I am simulating ADT Stanley Controller for an Autonomous Vehicle (Highway), and I would like to know what value is used for the friction coeffcient () in the implementation of ADT Stanley Controller for an Autonomous Vehicle (Highway). Can anybody help please?

Best, Kanat.I am simulating ADT Stanley Controller for an Autonomous Vehicle (Highway), and I would like to know what value is used for the friction coeffcient () in the implementation of ADT Stanley Controller for an Autonomous Vehicle (Highway). Can anybody help please?

Best, Kanat. I am simulating ADT Stanley Controller for an Autonomous Vehicle (Highway), and I would like to know what value is used for the friction coeffcient () in the implementation of ADT Stanley Controller for an Autonomous Vehicle (Highway). Can anybody help please?

Best, Kanat. vehicle dynamics modelling, friction coefficient MATLAB Answers — New Questions

​

Hi,

I have created a grid layout ([3,2]) in a tab in a programmatical app. The column width for the grid layout is set to ‘fit’ for both columns. In the first row, I have a uitable and a uiaxes next to each other and in the second row, I have a uipanel and another uiaxes next to one another. The final row contains a button.
The content of the uipanel in the second row, is a heatmap based on the correlations between variables. I am using a uipanel as a parent since heatmap cannot be the child of uiaxes.
When I debug the code, the heatmap fills the uipanel perfectly and everything runs as expected. However, if I remove the breakpoints and run the code in normal mode, the heatmap resizes for some reason and becomes very small in the uipanel.
This is the code used to create the gridlayout:
g3=uigridlayout(tab3,[3 2]);
g3.RowHeight = {‘fit’,’fit’,’fit’};
g3.ColumnWidth = {‘fit’,’fit’};

testdata=array2table(zeros(13,4),"RowNames",variables,"VariableNames",{‘Variable 1′,’Variable 2′,’Variable 3′,’Variable 4’});
t14=uitable(g3,"Data",testdata);
t14.ColumnEditable = repelem(false,4);
t14.Layout.Row=1;
t14.Layout.Column=1;
s1=uistyle(HorizontalAlignment=’right’);
addStyle(t14,s1);

ax1=uiaxes(g3);
ax1.Layout.Row=1;
ax1.Layout.Column=2;

ax_heat=uipanel(g3);
ax_heat.Layout.Row=2;
ax_heat.Layout.Column=1;

ax_box=uiaxes(g3);
ax_box.Layout.Row=2;
ax_box.Layout.Column=2;

The heatmap is calculated and assigned to the uipanel as follows:
R=corr(Data);
hm=heatmap(ax_heat,variables, variables,R,’Colormap’,jet);
Is there a way to "force" the size of the heatmap to fill the entire uipanel?
Why is the behaviour different between debugging (perfect) and normal mode?
Thanks in advance!Hi,

I have created a grid layout ([3,2]) in a tab in a programmatical app. The column width for the grid layout is set to ‘fit’ for both columns. In the first row, I have a uitable and a uiaxes next to each other and in the second row, I have a uipanel and another uiaxes next to one another. The final row contains a button.
The content of the uipanel in the second row, is a heatmap based on the correlations between variables. I am using a uipanel as a parent since heatmap cannot be the child of uiaxes.
When I debug the code, the heatmap fills the uipanel perfectly and everything runs as expected. However, if I remove the breakpoints and run the code in normal mode, the heatmap resizes for some reason and becomes very small in the uipanel.
This is the code used to create the gridlayout:
g3=uigridlayout(tab3,[3 2]);
g3.RowHeight = {‘fit’,’fit’,’fit’};
g3.ColumnWidth = {‘fit’,’fit’};

testdata=array2table(zeros(13,4),"RowNames",variables,"VariableNames",{‘Variable 1′,’Variable 2′,’Variable 3′,’Variable 4’});
t14=uitable(g3,"Data",testdata);
t14.ColumnEditable = repelem(false,4);
t14.Layout.Row=1;
t14.Layout.Column=1;
s1=uistyle(HorizontalAlignment=’right’);
addStyle(t14,s1);

ax1=uiaxes(g3);
ax1.Layout.Row=1;
ax1.Layout.Column=2;

ax_heat=uipanel(g3);
ax_heat.Layout.Row=2;
ax_heat.Layout.Column=1;

ax_box=uiaxes(g3);
ax_box.Layout.Row=2;
ax_box.Layout.Column=2;

The heatmap is calculated and assigned to the uipanel as follows:
R=corr(Data);
hm=heatmap(ax_heat,variables, variables,R,’Colormap’,jet);
Is there a way to "force" the size of the heatmap to fill the entire uipanel?
Why is the behaviour different between debugging (perfect) and normal mode?
Thanks in advance! Hi,

I have created a grid layout ([3,2]) in a tab in a programmatical app. The column width for the grid layout is set to ‘fit’ for both columns. In the first row, I have a uitable and a uiaxes next to each other and in the second row, I have a uipanel and another uiaxes next to one another. The final row contains a button.
The content of the uipanel in the second row, is a heatmap based on the correlations between variables. I am using a uipanel as a parent since heatmap cannot be the child of uiaxes.
When I debug the code, the heatmap fills the uipanel perfectly and everything runs as expected. However, if I remove the breakpoints and run the code in normal mode, the heatmap resizes for some reason and becomes very small in the uipanel.
This is the code used to create the gridlayout:
g3=uigridlayout(tab3,[3 2]);
g3.RowHeight = {‘fit’,’fit’,’fit’};
g3.ColumnWidth = {‘fit’,’fit’};

testdata=array2table(zeros(13,4),"RowNames",variables,"VariableNames",{‘Variable 1′,’Variable 2′,’Variable 3′,’Variable 4’});
t14=uitable(g3,"Data",testdata);
t14.ColumnEditable = repelem(false,4);
t14.Layout.Row=1;
t14.Layout.Column=1;
s1=uistyle(HorizontalAlignment=’right’);
addStyle(t14,s1);

ax1=uiaxes(g3);
ax1.Layout.Row=1;
ax1.Layout.Column=2;

ax_heat=uipanel(g3);
ax_heat.Layout.Row=2;
ax_heat.Layout.Column=1;

ax_box=uiaxes(g3);
ax_box.Layout.Row=2;
ax_box.Layout.Column=2;

The heatmap is calculated and assigned to the uipanel as follows:
R=corr(Data);
hm=heatmap(ax_heat,variables, variables,R,’Colormap’,jet);
Is there a way to "force" the size of the heatmap to fill the entire uipanel?
Why is the behaviour different between debugging (perfect) and normal mode?
Thanks in advance! uipanel, uigridlayout, heatmap, debugging MATLAB Answers — New Questions

​

One of the main problems is that there will never be a sign change on the interval so it’ll always execute the first part of the if statement. I commented out the err>errtol part for testing. I don’t know what i’m doing wrong for calculating using the bisection method. I have to use while loops.

% A scale is made with two springs, and when an object is attached to the
% two springs, the springs stretch and the ring at the end of the two
% springs is displaced downwards a distance x.
%
% The relationship between the weight of the object and the distance x is:
% W=(2k/l)(l-lo)(b+x)
% The initial spring length
% lo = sqrt(a^2+b^2)
% The stretched spring length
% l = sqrt(a^2+(b+x)^2)
% for the given scale a=8.0 in. b=5.0 m. and the spring constant k=16.0 lb/in.
% b=5.0 m.=196.85 in.
% Trying to find the deflection x.
%
% Have the user input lower and upper values of the starting
% interval (xl, xu), as well as the weight of the object
% Initialize the error tolerance (errtol)
% and the maximum number of iterations (maxiter)
%
% Check the interval to see if there’s a sign change
%
% while (iterations < maxiter) and (err > errtol)
% Calculate midpoint of the interval xr=(xl+xu)/2
% Calculate error estimate (err)
% Evaluate the function at the midpoint f(xr)
% If the sign of f(xr) is equal to the sign of f(xl)
% if f(xr)*f(xu)>0
% then xr becomes the new xl.
% else xr becomes the new xu.
% end while loop
%
% If err <= errtol
% then solution found, output result
% else display ‘root not found within tolerance

W = input(‘nWhat is the weight of the object attached to the ring in pounds (lb)? ‘);
xl = input(‘nWhat is the lower initial bracket estimate in inches? ‘); %always 0
xu = input(‘nWhat is the upper initial bracket estimate in inches? ‘); %always 10
a = 8.0;
b = 5.0 ;
lo = sqrt(a^2+b^2);
k = 16.0;
errtol = 0.005;
xr = (xl+xu)/2;
maxiter = 10;
iterations = 0;
f = @(x) (2*k/(sqrt(a^2+(b+x)^2)))*((sqrt(a^2+(b+x)^2))-lo)*(b+x);
err = abs((xu-xl)/xu);
xrold = abs((xu-xl)/xu);
while (iterations<maxiter) %|| (err>errtol)
iterations=iterations+1;
xr=(xl+xu)/2;
err = abs((xr-xrold)/xr)*100;
if f(xr)*f(xl)>0
xu = xr;
else
xl = xr;
end
xrold = xr;
endOne of the main problems is that there will never be a sign change on the interval so it’ll always execute the first part of the if statement. I commented out the err>errtol part for testing. I don’t know what i’m doing wrong for calculating using the bisection method. I have to use while loops.

% A scale is made with two springs, and when an object is attached to the
% two springs, the springs stretch and the ring at the end of the two
% springs is displaced downwards a distance x.
%
% The relationship between the weight of the object and the distance x is:
% W=(2k/l)(l-lo)(b+x)
% The initial spring length
% lo = sqrt(a^2+b^2)
% The stretched spring length
% l = sqrt(a^2+(b+x)^2)
% for the given scale a=8.0 in. b=5.0 m. and the spring constant k=16.0 lb/in.
% b=5.0 m.=196.85 in.
% Trying to find the deflection x.
%
% Have the user input lower and upper values of the starting
% interval (xl, xu), as well as the weight of the object
% Initialize the error tolerance (errtol)
% and the maximum number of iterations (maxiter)
%
% Check the interval to see if there’s a sign change
%
% while (iterations < maxiter) and (err > errtol)
% Calculate midpoint of the interval xr=(xl+xu)/2
% Calculate error estimate (err)
% Evaluate the function at the midpoint f(xr)
% If the sign of f(xr) is equal to the sign of f(xl)
% if f(xr)*f(xu)>0
% then xr becomes the new xl.
% else xr becomes the new xu.
% end while loop
%
% If err <= errtol
% then solution found, output result
% else display ‘root not found within tolerance

W = input(‘nWhat is the weight of the object attached to the ring in pounds (lb)? ‘);
xl = input(‘nWhat is the lower initial bracket estimate in inches? ‘); %always 0
xu = input(‘nWhat is the upper initial bracket estimate in inches? ‘); %always 10
a = 8.0;
b = 5.0 ;
lo = sqrt(a^2+b^2);
k = 16.0;
errtol = 0.005;
xr = (xl+xu)/2;
maxiter = 10;
iterations = 0;
f = @(x) (2*k/(sqrt(a^2+(b+x)^2)))*((sqrt(a^2+(b+x)^2))-lo)*(b+x);
err = abs((xu-xl)/xu);
xrold = abs((xu-xl)/xu);
while (iterations<maxiter) %|| (err>errtol)
iterations=iterations+1;
xr=(xl+xu)/2;
err = abs((xr-xrold)/xr)*100;
if f(xr)*f(xl)>0
xu = xr;
else
xl = xr;
end
xrold = xr;
end One of the main problems is that there will never be a sign change on the interval so it’ll always execute the first part of the if statement. I commented out the err>errtol part for testing. I don’t know what i’m doing wrong for calculating using the bisection method. I have to use while loops.

% A scale is made with two springs, and when an object is attached to the
% two springs, the springs stretch and the ring at the end of the two
% springs is displaced downwards a distance x.
%
% The relationship between the weight of the object and the distance x is:
% W=(2k/l)(l-lo)(b+x)
% The initial spring length
% lo = sqrt(a^2+b^2)
% The stretched spring length
% l = sqrt(a^2+(b+x)^2)
% for the given scale a=8.0 in. b=5.0 m. and the spring constant k=16.0 lb/in.
% b=5.0 m.=196.85 in.
% Trying to find the deflection x.
%
% Have the user input lower and upper values of the starting
% interval (xl, xu), as well as the weight of the object
% Initialize the error tolerance (errtol)
% and the maximum number of iterations (maxiter)
%
% Check the interval to see if there’s a sign change
%
% while (iterations < maxiter) and (err > errtol)
% Calculate midpoint of the interval xr=(xl+xu)/2
% Calculate error estimate (err)
% Evaluate the function at the midpoint f(xr)
% If the sign of f(xr) is equal to the sign of f(xl)
% if f(xr)*f(xu)>0
% then xr becomes the new xl.
% else xr becomes the new xu.
% end while loop
%
% If err <= errtol
% then solution found, output result
% else display ‘root not found within tolerance

W = input(‘nWhat is the weight of the object attached to the ring in pounds (lb)? ‘);
xl = input(‘nWhat is the lower initial bracket estimate in inches? ‘); %always 0
xu = input(‘nWhat is the upper initial bracket estimate in inches? ‘); %always 10
a = 8.0;
b = 5.0 ;
lo = sqrt(a^2+b^2);
k = 16.0;
errtol = 0.005;
xr = (xl+xu)/2;
maxiter = 10;
iterations = 0;
f = @(x) (2*k/(sqrt(a^2+(b+x)^2)))*((sqrt(a^2+(b+x)^2))-lo)*(b+x);
err = abs((xu-xl)/xu);
xrold = abs((xu-xl)/xu);
while (iterations<maxiter) %|| (err>errtol)
iterations=iterations+1;
xr=(xl+xu)/2;
err = abs((xr-xrold)/xr)*100;
if f(xr)*f(xl)>0
xu = xr;
else
xl = xr;
end
xrold = xr;
end bisection, while loop MATLAB Answers — New Questions

​

I am attempting to use AI to generate an initial design for a GUI. I would like to copy the code that is generated and input it directly into the Code View of the App Designer. I would then like to make further adjustments using some of the App Designer tools (i.e. Design View). However, I cannot copy the code directly over, as App Designer doesn’t let the user edit portions of the code. Is there a way to edit the grayed-out code? Or a way to easily integrate the generated code into an .mlapp file?I am attempting to use AI to generate an initial design for a GUI. I would like to copy the code that is generated and input it directly into the Code View of the App Designer. I would then like to make further adjustments using some of the App Designer tools (i.e. Design View). However, I cannot copy the code directly over, as App Designer doesn’t let the user edit portions of the code. Is there a way to edit the grayed-out code? Or a way to easily integrate the generated code into an .mlapp file? I am attempting to use AI to generate an initial design for a GUI. I would like to copy the code that is generated and input it directly into the Code View of the App Designer. I would then like to make further adjustments using some of the App Designer tools (i.e. Design View). However, I cannot copy the code directly over, as App Designer doesn’t let the user edit portions of the code. Is there a way to edit the grayed-out code? Or a way to easily integrate the generated code into an .mlapp file? appdesigner, app designer MATLAB Answers — New Questions

​

Hi,
I`m looking for function or source code for Triangular-weighted moving average filter to apply it and make my data processing.
High-frequency noise shall be removed from the measured signals using a triangular-weighted moving average with a smoothing width of 100 ms.

can someone share the experience ?Hi,
I`m looking for function or source code for Triangular-weighted moving average filter to apply it and make my data processing.
High-frequency noise shall be removed from the measured signals using a triangular-weighted moving average with a smoothing width of 100 ms.

can someone share the experience ? Hi,
I`m looking for function or source code for Triangular-weighted moving average filter to apply it and make my data processing.
High-frequency noise shall be removed from the measured signals using a triangular-weighted moving average with a smoothing width of 100 ms.

can someone share the experience ? filter, data processing MATLAB Answers — New Questions

​

I have code for a genetic algorithm as follows (which I got from a matlab example):
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon, [1,2])
the [1,2] parameter corresponds to IntCon (see https://www.mathworks.com/help/gads/ga.html#d122e40769), and it is restricting x(1) and x(2) to integer values (which I don’t want). I want to get rid of this but when I delete it and run:
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon)
I get this error:
Error using constrValidate (line 59)
Constraint function must return real value.
Error in gacommon (line 125)
[LinearConstr, Iterate,nineqcstr,neqcstr,ncstr] = constrValidate(NonconFcn, …
Error in ga (line 364)
NonconFcn,options,Iterate,type] = gacommon(nvars,fun,Aineq,bineq,Aeq,beq,lb,ub, …
Error in Model_Building_2 (line 101)
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon)
can anyone think of any reason why this happens? the code runs well with any variable in IntCon (ie it can be [3], [4], [2,3] or any other combination) as long as there is at least one. using empty brackets [] returns the same error as above.
thanks in advance!I have code for a genetic algorithm as follows (which I got from a matlab example):
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon, [1,2])
the [1,2] parameter corresponds to IntCon (see https://www.mathworks.com/help/gads/ga.html#d122e40769), and it is restricting x(1) and x(2) to integer values (which I don’t want). I want to get rid of this but when I delete it and run:
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon)
I get this error:
Error using constrValidate (line 59)
Constraint function must return real value.
Error in gacommon (line 125)
[LinearConstr, Iterate,nineqcstr,neqcstr,ncstr] = constrValidate(NonconFcn, …
Error in ga (line 364)
NonconFcn,options,Iterate,type] = gacommon(nvars,fun,Aineq,bineq,Aeq,beq,lb,ub, …
Error in Model_Building_2 (line 101)
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon)
can anyone think of any reason why this happens? the code runs well with any variable in IntCon (ie it can be [3], [4], [2,3] or any other combination) as long as there is at least one. using empty brackets [] returns the same error as above.
thanks in advance! I have code for a genetic algorithm as follows (which I got from a matlab example):
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon, [1,2])
the [1,2] parameter corresponds to IntCon (see https://www.mathworks.com/help/gads/ga.html#d122e40769), and it is restricting x(1) and x(2) to integer values (which I don’t want). I want to get rid of this but when I delete it and run:
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon)
I get this error:
Error using constrValidate (line 59)
Constraint function must return real value.
Error in gacommon (line 125)
[LinearConstr, Iterate,nineqcstr,neqcstr,ncstr] = constrValidate(NonconFcn, …
Error in ga (line 364)
NonconFcn,options,Iterate,type] = gacommon(nvars,fun,Aineq,bineq,Aeq,beq,lb,ub, …
Error in Model_Building_2 (line 101)
[x,fval] = ga(@objfun,4,A,b,Aeq,beq,lb,ub,@nonlcon)
can anyone think of any reason why this happens? the code runs well with any variable in IntCon (ie it can be [3], [4], [2,3] or any other combination) as long as there is at least one. using empty brackets [] returns the same error as above.
thanks in advance! genetic algorithm, ga, optimization, global optimization, optimisation, intcon MATLAB Answers — New Questions

​

Hello guys!
I am looking for a way to name a variable with a string name that will be changing according to the T and V values
My code is the following:
——————————-
T=15; % input variable T
V=1; % input variable V
load(‘FRF_T15_V1.mat’)
load(‘FRF_T15_V2.mat’)
load(‘FRF_T15_V3.mat’)
formatSpec = ‘FRF_T%d_V%d’;
filename = sprintf(formatSpec,T,V);
x=eval(filename);
XP=(x{3,3});
save (‘XP,’XP’)
—————————–
I would like for variable XP to be assigned according to the input values of T and V, e.g.,
FRF_T15_V1_XP=(x{3,3});
And then save it as
save (‘ FRF_T15_V1_XP,’ FRF_T15_V1_XP ‘)

Thanks in advance for your help!
Kind regards,
HugoHello guys!
I am looking for a way to name a variable with a string name that will be changing according to the T and V values
My code is the following:
——————————-
T=15; % input variable T
V=1; % input variable V
load(‘FRF_T15_V1.mat’)
load(‘FRF_T15_V2.mat’)
load(‘FRF_T15_V3.mat’)
formatSpec = ‘FRF_T%d_V%d’;
filename = sprintf(formatSpec,T,V);
x=eval(filename);
XP=(x{3,3});
save (‘XP,’XP’)
—————————–
I would like for variable XP to be assigned according to the input values of T and V, e.g.,
FRF_T15_V1_XP=(x{3,3});
And then save it as
save (‘ FRF_T15_V1_XP,’ FRF_T15_V1_XP ‘)

Thanks in advance for your help!
Kind regards,
Hugo Hello guys!
I am looking for a way to name a variable with a string name that will be changing according to the T and V values
My code is the following:
——————————-
T=15; % input variable T
V=1; % input variable V
load(‘FRF_T15_V1.mat’)
load(‘FRF_T15_V2.mat’)
load(‘FRF_T15_V3.mat’)
formatSpec = ‘FRF_T%d_V%d’;
filename = sprintf(formatSpec,T,V);
x=eval(filename);
XP=(x{3,3});
save (‘XP,’XP’)
—————————–
I would like for variable XP to be assigned according to the input values of T and V, e.g.,
FRF_T15_V1_XP=(x{3,3});
And then save it as
save (‘ FRF_T15_V1_XP,’ FRF_T15_V1_XP ‘)

Thanks in advance for your help!
Kind regards,
Hugo string, variable MATLAB Answers — New Questions

​

License checkout failed.
License Manager Error -9
Your username does not match the username in the license file.
To run on this computer, you must run the Activation client to reactivate your license.

Troubleshoot this issue by visiting:
https://www.mathworks.com/support/lme/R2020a/9

Diagnostic Information:
Feature: MATLAB
License path: /home/shishkina/.matlab/R2020a_licenses:/usr/local/MATLAB/R2020a/licenses/license.dat:/usr/local/MAT
LAB/R2020a/licenses/license_shishkina-Inspiron-5379_1096937_R2020a.lic
Licensing error: -9,57.License checkout failed.
License Manager Error -9
Your username does not match the username in the license file.
To run on this computer, you must run the Activation client to reactivate your license.

Troubleshoot this issue by visiting:
https://www.mathworks.com/support/lme/R2020a/9

Diagnostic Information:
Feature: MATLAB
License path: /home/shishkina/.matlab/R2020a_licenses:/usr/local/MATLAB/R2020a/licenses/license.dat:/usr/local/MAT
LAB/R2020a/licenses/license_shishkina-Inspiron-5379_1096937_R2020a.lic
Licensing error: -9,57. License checkout failed.
License Manager Error -9
Your username does not match the username in the license file.
To run on this computer, you must run the Activation client to reactivate your license.

Troubleshoot this issue by visiting:
https://www.mathworks.com/support/lme/R2020a/9

Diagnostic Information:
Feature: MATLAB
License path: /home/shishkina/.matlab/R2020a_licenses:/usr/local/MATLAB/R2020a/licenses/license.dat:/usr/local/MAT
LAB/R2020a/licenses/license_shishkina-Inspiron-5379_1096937_R2020a.lic
Licensing error: -9,57. matlab runnign MATLAB Answers — New Questions

​

I just downloaded MATLAB 2025a and no variables show up in the Workspace, even though they are actually saved in memory. For example, if I just open MATLAB and type x = 1, nothing happens. But when I type x, then MATLAB returns the value stored as 1. Nothing appears in the workspace, no named variables, variable types, the size or class, etc. If I right click on the Workspace and try to make a new variable, nothing happens. The "Save Workspace" and "Clear Workspace" are greyed out. Clicking "Refresh" also doesn’t do anything. See the attached screenshot.
I have tried digging into the MATLAB preferences to see what I am missing, but can’t find anything.
Note that I am running a 2024 MacBook Pro Sequoia 15.5.I just downloaded MATLAB 2025a and no variables show up in the Workspace, even though they are actually saved in memory. For example, if I just open MATLAB and type x = 1, nothing happens. But when I type x, then MATLAB returns the value stored as 1. Nothing appears in the workspace, no named variables, variable types, the size or class, etc. If I right click on the Workspace and try to make a new variable, nothing happens. The "Save Workspace" and "Clear Workspace" are greyed out. Clicking "Refresh" also doesn’t do anything. See the attached screenshot.
I have tried digging into the MATLAB preferences to see what I am missing, but can’t find anything.
Note that I am running a 2024 MacBook Pro Sequoia 15.5. I just downloaded MATLAB 2025a and no variables show up in the Workspace, even though they are actually saved in memory. For example, if I just open MATLAB and type x = 1, nothing happens. But when I type x, then MATLAB returns the value stored as 1. Nothing appears in the workspace, no named variables, variable types, the size or class, etc. If I right click on the Workspace and try to make a new variable, nothing happens. The "Save Workspace" and "Clear Workspace" are greyed out. Clicking "Refresh" also doesn’t do anything. See the attached screenshot.
I have tried digging into the MATLAB preferences to see what I am missing, but can’t find anything.
Note that I am running a 2024 MacBook Pro Sequoia 15.5. workspace, variable, variables, mac MATLAB Answers — New Questions

​

Hello,

I’m struggeling a litle bit with a thermal model based on the two and thre dimensional heat equation.
My aim is to estimate the HCT with the aid of "experimental data" and a grey-box model.
The thermal BC’s are quite simple, and illustrated below.

