Real-time adaptive input design for the determination of competitive adsorption isotherms in liquid chromatography

Abstract The adaptive input design (also called online redesign of experiments) for parameter estimation is very effective for the compensation of uncertainties in nonlinear processes. Moreover, it enables substantial savings in experimental effort and greater reliability in modeling. We present theoretical details and experimental results from the real-time adaptive optimal input design for parameter estimation. The case study considers separation of three benzoate by reverse phase liquid chromatography. Following a receding horizon scheme, adaptive D-optimal input designs are generated for a precise determination of competitive adsorption isotherm parameters. Moreover, numerical techniques for the regularization of arising ill-posed problems, e.g. due to scarce measurements, lack of prior information about parameters, low sensitivities and parameter correlations are discussed. The estimated parameter values are successfully validated by Frontal Analysis and the benefits of optimal input designs are highlighted when compared to various standard/heuristic input designs in terms of parameter accuracy and precision.

[1]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[2]  Biao Huang,et al.  Receding horizon experiment design with application in SOFC parameter estimation , 2010 .

[3]  Sebastian Engell,et al.  Optimization-based control of a reactive simulated moving bed process for glucose isomerization , 2004 .

[4]  Giuseppe Carlo Calafiore,et al.  Robot Dynamic Calibration: Optimal Excitation Trajectories and Experimental Parameter Estimation , 2001 .

[5]  Brian Armstrong,et al.  On Finding Exciting Trajectories for Identification Experiments Involving Systems with Nonlinear Dynamics , 1989, Int. J. Robotics Res..

[6]  Rohit S. Patwardhan,et al.  A moving horizon approach to input design for closed loop identification , 2014 .

[7]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[8]  Laurent Hascoët,et al.  The Tapenade automatic differentiation tool: Principles, model, and specification , 2013, TOMS.

[9]  Jan Swevers,et al.  Optimal robot excitation and identification , 1997, IEEE Trans. Robotics Autom..

[10]  John F. MacGregor,et al.  The analysis and design of binary vapour‐liquid equilibrium experiments. Part II: The design of experiments , 1977 .

[11]  J. Albersmeyer.  Adjoint-based algorithms and numerical methods for sensitivity generation and optimization of large scale dynamic systems , 2010 .

[12]  Sandro Macchietto,et al.  Model-based design of experiments for parameter precision: State of the art , 2008 .

[13]  A. Seidel-Morgenstern,et al.  Frontal analysis method to determine competitive adsorption isotherms. , 2001, Journal of chromatography. A.

[14]  Shamsul Qamar,et al.  Efficient and accurate numerical simulation of nonlinear chromatographic processes , 2011, Comput. Chem. Eng..

[15]  Hans Bock,et al.  Numerical methods for optimum experimental design in DAE systems , 2000 .

[16]  André Bardow,et al.  Optimal experimental design of ill-posed problems: The METER approach , 2008, Comput. Chem. Eng..

[17]  James C. Sutherland,et al.  Graph-Based Software Design for Managing Complexity and Enabling Concurrency in Multiphysics PDE Software , 2011, TOMS.

[18]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[19]  Guy A. Dumont,et al.  Moving-Horizon Predictive Input Design for Closed-Loop Identification , 2015 .

[20]  Roos D. Servaes,et al.  Optimal temperature input design for estimation of the square root model parameters: parameter accuracy and model validity restrictions. , 2002, International journal of food microbiology.

[21]  J. D. Stigter,et al.  On adaptive optimal input design: A bioreactor case study , 2006 .

[22]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[23]  René Schenkendorf,et al.  Online model selection approach based on Unscented Kalman Filtering , 2013 .

[24]  Harvey Arellano-Garcia,et al.  Online Model-Based Redesign of Experiments for Parameter Estimation Applied to Closed-loop Controller Tuning , 2013 .

[25]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[26]  Biao Huang,et al.  Constrained receding‐horizon experiment design and parameter estimation in the presence of poor initial conditions , 2011 .

[27]  Donald W. Marquaridt.  Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation , 1970 .

