AI Technique suitable for Temperature Distribution prediction.

Greetings,

I am a Mechanical Engineer by profession and am considering exploring a suitable AI/ML technique to predict the 2D temperature distribution of an arbitrary object for different heat generation rates.

So I am considering data from temperature sensors to give me temperature values at particular X/Y coordinates on my object, along with the corresponding cooling medium static pressure and flow rates for different heat generation rates of my object.

Now from these few spatial locations, I'd like to predict the temperature at other points on the object where no sensors are placed, given that I will train my model with known values of temperature at the non-sensor locations obtained from deterministic/analytical model of the problem.

In short my predictors would be:

1. Heat Generation
2. Pressure
3. Flow Velocity

at, say 5 locations, to predict temperature at 10 locations.

Further, if I would like to capture the temporal variation, how would I prepare my dataset and which AI technique would be best for this problem?

Thank you!

[Sam Chak]

Hi @Ibrahim Patel

I'm imagining how the spatial prediction probably look like. Unsure if the temperature gradient would affect the prediction accuracy or not. You didn't mention about how far the 10 target locations are away from the 5 sensor locations. But I guess that the 10 target locations must be difficult to reach, or maybe impossible to install the sensors. If there is a governing differential equation, perhaps fitting parameters of the DE to the spatial data would yield better predictions.

% Example
[X, Y] = meshgrid(0:0.25:4);
Z = 5*(X - 2).*exp(- (X - 2).^2 - (Y - 2).^2) + 32;
contour3(Z, 35)
xlabel('x')
ylabel('y')
zlabel('T')

[Ibrahim Patel]

So here's the concept I am trying to work on using AI. Given 44 temperature sensor reading (shown as different colored boxes above (my Input) I want to yield the image below; giving the whole temperature distribution at all missing locations of the Input image.

I guess CNN is suitable, but I don't know how to go about it. If anyone can suggest a suitable architecture for this problem please or possibly a code@Sam Chak, @Image Analyst .

Thanks!

[Ibrahim Patel]

I used nftool to solve the above problem. But I want a technique that if one sensor fails (temperature reading NaN) the distribution may still be obtained.

Any one care to suggest which technique can accommodate missing values in inputs of a trained model?

The nftool model gives NaN for all even if one value in input is NaN...

[Walter Roberson]

@Ibrahim Patel

Major parts of the processing for Neural Networks is matrix multiplications. A single NaN "pollutes" an entire row of results.

Observe:

A = magic(5)

A = 5×5

17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

B = rot90(A)

B = 5×5

15 16 22 3 9 8 14 20 21 2 1 7 13 19 25 24 5 6 12 18 17 23 4 10 11

C = flipud(B)

C = 5×5

17 23 4 10 11 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9

An = A; An(2,4) = nan

An = 5×5

17 24 1 8 15 23 5 7 NaN 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

orig1 = A * B

orig1 = 5×5

895 1000 975 820 535 1000 925 845 635 820 975 845 585 845 975 820 635 845 925 1000 535 820 975 1000 895

orig2 = orig1 * C

orig2 = 5×5

54775 52450 50425 58300 58675 57425 55550 51275 52950 57425 58825 58175 54925 51675 51025 52425 56900 58575 54300 52425 51175 51550 59425 57400 55075

mod1 = An * B

mod1 = 5×5

895 1000 975 820 535 NaN NaN NaN NaN NaN 975 845 585 845 975 820 635 845 925 1000 535 820 975 1000 895

mod2 = mod1 * C

mod2 = 5×5

54775 52450 50425 58300 58675 NaN NaN NaN NaN NaN 58825 58175 54925 51675 51025 52425 56900 58575 54300 52425 51175 51550 59425 57400 55075

Thus with even a single NaN, major portions of the output can become unusable. It is common for every input in a Neural Network to influence every output, so a single NaN can ruin the entire output.

Because of this, it is your responsibility to pre-process the data, and entire remove the samples that have NaN or else replace the NaN entries with something finite.

Neural Network algorithms are mostly not designed to be able to detect and fix-up calculations that involve nan.

[Ibrahim Patel]

Thanks @Walter Roberson

Answer 1

[Ibrahim Patel]

Thanks @Sam Chak. Actually I am considering exploring the AI approach to this problem.

You are right, the PDE approach would give better results.

Answer 2

[Diana]

This is an interesting discussion, not long ago I also discussed this and found a lot of useful comments for myself. Now I am interested in a slightly different direction of using AI. For example, in the field of visual data, accuracy is of paramount importance. Image annotation services are the cornerstone for achieving accuracy in machine learning and artificial intelligence. So I found out about an outsourcing image annotation company that has good reviews. Maybe this will be useful for you.