ECMI Modelling Week 2018

Modelling Problems and reports

• Optimization of plane assembly process, instructor: Maria Churilova
  Mathematical background: basic mechanics, optimization methods

  Nowadays parts of an aircraft are often made in different countries or even on different continents. Then they are brought together and assembled by special rivets and fasteners. The assembly process consists of several stages, it is very complicated and time-consuming. One of the assembly stages is installation of temporary fastening elements to make a qualitative connection of two or more parts of the future aircraft. Positions for these fastening elements remain the same (there is an approved template) for all aircrafts of one model. Thus, the template by which the temporary fasteners are installed must ensure a good connection of parts for all aircrafts assembled with it. The other important aspect is the assembly time. To reduce assembly time (and save a lot of money for the aircraft company) one should decrease the number of temporary fasteners without loss of assembly quality. For this task, we consider a test problem of airplane wing-to-fuselage junction. We provide the FEM code (exe file) which computes the resulting gap between connected parts for given set of fastener positions. The first part of this task is to create and improve the template for installation the given amount of fastening elements (for example, 30% of all possible fasteners are installed). The quality of this template can be verified on a set of 200 initial gaps. The second part of this task is to reduce the number of fastening elements without decreasing assembly quality. The main requirement for solution algorithm is less computational time – for real airplane junction models time of one calculation (one fastening template and one initial gap) is around 5 minutes, which makes a long search impossible. For test problem time of one calculation is less than 1 second.
  Report of the group

• Modelling drilling cuttings formation, instructor: Tatiana Pogarskaia

  Mathematical background: mechanics, stochastic processes

  This task appeared from the complex modelling of well drilling process. From one side there is the drill string, which consists of drilling pipes and a bit. The drill string is rotating, there is an engine on its top, and also it is pressing the bit into the soil by part of its own weight. From the other side, there is a drilling mud, that flows inside the string to the bit and then backwards in the annulus – from the bit to the surface. The soil cuttings, which come from the bit, are washed away with drilling mud. One of the problems that arose during this work is to calculate the amount of drilled cuttings in each period of time and their size/mass distribution. This data is then used to calculate the cuttings flow in the drilling mud and helps to estimate if the system parameters (drilling mud flow rate and rheological properties, string rotation speed and pressure on the bit, the well geometry) are chosen properly. As input data, the model of cuttings formation should take the bit diameter and type, the drilled soil type, drill string rotation speed and pressure on the bit, optional: drilling mud flow rate and rheological properties. As output, we would like to know the drilling speed (or the volume/mass of drilled soil per time period), minimum and maximum possible cutting size and distribution of all cuttings over sizes/mass. We understand that without proper experimental database (which unfortunately we do not have) these results can only be used for preliminary calculations. But our experience shows that even such model problems are very useful for development of well designs and related equipment.
  Report of the group

• Modeling groundwater flow in aquifers, instructor: Ercilia Sousa

  Mathematical background: Partial differential equations. Numerical analysis. Matlab programming skills.

  An aquifer is an underground layer of permeable water-bearing rock and it fills with water from rain that drains into the ground. In some areas, the water passes through the soil on top of the aquifer, and in others, it enters through joints and cracks in rocks. The water moves downward until it meets less permeable rock. Aquifers act as reservoirs for groundwater. Because aquifers fill with water that drains from the surface of the Earth, they can be contaminated by any chemical or toxic substance found on the surface. Therefore it is quite important to model groundwater transport to understand how long a contaminant plume will grow, remain stable, or shrink, as well as how easy or difficult it will be to remediate.
  Report of the group

• Wind power prediction, instructor: Tihomir Ivanov

  Mathematical background: Since there exist many different approaches for this problem, there are no specific requirements, but some knowledge in one of the following: PDE modelling, time series analysis, numerical analysis, would be helpful.

