lsqcurvefit doesn't curve fit

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Matthew Hunt 2019-2-13

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https://ww2.mathworks.cn/matlabcentral/answers/444769-lsqcurvefit-doesn-t-curve-fit

评论： Matthew Hunt 2019-2-13

I have a model which I want to paramtrise using lsqcurvefit. I have 10 parameters that I must find and I have 10 pieces of data (or more) that I can call on. I set up my function that I want to minimise including the function which includes the model. When I use 10 points I get the message that a minimum is possible and when I plot the solution using the parameters and compare it against the experimental data, I get completely different curves, the solution should overly the points I get but that just isn't the case.

Any idea why this would happen?

Mat

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回答（2 个）

Star Strider 2019-2-13

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Use as many data as you have. Also, nonlinear parameter estimation techniques are very sensitive to the initial estimates (that you give to the routine to start with), and an inaccurate set can cause the routine to end up in a local minimum rather than a minimum that is much closer to the correct parameters. Choosing the correct values can be challenging.

If you repeatedly have problems guessing the correct initial parameter values, use one of the Global Optimization Toolbox functions (such as the genetic algorithm ga function) to search out the best parameter set. Those take time, however they are usually succesful. (For ga, begin with a large initial population, so it has a better probability of discovering the best parameter set.)

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Matthew Hunt 2019-2-13

在 MATLAB Online 中打开

%This is the code for the inverse problem for the single particle model.
%The inverse problem will use the terminal voltage for the inverse problem
%This computes the constants for the Greens function:
N=15; %Number of terms used in Green's function
d=0.01; %Using the small different in the intevals to avoid infinity
f=@(x)tan(x)-x; %The transecendal equation 
mu_n=zeros(N,1); %array which stores the solutions
mu_n(1)=fzero(f,pi/2-d);
for i=0:N-1
    mu_n(i+2)=fzero(f,[(2*i+1)*pi/2+d (2*(i+1)+1)*pi/2-d]);
end
mu_n=mu_n(2:N+1);
%Import data as time and voltage:
load VoltageData.mat;
load('OCP_Cathode.mat'); %Load the OCP data for the cathode
load('OCP_aNODE.mat'); %Load OCP data for the anode;
SOC_a=OCP_Anode(:,1);
SOC_c=OCP_Cathode(:,1);
OCV_a=flip(OCP_Anode(:,2));
OCV_c=OCP_Cathode(:,2);
time=VoltageData(:,1);
voltage=VoltageData(:,2); 
%Import the applied current data
%Set it to the correct value:
I_app=ones(1,10);
Time=time/time(end);
%Get the data to be used:
t_data=linspace(0,Time(end),10);
L=length(Time);
V_data=interp1(Time,voltage,t_data);
%Choose initial conditions for the parameters:
X_0=0.5*ones(1,10);
X_0(5:10)=10^-7;
lb=zeros(1,10);
ub=ones(1,10);
%Set up the function for lsqcurvefit:
fun = @(X,t)terminal_voltage(V_data,I_app,mu_n,t_data,X,SOC_a,SOC_c,OCV_c,OCV_a)';
options=optimset('MaxFunEvals',100000,'TolX',10^-10);
x = lsqcurvefit(fun,X_0,t_data',V_data,lb,ub,options);
X=x;
%Compare the theoretical prediction to experimental data
SOC_anode=anode_c(I_app,mu_n,1,t_data,X);
SOC_cathode=cathode_c(I_app,mu_n,1,t_data,X);
O_plus=interp1(1-SOC_c,OCV_c,SOC_cathode);
O_minus=interp1(SOC_a,OCV_a,SOC_anode);
V=(eta_plus(SOC_cathode,I_app,X)-eta_minus(SOC_anode,I_app,X)+O_plus-O_minus);
plot(t_data,V);
hold on
plot(t_data,V_data,'ro');
title('Comparison of Theory and Experiment');
legend('Calculated Voltage', 'Experimental Voltage');
xlabel('Time');
ylabel('Terminal Voltage');

Matthew Hunt 2019-2-13

在 MATLAB Online 中打开

function G = Greens_fn(D,mu_n,r,t,r_bar)
%This is the Green's function for spherical diffusion equation
%Solution can be found in A.D. Polyanin. The Handbook of Linear Partial Differential Equations
%for Engineers and Scientists, Chapman & Hall, CRC 17
G=zeros(length(t),length(r_bar));
N_t=length(t);
N=length(mu_n); %Number of terms used in Green's function series
for i=1:N
    for j=1:N_t
    G_i(j,:)=(2*r_bar/r).*((1+mu_n(i)^-2).*sin(mu_n(i)*r).*sin(mu_n(i)*r_bar).*exp(-D*mu_n(i)^2*t(j))); %Ther series part of the Greens function
    G(j,:)=G(j,:)+G_i(j,:); %Adding uo the terms of the series
    end
end
for i=1:N_t
    G(i,:)=G(i,:)+3*r_bar.^2; %Adding the final part to give the Green's function
end
end

Matthew Hunt 2019-2-13

在 MATLAB Online 中打开

function V=terminal_voltage(V_exp,I_app,mu_n,t,X,SOC_a,SOC_c,OCV_c,OCV_a)
gamma_plus=X(5);
gamma_minus=X(6);
nu_plus=X(9);
nu_minus=X(10);
SOC_cathode=cathode_c(I_app,mu_n,1,t,X);
SOC_anode=anode_c(I_app,mu_n,1,t,X);
O_plus=interp1(1-SOC_c,OCV_c,SOC_cathode);
O_minus=interp1(SOC_a,OCV_a,SOC_anode);
V=eta_plus(SOC_cathode,I_app,gamma_plus,nu_plus)-eta_minus(SOC_anode,I_app,gamma_minus,nu_minus)+O_plus-O_minus-V_exp';

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Matt J 2019-2-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/444769-lsqcurvefit-doesn-t-curve-fit#answer_360878

编辑：Matt J 2019-2-13

You could have a bug in your model function, such that it is not implementing the curve you that you think it is. What happened when you used your model function code to generate a curve with known parameters? Did the curve look as expected?