Experimental and Theoretical Studies of Kinetics and Quality Parameters to Determine Spontaneous Combustion Propensity of U.S. Coals

Spontaneous combustion is one of the most serious problems to mine safety and production in the global coal industry. It is considered to be the trigger for fires and explosions in underground coal mines especially for gassy mines. Such thermal events are not easily detectable since they normally occur in inaccessible gob and sealed area. It is also difficult to find the most likely hot point accurately. Admittedly, determination of the propensity for spontaneous combustion before mining activity should be a necessary step in the design of a mine and ventilation plan. However, due to the complexity of the chemical and physical properties of coal, spontaneous combustion has not been fully understood.;Many methods and techniques have been developed for studying self-heating of coal. Each of the methods has its unique characteristics and index for assessing the propensity of self-ignition. However, all the reasonable candidate factors causing spontaneous combustion could not be examined thoroughly by any single method. Accountable relationships among the propensity indices of different methods should be established. The certainty for assessing the propensity of spontaneous combustion will be greatly improved by using the combination of various methods. On the other hand, spontaneous combustion is affected by many factors. According to a proximate analysis of coal, it is believed that sulfur and volatile matter in coal are the main intrinsic factors that cause the self-heating of coal. Their oxidation at lower temperatures than that of fixed carbon to initiate coal\u27s self-heating should be quantified.;In order for better understanding spontaneous combustion behavior, the following research has been done in this dissertation:;• Establishment of a coal spontaneous combustion testing facility that features adiabatic self-heating, thermogravimetric analyzer (TGA) and USBM self-heating temperature methods in the mine ventilation laboratory at West Virginia University.;• Correlation of U.S. coal rank and propensity for spontaneous combustion has been studied by classifying coal rank quantitatively. This quantified rank system provides a schematic view that reflects the relationship between rank and self-heating temperature of coal. As such, it can be used to serve as a quick estimate of self-heating potential of U.S. coals and as a cost effective way for initial risk assessment for any new mine development.;• Based on the law of energy conservation, a mathematical model has been developed to quantify the self-heating rate of coal and assist the adiabatic self-heating test when the testing period becomes impractically long. Then improvements have been made to the model by enhancing the model\u27s ability to consider the effects of sulfur, volatile matter and moisture contents in the coal - three important factors affecting a coal\u27s self-heating process. Heat release rates for pyrite oxidation and moisture condensation are built into the model

Optimal linear estimation under unknown nonlinear transform

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We consider a significant generalization in which the relationship between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$ is noisy, quantized to a single bit, potentially nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover $\beta^*$ in settings (i.e., classes of link function $f$) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between $y_i$ and $\langle \mathbf{x}_i,\beta^* \rangle$. We also consider the high dimensional setting where $\beta^*$ is sparse ,and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where $p \gg n$. For a broad class of link functions between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.Comment: 25 pages, 3 figure