find the slope of a smooth curve at a point

I want to find the slop of the curve at [maxdepth01 , maxload01] and draw the slope tangent to the zero axis .

s = load('matlab needed.mat')

s = struct with fields:
             A: [204196×1 double]
             B: [204196×1 double]
    maxdepth01: 1.9545e+03
     maxload01: 4.5054e+05

B = s.B;
A = s.A;
maxdepth01 = s.maxdepth01;
maxload01 = s.maxload01;
plot(B , A , "r--")
hold on
plot(maxdepth01 ,maxload01 ,"*")

[Mathieu NOE]

hello

so we have 2 data sets , i see one is the raw data (needed.mat) and one is smoothed ('matlab needed.mat')

still it's not clear what tangent / slope you want at the [maxdepth01 , maxload01] point

this is an angular point so we can either speak of the slope on the LHS (horizontal section) or after this point (vertical portion)

[soheil zare]

I have corrected the data. Overall I want the slope at the maximum load which is shown with a star like the picture below and the slope shown by a red line.

Answer 1

[Mathieu NOE]

hello

I tried to do the entire process from the raw data to the drawing of the tangent line

your amount of data is quite significant, I coud decimate this by a factor 100 without mpact on the result (just FYI)

the tangent line is drawn with xx, yy data

load('needed.mat')
samples = numel(depth01);

% decimation and smoothing
decim_factor = 100;
ind = 1:decim_factor:samples;
x = depth01(ind);
y = load01(ind);
xs = smoothdata(x,'gaussian',25);
ys = smoothdata(y,'gaussian',25);
  
% maxdepth01 ,maxload01 point detection = point of maximal distance to origin
[d_squared,ind] = max(xs.^2+ys.^2);
maxdepth01 = xs(ind);
maxload01 = ys(ind);

% slection of 33% of reamining samples after the maxdepth01 ,maxload01 point
ind2 = ind + (0:(numel(x)-ind)/20);
x2 = xs(ind2);
y2 = ys(ind2);

% Fit a polynomial p of degree "degree" to the (x,y) data:
degree = 1;
p = polyfit(x2,y2,degree);

% Evaluate the fitted polynomial p and plot the tangent line:
% find x coordinate crossing y = 0 
x0 = -p(2)/p(1);
xx = linspace(x0,maxdepth01,25);
yy = polyval(p,xx);
eqn = poly_equation(flip(p)); % polynomial equation (string)

figure(1);
plot(depth01 , load01 , "r*", xs, ys,'k')
hold on
plot(maxdepth01, maxload01, "c*", 'LineWidth', 2, 'MarkerSize', 40)
plot(x2,y2,'db',xx,yy,'--')
legend('raw data','data downsampled & smoothed','peak point','polyfit data' , eqn)


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


function eqn = poly_equation(a_hat)
eqn = " y = "+a_hat(1);
for i = 2:(length(a_hat))
    
    if sign(a_hat(i))>0
        str = " + ";
    else
        str = " ";
    end
    
    if i == 2
%         eqn = eqn+" + "+a_hat(i)+"*x";
        eqn = eqn+str+a_hat(i)+"*x";
        
    else
%         eqn = eqn+" + "+a_hat(i)+"*x^"+(i-1)+" ";
        eqn = eqn+str+a_hat(i)+"*x^"+(i-1)+" ";
    end
end
eqn = eqn+" ";
end
        

[soheil zare]

hi.although it seems so complicated but its ok. but there is a problem that the slope doesnt start from the maxload point.

[Mathieu NOE]

ok, corrected

% load('matlab needed.mat')
% plot(B , A , "r-")
% hold on
% plot(maxdepth01 ,maxload01 ,"db")
% hold off

clearvars;close all;clc;
load('needed.mat')
samples = numel(depth01);

% decimation and smoothing
decim_factor = 100;
ind = 1:decim_factor:samples;
x = depth01(ind);
y = load01(ind);
xs = smoothdata(x,'gaussian',25);
ys = smoothdata(y,'gaussian',25);
  
% maxdepth01 ,maxload01 point detection = point of maximal distance to origin
[d_squared,ind] = max(xs.^2+ys.^2);
maxdepth01 = xs(ind);
maxload01 = ys(ind);

% selection of small batch of samples after the maxdepth01 ,maxload01 point
ind2 = ind + (0:(numel(x)-ind)/20);
x2 = xs(ind2);
y2 = ys(ind2);

% Fit a polynomial p of degree "degree" to the (x,y) data:
degree = 1;
p = polyfit(x2,y2,degree);

% Evaluate the fitted polynomial p and plot the tangent line:
% find x coordinate crossing y = 0 
x0 = -p(2)/p(1);
xx = linspace(x0,maxdepth01,5);
yy = linspace(0,maxload01,5);

figure(1);
plot(depth01 , load01 , "r*", xs, ys,'k',xx,yy,'c--')
hold on
plot(maxdepth01, maxload01, "c*", 'LineWidth', 2, 'MarkerSize', 40)
legend('raw data','data downsampled & smoothed','tangent line','peak point')



        

[soheil zare]

hello.thanks for your answer .

can you help me to write a power function for the smoothed data after loadmax(unloading / descending ) part?

and also what should I do to select for example 10% of the descending after passing 5% from the max instead of choosing 33% after loadmax

thanks

[Mathieu NOE]

ok

the first part of the question is clear

but after it gets complicated especially at the end of a heavy work day

"10% of the descending after passing 5% from the max instead of choosing 33% after loadmax"

can you make a sketch where all those values are in the graph ? I am not sure to understand if we speak from x, y values and if we start from the max load point or from the end point ???

Answer 2

[Image Analyst]

Try this:

s = load('matlab needed.mat')

s = struct with fields:
             A: [204196×1 double]
             B: [204196×1 double]
    maxdepth01: 1.9545e+03
     maxload01: 4.5054e+05

B = s.B;
A = s.A;
maxdepth01 = s.maxdepth01;
maxload01 = s.maxload01;
subplot(2, 1, 1);
plot(B, A, "r--", 'LineWidth', 2);
hold on
plot(maxdepth01, maxload01, "r*", 'LineWidth', 2, 'MarkerSize', 20)
grid on;
fontSize = 12;
xlabel('B Depth', 'FontSize',fontSize);
ylabel('A Load', 'FontSize',fontSize);
title('Original Data', 'FontSize',fontSize);

% Find index of maxdepth01 on the x axis
[m, indexOfPeak] = min(abs(B - maxdepth01))

m = 0.1007

indexOfPeak = 130220

plot(B(1:indexOfPeak), A(1:indexOfPeak), "b-", 'LineWidth', 2);

% Find the angles from the peak point to the last point
angles = atan2d(A(indexOfPeak:end-1) - A(end), B(indexOfPeak:end-1) - B(end));
subplot(2, 1, 2);
plot(angles, 'b-', 'LineWidth', 2);
grid on;
title('Angle from last point to peak point', 'FontSize',fontSize);
xlabel('Index', 'FontSize',fontSize);
ylabel('Angle', 'FontSize',fontSize);

% It appears that the angle right at the peak point
% is the steepest of all the angles, so just report that.
angleAtPeak = max(angles)

angleAtPeak = 89.9384

% Get the slope there at the peak.
slope = tand(angleAtPeak)

slope = 930.0585