Need help to fit the data without error.

Question

tuhin 2024-3-4

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2090051-need-help-to-fit-the-data-without-error

编辑： Torsten 2024-3-13

% Data
rData = [5.3571429, 0.096854535; 10.714286, 0.055104186; 16.071429, 0.042811499; 21.428571, 0.024825886; 26.785714, 0.023279183; 32.142857, 0.016328542; 37.5, 0.0092185037; 42.857143, 0.0075624777; 48.214286, 0.0023514323; 53.571429, 0.001637045; 58.928571, -0.0024887011; 64.285714, -0.0034741333; 69.642857, -0.0056340032; 75, -0.0040906991; 80.357143, -0.0039738424; 85.714286, -0.0044593789; 91.071429, -0.0054884315; 96.428571, -0.0037277341; 101.78571, -0.0041691748; 107.14286, -0.0039292558; 112.5, -0.0037408923; 117.85714, -0.0040700255; 123.21429, -0.0028904555; 128.57143, -0.0022557232; 133.92857, -0.0020756487; 139.28571, -0.0020739949; 144.64286, -0.0015149035; 150, -0.0019796368; 155.35714, -0.00068430865; 160.71429, -0.00060721168; 166.07143, -0.00055972397; 171.42857, -0.0011788755; 176.78571, -0.00090675531; 182.14286, -0.00060012026; 187.5, 7.6071311e-6];
tData = [5.3571429, 0.081473653; 10.714286, -0.0076210718; 16.071429, -0.038565046; 21.428571, -0.014000405; 26.785714, -0.042161254; 32.142857, -0.071404281; 37.5, -0.066992712; 42.857143, -0.031355057; 48.214286, -0.02043848; 53.571429, -0.025259291; 58.928571, -0.019615094; 64.285714, -0.015185751; 69.642857, -0.012213914; 75, -0.0047624032; 80.357143, -0.00041652762; 85.714286, 0.0028162852; 91.071429, 0.00979253; 96.428571, 0.0080315783; 101.78571, 0.0034739882; 107.14286, 0.0021786814; 112.5, 0.0043349925; 117.85714, 0.0053397331; 123.21429, 0.0061087654; 128.57143, 0.0028425693; 133.92857, 0.002129577; 139.28571, 0.0068534431; 144.64286, 0.0071201038; 150, 0.0099290536; 155.35714, 0.0089545127; 160.71429, 0.0079282308; 166.07143, 0.0075533041; 171.42857, 0.01092774; 176.78571, 0.012219652; 182.14286, 0.01013098; 187.5, 0.0096622622];
% Define equations
syms x;
mu = sym('mu'); lambda = sym('lambda'); ke = sym('ke'); ko = sym('ko');
Alpha = @(mu, lambda) 1/(2*mu + lambda);
r = @(x) x;
theta = @(x) x;
% Define equations
eqn1 = x^2*diff(r(x), x, x) + x*diff(r(x), x) - r(x) + Alpha(mu, lambda)^-1*ke^2*x^2*r(x) - Alpha(mu, lambda)^-1*ko^2*x^2*theta(x) == 0;
eqn2 = x^2*diff(theta(x), x, x) + x*diff(theta(x), x) - theta(x) + mu^-1*ko^2*x^2*r(x) + mu^-1*ke^2*x^2*theta(x) == 0;
% Convert symbolic equations to function handles
eqn1_func = matlabFunction(eqn1);
eqn2_func = matlabFunction(eqn2);
% Define the model
funr = @(params, x) deval(ode45(@(x, y) [eqn1_func(params(1), params(2), params(3), params(4), x); eqn2_func(params(1), params(2), params(3), params(4), x)], [0.75, 187.5], [0.1625, 0]), x, 1);
% Fit the data with initial guess values
initialGuess = [15, 50, 0.01, 0.01];
fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1).', rData(:,2).');
Error using symengine>@(ke,ko,mu,x)(ke.^2.*x.^3)./mu+(ko.^2.*x.^3)./mu==0.0
Too many input arguments.

Error in solution>@(x,y)[eqn1_func(params(1),params(2),params(3),params(4),x);eqn2_func(params(1),params(2),params(3),params(4),x)] (line 17)
funr = @(params, x) deval(ode45(@(x, y) [eqn1_func(params(1), params(2), params(3), params(4), x); eqn2_func(params(1), params(2), params(3), params(4), x)], [0.75, 187.5], [0.1625, 0]), x, 1);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 104)
    odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in solution>@(params,x)deval(ode45(@(x,y)[eqn1_func(params(1),params(2),params(3),params(4),x);eqn2_func(params(1),params(2),params(3),params(4),x)],[0.75,187.5],[0.1625,0]),x,1) (line 17)
funr = @(params, x) deval(ode45(@(x, y) [eqn1_func(params(1), params(2), params(3), params(4), x); eqn2_func(params(1), params(2), params(3), params(4), x)], [0.75, 187.5], [0.1625, 0]), x, 1);

