Industrial Mathematics Initiatives:
An (inter)national need?
Graeme Wake
Centre for Mathematics in Industry
Massey University
Auckland, New Zealand
http://www.mathsinindustry.co.nz
g.c.wake@massey.ac.nz
ANZMC 2008
Key Reference:
Organisation for Economic Co-operation and Development : Global
Science Forum
Report on Mathematics in Industry July 2008
1
Views of Mathematics
Mathematics is the “software” of science, yet has a life of its
own.
The connections however sustain it.
Features of Mathematics are:
 Longevity - it lasts forever
 Open ended-ness
 Developed by abstraction
 Universality
However…
“We shall need a new breed of mathematical professionals
able to mediate between mathematics and applied
science. The cross-fertilization of ideas is crucial for the
health of the science and mathematics.” – Michael
Gromov, France: AMS Notices 1998.:
2
OECD Report: The challenge
• 3.2 The Academic Environment
• “The academic discipline of mathematics has
undergone intense intellectual growth, but its
applications to industrial problems have not
undergone a similar expansion. “
• “The degree of penetration of mathematics in
industry is in general unbalanced, with a
disproportionate participation from large
corporations and relatively little impact in smalland medium-sized enterprises. “
3
 Across the world there are a wide range of activities
in existence which are designed to spread the
problem-solving power of mathematics to industry
and society-at-large, in order to enhance the
knowledge and technical base of organisations.
 There are a range of models practised, and there
are a few notable examples where a high level of
activity has been obtained. This paper traverses the
options, and looks at what is achievable in a given
instance, such as in South Korea and the nearby
countries.
 As Director of the Australian and New Zealand
Mathematics-in-Industry Study Group 2004-6, I have
been privileged to help develop this in our region.
Also I have assisted with similar developments in
other neighbouring countries around the Pacific,
4
notably in Brunei, Thailand and South Korea.
Industrial Mathematics is a
distinctive activity:
starts from a client’s problems, which,
although not described by mathematics,
are possibly solvable using quantitative
techniques of analysis and/or
computation.
Illustrative case-study examples will be
described where spectacular results
have been obtained in medical and
engineering applications.
5
 This activity has positive spins-off for it serves to
* establish better links between industry and
academic mathematics.
* enhance the image of mathematics in the
community.
* provide improved university education of
mathematicians through
- expanded employment prospects for
mathematics graduates;
- fresh research problems for
mathematicians;
- innovative material for teaching courses.
6
The lot of an Applied
Mathematician
Applied Mathematics seems to be about finding answers to
problems. These are not written down in some great book
and in reality the hardest task for an applied
mathematician is finding good questions. There seem to
be three types of problems in the real world:
o The trivial
o The impossible
o The just solvable
The boundaries between them are very blurred. They vary
from person to person, and some of my strongest
memories are of problems that suddenly jump one from
category to another, and this is usually with the help of
colleagues!
7
Modelling Paradigms
The 10 commandments
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Simple models do better!
Think before you compute
A graph is worth 1000 equations
The best computer you’ve got is between your
ears!
Charge a low fee at first, then double it next
time
Being wrong is a step towards getting it right
Build a (hypothetical) model before collecting
data
Do experiments where there is “gross
parametric sensitivity”
Learn the biology etc.
Spend time on “decision support”
8
What is Industrial Mathematics?
 Means by which industry improves quality of products
 Starts with a problem posed by industry
 An equal partner with science and engineering at all
stages
 Must be meaningful to industry and non-mathematical
personnel
 The problem to be solved must be as stated
 Must include advances in industrial products or
processes in addition to containing advances in
the
mathematical sciences
 Will often include new theories, not just algorithms
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What skills are needed to be an Industrial Mathematician?
 Covers a vast range of the mathematical sciences:
o
o
o
o
o
o
o
o
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Data mining and analysis
Networks
Optimisation
Stochastic processes
Systems models – such as dynamical systems
Discrete and continuous models
Spatial patterns
Conservation principles
Etc
 Collaborative team work needing good communication skills
 All four stages of the modelling process:
o
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Formulation
Solution
Interpretation
Underpinning decision support
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What skills are needed for
Industrial Mathematics?
 Breadth in the mathematical sciences + depth in some area of
the mathematical sciences
 Breadth in science, technology and commerce
 Ability to abstract essential mathematical/analytical
characteristics from a situation and formulate them in a fashion
meaningful for the context
 Computational skills, including numerical methods, data
analysis and computational implementation, that lead to
accurate solutions
 Flexible problem solving skills
 Communication skills
 Ability to work in a team with other scientists, engineers,
managers and business people
 Dedication to see solutions implemented in a way that make a
difference for the enterprise
 Willingness to follow through to ascertain what real impact the
modelling/analysis has had in the enterprise
11
Why aren’t there more mathematical
scientists in industry?
