Post on 20-May-2020
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
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
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
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
Price of Electric Power
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ines
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Coal
Oil
Water Power
Nuclear
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LoadCost of Production €/MWh
PowerTWh/a
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Vesivoiman vaihteluvälinoin 74 TWh
Pohjoismaiden vesivoima
Pohjoismaidenlämpövoima
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
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
Rising Bubble in Liquid
Prof Heikki Haario LUT
Bubble
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
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
1150 5300 12970
1080
Large mill
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Lime Kiln
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Recovery Boiler
process
Electrfilter
Chemfilter
Chemwash
Bicarbonate NaOH
measurement
pump
El-power El-power
ash ash
Inverse scattering
• EM-trasmitter• Pulses with
different frequency• Measuring reflected
field on surface• Mathematical inversion theory• Underground structure
revealed1985
Windshield design
Heat treatmentRim frameSag bendingInverse problemTemperature distr form
heating rim
Sag bending
Planar glas
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
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
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
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
Hurricane track forecast
5-day track forecast
Estuary flow modelling
• Salinity penetration• Tidal flow effect• Salt water percolation into adjacent soil• Effect of dam and weir structures
Analysis of canopy shapeinduced spectral reflectance
• Developing algorithms to understand canopyshape induced spectral reflectance
• Ecology Lab, Department of Botany
Simple model
R = a0 + a1x1 + a2x2 + a3x3 + a4x4x1 = girth value, x2 = canopy area, x3 = occupancyx4 = height.
Questions
• Hookes law• Elastic deformation• Friction & dissipative deformation• Hysteresis?• Single yarn multiple yarn?
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
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
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