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Show COLLEGE OF ENGINEERING UNDERGRADUATE RESEARCH ABSTRACTS Nathan Yonkee Mikhail Skliar REDUCED DIMENSIONALTHERMAL MODEL IDENTIFICATION Nathan Yonkee (Mikhail Skliar) Department of Chemical Engineering University of Utah Thermal imaging is an emerging measurement modality that can noninvasively monitor a broad range of thermal processes. In this project, thermal images were used to identify an autoregressive model that adequately described the transient temperature evolution captured by a thermal camera. As a test case, we studied the heat transfer through a metal rod partially inserted into a tubular oven.The resulting temperature distribution was imaged using an infrared camera with a resolution of 320x240 pixels, yielding 76,800 pointwise temperature measurements. Three sets of data were collected, each corresponding to a different oven temperature. For each set, the metal rod was initially preheated inside of the oven, and then a length of the rod was removed while the base remained inside of the oven maintained at a fixed temperature. The three sets of data corresponded to oven temperatures of 175 °C, 225 °C, and 275 °C. Infrared images were collected every 90 seconds over a period of 75 minutes for each of the three sets. In order to model the transient cooling of the rod, a set of optimal orthonormal basis functions was identified using the imaging data. For each image, the longitudinal temperature distribution (274 pixels long) was estimated using the arithmetic mean of the corresponding radially distributed temperature measurements (50 pixels wide) and then the ambient temperature was subtracted from the data. All three sets of images were used together to identify a single set of three basis functions by using the singular value decomposition of the combined dataset.The singular value decomposition of the dataset identified which basis functions best described the data, in a least squares sense. This set of three basis functions described 9 7 % of all information contained in the combined dataset, while the 271 discarded basis functions described the remaining 3%. By using the identified basis functions, the high-dimensional thermal imaging data was represented parsimoniously and with little loss of useful information by a low-dimensional system. The temperature distribution of the rod was then modeled as a linear combination of the three basis functions. The transient evolution of the corresponding coefficients was described using an autoregressive model.Three separate models for each oven temperature were estimated. These models described their respective coefficient evolution with greater than 9 7 % correlation, in the least squares sense.The model parameters corresponding to an oven temperature of 175 °C described the coefficients corresponding to an oven temperature of 225 °C with a correlation of 9 4 % and described the coefficients corresponding to an oven temperature of 275 °C with a correlation of 90%. Any stable auto-regressive model, with no input signal, has a steady state value of zero. Because each of the autoregressive models was stable, they cannot be used to estimate the steady-state temperature distribution with any accuracy. |
