(434c) Sparse-Identification-Based Predictive Control of Nonlinear Processes Using Noisy Process Data

Chemical process systems consist of numerous control loops to ensure operational stability and maximize yield. In industrial settings, advanced process control techniques such as model predictive control (MPC) are utilized to maintain stable operation and optimal process conditions. However, chemical processes such as catalytic reactors and distillation columns exhibit highly complex process dynamics such as severe nonlinearities and sensor noise in measurements [1,2]. Hence, modeling such processes involves a number of challenges. As MPC requires an accurate process model to predict the process states over a defined prediction horizon in order to optimize a cost function, a well-conditioned model must first be obtained. As large-scale process networks generally cannot be modeled adequately using first-principles analyses, data-driven modeling has attracted much attention, especially in the recent literature, due to the advances in machine learning and computational resources [3]. The results of machine learning techniques such as neural networks, support vector machines, sparse identification, etc. have largely been excellent due to their ability to capture most nonlinearities via extensive hyper-parameter tuning. However, the handling of noise in the application of machine learning techniques is a major challenge where significant room for improvement exists. This is because “noisy data” in the context of machine learning typically refers to miscategorized labels in classification problems rather than regression problems [4]. Hence, the aforementioned accuracies are not necessarily observed when the methods are applied to chemical processes with high sensor noise. Based on an extensive literature review, this limitation holds for sparse identification, which is the method primarily studied and developed in this work.

In this work, a nonlinear process model is obtained for a chemical process from noisy industrial data using sparse identification, a recent method that models nonlinear dynamical systems as nonlinear first-order ordinary differential equations [5]. A high-fidelity process simulator, Aspen Plus Dynamics, is used to simulate a chemical plant, and the measured data is then taken as the industrial data. Gaussian noise is added to the data set to generate a noisy industrial data set, which is used to identify a process model using sparse identification. However, due to the combined challenges of modeling the industrial data set and noise, the sparse identification algorithm is modified to produce multiple models with each model dropping out a number of library terms during model identification. This is similar to a regularization term to prevent overfitting. It is found that the model identified without dropout exhibits poor long-term predictions and does not reach the correct steady-state value, while the best model identified with dropout is able to predict the steady-state correctly and capture most of the transient behavior fairly correctly as well, leading to a controller with lower convergence time and energy.

References:

[1] Chang, H.-C., Aluko, M., 1984. Multi-scale analysis of exotic dynamics in surface catalyzed reactions-I: justification and preliminary model discriminations. Chem. Eng. Sci. 39 (1), 37–50.

[2] Lévine, J., Rouchon, P., 1991. Quality control of binary distillation columns via nonlinear aggregated models. Automatica. 27 (3), 463–480.

[3] Wu, Z., Tran, A., Rincon, D., Christofides, P.D., 2019. Machine-learning-based predictive control of nonlinear processes. Part II: Computational implementation. AIChE Journal. 65:e16734.

[4] Han, B. , Yao, Q. , Yu, X. , Niu, G. , Xu, M. , Hu, W. , Tsang, I.W. , Sugiyama, M. , 2018. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In: Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems, pp. 8536–8546

[5] 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.