Removing noise from Hysteresis loops

Question

Sadia 2019-7-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/470461-removing-noise-from-hysteresis-loops

编辑： Sadia 2019-9-24

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Hi, I need a help in removing noise from Hysteresis loops, I have generated code which loads multiple files(containing Force and Displacement data) one by one and plots their Hysteresis loops but i need to remove noise and the smoothening curve should fit the orginal shape, I have used a filter in following code but it distorts the orginal shape of loops which effects the area under the curve for calculation of damping.This filter works well for one data file but disfigures the other file, so I want a solution that would work for my all files. Any help would be highly appreciated.

Following is my code:

clc
clear all
projectdir = 'F:\NUST\SAMPLE 9\Measured'
dinfo = dir(fullfile(projectdir))
dinfo([dinfo.isdir]) = []    %get rid of all directories including . and ..
%nfiles = length(dinfo)
folder = 'F:\NUST\IMAGE\hysteresis';
for j = 5 :6
    
  filename = fullfile(projectdir, dinfo(j).name)
  delimiter = ';';
startRow = 1000;
endRow = 2000;
formatSpec = '%*s%*s%f%f%f%f%f%f%f%f%f%[^\n\r]';
  f1 = fopen(filename, 'r')
  dataArray = textscan(f1, formatSpec, endRow-startRow+1, 'Delimiter', delimiter, 'EmptyValue' ,NaN,'HeaderLines', startRow-1, 'ReturnOnError', false);
  fclose(f1)
  %% Allocate imported array to column variable names
  Displacement = dataArray{:, 1}
Force = (dataArray{:, 2})*1000
%%%%%%%%%%%%%Plots%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure (j)
%plot(Testtime,Force)
%b=fir1(20,0.1,'low');
%[b,a]=butter(10,0.2,'low');
[b,a]=butter(10,0.2,'low');
%y1=filter(b,1,Force);%Fir
y2=filter(b,a,Force);%butter
plot(Displacement,y2)
%plot(Displacement,Force)
title(dinfo(j).name)
%title(['S1  R',sprintf('%d',j)])
xlabel('Displacement(mm)') 
ylabel('Force(N)')
%saveas(h,sprintf('FIG%d.png',j));
hold on
%saveas(plot, fullfile(folder, sprintf('fig%02d.jpg', j)));
pngFileName = sprintf('Fig_%d.jpg', j);
  fullFileName = fullfile(folder, pngFileName);
    
  % Then save it
  %saveas(gcf, fullFileName)
  
end

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Answer 1

Star Strider 2019-7-6

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/470461-removing-noise-from-hysteresis-loops#answer_382180

The easiest way to remove the noise is likely to fit your data to a function that describes the hysteresis.

See: Interpolation when y data is not strictly a function of x for an illustration of how to do that.

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Sadia 2019-7-6

在 MATLAB Online 中打开

Thank you Sir for your valuable replay. I have modified my code using your illustration but ascending and descending curves are very narrow, seems like they are not following the data accurately. i am attaching figures of both usng my old code and new one. and following is my modified code. kindly assesist me if I am doing something wrong.

clc
clear all
projectdir = 'F:\NUST\SAMPLE 9\Measured'
dinfo = dir(fullfile(projectdir))
dinfo([dinfo.isdir]) = []    %get rid of all directories including . and ..
%nfiles = length(dinfo)
folder = 'F:\NUST\IMAGE\hysteresis';
for j = 5 :6
    
