White-box Machine learning approaches to identify governing equations for overall dynamics of manufacturing systems: A case study on distillation column

Abstract Dynamical equations form the basis of design for manufacturing processes and control systems, however, identifying governing equations using mechanistic approach is tedious. Recently, Machine learning (ML) has shown promise to identify the governing dynamical equations for physical systems faster. This possibility of rapid identification of governing equations provides an exciting opportunity for advancing dynamical systems modeling. However, applicability of ML approach identifying governing mechanisms for dynamics of complex systems relevant to manufacturins systems has not been tested. We test and compare the efficacy of two white-box ML (SINDy and SymReg) approaches for predicting dynamics and structure of dynamical equations for overall dynamics in distillation column. Results demonstrate that a combination of ML approach should be used to identify full range of equations. In terms of physical law, few terms were interpretable as related to Fick’s law of diffusion and Henry’s law in SINDy whereas SymReg identified energy balance as driving dynamics.

[1]  A. Maarleveld,et al.  Dynamics and control of continuous distillation units , 1975 .

[2]  B. Retzbach.  Control of an Extractive Distillation Plant , 1986 .

[3]  Xinqiang You,et al.  Review of extractive distillation. Process design, operation, optimization and control , 2019, Chemical Engineering Research and Design.

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  William L. Bolles.  Distillation tray fundamentals, by M. J. Lockett, 1986, 226 pages, Cambridge University Press, Cambridge, England and New York, $54.50 (U.S.) , 1988 .

[6]  Sigurd Skogestad,et al.  Dynamics and Control of Distillation Columns - A Critical Survey , 1992 .

[7]  Antonios Armaou,et al.  Equation-free, coarse-grained computational optimization using timesteppers , 2006 .

[8]  Steven L. Brunton,et al.  Data-Driven Identification of Parametric Partial Differential Equations , 2018, SIAM J. Appl. Dyn. Syst..

[9]  S. Brunton,et al.  Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.

[10]  George E. Karniadakis,et al.  Hidden physics models: Machine learning of nonlinear partial differential equations , 2017, J. Comput. Phys..

[11]  Bengt Andersson,et al.  Mathematical Modeling in Chemical Engineering , 2014 .

[12]  Robert K. Niven,et al.  Synchronization control of oscillator networks using symbolic regression , 2016, Nonlinear Dynamics.

[13]  V. Venkatasubramanian.  The promise of artificial intelligence in chemical engineering: Is it here, finally? , 2018, AIChE Journal.

[14]  Lee A. Segel,et al.  Mathematics applied to deterministic problems in the natural sciences , 1974, Classics in applied mathematics.

[15]  Hari Om Gupta,et al.  ANN based estimator for distillation—inferential control , 2005 .

[16]  M. Lockett,et al.  Weeping from sieve trays , 1986 .

[17]  P. A. Taylor,et al.  Modelling and Dynamics of an Extractive Distillation Column , 1983, 1983 American Control Conference.

[18]  Rick Chartrand,et al.  Numerical Differentiation of Noisy, Nonsmooth Data , 2011 .

[19]  R. Sargent,et al.  The mathematical modelling of transient systems using differential-algebraic equations , 1988 .

[20]  Vijander Singh,et al.  ANN-based estimator for distillation using Levenberg-Marquardt approach , 2007, Eng. Appl. Artif. Intell..

[21]  Don W. Green,et al.  Perry's Chemical Engineers' Handbook , 2007 .

[22]  David M. Himmelblau,et al.  Modeling and control of a packed distillation column using artificial neural networks , 1995 .

[23]  Ridvan Berber,et al.  DYNAMIC SIMULATION OF A DISTILLATION COLUMN SEPARATING A MULTICOMPONENT MIXTURE , 1989 .

[24]  B. Wayne Bequette,et al.  Nonlinear system identification and model reduction using artificial neural networks , 2003, Comput. Chem. Eng..

[25]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Panagiotis D. Christofides,et al.  Machine learning-based modeling and operation for ALD of SiO2 thin-films using data from a multiscale CFD simulation , 2019, Chemical Engineering Research and Design.

[27]  Frank Noé,et al.  Reactive SINDy: Discovering governing reactions from concentration data. , 2019, The Journal of chemical physics.

[28]  Thomas J. McAvoy,et al.  An analytical approach to approximate dynamic modeling of distillation towers , 1987 .

[29]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[30]  Venugopal G. Krishnapura,et al.  Arma neuron networks for modeling nonlinear dynamical systems , 1997 .

[31]  Hod Lipson,et al.  Automated reverse engineering of nonlinear dynamical systems , 2007, Proceedings of the National Academy of Sciences.

[32]  William L. Luyben,et al.  Rigorous dynamic models of distillation columns , 1987 .

[33]  Rafiqul Gani,et al.  A generalized model for distillation columns—I: Model description and applications , 1986 .

[34]  Kamran Shafi,et al.  Prediction of dynamical systems by symbolic regression. , 2016, Physical review. E.

[35]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[36]  S. Osher,et al.  Sparse dynamics for partial differential equations , 2012, Proceedings of the National Academy of Sciences.

[37]  Hod Lipson,et al.  Distilling Free-Form Natural Laws from Experimental Data , 2009, Science.

[38]  Jay H. Lee,et al.  Machine learning: Overview of the recent progresses and implications for the process systems engineering field , 2017, Comput. Chem. Eng..

[39]  Rakesh Agrawal,et al.  New pressure drop correlation for sieve tray distillation columns , 1983 .