=xlsread('all data for fitting');
% Specify y variable from data file ,(Nu)column.
y=x(:,4);
% Specify a vector of starting conditions for the solvers
c0=[1;1;1;1];
% Perform a nonlinear regression
c=lsqnonlin(f,c0);

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Answer 1

Star Strider 2020-8-14

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/579642-nonlinear-least-squares-data-fit#answer_480048

在 MATLAB Online 中打开

The objective function needs to be coded as:

ffcn = @(c) f(c,x) - y;

with the complete lsqnonlin call being:

f=@(c,x) c(1).*(x(:,1).^c(2)).*(x(:,2).^c(3)).*(x(:,3).^c(4))./x(:,4)-1;
ffcn = @(c) f(c,x) - y; 
c0=[1;1;1;1];
C = lsqnonlin(ffcn, c0);

producing:

C =
   1.0308e-01
   1.3246e+00
   1.9801e-06
  -4.6017e-01

.

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MOHAMED ABDULAZIM 2020-8-18

在 MATLAB Online 中打开

I have tried to take the initial values from genetic algorithm and use them in the least square nonlinear fit but every time I try to run the script,an error message appears.

clc
clear all
% Create an anonymous function that describes the expected relationship
% between X and Y
f=@(c,x) c(1).*(x(:,1).^c(2)).*exp((x(:,3)*c(4))+(x(:,2)*c(3)));
% data set 
% Specify x variables from data file,Re,Theta and Beta columns.
x=xlsread('all data for fitting');
% Specify y variable from data file ,(Nu)column.
y=x(:,4);
% objective function 
ff=@(c)(f(c,x)-y)./y;
% maximum of objective function
ffmax=@(c)norm(ff(c));
% Identifying population size and number of parameters for genetic
% algorithm
PopSz = 500;
Parms = 4;
% Modifying the options of genetic algotithm optimization function
options = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-4, 'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf, 'PlotInterval',1);
% Genetic algorithm application
[theta,fval,exitflag,output] = ga(ffmax, Parms, [],[],[],[],-Inf(Parms,1),Inf(Parms,1),[],[],options);
% Specify a vector of starting conditions for the solvers(Least squre
% nnonlinear fit)
c0=[theta(1) ;theta(2);theta(3); theta(4)];
% Perform a nonlinear regression
c=lsqnonlin(ff,c0);
y1=f(c,x);
diff_Nu=y-y1;
Abs_diff_Nu=abs(diff_Nu);
perc_error=(Abs_diff_Nu./y);
x_line45=0:max(y);y_line45=0:max(y);
[max_error,I_max]=max(perc_error);
[min_error,I_min]=min(perc_error);
x_line_high=0:max(y); y_line_high=(max_error+1)*(0:max(y));
x_line_low=0:max(y); y_line_low=(1-max_error)*(0:max(y));
figure
plot(x_line45,y_line45,'k')
hold on
scatter(y,y1)
hold on
plot(x_line_high,y_line_high,'r')
hold on
plot(x_line_low,y_line_low,'r')
N=[y,y1];
header=['Nuact','Nufit'];
disp(header)
disp(N)

Here is the error:

Error using optimoptions (line 114)
Invalid solver specified. Provide a solver name or handle
(such as 'fmincon' or @fminunc).
Type DOC OPTIMOPTIONS for a list of solvers.
Error in bestfitever (line 20)
options = optimoptions('ga', 'PopulationSize',PopSz,
'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-4,
'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf,
'PlotInterval',1);

MOHAMED ABDULAZIM 2020-8-19

Did you try to run this script on your version?

Star Strider 2020-8-19

在 MATLAB Online 中打开

I used this:

D = xlsread('all data for fitting.xlsx');
x = D;
y = x(:,4);
f=@(c,x) c(1).*(x(:,1).^c(2)).*(x(:,2).^c(3)).*(x(:,3).^c(4));
ffcn = @(c) (f(c,x) - y)./y; 
ftns = @(c) norm(ffcn(c));
PopSz = 500;
Parms = 4;
opts = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-4, 'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf, 'PlotInterval',1);
t0 = clock;
fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
[theta,fval,exitflag,output] = ga(ftns, Parms, [],[],[],[],-Inf(Parms,1),Inf(Parms,1),[],[],opts)
t1 = clock;
fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
GA_Time = etime(t1,t0)
QQQ1 = datetime([zeros(1,5) GA_Time], 'Format','HH:mm:ss.SSS')
fprintf('\nElapsed Time: %23.15E s ', GA_Time)
fprintf(1,'\tRate Constants:\n')
for k1 = 1:length(theta)
    fprintf(1, '\t\tTheta(%d) = %12.5E\n', k1, theta(k1))
end

and when I ran that just now, got these parameter estimates:

theta =
     2.8517e+000   431.7000e-003    99.6000e-003  -324.6437e-003

with a fitness value of:

fval =
     5.5386e+000

.

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Nonlinear least-squares data fit

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