Software supporting optimal experimental design: A case study of binary diffusion using EFCOSS

Methods for optimal experimental design aim at minimizing uncertainty in parameter estimation problems. Despite their long tradition in applied mathematics and importance in practical applications, they are currently not widely used in computational science and engineering. To make the techniques of optimal experimental design more accessible to a broader community, we introduce a novel software environment called EFCOSS and demonstrate its ease of use and versatility in two case studies of binary diffusion experiments. Through the use of a component-based software architecture, integration of automatic differentiation technology and facilitated interfacing to optimization algorithms, EFCOSS minimizes the computational overhead for the user who can thus focus on model development and analysis itself. The presented case studies focus on diffusion experiments in liquids since these experiments are typically very demanding. The use of optimal experimental design techniques allows to reduce experimental time and effort significantly.

[1]  André Bardow,et al.  Ternary diffusivities by model-based analysis of Raman spectroscopy measurements , 2006 .

[2]  André Bardow,et al.  Model‐based measurement of diffusion using Raman spectroscopy , 2003 .

[3]  Sandro Macchietto,et al.  Curvature-Based Methods for Designing Optimally Informative Experiments in Multiresponse Nonlinear Dynamic Situations , 2005 .

[4]  Christian H. Bischof,et al.  An interactive environment for supporting the transition from simulation to optimization , 2003, Sci. Program..

[5]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[6]  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.

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

[8]  A. Tits,et al.  Nonlinear Equality Constraints in Feasible Sequential Quadratic Programming , 1996 .

[9]  Stefan Körkel,et al.  Numerische Methoden für Optimale Versuchsplanungsprobleme bei nichtlinearen DAE-Modellen , 2002 .

[10]  R. Byron Bird,et al.  Five decades of transport phenomena , 2004 .

[11]  Christian Bischof,et al.  Adifor 2.0: automatic differentiation of Fortran 77 programs , 1996 .

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

[13]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[14]  Niket S. Kaisare,et al.  Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing , 2006, Comput. Chem. Eng..

[15]  André Bardow,et al.  Concentration-dependent diffusion coefficients from a single experiment using model-based Raman spectroscopy , 2005 .

[16]  J. A. Rard,et al.  Isothermal diffusion coefficients of sodium chloride-magnesium chloride-water at 25.degree.C. 5. Solute concentration ratio of 1:1 and some Rayleigh results , 1993 .

[17]  Eric S. Fraga,et al.  A multi-agent system to facilitate component-based process modeling and design , 2008, Comput. Chem. Eng..

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

[19]  Konrad Hinsen,et al.  Numerical Python , 1996 .

[20]  J. Navarro-Laboulais,et al.  Practical identifiability analysis in dynamic gas-liquid reactors: Optimal experimental design for mass-transfer parameters determination , 2008, Comput. Chem. Eng..

[21]  Peter Spellucci,et al.  A new technique for inconsistent QP problems in the SQP method , 1998, Math. Methods Oper. Res..

[22]  Bobby Schnabel,et al.  A modular system of algorithms for unconstrained minimization , 1985, TOMS.

[23]  Johannes P. Schlöder,et al.  Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes , 2004, Optim. Methods Softw..

[24]  Christian H. Bischof,et al.  Algorithms and design for a second-order automatic differentiation module , 1997, ISSAC.

[25]  Christian Bischof,et al.  ADIC: an extensible automatic differentiation tool for ANSI-C , 1997 .

[26]  Matthias Reuss,et al.  Optimal Experimental Design for Parameter Estimation in Unstructured Growth Models , 1994 .

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

[28]  H. Martin Bücker,et al.  EFCOSS: An interactive environment facilitating optimal experimental design , 2010, TOMS.

[29]  H. Arellano-Garcia,et al.  Optimale Versuchsplanung in der chemischen Verfahrenstechnik , 2007 .

[30]  Elizabeth Eskow,et al.  Algorithm 738: a software package for unconstrained optimization using tensor methods , 1990, TOMS.

[31]  Eric Walter,et al.  Qualitative and quantitative experiment design for phenomenological models - A survey , 1990, Autom..

[32]  André Bardow,et al.  Direct determination of the concentration dependence of diffusivities using combined model-based Raman and NMR experiments , 2009 .

[33]  Jorge J. Moré,et al.  User Guide for Minpack-1 , 1980 .

[34]  A. D. Hall,et al.  The PORT Mathematical Subroutine Library , 1978, TOMS.

[35]  Bobby Schnabel,et al.  Algorithm 768: TENSOLVE: a software package for solving systems of nonlinear equations and nonlinear least-squares problems using tensor methods , 1997, TOMS.

[36]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[37]  Sandro Macchietto,et al.  Model-Based Design of Parallel Experiments , 2007 .

[38]  Michel Cabassud,et al.  Sequential experimental design strategy for kinetic parameters estimation , 1999 .

[39]  John Crank,et al.  The Mathematics Of Diffusion , 1956 .

[40]  Peter Spellucci,et al.  An SQP method for general nonlinear programs using only equality constrained subproblems , 1998, Math. Program..

[41]  M. Powell.  A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 1994 .

[42]  Wayne R. Cowell,et al.  Sources and development of mathematical software , 1984 .

[43]  Shengtai Li,et al.  Sensitivity analysis of differential-algebraic equations and partial differential equations , 2005, Comput. Chem. Eng..

[44]  Richard F. Sincovec,et al.  Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3] , 1979, TOMS.