# parameter optimization in function

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Elon Hendriksen 2022 年 7 月 22 日

Hi!
I have written a code in which a nonlinear pendulum is modelled. Now with measured data from a pendulum I would like to optimize my damping coefficient so that the model in matlab fits the measured data. Since the damping coeficient is in a separate function file I do not know how to tackle this. See script in attachment.
In F_nonlin the damping coefficient is currently 0.000035 and fits the curve quite well but as mentioned above I would like matlab to optimize this value automattically.
Thanks in advance for the help!
Kind regards, Elon

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### 回答 (2 件)

Alan Weiss 2022 年 7 月 22 日
Try putting the following code at the end of yours:
[dfinal,resnorm] = fminbnd(@(damping)trytofit(damping,x0,Acc_clean),0.00002,0.00005)
function delta = trytofit(damping,x0,Acc_clean)
tspan = Acc_clean(:,1)/1000-5.017;
[~, S] = ode45(@(t,y) F_nonlin(t,y,damping),tspan,x0);
delta = sum((S - Acc_clean(:,3)).^2,"all");
end
I changed the F_nonlin code as follows:
function dx = F_nonlin(~,x,Bfactor)
% Derivative function for a nonlinear pendulum model.
%
% States:
% x(1): theta
% x(2): d theta/dt
% system parameters:
g = 9.81; % gravitational constant (m/s^2)
m = 1.042; % mass pendulum
L = 0.210; % length pendulum
M = m*L;
K = m*g; %iets met g
B = Bfactor * 2 * sqrt(M*K); %0.000035 for fitted line
dx(1,1) = x(2);
dx(2,1) = -( K*sin(x(1)) + B*x(2)*abs(x(2)) ) / M;
I get the result dfinal = 3.1459e-05, pretty close to what you have.
My code searches for a minimum of the sum of squares of differences between the simulated pendulum and the data you have. The only thing it varies is the damping (Bfactor in F_nonlin, a scalar), so I use fminbnd to get the minimum.
Of course, it is possible I made an error somewhere, but I think that you see how I put the parameter Bfactor in the simulation to give something that a solver can vary to search for a minimum.
Alan Weiss
MATLAB mathematical toolbox documentation
##### 4 件のコメント表示非表示 3 件の古いコメント
Torsten 2022 年 7 月 22 日
In your code, L is an input variable to F_nonlin and you immediately overwrite that input by setting L to 0.21. One of these settings is superfluous.

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Rajiv Singh 2022 年 8 月 9 日

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