A comparison of advanced quasi Monte Carlo methods for multidimensional integrals in air pollution modeling

Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is very significant for improving the reliability of these models. Several efficient quasi-Monte Carlo algorithms – the van der Corput sequence and lattice rules based on different generating vectors have been used in our sensitivity studies of the model output results for some air pollutants with respect to the emission levels and some chemical reactions rates. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The numerical tests show that the van der Corput sequences under consideration are efficient for the multidimensional integrals under consideration and especially for computing small by value sensitivity indices.

[1]  I. Sloan,et al.  Lattice methods for multiple integration: theory, error analysis and examples , 1987 .

[2]  I. Sloan.  Lattice Methods for Multiple Integration , 1994 .

[3]  Zahari Zlatev,et al.  Computer Treatment of Large Air Pollution Models , 1995 .

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

[5]  H. Niederreiter,et al.  Monte Carlo and quasi-Monte Carlo methods 2000 : proceedings of a conference held at the Hong Kong Baptist University, Hong Kong SAR, China, November 27-December 1, 2000 , 2002 .

[6]  Stefka Fidanova.  Convergence Proof for a Monte Carlo Method for Combinatorial Optimization Problems , 2004, International Conference on Computational Science.

[7]  Ivan Tomov Dimov,et al.  Exact Error Estimates and Optimal Randomized Algorithms for Integration , 2006, Numerical Methods and Applications.

[8]  Stefano Tarantola,et al.  Estimating the approximation error when fixing unessential factors in global sensitivity analysis , 2007, Reliab. Eng. Syst. Saf..

[9]  I. Georgiev,et al.  An Immersed Interface FEM for Elliptic Problems with Local Own Sources , 2009 .

[10]  Rayna Georgieva,et al.  Monte Carlo algorithms for evaluating Sobol' sensitivity indices , 2010, Math. Comput. Simul..

[11]  Zahari Zlatev,et al.  Variance-Based Sensitivity Analysis of the Unified Danish Eulerian Model According to Variations of Chemical Rates , 2012, NAA.

[12]  Z. Zlatev,et al.  Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions , 2013 .

[13]  Nikolai Sergeevich Bakhvalov,et al.  On the approximate calculation of multiple integrals , 2015, J. Complex..

[14]  Frances Y. Kuo,et al.  Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation , 2016, Foundations of Computational Mathematics.

[15]  Ivan Georgiev,et al.  Mathematical modeling of the heat transfer during pyrolysis process used for end-of-life tires treatment , 2017 .

[16]  Ivan Ganchev,et al.  Conceptual and Analytical Models for Predicting the Quality of Service of Overall Telecommunication Systems , 2018, Autonomous Control for a Reliable Internet of Services.

[17]  Velizara Pencheva,et al.  ANALYSIS AND ASSESSMENT OF THE REGULARITY OF MASS URBAN PASSENGER TRANSPORT IN THE CONDITIONS OF THE CITY OF RUSE , 2018 .

[18]  Velizara Pencheva,et al.  Modelling passenger service rate at a transport hub serviced by a single urban bus route as a queueing system , 2019 .

[19]  Charles Pezerat,et al.  Sensitivity analysis and propagation of uncertainty for the simulation of vehicle pass-by noise , 2019 .

[20]  L. Kirilov,et al.  Structural Instability of Gold and Bimetallic Nanowires Using Monte Carlo Simulation , 2019, Recent Advances in Computational Optimization.

[21]  I. Georgiev,et al.  Numerical study of the influence of two-burner heating upon the heat transfer during pyrolysis process used for end-of-life tires (EOLT) treatment , 2019, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19.