Random exponential function between two values

Question

Nicola De Noni 2022-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/1721850-random-exponential-function-between-two-values

评论： Sam Chak 2022-5-18

Hello everyone! I’m trying to create a random vector with a maximum value of xmax_out = 65 and a minimum value of xmin_out = 16. This vector. However, I would like this vector to have an exponential shape, as shown, because I want to simulate the temperature that decreases in contact with a hot fluid to be cooled.

As you can see: I would like the temperature at time 0 (therefore origin of the x axis) to be equal xmax_out while at time t the temperature reaches the xmin_out value. In the project the cooling time is about 50 min.

I tried to use the following code to generate a decreasing random vector, but unfortunately it is linear.

% Temperature range
n = 50;                            % Length of time [min]
xmin_out = 16 + 273.15;            % Minimum outlet temperature [K]
xmax_out = 65 + 273.15;            % Maximum outlet temperature [K]
% Random Vector of temperature: 
T_out = sort((xmax_out-xmin_out)*rand(n,1)+xmin_out, "descend");

Thanks!

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Answer 1

Sam Chak 2022-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/1721850-random-exponential-function-between-two-values#answer_966145

编辑：Sam Chak 2022-5-18

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Hi @Nicola De Noni

Are you looking for an exponential decay like this?

t = linspace(0, 3000, 30001);
tmin = 50;
xmin = 16;
xmax = 65;
k = -log(xmin/65)/(60*tmin);
T = xmax*exp(-k*t);
plot(t/60, T, 'linewidth', 1.5)
grid on
xlabel('Time, t [min]')
ylabel('Temperature, T')

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Torsten 2022-5-18

编辑：Torsten 2022-5-18

在 MATLAB Online 中打开

The shape comes from an exponential, but it's not visible in the interval [0:50].

If you plot for

t = linspace(0,3000*10,3000)

, you'll see the exponential behaviour.

Sam Chak 2022-5-18

在 MATLAB Online 中打开

Hi @Nicola De Noni

Since the absolute Kelvin is just an additive reference, you can do this way:

t = linspace(0, 36000);     % 3000 seconds == 50 min; plot up to 600 min
tmin = 50;
xmin = 20;                  % Temperature [Kelvin]
xmax = 45;                  % Temperature [Kelvin]
k = -log((xmin)/(xmax))/(60*tmin);
Temp = (xmax)*exp(-k*t) + 273.15;
plot(t/60, Temp, 'linewidth', 1.5)
grid on
xlabel('Time, t [min]')
ylabel('Temperature, T [K]')