Computational statistical methods in chemical engineering

Abstract

Recent advances in theory and practice, have introduced a wide variety of tools from machine learning that can be applied to data intensive chemical engineering problems. This thesis covers applications of statistical learning spanning a range of relative importance of data versus existing detailed theory. In each application, the quantity and quality of data available from experimental systems are used in conjunction with an understanding of the theoretical physical laws governing system behavior to the extent they are available. A detailed generative parametric model for optical spectra of multicomponent mixtures is introduced. The application of interest is the quantification of uncertainty associated with estimating the relative abundance of mixtures of carbon nanotubes in solution. This work describes a detailed analysis of sources of uncertainty in estimation of relative abundance of chemical species in solution from optical spectroscopy. In particular, the quantification of uncertainty in mixtures with parametric uncertainty in pure component spectra is addressed. Markov Chain Monte Carlo methods are utilized to quantify uncertainty in these situations and the inaccuracy and potential for error in simpler methods is demonstrated. Strategies to improve estimation accuracy and reduce uncertainty in practical experimental situations are developed including when multiple measurements are available and with sequential data. The utilization of computational Bayesian inference in chemometric problems shows great promise in a wide variety of practical experimental applications. A related deconvolution problem is addressed in which a detailed physical model is not available, but the objective of analysis is to map from a measured vector valued signal to a sum of an unknown number of discrete contributions. The data analyzed in this application is electrical signals generated from a free surface electro-spinning apparatus. In this information poor system, MAP estimation is used to reduce the variance in estimates of the physical parameters of interest. The formulation of the estimation problem in a probabilistic context allows for the introduction of prior knowledge to compensate for a high dimensional ill-conditioned inverse problem. The estimates from this work are used to develop a productivity model expanding on previous work and showing how the uncertainty from estimation impacts system understanding. A new machine learning based method for monitoring for anomalous behavior in production oil wells is reported. The method entails a transformation of the available time series of measurements into a high-dimensional feature space representation. This transformation yields results which can be treated as static independent measurements. A new method for feature selection in one-class classification problems is developed based on approximate knowledge of the state of the system. An extension of features space transformation methods on time series data is introduced to handle multivariate data in large computationally burdensome domains by using sparse feature extraction methods. As a whole these projects demonstrate the application of modern statistical modeling methods, to achieve superior results in data driven chemical engineering challenges.