Extreme situations call for extreme theory

From a legislative perspective in 2004, we saw the introduction of a new subsidence management policy and approvals process implemented. Spurred on by a significant increase in the amount of underground coal mines operating throughout the Southern Coalfields, the NSW government further established an independent enquiry which resulted in a call for the increase in the use of peer reviewed science and independent expert opinion, when in the process of undergoing detailed environmental assessments that aim to address the full range of potential impacts on aspects such as water, biodiversity, air quality, noise, and subsidence.
The Australian Research Council’s Centre of Excellence for Mathematics and Statistics of Complex Systems or MASCOS is a research centre that develops mathematical and statistical techniques to improve understanding of the workings of complex systems. Besides theoretical research, MASCOS applies theory by conducting projects with industrial partners to solve real problems in complex systems. Since 2008, it has significantly expanded its industry outreach by targeting new industry sectors for specific projects using advanced mathematics and statistics, such as underground coal mining. MASCOS has a dedicated Industry Division led by Industry Projects Manager David Shteinman, an engineer with 24 years experience in the commercial and industrial applications of mathematics and statistics.
In collaboration with Mine Subsidence Engineering Consultants (MSEC Pty Ltd), MASCOS has established a two-stage project to develop statistical methods using extreme value theory (EVT) in order to improve prediction of the magnitude of ground subsidence due to underground coal mining, and the consequential impacts on structures. In effect a “bridge" has been built between some quite abstract statistical theory and the very real effects of mine subsidence.

What is EVT?
Extreme value theory refers to an area of statistics which provides a range of mathematically sound models that accurately describe the extreme levels of any process, such as extreme subsidence levels. A compelling feature about extreme value theory is that it allows credible prediction of the process being modelled beyond the range of the observed data. So, for example, 100-year return levels (the level expected to be exceeded on average once in 100 years) can easily be inferred from 30 years of observed data.

The Method
Stage 1: Exploratory Statistical Analysis, Dr Scott Sisson, UNSW Statistics
The first stage of this work was completed by Dr Scott Sisson of UNSW Statistics. This involved exploratory statistical analyses to quantify the probability that a future ground strain caused by mining exceeds a specified maximum tolerable subsidence (i.e. a trigger point). It was demonstrated that using EVT motivated models to describe the extreme tails of MSEC's observed strain data, resulted in more credible fits than based on alternative models based on the full dataset. As a consequence, the predictions of future extreme subsidence in excess of the trigger points are more reliable.

Stage 2: Develop Statistical Model, Dr Yao-ban Chan, MASCOS under the supervision of Dr Scott Sisson
The second stage of this project to be conducted by MASCOS Fellow Researcher, Dr Yao-ban Chan (under the supervision of Dr Sisson) will develop the statistical models more precisely. This involves the use of regression methods to improve accuracy and precision by the inclusion of relevant explanatory variables, such as the distance from the point of interest to the mine (a ‘far field’ analysis), and the modelling of the relationship of subsidence strain and curvature. Dr Chan is additionally simplifying the implementation of the EVT methods by supplying MSEC with programs written in the ‘R’ software package, with documentation for easy application.

Where to from here?
The results from Stage 1 were used in MSEC’s 2009 submissions to the NSW Government. Stage 2 and 3 results will assist MSEC in its consultancy advice to the Government and mining companies on the effects of proposed underground mines. Future projects with MSEC will include the modelling of more complex ground effects such as upwards movement of a valley floor (‘subsidence’) when mining occurs under the valley.

For further information regarding MASCOS and industrial applications of mathematics and statistics, please contact: David Shteinman on tel: +61 (0)2 9385 9915 or email: davids@complex.org.au