I generate dummy data via this matalb script:
% generate_dummy_tempdata_and_model_fixed.m
% Generate Dummy-data and prepare (2D/3D)
clc, close all, clear all
%% === Parameter ===
modellTyp = "3D"; % "2D" or "3D"
nx = 4; ny = 4; nz = 4; % Node count
dx = 0.02;dy = 0.03; dz = 0.04; % Node distance [m]
times = 0:1:30; % Time range [s]
T0 = 300; % Initial temperature [K]
dt = times(2) – times(1); % Time step [s]
%% === 1) Generate dummy-data and save as CSV ===
data = [];
switch modellTyp
case "2D"
for iy = 0:ny-1
for ix = 0:nx-1
x = ix * dx;
y = iy * dy;
Tcurve = T0 + 10 * sin(2*pi*times/60 + ix*0.3 + iy*0.5);
data = [data; x, y, Tcurve];
end
end
% Header ass string array
header = ["x","y", "t" + string(times)];
csvFile = ‘example_tempdata2D.csv’;
case "3D"
for iz = 0:nz-1
for iy = 0:ny-1
for ix = 0:nx-1
x = ix * dx;
y = iy * dy;
z = iz * dz;
Tcurve = T0 + 10 * sin(2*pi*times/60 + ix*0.2 + iy*0.3 + iz*0.4);
data = [data; x, y, z, Tcurve];
end
end
end
% Header as string array
header = ["x","y","z", "t" + string(times)];
csvFile = ‘example_tempdata3D.csv’;
end
% Bulid table and save
Ttbl_out = array2table(data, ‘VariableNames’, header);
writetable(Ttbl_out, csvFile);
disp([‘Dummy-data saved: ‘, csvFile]);
The core of the simulation is the transformation of the 2d and 3d diffusion equation into an ode.
I do it with this script:
function [A,B,C,D] = fHeat2D3D(theta, Ts)
% fHeat2D3D Continuous-time grey-box state-space for 2D/3D heat diffusion
% Signature for idgrey: fHeat2D3D(theta, Ts)
% Inputs:
% theta = [Lambda, rho, cp, hBot1, …, hBotN]
% Ts = sample time (ignored in continuous-time model)
% Globals: nx, ny, nz, dx, dy, dz, modellTyp, h_top

global nx ny nz dx dy dz modellTyp h_top

% Extract physical parameters
Lambda = theta(1);
rho = theta(2);
cp = theta(3);

% Determine expected number of bottom convection coefficients
if strcmp(modellTyp,’2D’)
expectedNbot = nx;
else
expectedNbot = nx * nz;
end
% Validate theta length
if length(theta) ~= 3 + expectedNbot
error(‘Theta must have length 3+%d (got %d)’, expectedNbot, length(theta));
end
% Extract bottom convection coefficients
hBot = theta(4:end);

% Number of states
if strcmp(modellTyp,’2D’)
N = nx * ny;
else
N = nx * ny * nz;
end

% Build A matrix (2D/3D Laplacian)
A = zeros(N);
dists = [dx, dx, dy, dy];
for idx = 1:N
tmp = idx – 1;
ix = mod(tmp, nx) + 1;
iy = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
iz = 1;
else
iz = floor(tmp / (nx * ny)) + 1;
end
diagSum = 0;
nbr = [-1,0; 1,0; 0,-1; 0,1];
for k = 1:4
x2 = ix + nbr(k,1);
y2 = iy + nbr(k,2);
if x2>=1 && x2<=nx && y2>=1 && y2<=ny
z2 = iz;
idx2 = x2 + (y2-1)*nx + (z2-1)*nx*ny;
K = Lambda / (rho * cp * dists(k)^2);
A(idx, idx2) = K;
diagSum = diagSum + K;
end
end
A(idx, idx) = -diagSum;
end

% Build B matrix
% Identify side (Dirichlet) nodes
side = false(N,1);
for idx = 1:N
tmp = idx – 1;
x = mod(tmp, nx) + 1;
y = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
side(idx) = (x == 1) || (x == nx);
else
z = floor(tmp / (nx * ny)) + 1;
side(idx) = (x==1)||(x==nx)||(y==1)||(y==ny);
end
end
Nside = sum(side);
B = zeros(N, Nside + 1 + expectedNbot);

% Side BC inputs
sidx = find(side);
for i = 1:Nside
B(sidx(i), i) = 1;
end
% Top convection BC
if strcmp(modellTyp,’2D’)
topIdx = find(~side & floor((0:N-1)/nx)==0);
else
topIdx = find(~side & floor((0:N-1)/(nx*ny))==nz-1);
end
for i = 1:numel(topIdx)
B(topIdx(i), Nside+1) = h_top;
end
% Bottom convection BC
if strcmp(modellTyp,’2D’)
botIdx = find(~side & floor((0:N-1)/nx)==ny-1);
else
botIdx = find(~side & floor((0:N-1)/(nx*ny))==0);
end
for i = 1:numel(botIdx)
B(botIdx(i), Nside+1+i) = hBot(i);
end

% Outputs and feedthrough
C = eye(N);
D = zeros(N, size(B,2));
end
Finally the ode ("function [A,B,C,D] = fHeat2D3D(theta, Ts)") is used as continuous-time state-space model to estimate the system parameter HTC(bottom), heat conductivity, density and specific heat capacity via idgrey and greyest.
% greybox_heat_diffusion.m
% Parametric continuous-time grey-box model for 2D/3D heat conduction

clear; clc; close all;
global nx ny nz dx dy dz modellTyp h_top t_env_top

%% === User setup ===
modellTyp = "2D"; % "2D" or "3D"
nx = 3; ny = 3; nz = 3; % Count of nodes in x, y, z direction(ignore nz for 2D)
dx = 0.02; dy = 0.03; dz = 0.04; % Distance between nodes [m]

dt = 1; % Time step [s]
times = 0:dt:60; % Time range [s]
csv2D = ‘example_tempdata2D.csv’;
csv3D = ‘example_tempdata3D.csv’;

% Fixed values / Top-HTC
t_env_top = 293; % Ambient free stream temperature [K]
h_top = 10; % HTC at the top edge [W/(m^2*K)]

%% === Initial guess of the model parameter ===
theta0.Lambda = 50; % Heat conduction [W/(m*K)]
theta0.rho = 7800;% Density [kg/m^3]
theta0.cp = 460; % Heat capacity [J/(kg*K)]
if modellTyp=="2D"
h_bot0 = 20*ones(nx,1);
else
h_bot0 = 20*ones(nx*nz,1);
end

%% === Read experimental data ===
if modellTyp=="2D"
Tdata = readtable(csv2D);
Texp = Tdata{:,3:end};
Nstates = nx*ny;
else
Tdata = readtable(csv3D);
Texp = Tdata{:,4:end};
Nstates = nx*ny*nz;
end
Nmeas = size(Texp,2);

%% === Calculate side indices ===
sideNodes = false(Nstates,1);
for idx=1:Nstates
tmp=idx-1; ix=mod(tmp,nx)+1; iy=floor(tmp/nx)+1;
if strcmp(modellTyp,"2D")
sideNodes(idx) = ix==1 || ix==nx;
else
iz=floor(tmp/(nx*ny))+1;
sideNodes(idx) = ix==1||ix==nx||iy==1||iy==ny;
end
end
sideIdx = find(sideNodes);

%% === Build input-matrix u ===
T_sideBC = Texp(sideIdx,:); % Side nodes – BC (experimental value)
T_topBC = t_env_top * ones(1,Nmeas);
u = [T_sideBC’ T_topBC’ zeros(Nmeas,length(h_bot0))];

%% === idgrey Setup ===
param0 = [theta0.Lambda theta0.rho theta0.cp h_bot0′];
order = [Nstates Nstates Nstates 0];

[A,B,C,D] = fHeat2D3D(param0, dt);

sysi = idgrey(‘fHeat2D3D’, param0, ‘c’, order, …
‘InputName’,[repmat({‘T_sideBC’},1,length(sideIdx)) {‘T_top’} repmat({‘T_bot’},1,length(h_bot0))], …
‘OutputName’, repmat({‘Tnode’},1,Nstates));

% Release parameters (all)
sysi.Structure.Parameters.Free = true;

%% === Parameter-estimation ===
data_id = iddata(Texp’, u, dt);
opt = greyestOptions(‘Display’,’on’,’InitialCondition’,’zero’);
sys_est = greyest(data_id, sysi, opt);

%% === Extract estimated values ===
th = sys_est.Structure.Parameters;
Lambda_est = th(1).Value; rho_est = th(2).Value; cp_est = th(3).Value;
hBot_est = [th(4:end).Value]’;

%% === Plots ===
Tsim = sim(sys_est, data_id);

% Plot h_bot
figure;
if strcmp(modellTyp,"2D")
plot(unique(Tdata.x), hBot_est, ‘o-‘, ‘LineWidth’, 2);
xlabel(‘x [m]’); ylabel(‘h_{bot} [W/m^2K]’);
title(‘HTC at the bottom edge (2D)’); grid on;
else
% 3D-Surface plot of h_bot at bottom surface
[Xq, Zq] = meshgrid(unique(Tdata.x), unique(Tdata.z));
hq = griddata(Tdata.x, Tdata.z, hBot_est, Xq, Zq, ‘natural’);

surf(Xq, Zq, hq);
xlabel(‘x [m]’); ylabel(‘z [m]’); zlabel(‘h_{bot} [W/m^2K]’);
title(‘HTC at bottom surface (3D)’); colorbar;
shading interp; view(30, 30);
end

