(147al) An Overview of the Application of and Advances in Sparse Identification in Process Systems Engineering

Research Interests

In the field of scientific and engineering research, the discovery of the dynamics of physical systems is of paramount importance and a building block of numerous fields such as process optimization and advanced process control. Many practical systems of interest follow dynamics that can be captured using differential equations—either ordinary or partial—that provide information on the system dynamics as functions of time and/or space. Due to the high nonlinearity and complexity of most practical engineering systems (e.g., catalytic reactors and distillation columns in the field of chemical engineering, or turbulent fluid flow in the field of mechanical engineering), it is often difficult to derive first-principles differential equations based on only knowledge of the physics of the system. With the increasing availability of data, advances in computing power, and accessibility of libraries typically used in data science and machine learning, a significant amount of effort has been expended on data-driven modeling of engineering systems. Some data-driven techniques that have recently been used successfully to model a variety of engineering systems of interest are neural networks [1-2] and sparse identification (SINDy) [3-5]. In the field of chemical engineering, SINDy has been used to build reduced-order models and subsequently model predictive controllers (MPC) for hydraulic fracturing [6] and nonlinear, multiscale reactors [7].

In the current work, we summarize recent advancements in the utilization of sparse identification of nonlinear dynamics (SINDy) for modeling and controlling nonlinear chemical process systems based on data. The two foci to address are the difficulties posed by time-scale multiplicities and noisy sensor data when employing SINDy. It provides a concise overview of innovative methods developed to overcome these challenges and presents modeling guidelines for applying these techniques to process systems engineering. To tackle the issue of model stiffness in two-time-scale systems, which can result in poorly conditioned controllers, we employed a reduced-order modeling approach that utilizes SINDy to capture the slow dynamics and nonlinear principal component analysis to establish an algebraic relationship between the fast and slow states. By doing so, the resulting model enables the utilization of a Lyapunov-based MPC that ensures closed-loop stability, provided that the separation between fast and slow dynamics is sufficiently large. Furthermore, we developed novel algorithms using subsampling, co-teaching, and ensemble learning to address the challenge of dealing with high levels of sensor noise in both simulated mathematical systems as well as large-scale systems using noisy industrial data from the process simulator, Aspen Plus Dynamics.

References:

[1] Ren, Y.M., Alhajeri, M.S., Luo, J., Chen, S., Abdullah, F., Wu, Z. and Christofides, P.D., 2022. A tutorial review of neural network modeling approaches for model predictive control. Comp. & Chem. Eng., 107956.

[2] Yun, S., Tom, M., Luo, J., Orkoulas, G. and Christofides, P.D., 2022. Microscopic and data-driven modeling and operation of thermal atomic layer etching of aluminum oxide thin films. Chem. Eng. Res. & Des., 177, 96-107.

[3] Brunton, S.L., Proctor, J.L., Kutz, J.N., 2016. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl. Acad. Sci. 113 (15), 3932–3937.

[4] Schaeffer, H., Caflisch, R., Hauck, C.D., Osher, S., 2013. Sparse dynamics for partial differential equations. Proc. Natl. Acad. Sci. 110 (17), 6634–6639.

[5] Ozolinš, V., Lai, R., Caflisch, R., Osher, S., 2013. Compressed modes for variational problems in mathematics and physics. Proc. Natl. Acad. Sci. 110 (46), 18368–18373.

[6] Narasingam, A., Sang-Il Kwon, J., 2018. Data-driven identification of interpretable reduced-order models using sparse regression. Comp. & Chem. Eng. 119, 101–111.

[7] Abdullah, F., Wu, Z., Christofides, P.D., 2021. Data-Based Reduced-Order Modeling of Nonlinear Two-Time-Scale Processes. Chem. Eng. Res. & Des., 166, 1-9.

Keywords: Process Automation & Control; Computing and Systems Engineering; Reactors