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Question 0 Hints and Tips
You may have realised that the distribution of data for the sluice performance does not look like a
polynomial – because of what we know about the system (i.e. the values can only be between 0 – 100%)
it clearly can’t move towards ± infinity at extreme values of x. So polyfit is useless; even if you can
generate a curve that seems to fit the data, the model is not based in reality and so is invalid.
It is also not a typical power law or exponential or saturation growth type function that have been
covered in the course material (none of which are polynomials either, again rendering polyfit useless
except for fitting a line – order 1 – to linearised data).
With that, here is a hint in three parts for question 0:
Part 1: There was a really good question on the forum earlier about whether y = logex or y = arctan(x)
could be linearised. Linearisation is a hugely important part of fitting models. As a general rule, it is
really easy to linearise any function that only contains one y and one x. So for these examples:
This is a general process that can be used across many different functions (maybe you can now see how
the substitutions we discussed in the workshops for the exponential and saturation-growth models have
come about).
Part 2: In a few years, when you become professional engineers and the decisions you make and
problems you solve could influence lives, there is very often not enough information to solve problems
straight off the bat in a prescriptive manner, so you will have to hunt around for ideas or take a step
back to think about the relative importance of approximations.
Remember also that Google is a great resource and there is a massive difference between using it
constructively and plagiarising from it. Don’t avoid Google just because others have plagiarised from it
or used information it yields without careful thought, possibly tarnishing the act of Googling in your
minds. We expect you to be able to extend a little beyond what has been explicitly mentioned in the
course. As long as you use it wisely, it is the first port of call for anyone solving a problem, not just
engineers.
Once you plot the data and have a careful look at how it is distributed, you will see that it looks like a
centrosymmetric distribution that asymptotes horizontally. So try some combination of “distribution
functions” “centrosymmetric” and “horizontal asymptotes” in Google and click on images to see what
you get. There’s at least a couple that we know of that show up – one is based around
Part 3: Now, as an engineer, you would know that finding gold is not a life-threatening scenario so you
can afford to make approximations, like just fitting a line or some piecewise-lines to the distribution
instead of the function above. A line doesn’t look like a great fit (and doesn’t obey the physical rules of
the system) but it will give you ball-park estimates of processing performance. Question 0 is only worth
a minute fraction of the marks and so it is not that vital if you get the function fit perfect or not.
While the performance of the sluice is the one common feature to all scenarios, in the end, it is likely
that other approximations made in other parts of the analysis of the whole prospecting problem will
actually lead to more errors in your estimate than approximating this distribution inexactly. The way
that the assignment has been broken down allows you to do any one of the questions well without too
much dependence (almost none) on the other questions.
At least in this assignment, we are less interested in whether you got the final answer exactly the same
as our solution. We are much more interested in whether you understand the processes you are
applying and can explain what their limitations are. So don’t panic if your fit is not perfect, because as
long as you are clear about the approximations that you make and explain why you made them and
what their limitations are (either in comments in your code or fprintf statements in your output), you
cannot be penalised for that – I said this very clearly in the workshop.

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