I have a question about Tavares calibration of EDEM

In this formula：I want to measure E50 and σ now

Assuming that I have conducted many experiments on particle size ranges, I have conducted 20 experiments with a particle size of 10mm and obtained the energy Ek of each stone fragmentation. Then, I divided it by the corresponding weight m of each stone to obtain the specific fragmentation energy E=(Ek/m), and arranged E in ascending order of specific fragmentation energy; Next, I perform a log operation on E to obtain the log (E) from small to large. I calculate the average value a and sample variance σ ^ 2 of 20 logs (E), and finally E50=10 ^ a. The sample variance σ is the variance I want. Is this feasible?

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Accepted answers

Renan

Hi @Jin1,

Assuming you have correctly measured the fracture energy of many different particles of the same size, you can calculate the probability of a particle having a fracture energy of E by dividing the number of times that energy appeared in your measurements by the total number of measurements you made.

After that, if you rearrange the equation you shared, you get:

ln(E) = sqrt(2)*sigma*inverf(2*P-1) + ln(E50)

which, in a log-log plot, is the equation of a line, y=ax+b, in which y = ln(E), a = sqrt(2)*sigma, x = inverf(2P-1) and b = ln(E50). If you plot your measurements in a log-log plot and find the equation of the line that best fits your data then you'll be able to calculate sigma and E50.

Best regards,

Renan

All comments

Renan

Hi @Jin1,

After that, if you rearrange the equation you shared, you get:

ln(E) = sqrt(2)*sigma*inverf(2*P-1) + ln(E50)

Best regards,

Renan

Another option is to notice that the fracture energy follows a lognormal distribution (as mentioned in the screenshot). This means that you can use the method explained here:

https://en.wikipedia.org/wiki/Log-normal_distribution#Estimation_of_parameters

to calculated

Jin1

OK， I can understand your approach. You've essentially transformed the probability function,

But I still have a question, for example, I got 20 sets of E (fracture energy/weight, Ek/m）, And I arranged him from small to large, obtaining the values of probabilities P and E. However, if I fit according to the function of P (E) and E * given in my comment, wouldn't it be not quite right? Because the variable in the above function is E *, and E * and E have a functional relationship, as shown below

look forward to your reply