# How to do a Multilabel classification where the label order is important?

I am doing carbon composite modelling for my college project. Each composite sample is created by stacking carbon fiber of different angles (0, 45, 90,-45). A sample can contain 8, 12 or 16 of such fibers. An actual sample would be named something like '0_90_-45_45_90_45_-45_0' or '90_-45_-45_-45_45_-45_0_45_90_-45_-45_-45_0_-45_90_0'. I have a bunch of data including continuous numerical like energy or reaction force, and some screenshots of the composite damage.

How can I train the model so that it can generate screenshot pictures and numerical data by inputting angles? More specifically I wish to know how to set the target variable in a proper way. My bet is set up a '1st/2nd...stack_angle' variable and restrict it to have discrete values from the 4 angles. But I don't know if, this way, the model would acknowledge the order of the angels is important (i.e.: "45_-45_90" behaves differently than "-45_90_45" in real world experiments). My supervisor says I should split the samples based on the number of stacks, then I have to deal with 8, 12, 16 stack samples separately.

I assume you're using an Instron hardness tester or something similar, where you apply a known force and measure the size of the resulting damaged region. It would probably be convenient to make several measurements of a given sample, perhaps doubling the applied force each time. Pay attention to the ratio of damaged region size to fiber layer thickness.

Use exclusively 16-layer samples. Ignore ±45° angles for now. That still leaves an interesting design space to explore.

Measure a "boring" stack, with all layers aligned.

Now introduce a top layer at 90°, and make sixteen measurements where you move that 90° layer down through the stack. Presumably at some point its effect becomes imperceptible, at least when applying small forces. Play a classification game with your data: given the hardness tester measurement, can you tell which of the 17 different samples was used? Which force level(s) let you win the game? Which samples are difficult to distinguish? Does an OLS linear model adequately capture the physics?

Now introduce another fourteen samples, where a pair of "boring" stacks are oriented 90° apart. So we have a 2 + 14 layer stack, another is 3 + 13, and so on.

Now start introducing thicker regions, with a fiber orientation change at two or more layers. Do your existing simple models still match observations? You might need to resort to XGBoost random forest at this point.

I recommend naming each sample with the "change in angle" at each layer. So a boring sample would be sixteen zeros, and another sample might be {0, 0, 90, 0, 0, 0, ...} to indicate a pair of aligned layers atop fourteen aligned layers.