Surrogate based sensitivity analysis of process equipment

Abstract The computational cost associated with the use of high-fidelity computational fluid dynamics (CFD) models poses a serious impediment to the successful application of formal sensitivity analysis in engineering design. Even though advances in computing hardware and parallel processing have reduced costs by orders of magnitude over the last few decades, the fidelity with which engineers desire to model engineering systems has also increased considerably. Evaluation of such high-fidelity models may take significant computational time for complex geometries. In many engineering design problems, thousands of function evaluations may be required to undertake a sensitivity analysis. As a result, CFD models are often impractical to use for design sensitivity analyses. In contrast, surrogate models are compact and cheap to evaluate (order of seconds or less) and can therefore be easily used for such tasks. This paper discusses and demonstrates the application of several common surrogate modelling techniques to a CFD model of flocculant adsorption in an industrial thickener. Results from conducting sensitivity analyses on the surrogates are also presented.

[1]  M. J. D. Powell,et al.  Radial basis functions for multivariable interpolation: a review , 1987 .

[2]  C. Fortuin,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory , 1973 .

[3]  Martin T. Hagan,et al.  Gauss-Newton approximation to Bayesian learning , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[4]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[5]  K.,et al.  Nonlinear sensitivity analysis of multiparameter model systems , 1977 .

[6]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machines , 2002 .

[7]  K. Shuler,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. III. Analysis of the approximations , 1975 .

[8]  Edwin R. Lewis Neural Nets, Modeling , 1988 .

[9]  Dirk Gorissen,et al.  Sequential modeling of a low noise amplifier with neural networks and active learning , 2009, Neural Computing and Applications.

[10]  D.A. Lowther,et al.  Selection of approximation models for electromagnetic device optimization , 2006, IEEE Transactions on Magnetics.

[11]  A. Saltelli,et al.  An alternative way to compute Fourier amplitude sensitivity test (FAST) , 1998 .

[12]  Martin Fodslette Møller,et al.  A scaled conjugate gradient algorithm for fast supervised learning , 1993, Neural Networks.

[13]  Murray Rudman,et al.  20 Years of AMIRA P266 “Improving Thickener Technology” - How Has It Changed The Understanding Of Thickener Performance? , 2009 .

[14]  David J. C. MacKay,et al.  Bayesian Interpolation , 1992, Neural Computation.

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

[16]  Phillip D. Fawell,et al.  The effect of flocculant solution transport and addition conditions on feedwell performance in gravity thickeners , 2009 .

[17]  J. Seinfeld,et al.  Automatic sensitivity analysis of kinetic mechanisms , 1979 .

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

[19]  Piet Demeester,et al.  A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design , 2010, J. Mach. Learn. Res..

[20]  R. Levine,et al.  An Algorithm for Finding the Distribution of Maximal Entropy , 1979 .

[21]  J. Mason,et al.  Algorithms for approximation , 1987 .

[22]  Roop L. Mahajan,et al.  Neural nets for modeling, optimization, and control in semiconductor manufacturing , 1999, Optics + Photonics.

[23]  Robert I. Cukier,et al.  Global nonlinear sensitivity analysis using walsh functions , 1981 .

[24]  Dirk Gorissen,et al.  A novel sequential design strategy for global surrogate modeling , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[25]  Yao Lin,et al.  An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design , 2004 .

[26]  John H. Seinfeld,et al.  Global sensitivity analysis—a computational implementation of the Fourier Amplitude Sensitivity Test (FAST) , 1982 .

[27]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[28]  Dirk Gorissen,et al.  Grid-enabled adaptive surrogate modeling for computer aided engineering , 2010 .

[29]  Timothy W. Simpson,et al.  Design and Analysis of Computer Experiments in Multidisciplinary Design Optimization: A Review of How Far We Have Come - Or Not , 2008 .

[30]  Joseph A. C. Delaney Sensitivity analysis , 2018, The African Continental Free Trade Area: Economic and Distributional Effects.

[31]  Ali H. Dogru,et al.  Sensitivity analysis of partial differential equations with application to reaction and diffusion processes , 1979 .

[32]  M. Palaniswami,et al.  Radar Localization with multiple Unmanned Aerial Vehicles using Support Vector Regression , 2005, 2005 3rd International Conference on Intelligent Sensing and Information Processing.

[33]  M. P. Schwarz,et al.  CFD modelling of thickeners at Worsley Alumina Pty Ltd , 2002 .

[34]  K. Shuler,et al.  Nonlinear sensitivity analysis of multiparameter model systems , 1977 .

[35]  K. Shuler,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II Applications , 1973 .

[36]  Nicolas Chapados,et al.  Extensions to Metric-Based Model Selection , 2003, J. Mach. Learn. Res..