% Comparison temperature-simulation vs. temperature-measurement
figure;
Nrow = ceil(sqrt(Nstates));
for i = 1:Nstates
subplot(Nrow, Nrow, i);
plot(times, Texp(i,:), ‘-‘, ‘LineWidth’, 1.5); hold on;
plot(times, Tsim.y(i,:), ‘:’, ‘LineWidth’, 1.5);
title(sprintf(‘Nodes %d’, i));
xlabel(‘Time [s]’); ylabel(‘T [°C]’);
legend(‘Experiment’, ‘Simulation’);
grid on;
end

% 3D-Point: final temperature distribution
if strcmp(modellTyp,"3D")
figure;
scatter3(Tdata.x, Tdata.y, Tdata.z, 50, Tsim.y(:,end), ‘filled’);
xlabel(‘x’); ylabel(‘y’); zlabel(‘z’);
title(‘Simulated temperature distribution at t=tend’);
colorbar; view(30,30);
end

%% End of the script
The call of the script "greybox_heat_diffusion.m" is not working properly and the function "fHeat2D3D" is not called correct.
For the averaging of the corne nodes (2D) respectively the corner & edge nodes (3D). I made this script:
function [A,B,C,D] = fHeat2D3D(theta, Ts)
% fHeat2D3D Continuous-time grey-box state-space for 2D/3D heat diffusion
% Signature for idgrey: fHeat2D3D(theta, Ts)
% Inputs:
% theta = [Lambda, rho, cp, hBot1, …, hBotN]
% Ts = sample time (ignored in continuous-time model)
% Globals: nx, ny, nz, dx, dy, dz, modellTyp, h_top

global nx ny nz dx dy dz modellTyp h_top

% Extract physical parameters
Lambda = theta(1);
rho = theta(2);
cp = theta(3);

% Determine expected number of bottom convection coefficients
if strcmp(modellTyp,’2D’)
expectedNbot = nx;
else
expectedNbot = nx * nz;
end
% Validate theta length
if length(theta) ~= 3 + expectedNbot
error(‘Theta must have length 3+%d (got %d)’, expectedNbot, length(theta));
end
% Extract bottom convection coefficients
hBot = theta(4:end);

% Number of states
if strcmp(modellTyp,’2D’)
N = nx * ny;
else
N = nx * ny * nz;
end

% Build A matrix (2D/3D Laplacian)
A = zeros(N);
dists = [dx, dx, dy, dy];
for idx = 1:N
tmp = idx – 1;
ix = mod(tmp, nx) + 1;
iy = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
iz = 1;
else
iz = floor(tmp / (nx * ny)) + 1;
end
diagSum = 0;
nbr = [-1,0; 1,0; 0,-1; 0,1];
for k = 1:4
x2 = ix + nbr(k,1);
y2 = iy + nbr(k,2);
if x2>=1 && x2<=nx && y2>=1 && y2<=ny
z2 = iz;
idx2 = x2 + (y2-1)*nx + (z2-1)*nx*ny;
K = Lambda / (rho * cp * dists(k)^2);
A(idx, idx2) = K;
diagSum = diagSum + K;
end
end
A(idx, idx) = -diagSum;
end

% Build B matrix
% Identify side (Dirichlet) nodes
side = false(N,1);
for idx = 1:N
tmp = idx – 1;
x = mod(tmp, nx) + 1;
y = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
side(idx) = (x == 1) || (x == nx);
else
z = floor(tmp / (nx * ny)) + 1;
side(idx) = (x==1)||(x==nx)||(y==1)||(y==ny);
end
end
Nside = sum(side);
B = zeros(N, Nside + 1 + expectedNbot);

% Side BC inputs
sidx = find(side);
for i = 1:Nside
B(sidx(i), i) = 1;
end
% Top convection BC
if strcmp(modellTyp,’2D’)
topIdx = find(~side & floor((0:N-1)/nx)==0);
else
topIdx = find(~side & floor((0:N-1)/(nx*ny))==nz-1);
end
for i = 1:numel(topIdx)
B(topIdx(i), Nside+1) = h_top;
end
% Bottom convection BC
if strcmp(modellTyp,’2D’)
botIdx = find(~side & floor((0:N-1)/nx)==ny-1);
else
botIdx = find(~side & floor((0:N-1)/(nx*ny))==0);
end
for i = 1:numel(botIdx)
B(botIdx(i), Nside+1+i) = hBot(i);
end

% Outputs and feedthrough
C = eye(N);
% === Corner and edge nodes averaging ===
for idx = 1:N
bcCount = nnz(B(idx,:)); % Count of BC-Input
if bcCount > 1
% Balanced averaging: scale A- and B-Line
A(idx,:) = A(idx,:) / bcCount;
B(idx,:) = B(idx,:) / bcCount;
end
end

D = zeros(N, size(B,2));(N, size(B,2));
end

I’m not sure if this is the rigth approach.

Maybe someone has a hint how can I get rid of the errors.
With best regards
SteffenHello,

I’m struggeling a litle bit with a thermal model based on the two and thre dimensional heat equation.
My aim is to estimate the HCT with the aid of "experimental data" and a grey-box model.
The thermal BC’s are quite simple, and illustrated below.

I generate dummy data via this matalb script:
% generate_dummy_tempdata_and_model_fixed.m
% Generate Dummy-data and prepare (2D/3D)
clc, close all, clear all
%% === Parameter ===
modellTyp = "3D"; % "2D" or "3D"
nx = 4; ny = 4; nz = 4; % Node count
dx = 0.02;dy = 0.03; dz = 0.04; % Node distance [m]
times = 0:1:30; % Time range [s]
T0 = 300; % Initial temperature [K]
dt = times(2) – times(1); % Time step [s]
%% === 1) Generate dummy-data and save as CSV ===
data = [];
switch modellTyp
case "2D"
for iy = 0:ny-1
for ix = 0:nx-1
x = ix * dx;
y = iy * dy;
Tcurve = T0 + 10 * sin(2*pi*times/60 + ix*0.3 + iy*0.5);
data = [data; x, y, Tcurve];
end
end
% Header ass string array
header = ["x","y", "t" + string(times)];
csvFile = ‘example_tempdata2D.csv’;
case "3D"
for iz = 0:nz-1
for iy = 0:ny-1
for ix = 0:nx-1
x = ix * dx;
y = iy * dy;
z = iz * dz;
Tcurve = T0 + 10 * sin(2*pi*times/60 + ix*0.2 + iy*0.3 + iz*0.4);
data = [data; x, y, z, Tcurve];
end
end
end
% Header as string array
header = ["x","y","z", "t" + string(times)];
csvFile = ‘example_tempdata3D.csv’;
end
% Bulid table and save
Ttbl_out = array2table(data, ‘VariableNames’, header);
writetable(Ttbl_out, csvFile);
disp([‘Dummy-data saved: ‘, csvFile]);
The core of the simulation is the transformation of the 2d and 3d diffusion equation into an ode.
I do it with this script:
function [A,B,C,D] = fHeat2D3D(theta, Ts)
% fHeat2D3D Continuous-time grey-box state-space for 2D/3D heat diffusion
% Signature for idgrey: fHeat2D3D(theta, Ts)
% Inputs:
% theta = [Lambda, rho, cp, hBot1, …, hBotN]
% Ts = sample time (ignored in continuous-time model)
% Globals: nx, ny, nz, dx, dy, dz, modellTyp, h_top

global nx ny nz dx dy dz modellTyp h_top

% Extract physical parameters
Lambda = theta(1);
rho = theta(2);
cp = theta(3);

% Determine expected number of bottom convection coefficients
if strcmp(modellTyp,’2D’)
expectedNbot = nx;
else
expectedNbot = nx * nz;
end
% Validate theta length
if length(theta) ~= 3 + expectedNbot
error(‘Theta must have length 3+%d (got %d)’, expectedNbot, length(theta));
end
% Extract bottom convection coefficients
hBot = theta(4:end);

% Number of states
if strcmp(modellTyp,’2D’)
N = nx * ny;
else
N = nx * ny * nz;
end