  Wind power is considered among the most promising sustainable energy sources. There has been a considerable growth in the installed electricity generation capacity worldwide in the last decades. A very important issue for the successful management and exploitation of this technology, however, is the necessity of accurate forecasts for generated power and, thus, wind speed. There exist different approaches, considering the time-horizon of the forecast. Broadly, they can be categorized as physically-based, statistically-based, and combined. In the current project, approaches for short- and mid-term forecasts will be considered. The main problems will be the following:

  • Propose physically-based and/or statistically-based models for forecasting wind speed;
  • Find a relation between wind speed and produced power;
  • Verify the applicability of the proposed forecasting procedures on the basis of numerical experiments, using real data.
  
  Report of the group

• Forecasting allergen’s concentrations, instructor: Marko Nedeljkov

  Mathematical background: partial differential equation, stochastics

  Allergies of different kinds are wide spread problem in our time and a large number of people suffers from pollen related allergies. Even with modern medical treatments, allergen avoidance is important for managing allergy. Knowledge about when certain pollen types are likely to be in the air helps allergy sufferers to plan activities and medication use. Since airborne pollen is transported by air masses it can easily spread and results in an increased risk for allergy symptoms in sensitive population. The importance of allergens forecasting is also recognized throughout the IPA Cross-Border Programme Croatia-Serbia. The project ”Real-time measurements and forecasting for successful prevention and management of seasonal allergies in Croatia-Serbia cross-border region (RealForAll)” started in July 2017 and in gathers together Biosense Institute University of Novi Sad, Faculty of Sciences University of Novi Sad, University of Osijek and Osijek Municipality in order to improve the relevant allergens forecasting and improve public health. Within this task, we will focus on the major pollen allergens (such as Ambrosia) in the Croatia-Serbia cross-border region. Based on the historical data, we will form the forecast of the allergens concentrations including both long-term and short-term predictions. Data consists of the historical daily pollen concentrations and meteorological data such as temperature and humidity which are highly relevant for pollen dissemination.
  Report of the group

• Storing your random objects, instructor: Thomas Götz

  Mathematical background:

  A problem that you might remember from your childhood: You have quite some wooden bricks for playing and constructing. In the evening you have to store them in a sort of container. If the bricks are arranged regularly, that’s easy. But what, if you just throw them into the container at random?
  Report of the group

• Imaging the body with light: mathematical and numerical challenges, instructor: Paola Causin

  Mathematical background: Calculus, Physics, Numerical Analysis, Matlab programming

  Diffuse optical tomography (DOT) is an emerging medical imaging technique in which the part of the body to be examined (typically, the brain or the breast) is illuminated by near-infrared light from an array of sources. The multiply-scattered light which emerges is collected by an array of detectors, forming one or more images that are numerically processed to obtain information about the tissue properties. Namely, since one can tune the wavelength of the light to coincide with weakest absorption from tissue water or oxy/de-oxygenated hemoglobin, one can attempt to localize absorption anomalies (primarily by the two forms of hemoglobin) and scattering in the tissue. To do this, a mathematical and numerical model of light propagation is used. This task is, however, highly complex since:

  1. tissue is a turbid medium with strong scattering, in which light follows an extremely complicated path, the signal strength attenuates rapidly, and propagation is inherently 3D
  2. the background properties are generally unknown and may be difficult to measure
  3. due to the physics of the propagation, the inverse problem (that is, compute the absorption coefficient from collected data) is severely ill-posed and appropriate techniques are required to handle it
  4. high computational efficiency is to be sought in order to obtain results in very short time spans and make DOT convenient when compared to other, more detailed but more time expensive/aggressive medical imaging techniques
  In this project, students will be given fundamentals of the DOT physical principles as well of the associated mathematical and numerical models. Then they will be asked to work on the different aspects of the mathematical model and numerical implementation in order to produce a self-contained code able to recognize anomalies within a tissue sample investigated by DOT (real data will also be provided).
  Report of the group

• Modeling effect of time delay for large network of seismic monitor, instructor: Christophe Picard

Mathematical background: linear algebra, signal processing, graphs.

