Surrogate model generation using self-optimizing variables

Abstract This paper presents the application of self-optimizing concepts for more efficient generation of steady-state surrogate models. Surrogate model generation generally has problems with a large number of independent variables resulting in a large sampling space. If the surrogate model is to be used for optimization, utilizing self-optimizing variables allows to map a close-to-optimal response surface, which reduces the model complexity. In particular, the mapped surface becomes much “flatter”, allowing for a simpler representation, for example, a linear map or neglecting the dependency of certain variables completely. The proposed method is studied using an ammonia reactor which for some disturbances shows limit-cycle behaviour and/or reactor extinction. Using self-optimizing variables, it is possible to reduce the number of manipulated variables by three and map a response surface close to the optimal response surface. With the original variables, the response surface would include also regions in which the reactor is extinct.

[1]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[2]  S. Skogestad,et al.  Analysis of instability in an industrial ammonia reactor , 1998 .

[3]  Sigurd Skogestad,et al.  Economic NMPC for heat-integrated chemical reactors , 2017, 2017 21st International Conference on Process Control (PC).

[4]  Sigurd Skogestad,et al.  Minimizing the complexity of surrogate models for optimization , 2016 .

[5]  Sigurd Skogestad,et al.  NULL SPACE METHOD FOR SELECTING OPTIMAL MEASUREMENT COMBINATIONS AS CONTROLLED VARIABLES , 2007 .

[6]  Sigurd Skogestad,et al.  Convex formulations for optimal selection of controlled variables and measurements using Mixed Integer Quadratic Programming , 2012 .

[7]  Dominique Bonvin,et al.  A Directional Modifier-Adaptation Algorithm for Real-Time Optimization , 2016 .

[8]  Sigurd Skogestad.  Plantwide control: the search for the self-optimizing control structure , 2000 .

[9]  Sigurd Skogestad,et al.  Optimal measurement combinations as controlled variables , 2009 .

[10]  Sigurd Skogestad,et al.  Optimal Selection of Controlled Variables , 2003 .

[11]  Nikolaos V. Sahinidis,et al.  A polyhedral branch-and-cut approach to global optimization , 2005, Math. Program..

[12]  Yi Cao,et al.  Self-optimizing control - A survey , 2017, Annu. Rev. Control..

[13]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[14]  David C. Miller,et al.  Learning surrogate models for simulation‐based optimization , 2014 .

[15]  Joel Andersson,et al.  A General-Purpose Software Framework for Dynamic Optimization (Een algemene softwareomgeving voor dynamische optimalisatie) , 2013 .

[16]  D. Krige.  A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[17]  Christodoulos A. Floudas,et al.  ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations , 2014, Journal of Global Optimization.

[18]  José Antonio Caballero,et al.  Large scale optimization of a sour water stripping plant using surrogate models , 2016, Comput. Chem. Eng..

[19]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[20]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[21]  Andrew J. T. Colin,et al.  The Implementation , 1972, Softw. Pract. Exp..

[22]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[23]  Martand Singhal,et al.  Improved Directional Derivatives for Modifier-Adaptation Schemes , 2017 .

[24]  I. Grossmann,et al.  An algorithm for the use of surrogate models in modular flowsheet optimization , 2008 .

[25]  S. Skogestad,et al.  VARIABLE REDUCTION FOR SURROGATE MODELLING , 2016 .

[26]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[27]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[28]  Heinz A. Preisig,et al.  Multi-scale modelling software framework facilitating simulation of interconnected scales using surrogate-models , 2016 .