Tstusmatemaatika Jaan Janno Inglisekeelne vaste Industrial mathematics or

Tööstusmatemaatika Jaan Janno

Inglisekeelne vaste: Industrial mathematics or mathematics in industry Tõlge tööstusmatemaatika ei ole päris täpne. Sõnal „industry“ on inglise keeles laiem tähendus kui sõnal „tööstus“ eesti keeles. „Industry“ hõlmab lisaks tööstuslikule tootmisele ka tehnoloogiat, majandust, rahandust, ökoloogiat, meditsiini, infotehnoloogiat jm

Tööstusmatemaatika tegeleb matemaatikaülesannetega, mis pärinevad tööstusest (ingl. vastena industry) ja seab eesmärgiks leida tööstuse jaoks sobivaid, sh efektiivsemaid lahendeid. Laiem mõiste on rakendusmatemaatika, mis lisaks eespooltoodule hõlmab ka matemaatika rakendamist teiste teadusharude (nt füüsika, bioloogia) teoeetiliste ülesannete lahendamisel.

Ajaloost Matemaatika rakendamisele tööstuses andis olulise tõuke elektronarvutite teke ja sellega seotud arvutusmatemaatika areng. Sellest ajast (1940 -ndate lõpp, 1950 ndate algus) pärineb ka mõiste „industrial mathematics“. Üsna pea algas ka organiseerumine. Pioneeriks sel alal USA. Üks vanemaid organisatsioone on SIAM (Society for Industrial and Applied Mathematics) loodi 1952.

Euroopas: ECMI (European Consortium for Mathematics in Industry), loodi 1987. a. Praegu on ECMI-l 111 institutsionaalset liiget. EU-MATHS-IN (European Service Network of Mathematics for Industry and Innovation) koondab rahvuslikke tööstusmatemaatika võrke ja keskusi COST Actions: https: //euro-math-soc. eu/industrial-mathematicalactivities-europe

Eestis: Tartu Ülikooli matemaatika Instituut (praegune MSI) on olnud ECMI liige 1993. aastast Tööstusmatemaatika alase tegevuse põhiline eestvedaja Eestis on olnud dotsent Peep Miidla Tema initsiatiivil loodi 2012. a MTÜ Eesti Tööstusmatemaatika Keskus Ksii https: //www. facebook. com/ksii 11/ Alates 2019. a on ECMI liikmeks ka TTÜ küberneetika instituut.

European Consortium for Mathematics in Industry (ECMI) - Euroopa Tööstusmatemaatika Konsortsium ECMI is a consortium of academic institutions and industrial companies that acts co-operatively with the following aims: To promote and support the use of mathematical modelling, simulation, and optimization in any activity of social or economic importance. To educate Industrial Mathematicians to meet the growing demand for such experts. To operate on a European scale.

ECMI tegevustest • Koostöörühmad tööstusega ESGI (European Study Groups with Industry). Üheks nädalaks koguneb rahvusvaheline matemaatikust koosnev rühm, kes tegeleb ettevõtete poolt esitatud rakendusülesannetega, pakkudes välja lahendusi. • Esimene ESGI toimus 1968. a Oxfordis ja praegu toimub neid igal aastal 5 -7 tk erinevates riikides.

ESGI Tartu Ülikoolis 4 -8. 02. 2019 Organisaator: Peep Miidla Üle 30 eksperdi erinevatest maadest 4 ülesannet ettevõtetelt

1. Ülesanne Swedbankilt Let’s consider the working schedules of support and servicing teams who have to complete incoming tasks in real time during fixed working hours longer than nominal 40 hour week. Such teams can be found throughout both the public and private sector, servicing either external or internal clients. It can be expected that the task flows for these teams will often vary over time and can be unevenly scattered in weeks and days. Nevertheless, the team leads and managers need to plan and design the work schedules of these teams so that robust task completion is guaranteed throughout the official servicing hours of the teams, even if the servicing hours are longer than usual 8 hour shifts or if they involve weekends. Moreover, the team leads will surely face several real world complications and constraints, such as unexpected illnesses or vacation seasons. In this ESGI problem, you are asked to model the work schedule of such teams under real world inspired constraints. The aim of the task is to provide team leads with a helper tool for compiling the individual work schedules of their team members based on task flow forecasts. The work schedules should be designed to maximise employee wellbeing, while providing robust performance and resilience to unexpected shocks. You are provided with an example description of real world complications and constraints, as well as, synthetic task flow data of two model teams for testing your methodology. You are expected to provide a proof-ofconcept implementation in a suitable programming language.