Recently the low interest in mathematics was the topic of a report in
Britain entitled “Low Interest in Mathematics set to Cripple British
Industry”. See “Mathematics Today”, IMA Bulletin, October 2003.
The same is true in other countries.
 The necessary skills (formulation, modelling, implementation and
decision support) are often not part of mathematical sciences
training in universities
 Collaboration between academics and industrialists requires
crossing cultural barriers with high investment costs
 Often industry hires well-trained scientists/engineers with strong
maths/stats background to take care of mathematical sciences
issues. Why?.....
 Industrial mathematics is often interdisciplinary and is not
appreciated by the mathematical sciences community
 We are not producing the right mix of graduates, especially at the
postgraduate level
12
Recommendations:
 Departments seeking to create new mathematical
sciences programs should consider including
industrial mathematics programs among the many
options offered
 Departments that wish to set up industrial
mathematics programs should start with a program
at the master’s level
 Staff in a department should start establishing
relationships with industry early, preferably with
stable local or regional industries, so as to make
industrial mathematics programs in the future
 Staff and postgraduate students should participate
in industrial mathematics workshops held nationally,
such as the ANZIAM one.
13
The Academic Perspective
Incentives for collaboration with industry
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Relevance of expertise to real world applications
Satisfaction arising from knowledge transfer
Source of interesting new problems?
Financial gain?
Disincentives
– “Dirty end” of science?
– Career structure
– Rating = f (research, teaching)
14
The Industry Perspective
Is mathematics actually relevant to industry?
What benefits can I expect?
What are the different mechanisms?
How much will it cost?
Why can’t I buy it today?
Only useful for long-term projects?
Will I actually understand the end result?
How can I protect our IPR?
What’s in it for academics?
15
Mathematics in Industry: Opportunities
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Options (Not mutually exclusive)
Regular industry days (monthly)
Theme days e.g.. Environmental Modelling, Petroleum,
Biology, Health
Student projects in Industry – Claremont style (funding)
Industrial Mathematics consulting office – on and off
campus
Mathematics in Industry Study Group –
OCIAM/ESGI/ANZIAM style
Dedicated Centre for Mathematics in Industry – e.g. the
Smiths’ Institute, Oxford
International linkages like that of OCCAM
http://www.maths.ox.ac.uk/occam
A newly-formed Oxford Centre for Collaborative
Applied Mathematics (OCCAM), funded for five years
from 1 October 2008 by the Global Research
Partnership of the King Abdullah University of Science
and Technology (KAUST).
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OCCAM, the Oxford Centre for Collaborative Applied Mathematics.
The objectives of OCCAM are to use focused teamwork and
innovative mathematical and computational methods to help
understand pressing, unsolved problems. OCCAM's primary focus
is within the following four interdisciplinary research areas:
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Methodologies
Resources, Energy and Environment
Biosciences and Bioengineering
Materials Science and Engineering
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Needs
• Commitment and Experience
• New staff member(s)/secondment??
• Industrial linkages and contacts – ex
students, friends etc
• Across departments
• Across ANZ – parent body
• Training for staff and graduate students
18
Problem Presenters MISG2005
•
Backyard Technology, Queensland
#5 Problem Sponsor
• Compac Sorting Equipment
#6 Problem Sponsor
• Environment Canterbury
#4 Problem Sponsor
• Fisher & Paykel
#7 Problem Sponsor
• Lincoln Ventures
#1 Problem Sponsor
• New Zealand Steel
#2 Problem Sponsor
• Transpower
#3 Problem Sponsor
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Problem 6: Mark McGuinness, Tim Marchant, Senaratne
Compac Sorting Equipment
“Modelling the physics of high speed product-weighing”
MISG 2005
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What we would like
• Mathematical model of the physical
process of weighing the fruit
• To be able to use the model to improve
the system design by testing different
scenarios
• Better signal processing for determining
the true weight of the fruit.
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Problem 4: Moderators: Heather North, Rod Weber,
Joanne Mann
• Factors Associated With Trends in
Bare Ground in the Central South
Island High Country
Jeromy Cuff
Environment Canterbury
Timaru
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High Country Example 1
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High Country Example 2
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High Country Example 3
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High Country Example 4
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High Country Example 5
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Some South Island Hill and
High Country Issues
• Bare ground creates surface erosion risk
– Extensive areas of LUC classes VII and VIII
land destocked in the 1960s - 1980s
– Objective was to improve ground cover
• Hieracium species have invaded tussock
grasslands
– Out competes resident vegetation but is not
persistent
– Doesn’t provide 100% cover
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MISG 2005 Challenge
• Create a mathematical model that identifies and
describes the main effects and interactions of
the factors influencing short and long term
ground cover trends in the high country.
