Solutions for composition analysis problem
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We are investigating recycled construction material separated in several size fractions. These consist of a mix of materials such as concrete, ceramics, gypsum, etc. One of the ideas is to make a model to estimate the material content of the size fractions as follows:
a) Composition analysis on the size fractions (data in terms of component metal oxides, e.g. CaO)
b) Composition analysis on the materials
c) Reconstruction of size fraction composition (a) using the composition of materials (b); Size fraction X = a * Concrete + b * Ceramics + c * gypsum + ... , which shall be performed for each metal oxide to obtain the full spectrum
Being quite the MATLAB leek, the question is: Is there an optimisation method available in MATLAB which returns to me the coefficients a, b, c, etc. in such a way that they yield the best approximation of the composition analysis of size fractions using composition analysis of component materials.
Any more required information I will gladly provide!
Thank you very much in advance.
rough93 on 25 Sep 2019
Gotcha, so for this application, you'll need to either know the metal oxide content of each material ahead of time through analysis testing or as standard info. and pull it into MATLAB. I'd set it up like this:
el1Concrete = 23.2; %percent of metal oxide 1 in concrete
el2Concrete = 76.8; %percent of metal oxide 2 in concrete
el1Ceramics = 100; %percent of metal oxide 1 in ceramics
Then, you'll need your size fractions and how much material is in each (through analysis, as you stated):
Size1Concrete = 5; %5 units of concrete in size1
Size1Ceramics = 2; %2 units of ceramics in size1
Size2Concrete = 18; %18 units of concrete in size1
For each size, you can perform calculations in order to find your X equation for each size fraction, then add them together for an overall answer.
TotalSize1 = Size1Concrete + Size1Ceramics; % total amount of units in size 1
X1 = el1Concrete * (Size1Concrete/TotalSize1) + el1Ceramics * (Size1Ceramics/TotalSize1);
TotalSize2 = Size2Concrete + Size2Ceramics; % total amount of units in size 2
X2 = el2Concrete * (Size2Concrete/TotalSize2) + el2Ceramics * (Size2Ceramics/TotalSize2);
X = X1 + X2;
Is this what you're looking for? I don't think you need to use any analytics methods to approximate the answer here, or at least if I understand your request correctly.