ESGI rühma aruanne esimese ülesande kohta: https: //sisu. ut. ee/sites/default/files/esgi 151/files/swedbank_esgi 151_ report. pdf

2. Ülesanne: Norma/Autoliv After stamping the products are transported to the heat treatment line and spread evenly on the conveyor to be fed to the furnace. Products are heated up to 880… 900°C and then dipped into the salt tank where they cool to 300… 400°C. The goal for ESGI 151 is to get the most effective production plan sequence by optimizing and minimizing the use of time and energy during change overs.

ESGI rühma aruanne teise ülesande kohta: https: //sisu. ut. ee/sites/default/files/esgi 151/files/report_norma. pdf

3. Ülesanne: Holon Technologies • There is a need to shift into more customer-centric model, as more insurance companies light up telematics technology. Imagine being able to predict an incident before it happens. Merging data analytics together with driver behavior is a game changing reality companies are just beginning to realize the benefits of. If actuaries can see patterns and trends, that’s where the magic begins to happen. • ESGI 151 brainstorm should construct a solution for classification of drivers according to the data from driving indicators. The objective function is to minimize the probability of causing traffic damage during the next insurance period or some other parameter according to new pattern, discovered in the data.

ESGI rühma aruanne kolmanda ülesande kohta: https: //sisu. ut. ee/sites/default/files/esgi 151/files/holontechnologies_r eport. pdf

4. Ülesanne: LHV pank LHV is researching options to develop a fully automated personal finance tool, which: - Provides an overview of a customer’s spending and helps forecast future spending - Acts as a personal finance advisor who makes personalised suggestions to help customers increase their savings The goal for ESGI is to suggest a theoretical framework for the second part of this project: building the personal finance advisor. Ideally, this would also result in a practical prototype.

ESGI rühma aruanne neljanda ülesande kohta: https: //sisu. ut. ee/sites/default/files/esgi 151/files/report_lhv. pdf

ECMI huvirühmad (Special interest groups) Rahvusvaheline koostöö spetsiifilistel TM teemadel Huvirühm annab ühesuguste huvidega teadlastele ja uurijatele nii ülikoolides kui ka ettevõtetes-organisatsioonides võimaluse ühineda ja koos taotleda Euroopa Liidu või teistest finantsallikatest rahastust uurimistöö läbiviimiseks. ECMI tegutseb siin ergutava vahendajana selliste rühmitiste moodustumisel, edastades oma kanalite kaudu informatsiooni olemasoleva kompetentsi kohta, samuti toetades neid rühmi rahaliselt.

Huvirühmad praeguse seisuga: • Shape and Size in Medicine, Biotechnology and Materials Science • Liquid Crystals, Elastomers and Biological Applications • Math for the Digital Factory • Numerical Weather Prediction • Computational Finance and Energy Markets • Sustainable Energies • Implantable devices and drug delivery systems • Net Campus for Modeling Education and Industrial Mathematics • Mathematics for Big Data • Modeling, Simulation and Optimization in Electrical Engineering (MSOEE)

Huvirühma loomine: • Describe the area of interest, the motivation and aims. There should be a clear interest in the activity from industry. If possible describe how the activity may lead to proposals for cooperative funding. • Identify a group of experts for an initial start-up group. These experts should come from more than one country in Europe and should include representative(s) from industry. • Describe potential activities for the first year. These might include workshops, industry days, minisymposia etc. • Nominate a contact person (moderator) who will be responsible for the programme of events and for reporting activities. The RIC requires an annual report which will be posted on the webpages.

