How can you apply Machine Learning to Comminution?

Summary

A key concept in the course ‘Simulation and Optimisation of Mineral Processing Plants’ is the application of Information Theory (IT). IT is both fundamental to mineral processing and (as far as I know) not taught elsewhere. As explained in previous articles, IT is an approach that leads to a ‘style’ of Machine Learning (ML). Indeed, the jump from IT to ML is so natural that it is difficult to define a boundary between the two subject areas.

In this article, I discuss the extension of IT to ML using comminution as an example.? The article is brief. A detailed lecture is provided in the Udemy course: ‘Information Theory (IT) as a basis for Machine Learning (ML)’. See Ref. 3.

Introduction

Before completing a PhD in Mineral Processing Engineering, I was a Physical Oceanographer.? As a Physical Oceanographer, I developed some novel mathematical approaches (which possibly could be labelled as ML).? As explained in a previous article (Ref. 1), the definition of ML is somewhat vague.? Here I mean a method of iterative improvement of mathematical models so that model development enables a model to match reality.

When I started my PhD I was introduced to modelling methods; and I was left wondering whether these models were the best approaches.? Certainly, they are particularly valuable in understanding process operations. However one has to question the purpose of a mathematical model.? Is it to:

1.?????? understand a process

2.?????? provide a practical model for optimisation, or

3.?????? provide a framework for a thesis or academic publication?

One would hope that all three objectives are synergistic, but this is not always the case.

What particularly confused me (at the time) was the use of rock breakage tests which would be used as input to predict product size distribution.? What confused me was that I wondered: “wouldn’t it be better for an operational plant to analyse the product size distribution to calibrate the models”.

Later, I realised that both approaches were of value with various strengths and weaknesses.? However, the idea of using product information still remains largely unexplored from an engineering viewpoint.

And so, the idea of using a product size distribution to calibrate or even construct a model is the focus of this article.

Proposed Udemy Course

Currently, there are two relevant courses:?

1.?????? Practical Introduction to Information Theory (Ref. 2) and

2.?????? Information Theory as a basis for Machine Learning (Ref. 3).

?In time, I am aiming to create a course:

“Introduction to Machine Learning for Mineral Processing”.

However, there are a number of courses I aim to create. The priority for courses depends on whether there is sufficient interest.? Currently, the response for already-available Udemy courses is not great.

As a compromise I added a ‘Machine Learning for Comminution’ lecture in course 2.

Methodology

Comminution is of course a complex process, so here I am only focusing on one aspect:? the aspect of the breakage function.

In order to demonstrate how ML can be applied I have to use simplifications, which themselves are making assumptions which are not valid. This compromise is required to highlight the ML approach. A complete and valid ML model would be quite complex to describe in a manageable article.

The Breakage Function (or matrix)

The basic idea is that we have a feed (F) and product (P).? These are related by:

Given a feed and product, can the breakage function be estimated?? Now before you read on, please think about the problem and draw your own conclusion.? There are three possible answers:

• No.
• Yes.
• I don’t know.

The answer I obtain the most is “I don’t know”; which is fine.? Now to pre-empt this article I am going to say ‘yes’, but before I do so I need to be very clear.? B cannot be estimated with high certainty.? B can be estimated using IT. The sub-question is whether B can be estimated sufficiently to be practical.

That is let us rewrite the equation:

Now if we estimate B2, the question is whether when applied to a different feed (F2), how good an estimate is P2 using:

Or indeed can we improve the estimate of B by using both equations.? The answer to this question is ‘yes’.

Solving equation 1 only to estimate the breakage function is an example of IT .? Using this estimate as a prior in equation (2) is an example of ML.

Figure 1 Visual explanation of IT and ML.?

IT is used for a single set of data to estimate the model. ML is used for a succession of data to improve the model using available data.

The methodology here of using IT for comminution is not totally original, and another author who worked on this problem is Otwinowski (2006), see Ref. 4.

Action plan

The purpose of this article is to demystify the concept of using an IT approach as a basis for ML for mineral processing. Direct courses are available by contacting the author.

An article providing a worked example will be provided if there is sufficient interest.

References

1.?????? LinkedIn article: What strategy can I use to apply Machine Learning to Mineral Processing?

2.?????? Udemy course: 'Practical Introduction to Information Theory'

3.?????? Udemy Course: ‘Information Theory (IT) as a basis for Machine Learning (ML)’

4.?????? Otwinowski 2006, ?Maximum entropy in comminution modelling