Bayesian design of experiments for complex chemical systems

Abstract

Engineering design work relies on the ability to predict system performance. A great deal of effort is spent producing models that incorporate knowledge of the underlying physics and chemistry in order to understand the relationship between system inputs and responses. Although models can provide great insight into the behavior of the system, actual design decisions cannot be made based on predictions alone. In order to make properly informed decisions, it is critical to understand uncertainty. Otherwise, there cannot be a quantitative assessment of which predictions are reliable and which inputs are most significant. To address this issue, a new design method is required that can quantify the complex sources of uncertainty that influence model predictions and the corresponding engineering decisions. Design of experiments is traditionally defined as a structured procedure to gather information. This thesis reframes design of experiments as a problem of quantifying and managing uncertainties. The process of designing experimental studies is treated as a statistical decision problem using Bayesian methods. This perspective follows from the realization that the primary role of engineering experiments is not only to gain knowledge but to gather the necessary information to make future design decisions. To do this, experiments must be designed to reduce the uncertainties relevant to the future decision. The necessary components are: a model of the system, a model of the observations taken from the system, and an understanding of the sources of uncertainty that impact the system. While the Bayesian approach has previously been attempted in various fields including Chemical Engineering the true benefit has been obscured by the use of linear system models, simplified descriptions of uncertainty, and the lack of emphasis on the decision theory framework. With the recent development of techniques for Bayesian statistics and uncertainty quantification, including Markov Chain Monte Carlo, Polynomial Chaos Expansions, and a prior sampling formulation for computing utility functions, such simplifications are no longer necessary. In this work, these methods have been integrated into the decision theory framework to allow the application of Bayesian Designs to more complex systems. The benefits of the Bayesian approach to design of experiments are demonstrated on three systems: an air mill classifier, a network of chemical reactions, and a process simulation based on unit operations. These case studies quantify the impact of rigorous modeling of uncertainty in terms of reduced number of experiments as compared to the currently used Classical Design methods. Fewer experiments translate to less time and resources spent, while reducing the important uncertainties relevant to decision makers. In an industrial setting, this represents real world benefits for large research projects in reducing development costs and time-to-market. Besides identifying the best experiments, the Bayesian approach also allows a prediction of the value of experimental data which is crucial in the decision making process. Finally, this work demonstrates the flexibility of the decision theory framework and the feasibility of Bayesian Design of Experiments for the complex process models commonly found in the field of Chemical Engineering.