Design of Dynamic Experiments: A Data-Driven Methodology for the Optimization of Time-Varying Processes

A new methodology for the design of experiments is presented that provides a way to optimize the operation of a variety of batch and semibatch or fed-batch processes without the use of a knowledge-driven or fundamental model describing the inner workings of the process, when one or more time-varying decision variables must be selected. The types of processes that can benefit from this approach include those producing specialty chemical, pharmaceutical, or food products whose production rate is not high enough to justify the development of a knowledge-driven model. The approach generalizes the classical and widely used Design of Experiments (DoE), which considers only decision variables, or factors, which are constant with time. The new approach, called the Design of Dynamic Experiments (DoDE), systematically designs experiments that explore a considerable number of dynamic signatures, called dynamic subfactors (DSFs), in the time dependency of the unknown decision variables or factors. Two example processes—a batch nonisothermal reactor and a semibatch penicillin fermentation process—amply demonstrate the utility of the method. In both cases, a small number of experiments lead to the quick and accurate optimization of the process. The calculated optimal operating conditions through the proposed DoDE approach are only slightly different from the optimum that would have been obtained if a knowledge-driven model were available.