smoothen curve plotted using discrete points

flowrate = [ 0 93 100 120 140 160 172 180 200 220 232 ] ;

head = [ 9.51 8.76 8.68 8.41 8.01 7.45 7.03 6.70 5.73 4.49 3.61 ] ;

cv20 = [ 0.8 1.1 2.2 4.1 6.6 9.9 13.9 18.6 24.1 30.3 37.2] ;

cv20new = smooth(cv20);

cv30 = [ 0.8 1 1.5 2.4 3.7 5.3 7.3 9.6 12.3 15.3 18.7 ] ;

cv30new = smooth(cv30);

cv40 = [ 0.8 0.9 1.3 1.8 2.7 3.7 5 6.4 8.2 10.1 12.3 ] ;

cv40new = smooth(cv40);

cv50 = [ 0.8 0.9 1.1 1.6 2.2 2.9 3.9 5 6.3 7.7 9.3 ] ;

cv50new = smooth(cv50);

cv60 = [ 0.8 0.8 1.1 1.4 1.9 2.5 3.3 4.2 5.2 6.4 7.7 ] ;

cv60new = smooth(cv60);

cv70 = [ 0.8 0.8 1 1.3 1.8 2.3 2.9 3.7 4.6 5.6 6.7] ;

cv70new = smooth(cv70);

cv80 = [ 0.8 0.8 1 1.3 1.7 2.1 2.7 3.4 4.2 5.1 6.1 ] ;

cv80new = smooth(cv80);

plot(flowrate,head)

title('Pump Performance Curves Estimates')

hold on

plot(flowrate,cv20new)

hold on

plot(flowrate,cv30new)

hold on

plot(flowrate,cv40new)

hold on

plot(flowrate,cv50new)

hold on

plot(flowrate,cv60new)

hold on

plot(flowrate,cv70new)

hold on

plot(flowrate,cv80new)

hold off

ylim([0.0 10.0])

i want my curve to be smoothened into a parabola like the below graph:

The curves for cv20,cv30 .. are not smoothening even after i used the smooth curve command.

Answer 1

[Mathieu NOE]

hello

this would be my suggestion - others methods I tried have not been successfull

flowrate = [ 0 93 100 120 140 160 172 180 200 220 232 ] ;
head = [ 9.51 8.76 8.68 8.41 8.01 7.45 7.03 6.70 5.73 4.49 3.61 ] ; 
cv20 = [ 0.8 1.1 2.2 4.1 6.6 9.9 13.9 18.6 24.1 30.3 37.2] ;
cv30 = [ 0.8 1 1.5 2.4 3.7 5.3 7.3 9.6 12.3 15.3 18.7 ] ;
cv40 = [ 0.8 0.9 1.3 1.8 2.7 3.7 5 6.4 8.2 10.1 12.3 ] ;
cv50 = [ 0.8 0.9 1.1 1.6 2.2 2.9 3.9 5 6.3 7.7 9.3 ] ;
cv60 = [ 0.8 0.8 1.1 1.4 1.9 2.5 3.3 4.2 5.2 6.4 7.7 ] ;
cv70 = [ 0.8 0.8 1 1.3 1.8 2.3 2.9 3.7 4.6 5.6 6.7] ;
cv80 = [ 0.8 0.8 1 1.3 1.7 2.1 2.7 3.4 4.2 5.1 6.1 ] ;

% plot
figure(1)
plot(flowrate,head,flowrate,cv20,flowrate,cv30,...
    flowrate,cv40,flowrate,cv50,flowrate,cv60,...
    flowrate,cv70,flowrate,cv80);
title('Pump Performance Curves Estimates')
ylim([0.0 10.0])

% plot
flowrate2 = linspace(min(flowrate),max(flowrate),100);
[cv20new] = my_opti_fminsearch(flowrate,cv20,flowrate2);
[cv20new] = my_opti_fminsearch(flowrate,cv20,flowrate2);
[cv30new] = my_opti_fminsearch(flowrate,cv30,flowrate2);
[cv40new] = my_opti_fminsearch(flowrate,cv40,flowrate2);
[cv50new] = my_opti_fminsearch(flowrate,cv50,flowrate2);
[cv60new] = my_opti_fminsearch(flowrate,cv60,flowrate2);
[cv70new] = my_opti_fminsearch(flowrate,cv70,flowrate2);
[cv80new] = my_opti_fminsearch(flowrate,cv80,flowrate2);

figure(2)
plot(flowrate,head,flowrate2,cv20new,flowrate2,cv30new,...
    flowrate2,cv40new,flowrate2,cv50new,flowrate2,cv60new,...
    flowrate2,cv70new,flowrate2,cv80new);
title('Pump Performance Curves Estimates')
ylim([0.0 10.0])

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [cvnew] = my_opti_fminsearch(flowrate,cv,flowrate2)

    cv = interp1(flowrate,cv,flowrate2);

    % fminsearch method
    x = flowrate2;
    a = cv(1);

    f = @(b,x) a  + b.*(x.^2);
    b_init = (cv(end) - a)./(flowrate(end).^2);

    obj_fun = @(params) norm(f(params(1),flowrate2)-cv);
    sol = fminsearch(obj_fun, [b_init]);
    b_sol = sol(1);
    cvnew = f(b_sol, flowrate2);


end

[Sujay Bharadwaj]

thanks this works although i am not quite sure why smooth() is not working. :(

[Mathieu NOE]

here you want all curves to be a perfect parabola , so none of the "smoothing" functions can do an exact parabola

the trick is indeed to fit a parabola equation to your data with the constant term always the same (so all curves have same origin)

all the best