@ Dr. Venkat Subramanian which models are the simple models you mentioned? Because I compared 5 different models and made a comparison between these and I found the Luo and Svendsen model most suitable for this problem. But even this model has unknown parameters which need to be determined and the only data I have is the experiment result, which they said I need to use to compare the population balance model with and use some of the data to find the population balance equation.

I copy pasted the breakup rate and daughter size distribution from the paper and inserted the data. Is it possible for this case.

(the experiment result is the bubble size distribution in a bioreactor, with an aeration of 0.25 vvm, an agitation speed of 250 rpm and an oil fraction (in water) of 30% (desity=  1230)

experiment_results.xlsx

@Axel Vogt thank you as well for your explanation. The scale is one thing I missed at first. The data after 130 is indeed something that makes no sence but this is only part of all the data I have and I shortened it because after 150 it is 100%, but other experimental data only becomes 100% at 150, so I need to do this for comparison reasons.

Do you know what the method and fitmethod is? and why the result with method brent and fitmethod lts is chosen by carl, while there are many other results to choose from.

The data is indeed disturbed a lot but this is due to the experimental data (which is not measured by me), I need to make an assesment of the used equipment because it need maintenance, so I know the data is not the best one to work with (unfortunatly)

@Carl Love First of all thank you very much for the response, this helps me a lot. This is the result I was looking for. The scale is indeed something I missed, so thanks for pointing this out.

I have one last question. You say the a,m1, m2,s1,s2 value: [a = .522164088988118, m1 = 22.7042491482519, m2 = 9.51958388629120, s1 = 6.47780713862839, s2 = 3.34678806698068]. In the maple file this is the result with the method brent and fitmethod lts.  With the notation: 'Sol'brent,lts.

Why is this the solution? Why is this method and fit method the right one?

@Markiyan Hirnyk Yes of course, I forgot to upload my mw file.The coefficient I found can never be correct, I did insert my excel file as well and it can clearly be seen the mean is not even close and I think a negative weight isn't possible eather.

data_fit.mw

data_linear.xlsx

@Markiyan Hirnyk statistic fit does not work, if I do so I get results that do not correspondent with the reality. Do you have perhaps any other ideas? I heard about dataFit in directSearch, But I do not know this nor do I have this packet. Anyone an idea if this could work?

@Markiyan Hirnyk I tried googling and in those results I have not found any example where you can find the maple code. I mostly understand population balancing but I was looking for a maple file with the actual code for a problem and if possible one related to my problem. It is so I can see the code and steps done in maple how to solve a population balance model if you have the formula (which I got out of other papers as I was instructed) till a solution with plots.

@Carl Love The X-axis is not linear. But I will insert a new excel file where the x-axis is linear if this helps. Is it possible to solve this problem whit an linear x-axis?

The data on the x-axis is not linear or logaritmic because of flaws in the equipment, that is the reason why I need to solve this problem so the equipment that they have used can be maintenanced.

data_linear.xlsx

@Carl Love when I use Fit(..., output= parametervalues) I get values of m1=0.91, m2=1.96, s1=1.96, s2=1.96 and a=-0.098

Can a (the weigth) be negative?

and how can the mean 1 and mean 2 be 0.91 and 1.96 of this graph? Or can this be right?

data_fit.mw

@Carl Love I missed indeed the() and you formula is correct, so the formula should be:

0.5*a*erfc(0.5*2^0.5*((-x+m1)/s1)) + (0.5-0.5*a)*erfc(0.5*2^0.5*((-x+m2)/s2))

with a solution:

-0.0493 erfc( -0.3589 x + 0.3301)+ 0.5493 erfc( -0.6492 x + 1.2771)

I this correct? And is it now possible to find m1, s1, m2, s2 and a?

data_fit.mw

@Markiyan Hirnyk I also have an other problem whit more difficult data. The original function is:

and the solution whe I fit the formula with my excel data is

now I do need to find m1, s1 and m2, s2 as mean and st dev of my 2 peaks in the graph and a the weight. in the figure below you can see the graph and mean 1 should be at around x=12 and for m2 at x=24. how do I get these values?

@Carl Love I have 4 sets of 150 numbers in data I need to transfer to maple for the fitting so, I need to calculate the parameters 4 times whit these numbers. Is this possible to copy paste? I use Excel 2007 and maple 18, does this match together? Because in the maple help page I found Maple support excel 97-2003