getting a approximation of a linear slope line of a curved set of data points

4 views (last 30 days)
Jon
Jon on 3 Aug 2023
Answered: Image Analyst on 3 Aug 2023
I am trying to plot a linear slope line for the area of the first illustration that rises. This is to get a approximation of the slope, although it has a slight curve I need this slope for an engineering calculation. I can't get theischange command to work for this and I don't know if at the start of the data a bunch of 0's are recorded. I can't eliminate these because it changes other graphs for this experiment. If you look at the second picture you'll understand what I trying to do. I have included my code at the end.
clc
clear
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di=5.05;
df=4.31;
Ao=(pi*di^2)/4;
Af=(pi*df^2)/4;
L=58.98;
Strain=abs(DeltaL)/L;
Stress=F/Ao;
plot(Strain,Stress,Marker=".")
xlabel('\epsilon (mm/mm)')
ylabel('\sigma (MPa')
title('Stress Strain Curve of Member in Tension')
[Lv,m,b] = ischange(Strain, 'linear', 'Threshold',0.01); % Change Points
Chs=nnz(Lv)
idxv = 1:find(Lv);
mdl=fitlm(Strain(idxv), Stress(idxv))
Slope = mdl.Coefficients.Estimate(2)
RSq = mdl.Rsquared.Ordinary
RSqAdj = mdl.Rsquared.Adjusted
[y,yci] = predict(mdl, Strain(idxv));
figure
plot(Strain,Stress,Marker=".")
xlabel('\epsilon (rad)')
ylabel('\sigma (Pa)')
title('Stress Strain Curve')
hold on
plot(Strain(Lv),Stress(Lv),"r+")
plot(Strain(idxv), y, '-r')
plot(Strain(idxv), yci, '--r')
hold off

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Accepted Answer

Image Analyst
Image Analyst on 3 Aug 2023
Ran in:
Try this:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
% Load data from mat file.
s = load('jon.mat')
s = struct with fields:
DeltaL: [725×1 double] F: [725×1 double]
F = s.F;
DeltaL = s.DeltaL;
%--------------------------------------------------------------------------
% Assign some parameters.
di=5.05;
df=4.31;
Ao=(pi*di^2)/4;
Af=(pi*df^2)/4;
L=58.98;
%--------------------------------------------------------------------------
% Compute Strain and Stress
Strain = abs(DeltaL) / L;
Stress = F / Ao;
%--------------------------------------------------------------------------
% Plot original data.
hFig1 = figure;
hFig1 =
Figure (1) with properties: Number: 1 Name: '' Color: [1 1 1] Position: [671 558 577 433] Units: 'pixels' Show all properties
plot(Strain, Stress, Marker=".")
xlabel('\epsilon (mm/mm)')
ylabel('\sigma (MPa)')
title('Stress Strain Curve of Member in Tension')
grid on;
fontsize(25, 'Points');
hFig1.WindowState = 'maximized';
%--------------------------------------------------------------------------
% Jon's way.
[Lv,m,b] = ischange(Strain, 'linear', 'Threshold',0.01); % Change Points
Chs=nnz(Lv);
Chs = 1
idexesToFit = 1:find(Lv);
%--------------------------------------------------------------------------
% Image Analyst's way.
% Fit between 0.05 and 0.45.
index1 = find(Stress > 0.05, 1, 'first')
index1 = 141
index2 = find(Stress > 0.45, 1, 'first')
index2 = 237
idexesToFit = index1 : index2;
% Indicate range where we're going to fit with colored vertical lines.
xline(Strain(index1), 'Color', 'm', 'LineWidth', 2);
xline(Strain(index2), 'Color', 'm', 'LineWidth', 2);
grid on;
%--------------------------------------------------------------------------
% Fit the data to a linear model.
mdl = fitlm(Strain(idexesToFit), Stress(idexesToFit))
mdl =
Linear regression model: y ~ 1 + x1 Estimated Coefficients: Estimate SE tStat pValue __________________ ___________________ _________________ _____________________ (Intercept) -0.240160898421624 0.00314929176093499 -76.2587008929026 5.07560089409645e-87 x1 26.4022829366629 0.159367662672624 165.669010223856 9.02277189285476e-119 Number of observations: 97, Error degrees of freedom: 95 Root Mean Squared Error: 0.00709 R-squared: 0.997, Adjusted R-Squared: 0.997 F-statistic vs. constant model: 2.74e+04, p-value = 9.02e-119
Slope = mdl.Coefficients.Estimate(2)
Slope = 26.4022829366629
RSq = mdl.Rsquared.Ordinary
RSq = 0.996550624964033
RSqAdj = mdl.Rsquared.Adjusted
RSqAdj = 0.996514315753128
[y, yci] = predict(mdl, Strain(idexesToFit));
%--------------------------------------------------------------------------
% Plot the fit over the original data.
hFig2 = figure;
plot(Strain, Stress, Marker=".") % Plot original data.
grid on;
hFig2.WindowState = 'maximized';
xlabel('\epsilon (rad)')
ylabel('\sigma (Pa)')
title('Stress Strain Curve')
hold on
plot(Strain(idexesToFit), Stress(idexesToFit),"r+")
plot(Strain(idexesToFit), y, '-r')
plot(Strain(idexesToFit), yci, '--r')
% Plot fit range.
xline(Strain(index1), 'Color', 'm', 'LineWidth', 2);
xline(Strain(index2), 'Color', 'm', 'LineWidth', 2);
hold off
fontsize(25, 'Points');

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