(12g) A New Dynamic Response Surface Methodology for Modeling the Dynamics of Nonlinear Processes

In the era of Big Data, there is an ever-increasing amount of measured process variables that have been collected and stored. However, such data have not yet resulted in accurate models for process optimization and control purposes. Often the information that might be extracted from them, a challenging task, might not be sufficient¹. In addition, most of the proposed modeling methodologies for extracting such information, such as PCA and PLS, are linear and static. However, the fact remains that both the input and output variables are time-varying and their true interrelationship is nonlinear.

Our research group has recently introduced two data-driven modeling methodologies that account for the nonlinearities and process dynamics. They generalize the classical Design of Experiments (DoE)^2,3 framework by considering dynamic input as well as dynamic output variables. They also accurately model nonlinear dependencies among the variables. The Design of Dynamic Experiments (DoDE)⁴ approach addresses the issue of dynamic inputs and the Dynamic Response Surface Methodology (DRSM)⁵ models time-varying outputs. These novel data-driven methodologies have been successfully applied to the modeling, optimization and control many batch processes^6-10.

In this paper, we present a new and more promising version of the DRSM methodology in order to accurately model dynamic data over the semi-infinite time horizon. The novelty of the new method rests on a nonlinear transformation of time, the independent variable. The new method has the following advantages in comparison with the previous DRSM approach. It is capable of:

1) Modeling both continuous as well as batch processes, handling semi-infinite as easily as finite time domains

2) Using data that are not equidistant in time

3) Using data segments that are of varied durations due to possible strong nonlinearities in dynamics

We have examined the accuracy of the new approach in two representative processes: a complex continuous polymerization process¹¹ and a semi-batch penicillin fermentation¹². In both cases, statistical measures prove the obtained DRSM model to be very accurate. We will also discuss how such DRSM models can be used for control and optimization purposes.

Reference

1. Reis MS, Braatz RD, Chiang LH. Big Data: Challenges and Future Research Directions. Chemical Engineering Progress. 2016;112(3):46-50.

2. Box GEP, Wilson KB. ON THE EXPERIMENTAL ATTAINMENT OF OPTIMUM CONDITIONS. Journal of the Royal Statistical Society Series B-Statistical Methodology. 1951;13(1):1-45.

3. Montgomery DC. Design and Analysis of Experiments.8th ed. New York: Wiley; 2013.

4. Georgakis C. Design of Dynamic Experiments: A Data-Driven Methodology for the Optimization of Time-Varying Processes. Industrial & Engineering Chemistry Research. 2013;52(35):12369-12382.

5. Klebanov N, Georgakis C. Dynamic Response Surface Models: A Data-Driven Approach for the Analysis of Time-Varying Process Outputs. Industrial & Engineering Chemistry Research. 2016;55(14):4022-4034.

6. Fiordalis A, Georgakis C. Data-driven, Using Design of Dynamic Experiments, versus Model-driven Optimization of Batch Crystallization Processes. Journal Of Process Control. 2013;23(2):179-188.

7. Georgakis C, Chin S, Hayot P, Wassick J, Chiang LH. Optimizing an Industrial Batch Process Using the Design of Dynamic Experiments Methodology. Paper presented at: AICHE Spring Meeting; April 10-14, 2016; Houston,TX.

8. Wang Z, Klebanov N, Georgakis C. DRSM Model for the Optimization and Control of Batch Processes. Paper presented at: Dynamics and Control of Process Systems, including Biosystems/IFAC2016; Trondhelm,Norway.

9. Wang Z, Georgakis C. Data-Driven Optimization Using an Evolutionary Design of Dynamic Experiments for Biopharmaceutical Processes. Paper presented at: AICHE Annual Meeting; Nov 13-18, 2016; San Francisco, CA.

10. Troup GM, Georgakis C. Process systems engineering tools in the pharmaceutical industry. Computers & Chemical Engineering. 2013;51:157-171.

11. Zacca JJ, Ray WH. Modeling of the liquid-phase polymerization of olefins in loop reactors. Chem. Eng. Sci. 1993;48(22):3743-3765.

12. Bajpai RK, Reuss M. A Mechanistic Model for Penicillin Production. J. Chem. Technol. Biotechnol. 1980;30(6):332-344.