% Build A matrix (2D/3D Laplacian)
A = zeros(N);
dists = [dx, dx, dy, dy];
for idx = 1:N
tmp = idx – 1;
ix = mod(tmp, nx) + 1;
iy = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
iz = 1;
else
iz = floor(tmp / (nx * ny)) + 1;
end
diagSum = 0;
nbr = [-1,0; 1,0; 0,-1; 0,1];
for k = 1:4
x2 = ix + nbr(k,1);
y2 = iy + nbr(k,2);
if x2>=1 && x2<=nx && y2>=1 && y2<=ny
z2 = iz;
idx2 = x2 + (y2-1)*nx + (z2-1)*nx*ny;
K = Lambda / (rho * cp * dists(k)^2);
A(idx, idx2) = K;
diagSum = diagSum + K;
end
end
A(idx, idx) = -diagSum;
end

% Build B matrix
% Identify side (Dirichlet) nodes
side = false(N,1);
for idx = 1:N
tmp = idx – 1;
x = mod(tmp, nx) + 1;
y = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
side(idx) = (x == 1) || (x == nx);
else
z = floor(tmp / (nx * ny)) + 1;
side(idx) = (x==1)||(x==nx)||(y==1)||(y==ny);
end
end
Nside = sum(side);
B = zeros(N, Nside + 1 + expectedNbot);

% Side BC inputs
sidx = find(side);
for i = 1:Nside
B(sidx(i), i) = 1;
end
% Top convection BC
if strcmp(modellTyp,’2D’)
topIdx = find(~side & floor((0:N-1)/nx)==0);
else
topIdx = find(~side & floor((0:N-1)/(nx*ny))==nz-1);
end
for i = 1:numel(topIdx)
B(topIdx(i), Nside+1) = h_top;
end
% Bottom convection BC
if strcmp(modellTyp,’2D’)
botIdx = find(~side & floor((0:N-1)/nx)==ny-1);
else
botIdx = find(~side & floor((0:N-1)/(nx*ny))==0);
end
for i = 1:numel(botIdx)
B(botIdx(i), Nside+1+i) = hBot(i);
end

% Outputs and feedthrough
C = eye(N);
D = zeros(N, size(B,2));
end
Finally the ode ("function [A,B,C,D] = fHeat2D3D(theta, Ts)") is used as continuous-time state-space model to estimate the system parameter HTC(bottom), heat conductivity, density and specific heat capacity via idgrey and greyest.
% greybox_heat_diffusion.m
% Parametric continuous-time grey-box model for 2D/3D heat conduction

clear; clc; close all;
global nx ny nz dx dy dz modellTyp h_top t_env_top

%% === User setup ===
modellTyp = "2D"; % "2D" or "3D"
nx = 3; ny = 3; nz = 3; % Count of nodes in x, y, z direction(ignore nz for 2D)
dx = 0.02; dy = 0.03; dz = 0.04; % Distance between nodes [m]

dt = 1; % Time step [s]
times = 0:dt:60; % Time range [s]
csv2D = ‘example_tempdata2D.csv’;
csv3D = ‘example_tempdata3D.csv’;

% Fixed values / Top-HTC
t_env_top = 293; % Ambient free stream temperature [K]
h_top = 10; % HTC at the top edge [W/(m^2*K)]

%% === Initial guess of the model parameter ===
theta0.Lambda = 50; % Heat conduction [W/(m*K)]
theta0.rho = 7800;% Density [kg/m^3]
theta0.cp = 460; % Heat capacity [J/(kg*K)]
if modellTyp=="2D"
h_bot0 = 20*ones(nx,1);
else
h_bot0 = 20*ones(nx*nz,1);
end

%% === Read experimental data ===
if modellTyp=="2D"
Tdata = readtable(csv2D);
Texp = Tdata{:,3:end};
Nstates = nx*ny;
else
Tdata = readtable(csv3D);
Texp = Tdata{:,4:end};
Nstates = nx*ny*nz;
end
Nmeas = size(Texp,2);

%% === Calculate side indices ===
sideNodes = false(Nstates,1);
for idx=1:Nstates
tmp=idx-1; ix=mod(tmp,nx)+1; iy=floor(tmp/nx)+1;
if strcmp(modellTyp,"2D")
sideNodes(idx) = ix==1 || ix==nx;
else
iz=floor(tmp/(nx*ny))+1;
sideNodes(idx) = ix==1||ix==nx||iy==1||iy==ny;
end
end
sideIdx = find(sideNodes);

%% === Build input-matrix u ===
T_sideBC = Texp(sideIdx,:); % Side nodes – BC (experimental value)
T_topBC = t_env_top * ones(1,Nmeas);
u = [T_sideBC’ T_topBC’ zeros(Nmeas,length(h_bot0))];

%% === idgrey Setup ===
param0 = [theta0.Lambda theta0.rho theta0.cp h_bot0′];
order = [Nstates Nstates Nstates 0];

[A,B,C,D] = fHeat2D3D(param0, dt);

sysi = idgrey(‘fHeat2D3D’, param0, ‘c’, order, …
‘InputName’,[repmat({‘T_sideBC’},1,length(sideIdx)) {‘T_top’} repmat({‘T_bot’},1,length(h_bot0))], …
‘OutputName’, repmat({‘Tnode’},1,Nstates));

% Release parameters (all)
sysi.Structure.Parameters.Free = true;

%% === Parameter-estimation ===
data_id = iddata(Texp’, u, dt);
opt = greyestOptions(‘Display’,’on’,’InitialCondition’,’zero’);
sys_est = greyest(data_id, sysi, opt);

%% === Extract estimated values ===
th = sys_est.Structure.Parameters;
Lambda_est = th(1).Value; rho_est = th(2).Value; cp_est = th(3).Value;
hBot_est = [th(4:end).Value]’;

%% === Plots ===
Tsim = sim(sys_est, data_id);

% Plot h_bot
figure;
if strcmp(modellTyp,"2D")
plot(unique(Tdata.x), hBot_est, ‘o-‘, ‘LineWidth’, 2);
xlabel(‘x [m]’); ylabel(‘h_{bot} [W/m^2K]’);
title(‘HTC at the bottom edge (2D)’); grid on;
else
% 3D-Surface plot of h_bot at bottom surface
[Xq, Zq] = meshgrid(unique(Tdata.x), unique(Tdata.z));
hq = griddata(Tdata.x, Tdata.z, hBot_est, Xq, Zq, ‘natural’);

surf(Xq, Zq, hq);
xlabel(‘x [m]’); ylabel(‘z [m]’); zlabel(‘h_{bot} [W/m^2K]’);
title(‘HTC at bottom surface (3D)’); colorbar;
shading interp; view(30, 30);
end

% Comparison temperature-simulation vs. temperature-measurement
figure;
Nrow = ceil(sqrt(Nstates));
for i = 1:Nstates
subplot(Nrow, Nrow, i);
plot(times, Texp(i,:), ‘-‘, ‘LineWidth’, 1.5); hold on;
plot(times, Tsim.y(i,:), ‘:’, ‘LineWidth’, 1.5);
title(sprintf(‘Nodes %d’, i));
xlabel(‘Time [s]’); ylabel(‘T [°C]’);
legend(‘Experiment’, ‘Simulation’);
grid on;
end

% 3D-Point: final temperature distribution
if strcmp(modellTyp,"3D")
figure;
scatter3(Tdata.x, Tdata.y, Tdata.z, 50, Tsim.y(:,end), ‘filled’);
xlabel(‘x’); ylabel(‘y’); zlabel(‘z’);
title(‘Simulated temperature distribution at t=tend’);
colorbar; view(30,30);
end

%% End of the script
The call of the script "greybox_heat_diffusion.m" is not working properly and the function "fHeat2D3D" is not called correct.
For the averaging of the corne nodes (2D) respectively the corner & edge nodes (3D). I made this script:
function [A,B,C,D] = fHeat2D3D(theta, Ts)
% fHeat2D3D Continuous-time grey-box state-space for 2D/3D heat diffusion
% Signature for idgrey: fHeat2D3D(theta, Ts)
% Inputs:
% theta = [Lambda, rho, cp, hBot1, …, hBotN]
% Ts = sample time (ignored in continuous-time model)
% Globals: nx, ny, nz, dx, dy, dz, modellTyp, h_top

global nx ny nz dx dy dz modellTyp h_top

% Extract physical parameters
Lambda = theta(1);
rho = theta(2);
cp = theta(3);

% Determine expected number of bottom convection coefficients
if strcmp(modellTyp,’2D’)
expectedNbot = nx;
else
expectedNbot = nx * nz;
end
% Validate theta length
if length(theta) ~= 3 + expectedNbot
error(‘Theta must have length 3+%d (got %d)’, expectedNbot, length(theta));
end
% Extract bottom convection coefficients
hBot = theta(4:end);

% Number of states
if strcmp(modellTyp,’2D’)
N = nx * ny;
else
N = nx * ny * nz;
end