  filename = fullfile(projectdir, dinfo(j).name)
  delimiter = ';';
startRow = 1000;
endRow = 2000;
formatSpec = '%*s%*s%f%f%f%f%f%f%f%f%f%[^\n\r]';
  f1 = fopen(filename, 'r')
  dataArray = textscan(f1, formatSpec, endRow-startRow+1, 'Delimiter', delimiter, 'EmptyValue' ,NaN,'HeaderLines', startRow-1, 'ReturnOnError', false);
  fclose(f1)
  Displacement = dataArray{:, 1}
  Force = (dataArray{:, 2})*1000
x = Displacement;
y = Force;
[cmin,cxix] = (min(x))
[cmax,cnix] = (max(x))
[fmin,fxix] = (min(y))
[fmax,fnix] = (max(y))
figure(j)
plot(x, y)
hold on
plot([cmin  cmax],  [fmin  fmax], '+r', 'MarkerSize', 5, 'LineWidth',1.5)
hold off
grid
text(cmin,fmin, sprintf('(%.3f, %.3f)',cmin, fmin), 'FontSize',8, 'FontName', 'Consolas', 'FontWeight', 'bold', 'VerticalAlignment','bottom', 'HorizontalAlignment','left')
text(cmax,fmax, sprintf('(%.3f, %.3f)',cmax, fmax), 'FontSize',8, 'FontName', 'Consolas', 'FontWeight', 'bold', 'VerticalAlignment','top', 'HorizontalAlignment','right')
xlabel('Displacement(mm)')
ylabel('Force(kN)')
Phi1 = @(b,I) -(b(1) .* atan(-b(2)*I+b(3)) - b(1).*I.*b(4));    % Descending
Phi2 = @(b,I)  (b(1) .* atan(-b(2)*I+b(3)) + b(1).*I.*b(4));    % Ascending
ixd = fix(length(x)/2);
vi2 = 1:ixd;
vi1 = ixd:length(x);
opts = statset('MaxIter', 5000, 'MaxFunEvals', 10000);
B1 = nlinfit(x(vi1), y(vi1), Phi1, ones(4,1),  opts )
B2 = nlinfit(x(vi2), y(vi2), Phi2, ones(4,1),  opts )
FitPhi1 = Phi1(B1,x);
FitPhi2 = Phi2(B2,x);
figure(j)
hpd1 = plot(x(vi1), y(vi1), '.b', x(vi2), y(vi2), '.b', 'LineWidth',1);
hold on
hpr1 = plot(x, FitPhi1, '-r', 'LineWidth', 1.5);
hpr2 = plot(x, FitPhi2, '-g', 'LineWidth', 1.5);
hold off
grid
legend([hpd1(1),hpr1,hpr2], 'Data', 'Descending', 'Ascending', 'Location', 'NW')
xlabel('Displacement(mm)')
ylabel('Force(kN)')
title(dinfo(j).name)
  
end

Star Strider 2019-7-6

在 MATLAB Online 中打开

Your data are definitely not easy to work with!

The data in your file compriseds one loop. There are many NaN values, so to eliminate them, I used:

dataArray = readmatrix('forceDisplacement.xlsx');
DispFrc = dataArray(:,3:4);
DispFrc = DispFrc(~any(isnan(DispFrc),2),:);
DispFrc = sortrows
Displacement = DispFrc(:,1);
Force = DispFrc(:,2);
x = Displacement;
y = Force;

It turns out that they are not neatly apportioned between the ascending and descending loops either, so simply dividing your matrix in half (that worked in applying my code to other problems) does not work with your data.

I instead used this to separate them:

ixd = gradient(x);
vi2 = ixd >  0;
vi1 = ixd <= 0;

and it appeared to work because the data you provided in your Excel file otherwise resulted in both limbs of they hysteresis loop very closely overlying each other. I could not distingush them using my existing code. I could only distinguish them using my revised ‘vi1’ and ‘vi2’ vectors based on the positive and negative gradients, and this was not optimal because the loops are supposed to approximate each other at thier extremes. Your data do not, and remain separated.

You applied my code correctly, however your data do not appear to have the characteristics my code requires to work easily with it. I am not certain what the problem is beyond that, or how to solve it.

I will do my best to work with you to solve these problems, if a solution exists.

Star Strider 2019-7-7

在 MATLAB Online 中打开

With respect to your earlier Comment, I use the readmatrix function (R2019a and later versions). It produces a double array, not a cell array. You posted an .xlsx spreadsheet, so the easiest way to import it is with readmatrix or xlsread.

Your ‘Hysteresis1.m’ file apparently creates a hysteresis loop and then attempts to analyse it. It requires the Communications Toolbox, that I do not have. If I substitute a randn call for awgn, I find that it simulates a hysteresis loop, then calls a function called ‘Hysteresis’ that is not supplied, so I cannot run it. I was also unable to find it with an Interweb search.

I discovered that sgolayfilt can smooth your data, however you have a number of data that are not unique, and this is causing problems with the analysis. Also, you have a number of cycles in your data, not just one, and those have varying amplitudes. My code was designed to analyse one complete cycle, and for that it works correctly.