• Such a model would be invaluable for
identifying land management options and could
be applied to help ensure soil conservation in
the Canterbury high country tussock grassland
ecosystems by identifying and quantifying the
important factors
• to prevent further deterioration in hign country condition and
• improve the condition of presently degraded lands
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Problem 7:Moderators: Clive Marsh, Andy Wilkins,
Jane Thredgold
Temperature Control for
Wash Water
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Steven Mansell
Kerry Newnham
Josh Cox
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Problem Summary
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Need to balance hot and cold intake to get correct
wash water temperature
Currently no feedback from bulk water - only from
mixing chamber
‘Abnormal’ operating conditions have been
identified
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Project Goals
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development of a closed loop transfer
function
confirmation of correct sensor position
discussion of sensitivity issues with regard to
above
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Fisher and Paykel Brainstorming
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Problem 1: Moderators: Sean Oughton, Tony
Roberts, Joanne Mann
Modelling the effects of porous
barriers on spray drift.
John-Paul Praat
Lincoln Ventures Ltd, Hamilton
Alison Forster and Jerzy. A. Zabkiewicz
Plant Protection ChemistryNZ, Rotorua
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Aim for the week:
Produce a model to predict
shelter effect on spray drift
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Aim for the week:
Produce a model to predict
shelter effect on spray drift
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Variables:
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Spray characteristics
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Environmental factors
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(eg. droplet size, release height)
(eg. wind velocity, wind direction)
Shelter characteristics
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(eg. porosity, width, height, length, leaf area
index, capture efficiency, shape of the crosssection area)
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Problem 3: Moderators: Kaye Marion, Bill Whiten,
Radneesh Suri
Optimising the relationship of
electricity spot price to real-time
input data
Conrad Edwards,
Transpower Ltd
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Problem summary
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New Zealand’s electricity market is based on a halfhourly spot market using ex-post locational marginal
prices.
A scheduling, pricing, and dispatch model “SPD” is a
linear program used to determine, from bids and
offers:
 dispatch in real-time, and then
 the corresponding nodal prices, ex-post
“Spring washers” are counter-intuitive but
mathematically predictable price patterns where
 some nodal prices can be >> highest generation offer
 some nodal prices can be negative
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Challenge for MISG2005
Develop an algorithmic means of identifying
occurrences of spring washers where
extreme prices are especially sensitive to
the constraint specification and other model parameters
Such an algorithm would then trigger a process of
checking the constraint and/or input data to determine
the actual sensitivity of the nodal price, and if necessary
an algorithm for correcting the constraint of parameter
causing the sensitivity with better measured values
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Problem 2: Moderators: Tim Marchant, Steve
Taylor, Alysha Nickerson
Development of empirical relationships
for metallurgical design of hot-rolled
steel products.
(New Zealand Steel Ltd, Glenbrook)
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Hot Rolled Coil
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MISG 2005 Objectives - Part 1
• Identify processing and product variables
which have a significant effect on product
mechanical properties
• Develop an empirical model enabling the
mechanical properties of hot-rolled coil
products to be predicted from the values of
the product and process variables
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If time allows:
• Develop a similar model for hot rolled
plate products.
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• Outcomes:
- Progress with all problems
- Ongoing collaborative arrangement in
most cases
- Industry-specific, in-house, one-off
workshops : This should have a national
focus.
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Conclusions of the OECD Report
• Conclusions and Recommendations
• “Industry faces problems that extend well
beyond the envelope of classical topics in
mathematics. Many of these problems have a
significant mathematical component, and the
intellectual challenges they pose fall in many
cases within topical areas of current research in
the mathematical sciences. Stronger links
between mathematics and industry will be
beneficial both to the partners and to national
economies. They will inspire new mathematics
and enhance the competitive advantage of
companies. ….”
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Proposal
• The proposed new Masters subject is Industrial
Mathematics and Statistics. Core components
and applications of Mathematics and Statistics are
combined to provide the quantitative
methodologies needed by modern technological
society. Industry often lacks the in-house
expertise that underpins experimental design,
data acquisition and analysis. The new MInfSc
subject will equip graduates with in-depth
understanding and a synergistic set of powerful
tools to model industrial systems and optimise
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decision making.
Discussion: Comments
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