Moving average

[vanatteveldt]

This is nog an original creation, but the post that it is based on (viewtopic.php?t=29679#p190249 and https://www.reddit.com/r/factorio/comme ... _included/) did not contain a detailed explanation or a .15 blueprint string, so I thought some people might find it useful.

Goal: give a moving average of a measurement like belt throughput, i.e. smooth or dampen the input signal so it doesn't fluctuate too much

Theory

theory

the idea is that every tick the value is a mix of the previous value (the memory) and the new input:

X_new = (1-s) * X_old + s * Input

Where s is a smoothing constant: setting it to .5 would mean that old and new are treated equally, so the current value contributes 1/16=6.25% of the value in 4 ticks. Since ticks are really quick in factorio, it is more reasonable to take a smoothing factor like .01, so the value of one second (60 ticks) ago contributes around 50% (.99 ^ 60).

This can be rewritten as:

X_new = X_old - X_old/z + Input/z (with z = 1/s; i.e. z=100 for a .01 mixing of new input)


Since factorio has integer calculus (only whole numbers, .99 is rounded down to zero) you don't really want to divide raw input by 100. Rather, you want to multiply everything with z:

z*X_new = z*O_old - X_old + input

And then scale down by z before displaying. You might even want to multiply the input by some amount to scale the amount up, e.g. multiply belt readings by 3600 to get items per minute instead of items per tick.

Overview:

This can be implemented in 3 combinators only, but I use slightly more to make it more understandable:



This displays the throughput of the belt as items/minute, counter courtesy of DaveMcW (viewtopic.php?f=193&t=19825&start=60#p282391)

All red wires are control, green wires are content

Implementation:

The main work is done by the central combinator, which embodies the main formula explained above: V_new = V_old - V_old/S + Input = V_old - V_old*N + Input

The addition is implemented by putting all components together on the input side.
- V_old is its own output (of the previous tick)
- V_old * N is the output of the bottom combinator (memory decay)
- Input is the V output of the top combinator (input)

Thus, every tick calculates a new version of V to which input is added and a fraction of the previous output is removed. The resulting variable V can be seen as the exponential average times the smoothing factor.

The combinator settings itself are the simple 'memory cell' / counter, where the output is copied to the input unless the red reset signal is nonzero:



Input: The topmost combinator scales up the input value (everything) and outputs it as V (for value):



Memory decay

The bottom combinator divides the current value of V by N, which is the negative value of the smoothing factor (so -100 if the smoothing factor is 100):



N is calculated by multiplying the constant value S by -1 in the constant and arithmetic combinators on the left hand side:




(the red signal is the reset signal: set to 1 to reset the counter, set back to zero to resume counting)

The final combinator scales down the value by dividing by the smoothing constant S:



In this case it ouputs to A because the counter wants its input on A, but of course you can put it on whatever you want.

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

Compact version

Here is a more compact version for 'copy paste' use. Input is anything on the green signal to the topleft; output is set on the bottom right, here A on the red signal:



(note that instead of a red reset signal this has a green control signal so you can reset by simply switching off the combinator; also, I manually calculate N=S*-1 to get rid of one combinator)

blueprint

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

As said above, none of this is original, but I hope the explanation and blueprint string might be of use. If there are any mistakes or inefficiencies please let me know!

[regular_human]

Excellent post, very informative. Thank you!

[AndrewIRL]

This is exactly what I needed and explained in detail such that I was able to modify it to get it to do what I wanted (smoother).

Very nice. Thanks for the current version blueprints.

[vanatteveldt]

Thanks both, glad you found it helpful! I learn a lot from all the posts on this board, so it's good to contribute something