I ended up getting unique values for your data, then filtering them, then doing the analysis. I use findpeaks to isolate the last (largest) cycle, provining the most data. This is about as good as I can get your data:

dataArray = readmatrix('forceDisplacement.xlsx');
DispFrc = dataArray(:,3:4);
DispFrc = DispFrc(~any(isnan(DispFrc),2),:);
Displacement = DispFrc(:,1);
Force = DispFrc(:,2);
x = Displacement;
y = Force;
[UDispFrc,ridx] = unique(DispFrc, 'rows', 'stable');
Ux = UDispFrc(:,1);
Uy = UDispFrc(:,2);
xf = sgolayfilt(Ux, 3, 7);
yf = sgolayfilt(Uy, 3, 7);
[xpks, xlocs] = findpeaks(xf);
[ypks, ylocs] = findpeaks(yf);
xfr = xf(xlocs(end-1):xlocs(end));
yfr = yf(xlocs(end-1):xlocs(end));
Phi1 = @(b,I) -(b(1) .* atan(-b(2)*I+b(3)) - b(1).*I.*b(4));    % Descending
Phi2 = @(b,I)  (b(1) .* atan(-b(2)*I+b(3)) + b(1).*I.*b(4));    % Ascending
ixd = fix(length(xfr)/2);
vi2 = 1:ixd;
vi1 = ixd:length(xfr);
opts = statset('MaxIter', 5000, 'MaxFunEvals', 10000);
B1 = nlinfit(xfr(vi1), yfr(vi1), Phi1, ones(4,1),  opts )
B2 = nlinfit(xfr(vi2), yfr(vi2), Phi2, ones(4,1),  opts )
FitPhi1 = Phi1(B1,xfr(vi1));
FitPhi2 = Phi2(B2,xfr(vi2));
figure
hpd1 = plot(xfr(vi1), yfr(vi1), '.r', xfr(vi2), yfr(vi2), '.g', 'LineWidth',1);
hold on
hpr1 = plot(xfr(vi1), FitPhi1, '-r', 'LineWidth', 1.5);
hpr2 = plot(xfr(vi2), FitPhi2, '-g', 'LineWidth', 1.5);
hold off
grid
legend([hpd1(1),hpr1,hpr2], 'Data', 'Descending', 'Ascending', 'Location', 'NW')
xlabel('x_1')
ylabel('y_1')

That is the best I can do.

To see the problems with your data in more detail, add ‘zf’ and this plot:

zf = linspace(0, 1, numel(Ux));
figure
plot3(xf, yf, zf)
grid
xlabel('xf')
ylabel('yf')

The inconsistent data are causing serious problems with the analysis of your data in my code.

Sadia 2019-7-7

在 MATLAB Online 中打开

Thank you so much sir for your precious time, one last request as I have multiple files to process with input argument of type "cell" not double array (R2015a), so could you please adjust my following code so that It may not give error. I have adjusted end and start rows so that i can select few cycles, you can change it. Pardon me for my lack of knoweledge in coding as that’s not within the area of my expertise. I highly appreciate your help.

projectdir = 'F:\NUST\SAMPLE 9\Measured'
dinfo = dir(fullfile(projectdir))
dinfo([dinfo.isdir]) = []    %get rid of all directories including . and ..
for j = 11:13  
  filename = fullfile(projectdir, dinfo(j).name)
  delimiter = ';';
startRow = 1000;%to get few cycles as their are 12 cycles rest are noise.
endRow = 2000;
formatSpec = '%*s%*s%f%f%f%f%f%f%f%f%f%[^\n\r]';
  f1 = fopen(filename, 'r')
  dataArray = textscan(f1, formatSpec, endRow-startRow+1, 'Delimiter', delimiter, 'EmptyValue' ,NaN,'HeaderLines', startRow-1, 'ReturnOnError', false);
  fclose(f1)
  %% Allocate imported array to column variable names
 DispFrc = dataArray(:,3:4);
DispFrc = DispFrc(~any(isnan(DispFrc),2),:);
Displacement = DispFrc(:,1);
Force = DispFrc(:,2);
x = Displacement;
y = Force;
.