How can i found the infelction point from the data and remove the data before the first and last infelction points.

I need to find the inflection point from the experimental data using matlab. Kindly help me for that. Thanks in advance

Answer 1

[Star Strider]

The data are quite noisy. After filtering them, it is not obvious what sort of inflection point you want or how to define it.

M1 = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1265285/data.xlsx')

M1 = 1430×2

0 32.2683 0.0050 32.2683 0.0100 32.2683 0.0150 32.2683 0.0200 32.2683 0.0250 32.2683 0.0300 32.2683 0.0350 32.2683 0.0400 32.2683 0.0450 32.2683

x = M1(:,1);
y = M1(:,2);
% yf = sgolayfilt(y, 3, 451);

Fs = 1/mean(diff(x))

Fs = 200

Fn = Fs/2;
L = numel(x);
NFFT = 2^nextpow2(L);
FTy = fft((y-mean(y)).*hann(L),NFFT)/L;
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);

figure
semilogy(Fv, abs(FTy(Iv))*2)
grid
xlim([0 10])

yf = lowpass(y, 0.5, Fs, 'ImpulseResponse','iir');

dyfdx = gradient(yf) ./ gradient(x);
d2yfdx2 = gradient(dyfdx) ./ gradient(x);

figure
yyaxis left
plot(x, y, 'DisplayName','Unfiltered Data')
hold on
plot(x, yf, '-r', 'DisplayName','Filtered Data')
hold off
ylabel('Data')
yyaxis right
plot(x, dyfdx, 'DisplayName','First Derivative Of Filtered Data')
hold on
plot(x, d2yfdx2, 'DisplayName','Second Derivative Of Filtered Data')
hold off
yline(0, '-g')
ylabel('Derivatives')
grid
legend('Location','best')

.

[JINU SUDHAKARAN Mr]

Thank you

[JINU SUDHAKARAN Mr]

The inflection points can be determined by the second derivative test. that is the point at which the second derivative reaches zero value. can yo help me to locate the points at which the second derivate reaches zero.. in my case, first point and last point is important. but its better to locate all points. i need to cut the data which is at the left side of the first inflection point. can you please help me to figure it out.

Also kindly guide me how i can do this process for two y values realted with one x values at the sam time.

Thanks in advance

[Star Strider]

Finding the second derivative zero-crossings is straightforward.

Try something like this —

M1 = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1265285/data.xlsx')

M1 = 1430×2

0 32.2683 0.0050 32.2683 0.0100 32.2683 0.0150 32.2683 0.0200 32.2683 0.0250 32.2683 0.0300 32.2683 0.0350 32.2683 0.0400 32.2683 0.0450 32.2683

x = M1(:,1);
y = M1(:,2);
% yf = sgolayfilt(y, 3, 451);

Fs = 1/mean(diff(x))

Fs = 200

Fn = Fs/2;
L = numel(x);
NFFT = 2^nextpow2(L);
FTy = fft((y-mean(y)).*hann(L),NFFT)/L;
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);

Fco = 0.5;

figure
plot(Fv, mag2db(abs(FTy(Iv))*2), 'DisplayName','Fourier Transform')
grid
xlim([0 10])
xlabel('Frequency')
ylabel('Magnitude (dB)')
xline(Fco, '-r', 'DisplayName',sprintf('Lowpass Filter Cutoff Frequency: %.2f',Fco))
legend('Location','best')

yf = lowpass(y, Fco, Fs, 'ImpulseResponse','iir');

dyfdx = gradient(yf) ./ gradient(x);
d2yfdx2 = gradient(dyfdx) ./ gradient(x);

d2zix = find(diff(sign(d2yfdx2)));
for k = 1:numel(d2zix)                                              % Second Derivative Zero-Crossings
    idxrng = max(1,d2zix(k)-1) : min(d2zix(k)+1, numel(x));
    xz(k,:) = interp1(d2yfdx2(idxrng), x(idxrng), 0);
    yfz(k,:) = interp1(x, yf, xz(k));
end

Function_Value_At_Inflection_Points = table(xz, yfz, 'VariableNames',{'x','y'})

Function_Value_At_Inflection_Points = 3×2 table
      x         y   
    ______    ______

    1.4709    34.213
    2.4326     36.47
     3.188    38.038

figure
yyaxis left
plot(x, y, 'DisplayName','Unfiltered Data')
hold on
plot(x, yf, '-r', 'DisplayName','Filtered Data')
hold off
ylabel('Data')
yyaxis right
plot(x, dyfdx, 'DisplayName','First Derivative Of Filtered Data')
hold on
plot(x, d2yfdx2, 'DisplayName','Second Derivative Of Filtered Data')
hold off
yline(0, '-g', 'DisplayName','Derivatives 0 Line')
for k = 1:numel(xz)
    xline(xz(k), '--m', sprintf('x = %.2f',xz(k)), 'DisplayName', sprintf('Inflection Points x = %.2f',xz(k)))
end
ylabel('Derivatives')
grid
legend('Location','best')

This entirely depends on how you want to define the inflection points and how you want to process the signal before calculating them.

.

[JINU SUDHAKARAN Mr]

Thanks

[JINU SUDHAKARAN Mr]

could you please explain the step by step for the denoising of the data... iam not familiar with that .so facing some difficulties for understanding in first steps for smoothening of data

Thanks in advance

[Star Strider]

Here, I simply calculated and plotted the Fourier transform, and then used that to choose the passband for the lowpass filter. That choice is a bit empirical, so I experimented until I got a filtered result that I liked. (I initially used the sgolayfilt function, however that did not produce the result that I wanted, so I went with a frequency-selective filtering approach.)

That is all there is to it. As to how I arrived at the approach I used, it is simply the result of my experience in such things.

[JINU SUDHAKARAN Mr]

THANK YOU

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

Answer 2

[Steven Lord]

The ischange, islocalmin, and/or islocalmax functions may be of use to you, as might the corresponding Live Editor Tasks Find Change Points and Find Local Extrema.