Industrial Mathematics Edward V Stansfield Thales Research

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Industrial MathematicsEdward V
StansfieldThales Research Technology (UK)
LtdIMA Vice President, EngineeringVisiting
Industrial Professor, University of Reading
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Overview

• Why mathematics?

• Some examples of its use
• Speech coding
• Passive emitter location
• Smart containers
• It can be entertaining!
• Summary and conclusions
• Questions

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Background

• Mathematics and physics were my favourite
  subjects at school
• A first degree in electrical engineering combined
  these two no regrets
• My career then mainly focused on the design
  development of
• communications systems
• navigation systems
• Both of these subjects require engineering
  maths applied maths

• As years rolled by, I had an increasing need for
  better maths skills
• So I studied for a second degree in maths,
  including some pure maths.
• I now use mathematics
• as an invaluable tool for my work
• as an interesting subject in itself
• for recreation and stimulation answering what
  if questions

This talk is thus about mathematics for work and
pleasure And remember todays pure is
tomorrows applied!!!
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Summary of technical topics

• During NATO employment 1971 - 1980
• Design specification of military
  communications systems
• For strategic tactical use over terrestrial
  satellite links
• Design of algorithms for medium rate and
  narrowband vocoders.

Quite a variety makes for an interesting career!
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Technical example 1 Speech coding (i)
Model of Speech Production
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Technical example 1 Speech coding (ii)
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Technical example 1 Speech coding (iii)
This technique originally developed for the
military is now widely used in mobile
telephones
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Technical example 2 Emitter location (ii)
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Technical example 2 Emitter location (iii)
Every measurement m is a known function f of
emitter location PE fk(PE) mk ek where ek
is the error in the kth measurement With K
measurements construct a measurement vector F(PE)
M E where F( ) is a known matrix and E is
error vector M Make a guess G for the emitter
position PE G D where D is the error in the
guess. Now determine position error vector D from
measurement vector M

• One method
• Linearise equations about G
• Solve for D
• Update the guess G
• Repeat until small error D

C F(G) A ?GF F(PE) F(GD) ?
F(G) AD F(PE) M E ? C AD E ? AD B
where B M C
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Technical example 3 Smart container (i)
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Technical example 3 Smart container (ii)
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Technical example 3 Smart container (iii)
Vibration plots and intermediate analysis results
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Mathematics for fun Kamikaze pelican (i)
The trains are 60 miles apart when the pelican
decides to fly off towards the other train at 50
mph. When it gets there, it changes its mind and
flies back to the first train, then changes its
mind again and flies back to the second train,
and so on. Eventually the two trains meet
buffer beam to buffer beam.
The question is how far does the pelican fly
before the two trains meet?
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Mathematics for fun Kamikaze pelican (ii)
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Mathematics for fun Kamikaze pelican (iii)
There is a hard way to solve this Distance
apart is 60 miles. Closing speed of pelican and
train is 60 mph. Meet up after 60 minutes.
Pelican travelled 50 miles. Each train travelled
10 miles. Trains 40 miles apart. Closing
speed still 60 mph. Meet again after 40
minutes. Pelican travelled another 50?2/3
miles. Each train travelled another 10?2/3
miles. Distance apart now 40 - 20?2/3 40?2/3
miles. Closing speed still 60 mph. Meet up
again after 40?2/3 minutes. Pelican travelled
another 50?(2/3)2 miles And so on Total
pelican distance 50?1 2/3 (2/3)2 (2/3)3
(2/3)4 (2/3)5 ? Miles And there is an
easy way The trains meet after 3 hours so
Pelican flies just 3?50 150 miles And the
point of the exercise is one way to prove that
Limit of 1 2/3 (2/3)2 (2/3)3 (2/3)4
(2/3)5 3
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Summary Conclusions

• Mathematics has underpinned an interesting career
• Communications
• Navigation
• Radar
• Security

• Basic requirements are
• Interest in how things work
• Mathematical modelling skills
• Understanding system design
• Performance analysis

And it can be fun!
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Questions ?