(269d) Bayesian Experimental Designs: A Decision Theoretic Framework Applied to Industrial Case Studies

Experimental design theories provide a systematic method for determining the operating conditions under which experiments will yield the greatest amount of information about a process. Its value in all aspects of process design, from product development to industrial scale-up, cannot be overstated. Efficient experimental designs minimize both the time and resources spent, while also maximizing the information gained. The classical approach to experimental design does not take full advantage of prior knowledge, such as the physics and chemistry that drive the process, and for this reason the most efficient designs are not identified. Model based approaches such as Bayesian Designs[1] provide the necessary framework to comprehensively represent prior knowledge, by using process models and probabilistic descriptions of model inadequacy, measurement errors, and parametric uncertainty. Combined with decision theory, these Bayesian Designs can be tailored to produce efficient designs for a specific study on a specific system.

While the Bayesian Design theory has been well developed and several applications have been demonstrated[2,3], the current literature focuses on either the application or the computational methods rather than an evaluation of the results. In addition, most examples utilize linear-Gaussian models even though the process response is known to be nonlinear in the parameters. This negates the biggest advantages of the Bayesian approach. In this work, Bayesian Designs are computed within a Decision Theoretic framework using full process models and an unrestricted (non-Gaussian) characterization of parametric uncertainty. The performance of Classical Designs and Bayesian Designs is presented for two industrial case studies: a gasification kinetics study and a solids separation study. The efficacy of both strategies is compared using both simulations and experimental results, in order to quantify the benefits of a model based approach to experimental design.

[1] Chaloner, K. and I. Verdinelli, Bayesian experimental design: A review. Statist. Sci., 1995. 10(3): p. 273-304.

[2] Murphy, E.F., S.G. Gilmour, and M.J.C. Crabbe, Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach. Journal of Biochemical and Biophysical Methods, 2003. 55(2): p. 155-178.

[3] Nabifar, A., et al., Optimal Bayesian Design of Experiments Applied to Nitroxide-Mediated Radical Polymerization. Macromolecular Reaction Engineering. DOI: 10.1002/mren.200900071