GUI-HDMR - A software tool for global sensitivity analysis of complex models

The high dimensional model representation (HDMR) method is a set of tools which can be used to construct a fully functional metamodel and to calculate variance based sensitivity indices very efficiently. Extensions to the existing set of random sampling (RS)-HDMR tools have been developed in order to make the method more applicable for complex models with a large number of input parameters as often appear in environmental modelling. The HDMR software described here combines the RS-HDMR tools and its extensions in one Matlab package equipped with a graphical user interface (GUI). This makes the HDMR method easily available for all interested users. The performance of the GUI-HDMR software has been tested in this paper using two analytical test models, the Ishigami function and the Sobol' g-function. In both cases the model is highly non-linear, non-monotonic and has significant parameter interactions. The developed GUI-HDMR software copes very well with the test cases and sensitivity indices of first and second order could be calculated accurately with only low computational effort. The efficiency of the software has also been compared against other recently developed approaches and is shown to be competitive. GUI-HDMR can be applied to a wide range of applications in all fields, because in principle only one random or quasi-random set of input and output values is required to estimate all sensitivity indices up to second order. The size of the set of samples is however dependent on the problem and can be successively increased if additional accuracy is required. A brief description of its application within a range of modelling environments is given.

[1]  Herschel Rabitz,et al.  Efficient Implementation of High Dimensional Model Representations , 2001 .

[2]  Saltelli Andrea,et al.  Sensitivity Analysis for Nonlinear Mathematical Models. Numerical ExperienceSensitivity Analysis for Nonlinear Mathematical Models. Numerical Experience , 1995 .

[3]  Alison S. Tomlin,et al.  The effects of parametric uncertainties in simulations of a reactive plume using a Lagrangian stochastic model , 2009 .

[4]  A. M. Dunker,et al.  Efficient calculation of sensitivity coefficients for complex atmospheric models , 1981 .

[5]  Stefano Tarantola,et al.  Calculating first-order sensitivity measures: A benchmark of some recent methodologies , 2009, Reliab. Eng. Syst. Saf..

[6]  Stefano Tarantola,et al.  Variance‐Based Methods , 2008 .

[7]  Robert W. Bilger,et al.  An experimental study of a reactive plume in grid turbulence , 1996, Journal of Fluid Mechanics.

[8]  Tamás Turányi,et al.  Mathematical Tools for the Construction, Investigation and Reduction of Combustion Mechanisms , 1998 .

[9]  Peter C. Young,et al.  State Dependent Parameter metamodelling and sensitivity analysis , 2007, Comput. Phys. Commun..

[10]  J. Eichhorn.  Validation of a Microscale Pollution Dispersal Model , 1996 .

[11]  H. Rabitz,et al.  Efficient input-output model representations , 1999 .

[12]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[13]  H. Rabitz,et al.  General foundations of high‐dimensional model representations , 1999 .

[14]  John P. Norton.  Algebraic sensitivity analysis of environmental models , 2008, Environ. Model. Softw..

[15]  Gemma Manache,et al.  Identification of reliable regression- and correlation-based sensitivity measures for importance ranking of water-quality model parameters , 2008, Environ. Model. Softw..

[16]  Shuangzhe Liu,et al.  Global Sensitivity Analysis: The Primer by Andrea Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana, Stefano Tarantola , 2008 .

[17]  Andrea Saltelli,et al.  An effective screening design for sensitivity analysis of large models , 2007, Environ. Model. Softw..

[18]  Alison S. Tomlin,et al.  A Lagrangian stochastic model for predicting concentration fluctuations in urban areas , 2007 .

[19]  T. Ishigami,et al.  An importance quantification technique in uncertainty analysis for computer models , 1990, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis.

[20]  Margaret MacDougall,et al.  Comprehensive sensitivity analysis of an SO2 deposition model for three measurement sites: Consequences for SO2 deposition fluxes , 2005 .

[21]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[22]  F. J. Davis,et al.  Illustration of Sampling‐Based Methods for Uncertainty and Sensitivity Analysis , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[23]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[24]  F. E. Satterthwaite.  Random Balance Experimentation , 1959 .

[25]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[26]  A. O'Hagan,et al.  Probabilistic sensitivity analysis of complex models: a Bayesian approach , 2004 .

[27]  Herschel Rabitz,et al.  Ratio control variate method for efficiently determining high‐dimensional model representations , 2006, J. Comput. Chem..

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

[29]  Mehmet T. Odman,et al.  Extension and evaluation of sensitivity analysis capabilities in a photochemical model , 2008, Environ. Model. Softw..

[30]  H. Rabitz,et al.  High Dimensional Model Representations , 2001 .

[31]  T. Ziehn,et al.  A global sensitivity study of sulfur chemistry in a premixed methane flame model using HDMR , 2008 .

[32]  Stefano Tarantola,et al.  Random balance designs for the estimation of first order global sensitivity indices , 2006, Reliab. Eng. Syst. Saf..

[33]  Herschel Rabitz,et al.  Global uncertainty assessments by high dimensional model representations (HDMR) , 2002 .

[34]  Peter A. Vanrolleghem,et al.  Uncertainty in the environmental modelling process - A framework and guidance , 2007, Environ. Model. Softw..

[35]  Panos G Georgopoulos,et al.  Correlation method for variance reduction of Monte Carlo integration in RS‐HDMR , 2003, J. Comput. Chem..

[36]  Tamás Turányi,et al.  Chapter 4 Mathematical tools for the construction, investigation and reduction of combustion mechanisms , 1997 .

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

[38]  J. F. Griffiths,et al.  A global sensitivity study of cyclohexane oxidation under low temperature fuel-rich conditions using HDMR methods , 2009 .

[39]  Alison S. Tomlin,et al.  Global sensitivity analysis of a 3D street canyon model—Part I: The development of high dimensional model representations , 2008 .

[40]  H. Rabitz,et al.  Practical Approaches To Construct RS-HDMR Component Functions , 2002 .

[41]  Armistead G. Russell,et al.  Effects of uncertainties in parameters of a Lagrangian particle model on mean ground-level concentrations under stable conditions , 2004 .

[42]  Anthony J. Jakeman,et al.  Ten iterative steps in development and evaluation of environmental models , 2006, Environ. Model. Softw..

[43]  M. Kramer,et al.  Sensitivity Analysis in Chemical Kinetics , 1983 .

[44]  Alison S. Tomlin,et al.  Global sensitivity analysis of a 3D street canyon model—Part II: Application and physical insight using sensitivity analysis , 2008 .

[45]  R. J. Kee,et al.  Chemkin-II : A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics , 1991 .

[46]  I. Sobol,et al.  About the use of rank transformation in sensitivity analysis of model output , 1995 .

[47]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .