(610g) Reduced-Order Modeling of CFD and FEA Simulations for Predicting the Impacts of Control Actions and Cyberattacks on Materials

Modern chemical processes rely extensively on control to manipulate processes toward desired states. These control systems represent an interface between the virtual computing environment and the physical system (the so-called cyber-physical system [1]), and this means that control actions directly impact the physical state of a process. Understanding the behavior of this interaction is important when considering problems in safety and security; however, direct testing of a process is often not possible. Therefore, simulation methods can be used to develop an understanding of how control actions affect process equipment. A comprehensive method for representing a wide variety of equipment involves continuum mechanics methods such as computational fluid dynamics (CFD) and finite element analysis (FEA). Previous research has indicated that such simulations could be used to develop intuition of the impacts of control actions on process equipment that might not be immediately evident, and would allow for a wide variety of situations to be considered [2]. However, these methods can be computationally expensive which limits how they could be applied to study a process. Thus, reduced-order models can be derived from CFD and FEA results to adequately represent system dynamics and allow for a wide variety of test cases to be studied offline.

Motivated by this, this work initially considers a coupled CFD/FEA simulation of a steam methane reforming tube created using ANSYS simulation software for developing reduced-order models for the fluid and for the solid equipment wall behavior. These are then used in analyzing how the fluid and solid evolve in response to a control system cyberattack and the use of an advanced control law. The CFD/FEA simulation builds on work done by Lao, et al. [5], in which closed-loop CFD simulations of the steam methane process were performed, where our goal is to use the CFD simulations of a reduced-size reforming tube with FEA simulations to investigate the equivalent stress (also known as von Mises stress) of the reactor walls. After verifying that the results of these CFD/FEA simulations were independent with respect to mesh and time step size, reduced-order autoregressive with exogenous terms (ARX) models were created to relate the control input (the temperature applied to the reactor) to variables which were desired to be predicted (equivalent stress and outlet hydrogen mole fraction). The resulting models are capable of representing the desired process and equipment dynamics in the CFD/FEA simulation and allow for the simulation of the equipment response (maximum equivalent stress variation over time) with reasonable computation time.

A cyberattack scenario is considered because cyberattacks represent an increasing threat to the interconnected chemical processes that exist today, and the strong interactions between the cyber and physical systems means that an attacker could directly drive a system towards an unsafe state that damages process equipment by manipulating the process control system [3]. Here, a cyberattack that provides false sensor measurements is simulated directly within the CFD simulation using a user-defined function. Impacts of the cyberattacks on the equipment compared to the hydrogen mole fraction at the tube outlet are compared. The advanced control scenario simulated using the reduced-order models obtained from the CFD/FEA simulation involves an advanced control method called economic model predictive control (EMPC), which optimizes control inputs based on an economic objective function and allows for varying operation in a safe region around the steady-state [4]. Cases in which the controller operates the process at a high-temperature steady-state (to maximize the outlet hydrogen mole fraction), and in which a constraint intended to represent a feedstock limitation applied periodically to facilitate a time-varying control action, are applied to demonstrate the impact of these control input profiles on the maximum equivalent stress in the tube wall.

This talk concludes with discussion of FEA modeling with advanced control considering equipment stress for another process known as powder bed fusion (PBF), which is an additive manufacturing process used to create metal components by melting successive layers of powder. FEA simulations were developed to represent the buildup of stresses components during the PBF process by using work done by Hussein, et al. [6], Zeng, et al. [7], and Goldak, et al. [8]. The computational intensity of these simulations means that only small and simple components can be directly simulated, and necessitate the use of reduced-order modeling techniques to simulate a wider variety of created components under advanced control strategies, and particularly those which constrain equipment behavior such as stresses in the part during the part construction. By using these situations as illustrative examples, this work demonstrates how reduced-order modeling techniques can be employed to represent processes with phenomena captured by CFD and FEA simulations.

REFERENCES:

[1] Chen, H. “Applications of Cyber-Physical System: A Literature Review.” Journal of Industrial Integration and Management. Vol. 2, No. 3, 1750012. (2017)

[2] Nieman, K., Oyama, H., Wegener, M., and Durand, H. “Predict the Impact of Cyberattacks on Control Systems.” Chemical Engineering Progress. September 2020.

[3] Davis, J., “Cybersecurity for Manufacturers: Securing the Digitized and Connected Factory,” Mahoney, T.C. (ed.), MForesight. (2017).

[4] Ellis, M., Durand, H., Christofides, P. D. “A tutorial review of economic model predictive control methods.” Journal of Process Control. Volume 24, Issue 8, Pages 1156-1178. (2014)

[5] Lao, L., Aguirre, A., Tran, A., Wu, Z., Durand, H., Christofides, P.D. “CFD modeling and control of a steam methane reforming reactor.” Chemical Engineering Science. Vol. 148, Pages 78-92. (2016)

[6] Hussein, A., Hao, L., Yan, C., and Everson, R. “Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting.” Materials and Design. Volume 52, Pages 638-647. (2013)

[7] Zeng, K., Pal, D., Gong, H., Patil, N., and Stucker, B. “Comparison of 3DSIM thermal modelling of selective laser melting using new dynamic meshing method to ANSYS.” Materials Science and Technology. Volume 31, Pages 945-956. (2014)

[8] Goldak, J., Chakravarti, A., and Bibby, M. “A New Finite Element Model for Welding Heat Sources.” Metallurgical Transactions B. Volume 15B, Pages 299-305. (1984)