(193h) Online Adaptive Sparse Identification of Systems (OASIS): Application to CSTR

Despite the proven success of “black-box” machine learning models in many applications, the integration of these models with physical laws has seen rapid growth lately. This is driven by the limitations of black-box models to generalize on the entire state space and a need to develop a complete understanding of the physical mechanisms that govern the dynamical system of interest. In recent times, Sparse Identification of Nonlinear Dynamics (SINDy) has been extensively used for data-driven discovery of underlying dynamics by constraining the model structure based on a priori knowledge such as symmetries and conservation laws [1-3]. The SINDy algorithm essentially balances model complexity and prediction accuracy by solving a regularization problem offline. However, for a complex system, very often, a large number of samples may be required to obtain accurate models, which is not always feasible. Moreover, in the case of systems with parameter uncertainties and evolving dynamics there is a need for online model adaptation as new data becomes available. This is particularly useful because re-training the model may not be fast enough to cope with real-time demands in case of process control and also, offline trained models can be significantly improved when adopted online [4, 5].

Motivated by these considerations, in this work, we developed a systematic procedure for the online identification of nonlinear dynamical systems that usually require a large amount of data in the case of traditional data-driven identification methods. Specifically, instead of the conventional way of using SINDy for the overall system identification, we applied SINDy only as a part of the method for identifying the initial potential terms from a large library of candidate functions. The method developed is a three-step process: in the first step, a parsimonious model from the initial data is generated using SINDy based on Sequential Thresholding Least squares, eliminating the unessential functions from the library. In the next step, as new data becomes available it is regressed onto the updated function library to re-estimate the values of function coefficients. In the final step, machine learning based stepwise feature selection is implemented to retain only the most informative features in the model, thereby reducing the run time and complexity associated with more parameters [6]. The method suggested is demonstrated for the online identification of a non-isothermal Continuous Stirred Tank Reactor (CSTR) system with second-order kinetics, having coupled dynamics between concentration and temperature. The advantage of SINDy to incorporate a priori knowledge, such as the reaction dependence on the Arrhenius rate constant has been utilized by including a temperature dependent exponential term in the candidate library. To highlight the significance of the proposed method, we compared the CSTR system models identified using this online approach with its offline counterpart. The results show that, for the accurate estimation of the model, the former method used only about half of the data samples required by the latter one. When compared to the original SINDy algorithm, the total time taken to identify the model using the proposed approach is approximately 60% lesser, thus demonstrating its applicability for online identification and model-based controller design.

Literature cited:

[1] Brunton, S.L., Proctor, J.L. and Kutz, J.N., 2016. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932-3937.

[2] Narasingam, A., and Kwon, J.S.-I., 2018. Data-driven identification of interpretable reduced order models using sparse regression. Computers and Chemical Engineering, 106 (2017) 501–511.

[3] Hoffmann, M., Frohner, C., and Noe, F., 2019. Reactive SINDy: Discovering governing reactions from concentration data. J.Chem.Phys.150, 025101(2019); doi:10.1063/1.5066099.

[4] Pitchaiah, S., and Armaou, A., 2008. Online System-Identification Using Subspace algorithms for the control of Microscopic processes. American Control Conference, Seattle.

[5] Varshney, A., Pitchaiah, S., and Armaou, A., 2009. Feedback control of dissipative PDE systems using adaptive model reduction. AIChE J, vol. 55, no. 4, pp. 906–918, 2009.

[6] Tourassi, G.D., Frederick, E.D., Markey, M.K., and Floyd J, C.E., 2001. Application of the mutual information criterion for feature selection in computer-aided diagnosis. Med Phys 28: 2394–2402.