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Abstracts and Talk Materials
Mathematical Modeling in Industry XVIII
August 6 - 16, 2014

Bradley K. Alpert (National Institute of Standards and Technology)

Team 1: Mathematical Challenges in High-Throughput Microcalorimeter Spectroscopy

Keywords of the presentation: ordinary differential equations, Fourier analysis, statistical estimation, fast algorithms; transition-edge sensors, microcalorimeters, single-photon spectroscopy, optimal filtering, multiplexing, pulse pile-up

In recent years, microcalorimeter sensor systems have been developed at NIST, NASA, and elsewhere to measure the energy of single photons in every part of the electromagnetic spectrum, from microwaves to gamma rays. These microcalorimeters have demonstrated relative energy resolution, depending on the energy band, of better than 3 x 10^(-4), providing dramatic new capabilities for scientific and forensic investigations. They rely on superconducting transition-edge sensor (TES) thermometers and derive their exquisite energy resolution from the low thermal noise at typical operating temperatures near 0.1 K. They also function in exceptionally broad energy bands compared to other sensor technologies. At present, the principal limitation of this technology is its relatively low throughput, due to two causes: (1) limited collection area, which is being remedied through development of large sensor arrays; and (2) nonlinearity of detector response to photons arriving in rapid succession. Both introduce mathematical challenges, due to variations in sensor dynamics, nonstationarity of noise when detector response nears saturation, crosstalk between nearby or multiplexed sensors, and algorithm-dependent noise of multiplexing. Although there are certain inherent limitations on calibration data, this environment is extremely data-rich and we will exploit data to attack one of these mathematical challenges.

Albert B. Gilg (Siemens AG)

Team 6: Prediction Under Uncertainties (Siemens and TU Munich)

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.

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