Mathematics in industry, research and managing of

development

Matti HeilioLappeenranta University of Technology

Mathematical technology

• Industrial processes• Commerce and business operations• Finance and insurance• Government, administration, services• Environment, ecology• Media, entertainment• Biosciences

Mathematics everywherekey resource for innovation, development, competitive production

Applications everywhere engineering, applied sciences, biomedical, finance, media

Demands for education, contents, methods and practices

?

Invisible Mathematics

• “it is done by computer….”• Crucial methods concealed in

the software lines, heart of algorithms or wired on micro chips

• Banknote cash machine• Medical imaging• DNA-identification• Simulator games

Medicine

• pharmacokinetics• Infection mechanisms, epidemiology• Instrumentation, diagnostics• Planning of surgical operations

Y’(t) = b - aY(t)

Environment and ecology• Climate and weather models• Interaction atmosphere - ocean• Flow phenomena, tornadoes• Spreading of pollution, pests• Flows and bioprocesses in ground• Dynamics of ecosystem

Fish ecology

• Predator-prey relations• Dynamical systems• Many species, more complex

dynamics• Effects of fishing• Oscillations, extinction

Humanistic and social sciences

• Large data-masses• Analysis of multivariate data• Archeology and dating techniques• Analysis of linquistic structures• Informatics, data-mining,

search engines

Administration and government

• Large scale systems in society. Traffic, delivery networks, logistics, data communication, energy, water and sewage networks

• Population registers, social security, health insurance, work pensionregisters, real estate database.

• Planning, monitoring and control

Corporate Management

• Management information systems• Production planning,

operations research• Econometric models• Financial instruments• Electronic trading systems• Insurance industry,

risk management

Drying concrete

Aluminium foil on 5 faces

free face

Neutron source Intensitymeasurement

Measurement of moisture

∂w/∂t = ∂/∂x[D(w,t)∂w/∂x]

X=0 X=1

Drying history

Modelling challenge

• Modelling of moisture transport D=D(w,t)• First attempt

D= a0+ a1w+ a2w2+ a3w3

• Second attemptD= awp(t) + be-m(w-c) , p(t)= p0+p1(1-t)d

Boundary conditions?Porous medium, capillary effect, vapour, convection, Darcy law…

Glass roof

• New building project• High aula space• Office windows• Ventilation channels• Effect of sunlight• Air flow field• Comfort level

Interior 3D image

• Room space with furniture etc• Set of 2d photos• Several camera

positions• Construct 3d model

of the interior• Architecture,

interior design

Packaging industry

Applied geometry??

Measuring cardboard strength

Load curves

Hollywood Mathematics

• Visualization• Animation• Virtual reality• Special effects

Modelling alien skin

• Gollum from “The Lord of the Rings”

• A technique to simulatesubsurface scattering

• Computer graphics Labin San Diego

• Henrik Wann JensenPhD fromDTU/Denmark

Titanic movie special effects

Southampton

Paper process overview

Paper Machine Head Box

Process variation

Cross direction measurement

Paper quality measurement

Paper web sample 1500m

Paper Machine Drying Section

Heat Exchanger

Metal sheet deformation

Metal Sheet Press Joints

Press Joint

Application Areas

• Design and planning • Industrial research• Measurement and testing• Experiments and data analysis • Production control systems• Intelligent data processing• Reliability engineering

Application Areas II

• Product design and geometry• Manufacturing systems• Flow systems• Chemical reactions and processes• Materials behavior• Information, signals and image analysis

Industrial Sectors

• Traffic and transportation

• Metal • Food and brewing • Semiconductor • Chemical

processes• Oil

• Energy• Information and

digital media• Finance,

insurance• Trade

Models are Used to

• gain understanding by testing assumptions

• forecast system behavior, evaluate performance

• replace experiments or laboratory trials• analyze what-if situations, sensitivity,

exceptional circumstances.

and

• analyze risk factors and failure mechanisms

• create virtual and/or visualized images • optimize values of design parameters• intelligent analyses on measurement

data• manage large information systems,

networks, data-bases

How to call it?

• Mathematics for technology • Industrial mathematics• Mathematical technology• Mathematics as technology

Theory of waveletsAdaptive/nonlinear filtersOptimal shape designFuzzy logic and controlStochastic controlEvolutionary algorithmsInversion theoryFEM methodsAdaptive grids/multigridDomain decomposition

Bayesian methodsMCMCPercolation theoryMultibody dynamicsModel reductionPerturbation analysisCoupled system modelsSystems identificationSignals analysis, ICAMolecular dynamics

Math Toolbox for R&D

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KäytössäSuunnitteilla

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Nordic Power lines

Spot-price 2000-2004

Electicity price variation, NZ

Hydro storagewater level

Price of Electric Power

CHP

Gas

turb

ines

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Coal

Oil

Water Power

Nuclear

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LoadCost of Production €/MWh

PowerTWh/a

Impo

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Vesivoiman vaihteluvälinoin 74 TWh

