I have force and displacement data of 15 loop of cyclic loading in excel file. How can I calculate the Hysteresis area in every cycle (the area between loading and unloading in cyclic loading in force vs displacement graph)? I want to compare these areas. actually we can solve it using Trapezoidal Rule (area = { [ f(a)+f(b) ] /2 } * (b-a)) but does anyone know a MATLAB code or a Macro for this calculation?vthank you
It's a very easy process if you have Originlab software (version 8.6 and upper). Take the polygon area of the individual curves. See the attached file.
Dear Parinaz,
You can do it directly in Excel without any coding just simply apply a trapezoidal rule to the upload and download parts of your curve, and subtract the two areas. You also can use the trapz() function in MATLAB as indicated by the gentlemen above, or I could write you a small macro which does it. Just send me your data to [email protected].
cheers, Andras
If you have enough data points and your curves are well-behaved - and it looks like it - use the TREND function in Excel to curve fit each half of your graph (up and down), subtract the functions to get a difference function, then use the SUMPRODUCT function to build the integral over your range. This is effectively the trapezoidal method with higher precision.
Dear friends ,
I think I should mentioned in my question that my main problem was categorizing the data of each cycle separately in excel or Matlab. i know how to use tapz code in Matlab and that it is easier in excel. Dear David unfortunately it is not possible to use trend function.we do not have just one well-behaved curve as you can see in the attached picture the curves are knotted to each other.
There are 100 sample for every second and in some rates and duration I have 600000 data. the start and end point of cycles are not the same in different cycles . I decided to write a code for separating the data of every loop using sign change of the trapz area ( positives =loading curve , negatives =unloading curve) but it did not work properly because of the data sign variations in beginning and end of cycles( because y values do not have a minimum to maximum and then maximum to minimum trend! there irregularities in start and end in y values) .anyway although it took too much time but i did it in excel without any code.
Thank you for sharing your answers.
Dear Parinaz, I have come across a similar problem, and wondering if you have already reached a solution?
I chose the difficult way because my data was not proper for writing a code: I separated the data of each loop ( by checking the data) then used trapezoidal rule step by step.
It's a very easy process if you have Originlab software (version 8.6 and upper). Take the polygon area of the individual curves. See the attached file.
You can use matlab,, to get it done. simply plot the curve in matlab.
plot various lines various lines of x=0:0.01:n to match you trapezium requirement.
determine the points where the curve meets the x=0:0.01:n lines. those points will give you the other dimensions of the trapezium.
you can then deploy the ordinary trapezium formular to iterate the area under the curve.
hope you can generate the matlab code from that.
Dear Parinaz,
I suggest you the use of Gauss's formula for areas. It's more effective and general.
Use X coordinates for displacements and Y coordinates for forces.
Attached, please find a fragment of code in FORTRAN.
It will be easy to rewrite it in another language.
Regards,
Luiz Eduardo
Dear Madan Kumar,
The simplest way to do it is to use trapz() function in matlab:
https://fr.mathworks.com/help/matlab/ref/trapz.html
Or juste follow the other answers above.
Regards,
Izem Amazigh
Are the overlapped parts in hysteresis loops additive or should we consider that area only once?
http://www.ece.northwestern.edu/local-apps/matlabhelp/techdoc/ref/trapz.html
follow the above link
In case of symmetrical hysteresis loops, the area can be directly calculated by algebraic formula. See details in my recent article Article An improved parametric model for hysteresis loop approximation
Take attention to the “Supplementary material” that accompanies this article.- Badges
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