Move the item, and both sides take the same logarithm.
log(V-V(t))= log(V-V 0)-t/τ
The above v, V(t) and t are known, and V0 and τ are unknown.
Let y=log(V-V(t))
x=t
Then kx+b=y
Where k =- 1/τ and b = log (v-v0).
The above process is to turn nonlinearity into linearity.
Substituting each data into the membership degree, the binary linear equations are obtained.
Equation 6 and variable 2 can be solved by least square method.
The following is the Matlab code:
v = 14;
t=[0.3,0.5, 1.0,2.0,4.0,7.0];
Vt=[5.6873,6. 1434,7. 1633,8.8626, 1 1.0328, 12.6962];
y = log(V-Vt);
A=[t(:),ones(size(t(:)))];
kb = A \ y(:);
τ=- 1/kb( 1)
V0=V-exp(kb(2))
Below%% is the result of fitting.
Vt_fit=V-(V-V0)*exp(-t/tau)
plot(Vt,Vt_fit,' * ',Vt,Vt,' r ')
Xlabel ("vt raw data")
Ylabel ("Ventricular tachycardia fitting data")
%%%%%%%%%%%%%%%
Fill in the blanks:
Methods: The nonlinear problem was transformed into a linear problem.
V0=5.000 1
τ= 3.6 165