[28]  D. M. Titterington,et al.  Recent advances in nonlinear experiment design , 1989 .

[29]  Costas Kravaris,et al.  Advances and selected recent developments in state and parameter estimation , 2013, Comput. Chem. Eng..

[30]  M. Foracchia,et al.  POPED, a software for optimal experiment design in population kinetics , 2004, Comput. Methods Programs Biomed..

[31]  J. Kiefer,et al.  Optimum Designs in Regression Problems , 1959 .

[32]  Graham C. Goodwin,et al.  Dynamic System Identification: Experiment Design and Data Analysis , 2012 .

[33]  André Bardow,et al.  Optimal Experimental Design for the Characterization of Liquid–Liquid Equilibria , 2014 .

[34]  Jay H. Lee,et al.  Repetitive model predictive control applied to a simulated moving bed chromatography system , 2000 .

[35]  Håkan Hjalmarsson,et al.  Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design , 2009, Autom..

[36]  Jürgen Hubbuch,et al.  High Throughput Screening for the Design and Optimization of Chromatographic Processes - Miniaturization, Automation and Parallelization of Breakthrough and Elution Studies , 2008 .

[37]  Sandro Macchietto,et al.  The optimal design of dynamic experiments , 1989 .

[38]  Hassan Hammouri,et al.  Optimal input design for online identification: a coupled observer-MPC approach , 2008 .

[39]  P. I. Barton,et al.  Design, Execution, and Analysis of Time-Varying Experiments for Model Discrimination and Parameter Estimation in Microreactors , 2014 .

[40]  Günter Wozny,et al.  Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design , 2015, Comput. Chem. Eng..

[41]  HascoetLaurent,et al.  The Tapenade automatic differentiation tool , 2013 .

[42]  Massimiliano Barolo,et al.  Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch , 2011, Medical & Biological Engineering & Computing.

[43]  Pascal Dufour,et al.  Observer and model predictive control for on-line parameter identification in nonlinear systems , 2013 .

[44]  Raman K. Mehra,et al.  Optimal input signals for parameter estimation in dynamic systems--Survey and new results , 1974 .

[45]  Sebastian F. Walter,et al.  Adjoint-based optimization of experimental designs with many control variables , 2014 .

[46]  Tor Arne Johansen,et al.  On Tikhonov regularization, bias and variance in nonlinear system identification , 1997, Autom..

[47]  Michel Kinnaert,et al.  A systematic approach to SMB processes model identification from batch experiments , 2007 .

[48]  Massimiliano Barolo,et al.  Online Model-Based Redesign of Experiments for Parameter Estimation in Dynamic Systems , 2009 .

[49]  A. E. Hoerl,et al.  Ridge Regression: Applications to Nonorthogonal Problems , 1970 .

[50]  E. Haber,et al.  Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems , 2010 .

[51]  Steven M Cramer,et al.  Use of MiniColumns for linear isotherm parameter estimation and prediction of benchtop column performance. , 2015, Journal of chromatography. A.

[52]  Günter Wozny,et al.  Model‐based identifiable parameter determination applied to a simultaneous saccharification and fermentation process model for bio‐ethanol production , 2013, Biotechnology progress.

[53]  G. Verghese,et al.  Subset selection for improved parameter estimation in on-line identification of a synchronous generator , 1999 .

[54]  Günter Wozny,et al.  Experimental evaluation of an approach to online redesign of experiments for parameter determination , 2013 .

[55]  Todd D. Murphey,et al.  Real-time trajectory synthesis for information maximization using Sequential Action Control and least-squares estimation , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[56]  Anita M. Katti,et al.  Fundamentals of Preparative and Nonlinear Chromatography , 1994 .

[57]  Harvey Arellano-Garcia,et al.  Handling Uncertainty in Model-Based Optimal Experimental Design , 2010 .

[58]  E. Haber,et al.  Optimal Experimental Design for the Large‐Scale Nonlinear Ill‐Posed Problem of Impedance Imaging , 2010 .

[59]  Vivek Dua,et al.  A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors , 2016, Comput. Chem. Eng..