% Build A matrix (2D/3D Laplacian)
A = zeros(N);
dists = [dx, dx, dy, dy];
for idx = 1:N
tmp = idx – 1;
ix = mod(tmp, nx) + 1;
iy = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
iz = 1;
else
iz = floor(tmp / (nx * ny)) + 1;
end
diagSum = 0;
nbr = [-1,0; 1,0; 0,-1; 0,1];
for k = 1:4
x2 = ix + nbr(k,1);
y2 = iy + nbr(k,2);
if x2>=1 && x2<=nx && y2>=1 && y2<=ny
z2 = iz;
idx2 = x2 + (y2-1)*nx + (z2-1)*nx*ny;
K = Lambda / (rho * cp * dists(k)^2);
A(idx, idx2) = K;
diagSum = diagSum + K;
end
end
A(idx, idx) = -diagSum;
end

% Build B matrix
% Identify side (Dirichlet) nodes
side = false(N,1);
for idx = 1:N
tmp = idx – 1;
x = mod(tmp, nx) + 1;
y = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
side(idx) = (x == 1) || (x == nx);
else
z = floor(tmp / (nx * ny)) + 1;
side(idx) = (x==1)||(x==nx)||(y==1)||(y==ny);
end
end
Nside = sum(side);
B = zeros(N, Nside + 1 + expectedNbot);

% Side BC inputs
sidx = find(side);
for i = 1:Nside
B(sidx(i), i) = 1;
end
% Top convection BC
if strcmp(modellTyp,’2D’)
topIdx = find(~side & floor((0:N-1)/nx)==0);
else
topIdx = find(~side & floor((0:N-1)/(nx*ny))==nz-1);
end
for i = 1:numel(topIdx)
B(topIdx(i), Nside+1) = h_top;
end
% Bottom convection BC
if strcmp(modellTyp,’2D’)
botIdx = find(~side & floor((0:N-1)/nx)==ny-1);
else
botIdx = find(~side & floor((0:N-1)/(nx*ny))==0);
end
for i = 1:numel(botIdx)
B(botIdx(i), Nside+1+i) = hBot(i);
end

% Outputs and feedthrough
C = eye(N);
% === Corner and edge nodes averaging ===
for idx = 1:N
bcCount = nnz(B(idx,:)); % Count of BC-Input
if bcCount > 1
% Balanced averaging: scale A- and B-Line
A(idx,:) = A(idx,:) / bcCount;
B(idx,:) = B(idx,:) / bcCount;
end
end

D = zeros(N, size(B,2));(N, size(B,2));
end

I’m not sure if this is the rigth approach.

Maybe someone has a hint how can I get rid of the errors.
With best regards
Steffen Hello,

I’m struggeling a litle bit with a thermal model based on the two and thre dimensional heat equation.
My aim is to estimate the HCT with the aid of "experimental data" and a grey-box model.
The thermal BC’s are quite simple, and illustrated below.

I generate dummy data via this matalb script:
% generate_dummy_tempdata_and_model_fixed.m
% Generate Dummy-data and prepare (2D/3D)
clc, close all, clear all
%% === Parameter ===
modellTyp = "3D"; % "2D" or "3D"
nx = 4; ny = 4; nz = 4; % Node count
dx = 0.02;dy = 0.03; dz = 0.04; % Node distance [m]
times = 0:1:30; % Time range [s]
T0 = 300; % Initial temperature [K]
dt = times(2) – times(1); % Time step [s]
%% === 1) Generate dummy-data and save as CSV ===
data = [];
switch modellTyp
case "2D"
for iy = 0:ny-1
for ix = 0:nx-1
x = ix * dx;
y = iy * dy;
Tcurve = T0 + 10 * sin(2*pi*times/60 + ix*0.3 + iy*0.5);
data = [data; x, y, Tcurve];
end
end
% Header ass string array
header = ["x","y", "t" + string(times)];
csvFile = ‘example_tempdata2D.csv’;
case "3D"
for iz = 0:nz-1
for iy = 0:ny-1
for ix = 0:nx-1
x = ix * dx;
y = iy * dy;
z = iz * dz;
Tcurve = T0 + 10 * sin(2*pi*times/60 + ix*0.2 + iy*0.3 + iz*0.4);
data = [data; x, y, z, Tcurve];
end
end
end
% Header as string array
header = ["x","y","z", "t" + string(times)];
csvFile = ‘example_tempdata3D.csv’;
end
% Bulid table and save
Ttbl_out = array2table(data, ‘VariableNames’, header);
writetable(Ttbl_out, csvFile);
disp([‘Dummy-data saved: ‘, csvFile]);
The core of the simulation is the transformation of the 2d and 3d diffusion equation into an ode.
I do it with this script:
function [A,B,C,D] = fHeat2D3D(theta, Ts)
% fHeat2D3D Continuous-time grey-box state-space for 2D/3D heat diffusion
% Signature for idgrey: fHeat2D3D(theta, Ts)
% Inputs:
% theta = [Lambda, rho, cp, hBot1, …, hBotN]
% Ts = sample time (ignored in continuous-time model)
% Globals: nx, ny, nz, dx, dy, dz, modellTyp, h_top

global nx ny nz dx dy dz modellTyp h_top

% Extract physical parameters
Lambda = theta(1);
rho = theta(2);
cp = theta(3);

% Determine expected number of bottom convection coefficients
if strcmp(modellTyp,’2D’)
expectedNbot = nx;
else
expectedNbot = nx * nz;
end
% Validate theta length
if length(theta) ~= 3 + expectedNbot
error(‘Theta must have length 3+%d (got %d)’, expectedNbot, length(theta));
end
% Extract bottom convection coefficients
hBot = theta(4:end);

% Number of states
if strcmp(modellTyp,’2D’)
N = nx * ny;
else
N = nx * ny * nz;
end

% Build A matrix (2D/3D Laplacian)
A = zeros(N);
dists = [dx, dx, dy, dy];
for idx = 1:N
tmp = idx – 1;
ix = mod(tmp, nx) + 1;
iy = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
iz = 1;
else
iz = floor(tmp / (nx * ny)) + 1;
end
diagSum = 0;
nbr = [-1,0; 1,0; 0,-1; 0,1];
for k = 1:4
x2 = ix + nbr(k,1);
y2 = iy + nbr(k,2);
if x2>=1 && x2<=nx && y2>=1 && y2<=ny
z2 = iz;
idx2 = x2 + (y2-1)*nx + (z2-1)*nx*ny;
K = Lambda / (rho * cp * dists(k)^2);
A(idx, idx2) = K;
diagSum = diagSum + K;
end
end
A(idx, idx) = -diagSum;
end

% Build B matrix
% Identify side (Dirichlet) nodes
side = false(N,1);
for idx = 1:N
tmp = idx – 1;
x = mod(tmp, nx) + 1;
y = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
side(idx) = (x == 1) || (x == nx);
else
z = floor(tmp / (nx * ny)) + 1;
side(idx) = (x==1)||(x==nx)||(y==1)||(y==ny);
end
end
Nside = sum(side);
B = zeros(N, Nside + 1 + expectedNbot);

% Side BC inputs
sidx = find(side);
for i = 1:Nside
B(sidx(i), i) = 1;
end
% Top convection BC
if strcmp(modellTyp,’2D’)
topIdx = find(~side & floor((0:N-1)/nx)==0);
else
topIdx = find(~side & floor((0:N-1)/(nx*ny))==nz-1);
end
for i = 1:numel(topIdx)
B(topIdx(i), Nside+1) = h_top;
end
% Bottom convection BC
if strcmp(modellTyp,’2D’)
botIdx = find(~side & floor((0:N-1)/nx)==ny-1);
else
botIdx = find(~side & floor((0:N-1)/(nx*ny))==0);
end
for i = 1:numel(botIdx)
B(botIdx(i), Nside+1+i) = hBot(i);
end

% Outputs and feedthrough
C = eye(N);
D = zeros(N, size(B,2));
end
Finally the ode ("function [A,B,C,D] = fHeat2D3D(theta, Ts)") is used as continuous-time state-space model to estimate the system parameter HTC(bottom), heat conductivity, density and specific heat capacity via idgrey and greyest.
% greybox_heat_diffusion.m
% Parametric continuous-time grey-box model for 2D/3D heat conduction

clear; clc; close all;
global nx ny nz dx dy dz modellTyp h_top t_env_top

%% === User setup ===
modellTyp = "2D"; % "2D" or "3D"
nx = 3; ny = 3; nz = 3; % Count of nodes in x, y, z direction(ignore nz for 2D)
dx = 0.02; dy = 0.03; dz = 0.04; % Distance between nodes [m]

dt = 1; % Time step [s]
times = 0:dt:60; % Time range [s]
csv2D = ‘example_tempdata2D.csv’;
csv3D = ‘example_tempdata3D.csv’;