Error in solution>@(params,x)funr(params,x) (line 20)
fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1).', rData(:,2).');

Error in lsqcurvefit (line 256)
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Caused by:
    Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.
fit2 = lsqcurvefit(@(params, x) funr(params, x), initialGuess, tData(:,1).', tData(:,2).');
% Plot the fitted functions
x_values = linspace(1, 187.5, 1000);
r_fit = funr(fit, x_values);
theta_fit = funr(fit2, x_values);
figure;
plot(x_values, r_fit, 'r', 'LineWidth', 2);
hold on;
scatter(rData(:,1), rData(:,2), 'b');
xlabel('x');
ylabel('r(x)');
title('Fitted r(x) vs. Data');
legend('Fitted r(x)', 'Data');
figure;
plot(x_values, theta_fit, 'g', 'LineWidth', 2);
hold on;
scatter(tData(:,1), tData(:,2), 'b');
xlabel('x');
ylabel('theta(x)');
title('Fitted theta(x) vs. Data');
legend('Fitted theta(x)', 'Data');

Getting folowwing errors:

Error using symengine>@(ke,ko,mu,x)(ke.^2.*x.^3)./mu+(ko.^2.*x.^3)./mu==0.0

Too many input arguments.

Error in test5>@(x,y)[eqn1_func(params(1),params(2),params(3),params(4),x);eqn2_func(params(1),params(2),params(3),params(4),x)] (line 21)

funr = @(params, x) deval(ode45(@(x, y) [eqn1_func(params(1), params(2), params(3), params(4), x); eqn2_func(params(1), params(2), params(3), params(4), x)], [0.75, 187.5], [0.1625, 0]), x, 1);

Error in odearguments (line 92)

f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in test5>@(params,x)deval(ode45(@(x,y)[eqn1_func(params(1),params(2),params(3),params(4),x);eqn2_func(params(1),params(2),params(3),params(4),x)],[0.75,187.5],[0.1625,0]),x,1) (line 21)

funr = @(params, x) deval(ode45(@(x, y) [eqn1_func(params(1), params(2), params(3), params(4), x); eqn2_func(params(1), params(2), params(3), params(4), x)], [0.75, 187.5], [0.1625, 0]), x, 1);

Error in test5>@(params,x)funr(params,x) (line 25)

fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1).', rData(:,2).');

Error in lsqcurvefit (line 225)

initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Error in test5 (line 25)

fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1).', rData(:,2).');

Caused by:

Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

4 个评论
显示 2更早的评论隐藏 2更早的评论

tuhin 2024-3-4

But eqn 1 and 2 are differential equations. This is the actual equations:

(*Define the equations*)

\[Alpha][\[Mu]_, \[Lambda]_] := 1/(2*\[Mu] + \[Lambda]);

eqns[\[Mu]_, \[Lambda]_, ke_, ko_] := {

x^2*r''[x] + x*r'[x] - r[x] + \[Alpha][\[Mu], \[Lambda]]^-1*ke^2*x^2*r[x] - \[Alpha][\[Mu], \[Lambda]]^-1*ko^2*x^2*\[Theta][x] == 0,

x^2*\[Theta]''[x] + x*\[Theta]'[x] - \[Theta][x] + \[Mu]^-1*ko^2*x^2*r[x] + \[Mu]^-1*ke^2*x^2*\[Theta][x] == 0};

I want to use and solve this two coupled differential eqns (with four boundary conditions) and fit it with the experimental data of r(x) vs x and \theta(x) vs x. For this I want to tune those four parameters mu; lambda; ke; ko. Please let me know if you need more clarifications.

Walter Roberson 2024-3-4

Your latex doesn't make sense.

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Answer 1

Torsten 2024-3-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2090051-need-help-to-fit-the-data-without-error#answer_1420881

编辑：Torsten 2024-3-5

在 MATLAB Online 中打开

I assumed you start integration at x = 5.3571429.

You will need to specify dr/dx and dtheta/dx in the y0-vector below.

