Optimization methods for the multivariate analysis of infrared spectral and interferogram data

Improvements to spectrometer hardware and design have made infrared spectroscopy a viable choice for monitoring chemical species outside the laboratory. The spectral data obtained from this type of measurement often contain analyte information hidden by multiple chemical constituents with overlapping spectral bands in addition to variations in spectral background signatures. A combination of signal processing and multivariate analysis is needed to meet these challenges. This dissertation describes research applying numerical optimization methods to enhance existing strategies for analyzing spectral and interferogram data.;An experimental design study of the factors that influence the pattern recognition performance of bandpass filtered Fourier transform infrared interferograms is described. The limit of detection of a target analyte is directly related to the ability to choose optimal settings for interferogram segment length, interferogram segment position, filter bandpass position, and filter bandpass width. Using analysis of variance techniques to interpret the main and interaction effects among the interferogram and filter variables, a protocol for designing near-optimal filters is developed.;An improved response function for the Simplex optimization of piecewise linear discriminants is described. The limit of detection of a target analyte is directly affected by the degree to which the discriminants are optimally positioned. A new response function is developed that guides the discriminant placement procedure to produce discriminants with better predictive abilities than previous response functions.;The application of genetic algorithms (GAs) to the optimization of piecewise linear discriminants is described. GA configurations are developed using experimental design methods to be stable for a wide variety of discriminant optimization problems. On average, the best piecewise linear discriminant optimized by a GA is observed to classify 11% more analyte-active patterns correctly in prediction than an unoptimized piecewise linear discriminant.;Simplex optimization, simulated annealing, generalized simulated annealing, a real-coded GA, and a Simplex-GA hybrid are compared for their ability to optimize piecewise linear discriminants. Discriminants optimized with Simplex optimization are found to outperform discriminants positioned by use of the other methods.;A protocol based on a GA for coupling bandpass digital filtering and partial least-squares (PLS) regression is described. Calibration models based on bandpass digital filters and PLS regression parameters found by the GA are found to perform better than calibration models based on grid searches.