In order to study the behavior and composition of the underground floor, drilling companies need precise timing and positioning information of their equipments. Those equipments are link in a network and are generally connected to a global positioning system for synchronization. However there are no guarantee that the instruments will remain synchronized and some of them my deviate in time. Hence, the periods to which the vibration of the underground floor are caught might not be completely accurate, making the precise localisation of the events impossible. The goal of this project is to model the effect of de-synchronization between the different instruments and how the de-syncrhonization events can be detected from the recorded signal logs.
Report of the group

• Modelling of Ice around Cooling Pipes, instructor: Jürgen Dölz

  Mathematical background: stationary heat equation, Bernoulli's free boundary problem, boundary integral equations

  The modelling of ice around cooling pipes is an important task in engineering. For example, when tunnelling closely under supporting structures like train lines, highways or houses, the ground where the tunnel is dug is often frozen by such pipes. This improves stability of the surrounding soil during digging and prevents the tunnel from collapsing. To predict the necessary cooling for such tasks, it is crucial to know how the ice around cooling pipes behaves. In this project, we will model the layer of ice around cooling pipes in the steady state. Therefore, we will transform the problem into Bernoulli's free boundary problem, which we will then solve using numerical methods based on boundary integral equations.
  Report of the group

• The espresso-coffee problem, instructor: Milana Čolić

  Mathematical background: Calculus, Modeling with PDE’s, Numerical Analysis

  Preparation of espresso-coffee is a process which, besides pleasure, posseses extraordinary complexity. In brief, a stream of hot water is forced to flow through the bounded layer of coffee in granules. Afterwards it is collected in the cup. The flow of water (percolation) is accompanied by the extraction of soluble substance of coffee, as well as the transport of the solid phase which becomes the part of the coffee emulsion. The goal of the project is to study the basic aspects of the percolation process, to establish the mathematical model and possibly perform some numerical simulation.
  Report of the group

• Diffusion and anomalous diffusion models: simulation and application to biological data, instructor: Michal Balcerek

  Mathematical background: probability theory, stochastic processes and time series, modelling of random variables and stochastic processes in Matlab (preferably).

  Movement of the particles in a cell is a very complex dynamical process resulting from an intricate interplay of multiple components. At first sight, the trajectories of migrating particles resemble those of thermally driven Brownian particles. However, by analyzing the trajectories of various particles, one can show experimentally that anomalous dynamics characterizes such movements. In fact, the characteristic properties of such anomalous diffusion can indicate differences between types of particles or even if some extracellular component, such as an catalyst, e.g. a medication, is present. In effect, there has been a great interest in long-range dependent and self-similar processes, in particular fractional Brownian motion (FBM), fractional stable motion (FSM) and autoregressive fractionally integrated moving average (ARFIMA). Such processes serve as basic stochastic models for fractional anomalous dynamics or the, so called, anomalous diffusion. The issue of distinguishing between normal and anomalous diffusion, as such, concerns many fields of science. In the case of classical diffusion, the second moment is linear in time, whereas anomalous diffusion processes exhibit distinct deviations from this fundamental property. The aim of this project is the application of various methods to find the best possible model to describe the data from a living cell.
  Report of the group

• Modelling human interactions across a city with graphs, instructor: Olivera Novović

  Mathematical background: graph theory, linear algebra, probability theory

  Connectivity graphs inferred from mobile phone data uncover pulse of human interaction. In the recent years many innovative applications based on this rich data emerged, such as urban sensing, transport planning, social analysis and monitoring epidemics of infectious diseases Anonymous mobile communication data from telecom operators can be utilized for sensing activities occurring within a city and can further fit into wider vision of smart cities that aims at monitoring and optimizing urban landscapes. The goal of the project is to provide students with hands-on experience in working with real-world telecom data on a city level. Project will include introduction into NetworkX and Pandas Python library. Students will then develop entire workflow on Telecom Italia data sets through steps:

  1. Aggregating raw data in defined spatial/temporal resolution
  2. Representing aggregated data as weighted graph, where nodes are spatial units and edges represent communication links with corresponding strength
  3. Edges filtering based on probability and measured statistical significance of having link between nodes
  4. Deeper analysis of obtained graphs, extracting information on global and local graph properties
  5. Visual presentation of graphs in spatial context and obtained results of the analysis
  Through the lenses of graph theory students will model human interactions across a city and discover properties that can serve for detecting the patterns and deviations from typical observations.
  Report of the group