rData = [5.3571429, 0.096854535; 10.714286, 0.055104186; 16.071429, 0.042811499; 21.428571, 0.024825886; 26.785714, 0.023279183; 32.142857, 0.016328542; 37.5, 0.0092185037; 42.857143, 0.0075624777; 48.214286, 0.0023514323; 53.571429, 0.001637045; 58.928571, -0.0024887011; 64.285714, -0.0034741333; 69.642857, -0.0056340032; 75, -0.0040906991; 80.357143, -0.0039738424; 85.714286, -0.0044593789; 91.071429, -0.0054884315; 96.428571, -0.0037277341; 101.78571, -0.0041691748; 107.14286, -0.0039292558; 112.5, -0.0037408923; 117.85714, -0.0040700255; 123.21429, -0.0028904555; 128.57143, -0.0022557232; 133.92857, -0.0020756487; 139.28571, -0.0020739949; 144.64286, -0.0015149035; 150, -0.0019796368; 155.35714, -0.00068430865; 160.71429, -0.00060721168; 166.07143, -0.00055972397; 171.42857, -0.0011788755; 176.78571, -0.00090675531; 182.14286, -0.00060012026; 187.5, 7.6071311e-6];

tData = [5.3571429, 0.081473653; 10.714286, -0.0076210718; 16.071429, -0.038565046; 21.428571, -0.014000405; 26.785714, -0.042161254; 32.142857, -0.071404281; 37.5, -0.066992712; 42.857143, -0.031355057; 48.214286, -0.02043848; 53.571429, -0.025259291; 58.928571, -0.019615094; 64.285714, -0.015185751; 69.642857, -0.012213914; 75, -0.0047624032; 80.357143, -0.00041652762; 85.714286, 0.0028162852; 91.071429, 0.00979253; 96.428571, 0.0080315783; 101.78571, 0.0034739882; 107.14286, 0.0021786814; 112.5, 0.0043349925; 117.85714, 0.0053397331; 123.21429, 0.0061087654; 128.57143, 0.0028425693; 133.92857, 0.002129577; 139.28571, 0.0068534431; 144.64286, 0.0071201038; 150, 0.0099290536; 155.35714, 0.0089545127; 160.71429, 0.0079282308; 166.07143, 0.0075533041; 171.42857, 0.01092774; 176.78571, 0.012219652; 182.14286, 0.01013098; 187.5, 0.0096622622];

initialGuess = [15, 50, 0.01, 0.01,...

rData(1,2),(rData(2,2)-rData(1,2))/(rData(2,1)-rData(1,1)),...

tData(1,2),(tData(2,2)-tData(1,2))/(tData(2,1)-tData(1,1))];

options = optimset('MaxFunEvals',10000,'MaxIter',10000);

fit = lsqnonlin( @(params)fitfun(params,rData,tData), initialGuess,[0 0 0 0 -Inf -Inf -Inf -Inf],[],options)

Local minimum found. Optimization completed because the size of the gradient is less than the value of the optimality tolerance.

fit = 1×8

1.0e+03 * 2.6450 0.0499 0.0000 0.0000 0.0001 -0.0000 0.0000 -0.0000

norm(fitfun(initialGuess,rData,tData))

ans = 3.4186

norm(fitfun(fit,rData,tData))

ans = 0.1558

[T,Y] = odefun(fit,rData,tData);

figure(1)

hold on

plot(rData(:,1),rData(:,2),'o')

plot(T,Y(:,1))

hold off

figure(2)

hold on

plot(tData(:,1),tData(:,2),'o')

plot(T,Y(:,3))

hold off

function res = fitfun(params,rData,tData)

[T,Y] = odefun(params,rData,tData);

res = [rData(:,2)-Y(:,1);tData(:,2)-Y(:,3)];

end

function [T,Y] = odefun(params,rData,tData)

mu = params(1);

lambda = params(2);

ke = params(3);

ko = params(4);

fun = @(x,y)[y(2);(-x*y(2)+y(1)-ke^2*x^2/(2*mu+lambda)*y(1)+ko^2*x^2*y(3)/(2*mu+lambda))/x^2;...

y(4);(-x*y(4)+y(3)-ko^2/mu*x^2*y(1)-ke^2/mu*x^2*y(3))/x^2];

tspan = rData(:,1);

y0 = [params(5);params(6);params(7);params(8)]; %[r,dr/dx,theta,dtheta/dx]

[T,Y] = ode45(fun,tspan,y0);

end

9 个评论
显示 7更早的评论隐藏 7更早的评论

tuhin 2024-3-13

Till now, I was varying those four parameters of mu, lamda, ke and ko for these two fittings (i.e. r(x) vs x and t(x) vs x). That means I am getting Ke_r, Ko_r, mu_r and lamda_r for r(x) vs x. For, t(x) vs x I am getting ke_t, ko_t, mu_t and lamda_t. Now I want the ke_r should be same as ke_t and ko_r should be same as ko_t. For that I want to change the script.

Torsten 2024-3-13

编辑：Torsten 2024-3-13

You have one fit in your code above from which you get Ke, Ko, mu and lamda by solving 4 differential equations for r, r', t and t' simultaneously. I don't know what you mean by

Till now, I was varying those four parameters of mu, lamda, ke and ko for these two fittings (i.e. r(x) vs x and t(x) vs x). That means I am getting Ke_r, Ko_r, mu_r and lamda_r for r(x) vs x. For, t(x) vs x I am getting ke_t, ko_t, mu_t and lamda_t.

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