I've been thinking about solar collectors where several independent mirrors to focus the light on a solar collector, similar to the following design from Energy Innovations.

Because there will be flaws in the assembly of this solar array, I am proceeding with the following assumptions (or lack thereof):

• The software knows the "position" of each mirror, but doesn't know how this position relates to the real world or to other mirrors. This will account for poor mirror calibration or other environmental factors which may effect one mirror but not the others.

• If a mirror moves 10 units in one direction, and then 10 units in the opposite direction, it will end up where it originally started.

I would like to use machine learning to position the mirrors correctly and focus the light on the collector. I expect I would approach this as an optimization problem, optimizing the mirror positions to maximize the heat inside the collector and the power output.

The problem is finding a small target in a noisy high-dimensional space (considering each mirror has 2 axis of rotation). Some of the problems I anticipate are:

• cloudy days, even if you stumble upon the perfect mirror alignment, it might be cloudy at the time

• noisy sensor data

• the sun is a moving target, it moves along a path, and follows a different path every day - although you could calculate the exact position of the sun at any time, you wouldn't know how that position relates to your mirrors

My question isn't about the solar array, but possible machine learning techniques that would help in this "small target in a noisy high dimensional-space" problem. I mentioned the solar array because it was the catalyst for this question and a good example.

What machine learning techniques can find such a small target in a noisy high-dimensional space?

EDIT:

A few additional thoughts:

• Yes, you can calculate the suns position in the real world, but you don't know how the mirrors position is related to the real world (unless you've learned it somehow). You might know the suns azimuth is 220 degrees, and the suns elevation is 60 degrees, and you might know a mirror is at position (-20, 42); now tell me, is that mirror correctly aligned with the sun? You don't know.

• Lets assume you have some very sophisticated heat measurements, and you know "with this heat level, there must be 2 mirrors correctly aligned". Now the question is, which two mirrors (out of 25 or more) are correctly aligned?

• One solution I considered was to approximate the correct "alignment function" using a neural network which would take the suns azimuth and elevation as input and output a large array with 2 values for each mirror which correspond to the 2 axis of each mirror. I'm not sure what the best training method is though.