# Math Modeling in Indudustry Team 6

In real-life applications critical areas are often non- accessible for measurement and thus for inspection and control. For proper and safe operations one has to estimate their condition and predict their future alteration via inverse problem methods based on accessible data. Typically such situations are even complicated by unreliable or flawed data such as sensor data rising questions of reliability of model results. We will analyze and mathematically tackle such problems starting with physical vs. data driven modeling, numerical treatment of inverse problems, extension to stochastic models and statistical approaches to gain stochastic distributions and confidence intervals for safety critical parameters.

As project example we consider a blast furnace producing iron at temperatures around 2,000 °C. It is running several years without stop or any opportunity to inspect its inner geometry coated with firebrick. Its inner wall is aggressively penetrated by physical and chemical processes. Thickness of the wall, in particular evolvement of weak spots through wall thinning is extremely safety critical. The only available data stem from temperature sensors at the outer furnace surface. They have to be used to calculate wall thickness and its future alteration. We will address some of the numerous design and engineering questions such as placement of sensors, impact of sensor imprecision and failure.

References:

1. F. Bornemann, P. Deuflhard, A. Hohmann, "Numerical Analysis”, de Gruyter, 1995

2. A. C. Davison,” Statistical Models”, Cambridge University Press, 2003

3. William H. Press, “Numerical Recipes in C”, Cambridge University Press, 1992

4. http://en.wikipedia.org/wiki/Blast_furnace#Modern_process

Prerequisites:

Computer programming experience in a language like C or C++; Knowledge about Numerical Linear Algebra,

Stochastic and Statistics (see references)