ECMI haridusprogramm • üliõpilaste ja õppejõudude vahetus ECMI partnerülikoolide vahel • üliõpilaste modelleerimisnädalate organiseerimine (modelling weeks) • ECMI magistriõppe näidiskava haldamine, vastavate diplomite ja sertifikaatide väljastamine • ECMI õppekeskuse (ECMI teaching center) staatuse andmine partnerülikoolidele

ECMI magistriõppe näidisprogramm (ECMI model master) Kaks spetsialiteeti: Tehnomatemaatika (technomathematics): orienteeritud tehnilistele aladele nagu mehaanika, farmaatsia, elektroonika, keemia, füüsika, biotehnoloogia, ehitus jm Ökonomatemaatika (economathematics): orienteeritud majandusele, rahandusele, statistikale, andmeanalüüsile

Eeldused immatrikuleerimiseks: On läbinud 180 ainepunktise bakalaureuseõppe, sh on läbinud 60 EAP matemaatika aineid tehnomatemaatika jaoks ja 54 EAP matemaatika aineid ökonomatemaatika jaoks. hea inglise keele oskus

Põhinõuded: Kaheaastane magistriprogramm Kaks spetsialiteeti: tehnomatemaatika (technomathematics) ja ökonomatemaatika (economathematics) Kava on inglisekeelne Vähemalt üks semester peab olema läbitud mõnes teises ECMI partnerülikoolis

Õppekava peab sisaldama: Regulaarset modelleerimiseminari, vähemalt 6 EAP Teisi modelleerimistegevusi (suvekoolid, tööstusprojektid, osavõtt koostöörühmadest tööstusega, st ESGI, jm), 0 – 9 EAP Osavõtt ECMI modelleerimisnädalast, 3 EAP Lõputöö peab olema seotud reaalse tööstusmatemaatika probleemiga, soovitavalt tehtud koostöös mingi ettevõtte või organisatsiooniga ja peab omama mittetriviaalset matemaatilist sisu, 30 EAP Viide täpsematele nõuetele: https: //ecmiindmath. org/education/ecmi-model-master-inmathematics-for-industry/

ECMI sertifikaat (magistriõppe diplomi lisa) väljastatakse, kui Magistriõppe programm vastab eeltoodud tingimustele Programmi õpetav ülikool on ECMI õppekeskuse (ECMI educational center) või ECMI provisionaalse õppekeskuse staatuses. Selleks hinnatakse õppekava ECMI ekspertide poolt. Täpsemalt: https: //ecmiindmath. org/education/ecmi-teaching-centres/how-toenter-the-ecmi-educational-network/

ECMI õppekeskused praeguse seisuga: University of Kaiserslautern, Technical University of Dresden, Johannes Kepler University, University of Milan, Technical University of Eindhoven, Technical University of Denmark, University of Oxford, University of Strathclyde, Lappeenranta University of Technology, Chalmers University of Technology, Lund University, The Norwegian University of Science and Technology, University Carlos III of Madrid, Sofia University “St. Kliment Ohridski”, Wroclaw University of Science and Technology, University of Lisbon – Instituto Superior Técnico, University of Coimbra, University of Novi Sad, University of Verona, University of Grenoble-Alpes, Eötvös Loránd University

ECMI modelleerimisnädalad tudengitele Moodustab osa magistriõppe näidisprogrammist. Erinevate riikide tudengid tulevad kokku ja veedavad ühe nädala partnerülikooli juures töötades reaalalust pärinevate probleemide kallal. Igat rühma juhub ECMI instruktor, kes tutvustab probleemi ja juhendab tudengeid. Tudengid presenteerivad oma tulemusi nädala lõpus ja kirjutavad aruanded.

Näiteid 2019. a Grenobles toimunud modelleerimisnädala ülesanetest: Project 1 - Modelling the effects of an earthquake on buildings. Instructor: Sanja Ružičić - Faculty of Sciences University of Novi Sad An earthquake is a sudden movement of the ground caused by the release of stress accumulated along geologic faults or by volcanic activity. Some of them have caused a great devastation and destruction of people's properties. It is known that building suffers the greatest damage if a frequency of the ground motion is close to its own frequency. In that case we say that the building and the ground motion are in resonance. Even though the resonance can cause a major damage, its effects can be reduced. So, nowadays it should be imperative to design the buildings that will resist the earthquakes forces and that are more likely to suffer reparable damage. It is natural to assume that the earthquake ground motion is characterized by its duration, displacement from the equilibrium point, velocity and acceleration which is a critical factor in determining how much damage a building will suffer. The aim of this project is to give the mathematical model and investigate how an earthquake effects the buildings of different structures since different buildings respond in widely differing manners to the same earthquake ground motion. It is expected that some numerical simulations will be performed.

