MATLAB: How to use LSQNONLIN or LSQCURVEFIT when the function has a derivative form

fit lsqnonlin least squares method

I would like to use the least squares method to determine specific parameters. Knowing the time step, dt, time,t(i), and displacement, u(i), for every step i, the equation is the following:

F0(i)=k1*u(i)^k2

F1(i)=(F1(i-1)+k3*u(i)-k3*u(i-1))*(k4/(k4+k3*dt))

Y(i)=F0(i)+F1(i)=(k1*u(i)^k2)+(F1(i-1)+k3*u(i)-k3*u(i-1))*(k4/(k4+k3*dt))

or if it is more convenient for anyone (assuming that dF1(i)/dt=(F1(i)-F1(i-1))/dt) :

Y(i)=(k1*u(i)^k2)+(k4*u(i)-(k4/k3)*dF1(i)/dt)

Y_exp is the expected output, and the parameters I want to determine are the k1,k2,k3,k4. The thing that worries me the most, is the dependence of time step i on i-1 time step.

ANY IDEAS?

Best Answer

It’s difficult for me to follow what you’re doing. If you want to fit a (perhaps kinetic) differential equation to data, you can use the techniques in Monod kinetics and curve fitting.

Related Solutions

MATLAB: Unable to perform assignment because the left and right sides have a different number of elements. Line “u(i) = u(I+1) + acceleration * dt” seems to be the problem.

When I ran your code, I got the same error. I tracked it down to your use of ‘spring’ as a variable name, as well as noting that in your ‘fres’ assignments that use it, you did not initially capitalise it.. This is actually the name of a colormap, so was creating a (64x3) matrix for your variable, and that was throwing the error. I corrected it to ‘Spring’ everywhere, and still got the error. What I find interesting is that as a general rule, MATLAB is case-sensitive, so ‘Spring’ and ‘spring’ should not be the same. (I am running this on R2019a.) I finally changed it to ‘SpringK’ everywhere, and the error disappeared.

The changes are:

SpringK = 200;

and:

    if u(i-2) <= 0 && u(i-1) >= 0
        fres = (mass*g*(sind(angle)) - (staticf*cosd(angle)));
    elseif (u(i-2) >= 0 && u(i-1) >= 0 && displacement_data(i-1) < Initial) || (u(i-2) < 0 && u(i-1) < 0 && displacement_data(i-1) < Initial)
        fres = mass*g*(sind(angle) + multiplier*(dynamicf*cosd(angle)));
    elseif u(i-2) >= 0 && u(i-1) <= 0
        fres = mass*g*(sind(angle) + staticf*cosd(angle)) - SpringK*(displacement_data(i-1) - Initial);
    elseif u(i-2) >=0 && u(i-1) >= 0 && displacement_data(i-1) >= Initial || u(i-2) < 0 && u(i-1) < 0 && displacement_data(i-1) >= Initial
        fres = mass*g*(sind(angle) + multiplier*(dynamicf*cosd(angle))) - SpringK*(displacement_data(i-1) - Initial);
    end

We are left with one error:

Undefined function or variable 'acceleration_data'.
    fprintf('%.4f\t\t%.4f\t\t%.4f\t\t%.4f\n', displacement_data(i-1), acceleration_data(i-1),
    time_data(i), u(i-1));

I defer to you to solve that.

MATLAB: Define the ODE equals the matrix. Runge Kutta 4

Change

xinital= [ 0 0 -2 0.4]

xinital= [ 0 0 -2 0.4]'

xinital= [ 0;0;-2;0.4]

Best Answer

Related Solutions

MATLAB: Unable to perform assignment because the left and right sides have a different number of elements. Line “u(i) = u(I+1) + acceleration * dt” seems to be the problem.

MATLAB: Define the ODE equals the matrix. Runge Kutta 4

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