The first generalization called the Design of Dynamic Experiments (DoDE), enables the design of experiments where some or all of the factors representing operating conditions can be functions of time. In the Figure to the right, a set of experiments is defined where the pH of the bioreactor is a quadratic function of time. All profiles are within the shaded area, describing the experimental domain. Not all experiments have the same duration, implying that the batch duration is one of the traditional factors in the DoDE design. DoDE designs can have both conventional factors as well as dynamic factors, which have a dependence on time.
The second generalization, called Dynamic Response Surface Methodology (DRSM), enables the modeling of time-resolved data from a set of experiments. It allows us to effectively and efficiently capture the dynamic characteristics of a process in a data-driven model. These DRSM models can be used to optimize the operation of the process, and their β(t) parametric functions reveal essential information about the inner workings of the process. For example, suppose a β(t) parametric function has positive values at the beginning of the batch but almost zero values during the later stages. In that case, it is implied that the corresponding factor influences the measured output positively at earlier but not at later times.
If one measures the compositions of the species involved in a complex reaction, the estimated DRSM models for each set of measurements can be used through a machine learning algorithm to identify the reaction stoichiometry the species are involved in. At the same time, the kinetic models for all reactions are estimated quite accurately.
This is quite useful when detailed composition measurements reveal the presence of species other than the reactants and expected products, and one wonders about the reaction pathways giving rise to such unexpected intermediates and byproducts, which could have a detrimental impact.
Dr. Christos Georgakis is Professor Emeritus of Chemical and Biological Engineering at Tufts University, where he has also been the Gordon Senior Faculty Fellow in Systems Engineering. In 2017, he was recognized with Tufts University’s Distinguished Senior Scholar Award.
Professor Georgakis has 50 years of experience as an educator, researcher, and industry consultant in Process Systems Engineering.
We will be more than happy to talk to you.
Process Cybernetics LLC (ProCyber for short) brings two recent statistical learning algorithms that generalize the traditional design of experiments (DoE) methodology to industrial practice.
Both generalizations aim to extend the power of DoE with respect to process dynamics. The first generalization called the Design of Dynamic Experiments (DoDE), enables the design of experiments where some or all of the factors representing operating conditions can be functions of time. The second generalization, called Dynamic Response Surface Methodology (DRSM), enables the modeling of time-resolved data from a set of experiments. It allows us to effectively and efficiently capture the dynamic characteristics of a process in a data-driven model.
In the cases where a detailed knowledge-driven model is not at hand, describing the inner workings of a process, a data-driven model can be quickly estimated to represent the essential characteristics of the process accurately. The innovative character of the DoDE and DRSM algorithms is the best way to describe the dynamic characteristics of the process in a data-driven model, something not possible in the DoE and RSM framework.
These novel modeling strategies are presently complemented by our partial understanding of our processes through material and energy balances to produce powerful hybrid models. These models effectively combine our incomplete knowledge and the power of data to model, optimize, and control both batch and continuous processes quickly. In effect, we are combining modern advances in data science and machine learning with traditional material and energy balances, the most prudent approach to improving chemical and biological processes. Instead of throwing out old and tested tools for the new and fanciful ones, we combine them for a doubling of benefits.
We have collaborated with a series of big and medium-sized companies to benchmark these algorithmic technologies. We have applied them in bulk chemicals and specialty products as well as in pharmaceuticals and biopharmaceuticals. We are ready to help your company benefit from these advances. Give us a call at 617-223-1793 or drop us an email at <c.georgakis@gmail.com>.
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