Pohjoismaiden vesivoima

Pohjoismaidenlämpövoima

Tree

Veneer cutting

• Veneer cutting• Log spinnig between

spools• Cutting blade• Wood sheets

plywood• Irregular shapes

Optimal centering

• Irregular shapes• Optiomization of

material usage• Centering strategy• Find optimal spool

positions

Simulated logsRandom radiusSpline fitting

Artificial logs

Forest seen from satelliteTuomo Kauranne, LUT

Branch Knots

Wood product quality

Branch/knot accumulation

Log size analysis

A B C

2 000 000 logs

Log-tomo

Measuring gates

Pre-prosessing at sawmill

Log data time series

Perturbed time series

X1 Heilahdusliikkeen pituusX2 PoikittaiskallistusX3 PoikittaiskalistusX4 Iskutaajuus

X4 Ilman nopeusX6 Syöttömäärä

Y Kuoripitoisuus

Pneumaattinen tärylajittelu

Security gate

• Transmitting/receiving antenna coils• Signal scattered from metal objects• Signal analysis, pattern recognition

coils

Shielding MRI device

• MRI diagnosticimaging

• Electromagneticfield

• Homogenous fieldrequired

• Harmful radiation• Protective shield

Shield optimization

• EM field distortedby the metal shield

• Shield design • Try to make total

field homogenous• Parametrized form• Shape optimization

Gear design• Wrist watch• Weed-day display• Non-linear movement• Fast advancement at

midnight• Off center axis• Noncircular rim• Tooth design

Optimal shape design

• Optimaalisen muodon etsintä

• Rakennesuunnittelu• Sillat, koneenosat,

lentokonesuunnittelu, potkuri, sylinterin palotila

Optimal shape design

Pump chamber

Armour penetrating projectile

Head box design

University of Jyvaskyla

Head box shape design

University of Jyvaskyla

Rising Bubble in Liquid

Prof Heikki Haario LUT

Bubble

Wake dynamics

Simulation of Atmosphere

Press valve

Velocity

Pressure

The bottom of the box has several holes (diam 5 mm) in a regular grid. Assume 25 holes at 5cm distance. The air is entering the narrow slit (3 mm) between the bottomand the plane and it is escaping at all four edges

Airbox problem

Pressure, turbulence intensity

Pathlines

Pressure at gap bottom

digest wash delign

Material flow componentsChips/fiberWaterLiqour

evaporation

water

water/steam

Four tank baby model

Washing

Power Boiler

Steamturbines

Watertreatment

Woodhandlingand debarking

To pulp line

Bark and wood waste

Bleaching

Recovery Boiler

Digesting Oxygendelignification& Screening

Evaporation Recausticizing

Lime Kiln

DS

DS

burned lime

Electricity

14744

6063BDt/d

1417BDt/d

2829BDt/d3143

ADt/d3237

BDt/d3311

BDt/d97.9 % 0.032 %2.996 %4.487 %

83.7%

1034 t H2O/h

16.91 %

316t/h

249.8 MW

5491 t DS/d

841 t/h

11675m3/d135g/l Na2O

972 t/d

BDt/d

3143 BDt/d

White liquorAA

BDt/d2592

11063 m3/dWhite liquor to cooking5038 tDS/d

176 t/h

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1080

Large mill

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Fiberline

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Recovery Boiler

process

Electrfilter

Chemfilter

Chemwash

Bicarbonate NaOH

measurement

pump

El-power El-power

ash ash

Inverse Problems

Inverse scattering

• EM-trasmitter• Pulses with

different frequency• Measuring reflected

field on surface• Mathematical inversion theory• Underground structure

revealed1985

Extrusion of plastic profiles

• Elastis/plasticdeformation

• Die design

?Inverse die design

1983

Windshield design

Heat treatmentRim frameSag bendingInverse problemTemperature distr form

heating rim

Sag bending

Planar glas

Ozone hole

Heikki Haario

Light emission measurement

Profile of atmospheric gases

Cross section imaging

Dental imaging

Dental tomography

• Limited angle tomography• Bayesian methods used• Existing images prior data

Algae growth model

Heikki Haario, LUT

Statistical analysis of modelreliability

Bayesian methods

Bayes, MCMC and Model Fitting

• Observations for 4 algae groups over 8 yearswith 8 control variables like temperature T, irradiation I, solids CS, nutrition N, P, ..., and

• 60 parameters to estimate, highly correlated• Bayesian methods with MCMC • data and prior information on the parameters

model + confidence zone

Algae Growth model

Blue Green Algae observations 1997 together with 95% limits of the fitted model

Heikki Haario, LUT

Sterilization of juice in a heatbath

T=94˚C

B= microbe density

Microbe reduction

Reliability of model prediction

Heikki Haario, V-M Taavitsainen

Glass roof

• New building project• High aula space• Office windows• Ventilation channels• Effect of sunlight• Air flow field• Comfort level

Garden irrigation

• Pipe network + sprinklers• Water flow, pressure losses etc.• Challenge, even spreading of water

Interior 3D image

• Room space with furniture etc• Set of 2d photos• Several camera

positions• Construct 3d model

of the interior• Architecture,

interior design

Restoration of Color Images

• limited amount of the color data and the graylevels

• Black and white photos of the full frescoes

• Fragments of the frescoes with originalcolors

• 8% of the originalinformation distributedrandomly

University of Padova, MANTEGNA Project, www.progettomantegna.it/

Electrochemical drilling

The Centre for Analysis, Scientific computing and ApplicationsEindhoven University of Technology

Drilling by etching/corrosion

Numerical Simulation of Electrochemical DrillingMarc Noot, CASA, Eindhoven

BEM simulation for glassparisons

K. Wang, R.M.M. Mattheij, H.G.ter Morsche

Mathematical Geoscience

Surging glaciers:advance of a glacieroccurring repeatedly

Temporary increasein velocity 5km/year

www2.maths.ox.ac.uk/mgg/

Fraunhofer ITWM, Kaiserslautern

Transport ProcessesFlow and Material SimulationImage ProcessingSystem Analysis, Prognosis and Control OptimizationFinancial MathematicsMathematical Methods for Dynamics andDurabilityHigh Performance and Visualization

www.itwm.fraunhofer.de/

Fraunhofer ITWM, Kaiserslautern

Technology- and Placement-Assistant for vertically integratedSystems

Optimal utilization of colored gemstones

Fraunhofer ITWM, Optimization

Multi-period supply chaindesign for the distribution of spare parts

Galileo-based localisationsystems for applications in trafficand security

Advanced material modelling

www.itwm.fraunhofer.de/

Diaper math

• Water absorbing tissue• Mixture of fibers and

absorbing grains

• Surface non-vowen textile• Model for water flow in unusual material• Optimal structure

Diaper equation ☺

• Water flow in porous medium• Absorbing grains and capillary effects• Project at University of Kaiserslautern

∂c/∂t = ∇ [(A-B cG) eβc ∇c] - ∂cG/∂t

∂cG/∂t = KGc-KcG

Non-woven textile

-liquid polymer-small nozzles-many holes-fluttering-fiber formation, tapering

Atmosphere simulation

Hurricane track forecast

5-day track forecast

Vadodara/Baroda

Gujarat

Inaugurationceremony

Estuary flow modelling

• Salinity penetration• Tidal flow effect• Salt water percolation into adjacent soil• Effect of dam and weir structures

Empirical Modelling of TyreLoad-Deflection behaviour

Power transfer capacity of electrical networks

GETCO Co Gujarat

Analysis of canopy shapeinduced spectral reflectance

• Developing algorithms to understand canopyshape induced spectral reflectance

• Ecology Lab, Department of Botany

Sample data on Bamboo

Reflectance spectra

Simple model

R = a0 + a1x1 + a2x2 + a3x3 + a4x4x1 = girth value, x2 = canopy area, x3 = occupancyx4 = height.

Fabric Tensile properties whencut at an angle

Textile Engineering Department

Fabric cut in an angle

Questions

• Hookes law• Elastic deformation• Friction & dissipative deformation• Hysteresis?• Single yarn multiple yarn?

Simple model

mx” = -k(θ)x - α(θ)x’+ F

α=20º

α=30º

ECMI nodes

MS in Technomathematics

2 year programmeExchange of ideasCurriculum developmentStudent/staff exchangeModelling week

Modelling weekDay 1• real-world problems presented• international teams of 5 studentsDay 2-5• understanding the context• building the model, computing experiments• evaluation and checking Day 6• final presentation 20 min/teamAfterwards written report proceedings

MWeek 2006 Copenhagen

• Modeling the goal kick• Dynamic settling and transport of heavy

particles in slurry flows. • Simulation and Optimization of

Semiconductor Devices• Optimization of Operative Control in Water

Distribution Systems• Paint drying with UV rays: an inverse problem• Models for a fishing rod and the action of

casting with a bait. • Detection of root rot in living trees

Manufacturing ophthalmiclenses

-automated machining-accuracy-optimal movemetns-smooth curvatureinterpolation

Smooth curvature interpolationTask is to model theSurface and compute the trajectory of thecutting edge

Modelling week2004, LUT

Development of Math Education

• Curriculum Development• Novi Sad, Serbia• Dar es Salaam, Kigali• Baroda, India• Web-supported education on

mathematical modelling• National consortium of 9 universities

CIMO, Finnish Centre for International Mobility2 year projectcurriculum development for applied & industrial mathematics

Lappeenranta Univ of TechTampere Univ of TechUniversity of Dar es SalaamKigali Inst of Science &Tech

Simulation and design

HIL simulation: Part of the systemhardware replaced by a simulationmodel

Timber manipulator

Lab of Machine Design, LUT

ECMI 2010 ConferenceWuppertal

• Display the role of mathematics as a generic resource for industry and business in their broadest sense.

• People from business, science and government will attend

• promotes the application of innovative mathematics to industry, and emphasiseindustrial sectors where math is at work

• opportunities for mathematicians to gain insight and new ideas

www.ecmi-indmath.org

ICIAM 2011, Vancouver• industrial and applied mathematics• industrial applications of math and

computational science