% Fixed values / Top-HTC
t_env_top = 293; % Ambient free stream temperature [K]
h_top = 10; % HTC at the top edge [W/(m^2*K)]

%% === Initial guess of the model parameter ===
theta0.Lambda = 50; % Heat conduction [W/(m*K)]
theta0.rho = 7800;% Density [kg/m^3]
theta0.cp = 460; % Heat capacity [J/(kg*K)]
if modellTyp=="2D"
h_bot0 = 20*ones(nx,1);
else
h_bot0 = 20*ones(nx*nz,1);
end

%% === Read experimental data ===
if modellTyp=="2D"
Tdata = readtable(csv2D);
Texp = Tdata{:,3:end};
Nstates = nx*ny;
else
Tdata = readtable(csv3D);
Texp = Tdata{:,4:end};
Nstates = nx*ny*nz;
end
Nmeas = size(Texp,2);

%% === Calculate side indices ===
sideNodes = false(Nstates,1);
for idx=1:Nstates
tmp=idx-1; ix=mod(tmp,nx)+1; iy=floor(tmp/nx)+1;
if strcmp(modellTyp,"2D")
sideNodes(idx) = ix==1 || ix==nx;
else
iz=floor(tmp/(nx*ny))+1;
sideNodes(idx) = ix==1||ix==nx||iy==1||iy==ny;
end
end
sideIdx = find(sideNodes);

%% === Build input-matrix u ===
T_sideBC = Texp(sideIdx,:); % Side nodes – BC (experimental value)
T_topBC = t_env_top * ones(1,Nmeas);
u = [T_sideBC’ T_topBC’ zeros(Nmeas,length(h_bot0))];

%% === idgrey Setup ===
param0 = [theta0.Lambda theta0.rho theta0.cp h_bot0′];
order = [Nstates Nstates Nstates 0];

[A,B,C,D] = fHeat2D3D(param0, dt);

sysi = idgrey(‘fHeat2D3D’, param0, ‘c’, order, …
‘InputName’,[repmat({‘T_sideBC’},1,length(sideIdx)) {‘T_top’} repmat({‘T_bot’},1,length(h_bot0))], …
‘OutputName’, repmat({‘Tnode’},1,Nstates));

% Release parameters (all)
sysi.Structure.Parameters.Free = true;

%% === Parameter-estimation ===
data_id = iddata(Texp’, u, dt);
opt = greyestOptions(‘Display’,’on’,’InitialCondition’,’zero’);
sys_est = greyest(data_id, sysi, opt);

%% === Extract estimated values ===
th = sys_est.Structure.Parameters;
Lambda_est = th(1).Value; rho_est = th(2).Value; cp_est = th(3).Value;
hBot_est = [th(4:end).Value]’;

%% === Plots ===
Tsim = sim(sys_est, data_id);

% Plot h_bot
figure;
if strcmp(modellTyp,"2D")
plot(unique(Tdata.x), hBot_est, ‘o-‘, ‘LineWidth’, 2);
xlabel(‘x [m]’); ylabel(‘h_{bot} [W/m^2K]’);
title(‘HTC at the bottom edge (2D)’); grid on;
else
% 3D-Surface plot of h_bot at bottom surface
[Xq, Zq] = meshgrid(unique(Tdata.x), unique(Tdata.z));
hq = griddata(Tdata.x, Tdata.z, hBot_est, Xq, Zq, ‘natural’);

surf(Xq, Zq, hq);
xlabel(‘x [m]’); ylabel(‘z [m]’); zlabel(‘h_{bot} [W/m^2K]’);
title(‘HTC at bottom surface (3D)’); colorbar;
shading interp; view(30, 30);
end

% Comparison temperature-simulation vs. temperature-measurement
figure;
Nrow = ceil(sqrt(Nstates));
for i = 1:Nstates
subplot(Nrow, Nrow, i);
plot(times, Texp(i,:), ‘-‘, ‘LineWidth’, 1.5); hold on;
plot(times, Tsim.y(i,:), ‘:’, ‘LineWidth’, 1.5);
title(sprintf(‘Nodes %d’, i));
xlabel(‘Time [s]’); ylabel(‘T [°C]’);
legend(‘Experiment’, ‘Simulation’);
grid on;
end

% 3D-Point: final temperature distribution
if strcmp(modellTyp,"3D")
figure;
scatter3(Tdata.x, Tdata.y, Tdata.z, 50, Tsim.y(:,end), ‘filled’);
xlabel(‘x’); ylabel(‘y’); zlabel(‘z’);
title(‘Simulated temperature distribution at t=tend’);
colorbar; view(30,30);
end

%% End of the script
The call of the script "greybox_heat_diffusion.m" is not working properly and the function "fHeat2D3D" is not called correct.
For the averaging of the corne nodes (2D) respectively the corner & edge nodes (3D). I made this script:
function [A,B,C,D] = fHeat2D3D(theta, Ts)
% fHeat2D3D Continuous-time grey-box state-space for 2D/3D heat diffusion
% Signature for idgrey: fHeat2D3D(theta, Ts)
% Inputs:
% theta = [Lambda, rho, cp, hBot1, …, hBotN]
% Ts = sample time (ignored in continuous-time model)
% Globals: nx, ny, nz, dx, dy, dz, modellTyp, h_top

global nx ny nz dx dy dz modellTyp h_top

% Extract physical parameters
Lambda = theta(1);
rho = theta(2);
cp = theta(3);

% Determine expected number of bottom convection coefficients
if strcmp(modellTyp,’2D’)
expectedNbot = nx;
else
expectedNbot = nx * nz;
end
% Validate theta length
if length(theta) ~= 3 + expectedNbot
error(‘Theta must have length 3+%d (got %d)’, expectedNbot, length(theta));
end
% Extract bottom convection coefficients
hBot = theta(4:end);

% Number of states
if strcmp(modellTyp,’2D’)
N = nx * ny;
else
N = nx * ny * nz;
end

% Build A matrix (2D/3D Laplacian)
A = zeros(N);
dists = [dx, dx, dy, dy];
for idx = 1:N
tmp = idx – 1;
ix = mod(tmp, nx) + 1;
iy = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
iz = 1;
else
iz = floor(tmp / (nx * ny)) + 1;
end
diagSum = 0;
nbr = [-1,0; 1,0; 0,-1; 0,1];
for k = 1:4
x2 = ix + nbr(k,1);
y2 = iy + nbr(k,2);
if x2>=1 && x2<=nx && y2>=1 && y2<=ny
z2 = iz;
idx2 = x2 + (y2-1)*nx + (z2-1)*nx*ny;
K = Lambda / (rho * cp * dists(k)^2);
A(idx, idx2) = K;
diagSum = diagSum + K;
end
end
A(idx, idx) = -diagSum;
end

% Build B matrix
% Identify side (Dirichlet) nodes
side = false(N,1);
for idx = 1:N
tmp = idx – 1;
x = mod(tmp, nx) + 1;
y = floor(tmp / nx) + 1;
if strcmp(modellTyp,’2D’)
side(idx) = (x == 1) || (x == nx);
else
z = floor(tmp / (nx * ny)) + 1;
side(idx) = (x==1)||(x==nx)||(y==1)||(y==ny);
end
end
Nside = sum(side);
B = zeros(N, Nside + 1 + expectedNbot);

% Side BC inputs
sidx = find(side);
for i = 1:Nside
B(sidx(i), i) = 1;
end
% Top convection BC
if strcmp(modellTyp,’2D’)
topIdx = find(~side & floor((0:N-1)/nx)==0);
else
topIdx = find(~side & floor((0:N-1)/(nx*ny))==nz-1);
end
for i = 1:numel(topIdx)
B(topIdx(i), Nside+1) = h_top;
end
% Bottom convection BC
if strcmp(modellTyp,’2D’)
botIdx = find(~side & floor((0:N-1)/nx)==ny-1);
else
botIdx = find(~side & floor((0:N-1)/(nx*ny))==0);
end
for i = 1:numel(botIdx)
B(botIdx(i), Nside+1+i) = hBot(i);
end

% Outputs and feedthrough
C = eye(N);
% === Corner and edge nodes averaging ===
for idx = 1:N
bcCount = nnz(B(idx,:)); % Count of BC-Input
if bcCount > 1
% Balanced averaging: scale A- and B-Line
A(idx,:) = A(idx,:) / bcCount;
B(idx,:) = B(idx,:) / bcCount;
end
end

D = zeros(N, size(B,2));(N, size(B,2));
end

I’m not sure if this is the rigth approach.

Maybe someone has a hint how can I get rid of the errors.
With best regards
Steffen thermal, grey-box, matlab, ode MATLAB Answers — New Questions

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