Project 2 - Drug delivery into the eye: therapeutic lenses versus intracameral implants. Instructor: José Augusto Ferreira - Centre for Mahematics of University of Coimbra Treatment of Glaucoma Topical drops and ointments are the conventional drug delivery formulations to treat eye diseases. However, due to several eye barriers only a small amount of drug reaches the anterior chamber. New drug delivery systems were proposed to avoid eye barriers, like therapeutic contact lens that increases the residence time of the drug in the cornea, and biodegradable intracameral implants that are placed in the anterior chamber. Both drug delivery systems are made of polymers that lead to a controlled drug release. This project aims to analyse the efficacy of the delivery systems: a therapeutic lens and a biodegradable intracameral implant. We consider that the increase of IOP is due to the decrease of the porosity of the trabecular meshwork. From mathematical point of view, the efficacy is measured considering the drug mass that reaches the trabecular meshwork. The mathematical models that describe the drug release from these drug delivery systems and their transport until the target are defined by systems of partial differential equations (PDEs) that are completed with interface, boundary and initial conditions. It should be pointed out that the aqueous humor dynamics has an important role in the drug transport in the anterior chamber.

Project 3 - Checking the "evenness" of a floor. Instructor: Thomas Goetz - University of Koblenz-Landau According to the German DIN-standard 18202 the "evenness" of a floor in building is measured by laying a measuring stick of length L (L=0. 1 m, 1 m 2 m or 4 m) on the floor and measuring the gap (pitch) between the stick and the actual surface of the floor. Accoring to the DIN 18202, this pitch has to be below a certain threshold depending on the desired quality of the floor and depending on the length of the measuring stick. The company CHEMICON is construction floor in building and the need to ensure that the final floor satisfies the criteria of the DIN standard. Since manual measurements (using the stick and measuring the gap) a extremely time consuming, the want to use a laser scanner taking images of the surface. Based on this ditialized surface image, it has to be checked whether the DIN standard is satiesfied or not. For the given project we do have some real data from actual laser scans of various buildings.

ECMI muudest tegevustest • Konverentsid: ECMI konverents iga kahe aasta tagant (2020. a konverents on edasi lükatud 2021. a), • Publikatsioonid: ECMI Journal of Mathematics in Industry (1. 1 ajakiri), Springer subseries The European Consortium for Mathematics in Industry of the “Mathematics in Industy” series, Annual report, Newsletter, blogi ECMI kodulehel

ECMI blog kodulehel. Näiteid minu postitustest: https: //ecmiindmath. org/2018/01/26/applying-non-parametricmethods-on-environmental-data/ https: //ecmiindmath. org/2018/01/17/energy-prediction-models-forwireless-sensor-nodes/ https: //ecmiindmath. org/2018/01/23/recovering-parameters-ofgeneralized-fractional-diffusion-models/

Tööstusmatemaatika vajaduse uuring 2007. a Eesti ettevõtete hulgas (P. Miidla poolt teostatud) • Piimatööstusettevõte: pakendi optimeerimine, juust kas bloki või silindrina, logistika (piima kokkuost, mahutite tühjendamine) • Spektromeetreid tootev ettevõte: kiire Fourier teisendus, aegrea korrastamine • Kaardirakenduste ja geo-infosüsteemide ettevõte: positsioneerimise tarkvara, rändkaupmehe ülesanne • Inseneribüroo: optimeerimisülesanded (maksumus), ehitusjärjekord • Klaaspakette tootev ettevõte: tootmise planeerimine, logistika • Tööstuselektrooniat tootev ettevõte: logistika, lainejootmine (vigade minimeerimine), lao optimeerimine

Tööstusmatemaatika vajaduse uuring (jätk) • Ehitusettevõte: optimeerimisülesanded, • Õlletehas: logistika, tootmise planeerimine