Prediction of Upward Flame Spread over Polymers

In this work, the existing understanding of flame spread dynamics is enhanced through an extensive study of the heat transfer from flames spreading vertically upwards across 5 cm wide, 20 cm tall samples of extruded Poly (Methyl Methacrylate) (PMMA). These experiments have provided highly spatially resolved measurements of flame to surface heat flux and material burning rate at the critical length scale of interest, with a level of accuracy and detail unmatched by previous empirical or computational studies. Using these measurements, a wall flame model was developed that describes a flame’s heat feedback profile (both in the continuous flame region and the thermal plume above) solely as a function of material burning rate. Additional experiments were conducted to measure flame heat flux and sample mass loss rate as flames spread vertically upwards over the surface of seven other commonly used polymers, two of which are glass reinforced composite materials. Using these measurements, our wall flame model has been generalized such that it can predict heat feedback from flames supported by a wide range of materials. For the seven materials tested here – which present a varied range of burning behaviors including dripping, polymer melt flow, sample burnout, and heavy soot formation – model-predicted flame heat flux has been shown to match experimental measurements (taken across the full length of the flame) with an average accuracy of 3.9 kW m-2 (approximately 10 – 15 % of peak measured flame heat flux). This flame model has since been coupled with a powerful solid phase pyrolysis solver, ThermaKin2D, which computes the transient rate of gaseous fuel production of constituents of a pyrolyzing solid in response to an external heat flux, based on fundamental physical and chemical properties. Together, this unified model captures the two fundamental controlling mechanisms of upward flame spread – gas phase flame heat transfer and solid phase material degradation. This has enabled simulations of flame spread dynamics with a reasonable computational cost and accuracy beyond that of current models. This unified model of material degradation provides the framework to quantitatively study material burning behavior in response to a wide range of common fire scenarios.

Thermal Tracking and Estimation for Microprocessors

Due to increasing integration density and operating frequency of today's high performance processors, the temperature of a typical chip can easily exceed 100 degrees Celsius. However, the runtime thermal state of a chip is very hard to predict and manage due to the random nature in computing workloads, as well as the process, voltage and ambient temperature variability (together called PVT variability). The uneven nature (both in time and space) of the heat dissipation of the chip could lead to severe reliability issues and error-prone chip behavior (e.g. timing errors). Many dynamic power/thermal management techniques have been proposed to address this issue such as dynamic voltage and frequency scaling (DVFS), clock gating and etc. However, most of such techniques require accurate knowledge of the runtime thermal state of the chip to make efficient and effective control decisions. In this work we address the problem of tracking and managing the temperature of microprocessors which include the following sub-problems: (1) how to design an efficient sensor-based thermal tracking system on a given design that could provide accurate real-time temperature feedback; (2) what statistical techniques could be used to estimate the full-chip thermal profile based on very limited (and possibly noise-corrupted) sensor observations; (3) how do we adapt to changes in the underlying system's behavior, since such changes could impact the accuracy of our thermal estimation. The thermal tracking methodology proposed in this work is enabled by on-chip sensors which are already implemented in many modern processors. We first investigate the underlying relationship between heat distribution and power consumption, then we introduce an accurate thermal model for the chip system. Based on this model, we characterize the temperature correlation that exists among different chip modules and explore statistical approaches (such as those based on Kalman filter) that could utilize such correlation to estimate the accurate chip-level thermal profiles in real time. Such estimation is performed based on limited sensor information because sensors are usually resource constrained and noise-corrupted. We also took a further step to extend the standard Kalman filter approach to account for (1) nonlinear effects such as leakage-temperature interdependency and (2) varying statistical characteristics in the underlying system model. The proposed thermal tracking infrastructure and estimation algorithms could consistently generate accurate thermal estimates even when the system is switching among workloads that have very distinct characteristics. Through experiments, our approaches have demonstrated promising results with much higher accuracy compared to existing approaches. Such results can be used to ensure thermal reliability and improve the effectiveness of dynamic thermal management techniques.

SEMIPARAMETRIC METHODS IN THE ESTIMATION OF TAIL PROBABILITIES AND EXTREME QUANTILES

In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, natural disaster insurance actuary, quality control schemes, etc. A useful way to make an assessment of extreme events is to estimate the probabilities of exceeding large threshold values and extreme quantiles judged by interested authorities. Such information regarding extremes serves as essential guidance to interested authorities in decision making processes. However, in such a context, data are usually skewed in nature, and the rarity of exceedance of large threshold implies large fluctuations in the distribution's upper tail, precisely where the accuracy is desired mostly. Extreme Value Theory (EVT) is a branch of statistics that characterizes the behavior of upper or lower tails of probability distributions. However, existing methods in EVT for the estimation of small threshold exceedance probabilities and extreme quantiles often lead to poor predictive performance in cases where the underlying sample is not large enough or does not contain values in the distribution's tail. In this dissertation, we shall be concerned with an out of sample semiparametric (SP) method for the estimation of small threshold probabilities and extreme quantiles. The proposed SP method for interval estimation calls for the fusion or integration of a given data sample with external computer generated independent samples. Since more data are used, real as well as artificial, under certain conditions the method produces relatively short yet reliable confidence intervals for small exceedance probabilities and extreme quantiles.