Abstract
An optimization version of the van der Corput sequence has 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. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is very significant for improving the reliability of these models. Clearly, the progress in the area of air pollution modeling, is closely connected with the progress in reliable algorithms for multidimensional integration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Antonov, I., Saleev, V.: An economic method of computing \(LP_{\tau }\)-sequences. USSR Comput. Math. Phy. 19, 252–256 (1979)
Bahvalov, N.: On the approximate computation of multiple integrals. Vestn. Mosc. State Univ. 4, 3–18 (1959)
Bakhvalov, N.: On the approximate calculation of multiple integrals. J. Complex. 31(4), 502–516 (2015)
Bratley, P., Fox, B.: Algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 14(1), 88–100 (1988)
Cukier, R., Fortuin, C., Shuler, K., Petschek, A., Schaibly, J.: Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I: theory. J. Chem. Phys. 59, 3873–3878 (1973)
Dimitriu, G.: Global sensitivity analysis for a chronic myelogenous leukemia model. In: Proceedings of the 9th International Conference NMA’2018, Borovets, Bulgaria, 20–24 Aug 2018, LNCS 11189. Springer (2019). https://doi.org/10.1007/978-3-030-10692-8_42
Dimov, I.T., Atanassov, E.: Exact error estimates and optimal randomized algorithms for integration. LNCS 4310, 131–139 (2007)
Dimov, I.T., Farago, I., Havasi, A., Zlatev, Z.: Operator splitting and commutativity analysis in the Danish Eulerian model. Math. Comp. Sim. 67, 217–233 (2004)
Dimov, I., Georgieva, R.: Monte Carlo algorithms for evaluating Sobol’ sensitivity indices. Math. Comput. Simul. 81(3), 506–514 (2010). ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2009.09.005
Dimov, I.T., Georgieva, R., Ostromsky, T., Zlatev, Z.: Variance-based sensitivity analysis of the unified Danish Eulerian model according to variations of chemical rates. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) Proceedings of the NAA 2012, LNCS 8236, pp. 247–254. Springer (2013)
Dimov, I.T., Georgieva, R., Ostromsky, T., Zlatev, Z.: Sensitivity studies of pollutant concentrations calculated by UNI-DEM with respect to the input emissions. Cent. Eur. J. Math. 11(8), 1531–1545 (2013). (Numerical Methods for Large Scale Scientific Computing)
Dimov, I.T., Ostromsky, T., Zlatev, Z.: Challenges in using splitting techniques for large-scale environmental modeling. In: Farago, I. (ed.) Advances in Air Pollution Modeling for Environmental Security, NATO Science Series, pp. 115–132. Springer (2005)
Doukovska, L.: Constant false alarm rate detectors in intensive noise environment conditions. Cybern. Inf. Technol. 10(3), 31–48 (2010)
Georgiev, I., Kandilarov, J.: An immersed interface FEM for elliptic problems with local own sources. In: AIP Conference Proceedings, vol. 1186, no. 1, pp. 335–342. American Institute of Physics (2009)
Georgiev, I.R., Zheleva, I., Filipova, M.: Numerical study of the influence of two-burner heating upon the heat transfer during pyrolysis process used for end-of-life tires (EOLT) treatment. In: AIP Conference Proceedings, vol. 2164
Gocheva-Ilieva, Snezhana G., Ivanov, Atanas V., Livieris, Ioannis E.: High performance machine learning models of large scale air pollution data in urban area. Cybern. Inf. Technol. 20(6), 49–60 (2020)
Gocheva-Ilieva, S.G., Ivanov, A.V., Voynikova, D.S., et al.: Time series analysis and forecasting for air pollution in small urban area: an SARIMA and factor analysis approach. Stoch. Environ. Res. Risk Assess. 28, 1045–1060 (2014)
Gocheva-Ilieva, S.G., Voynikova, D.S., Stoimenova, M.P., Ivanov, A.V., Iliev, I.P.: Regression trees modeling of time series for air pollution analysis and forecasting. Neural Comput. Appl. 31(12), 9023–9039 (2019)
Hamdad, H., Pézerat, C., Gauvreau, B., Locqueteau, C., Denoual, Y.: Sensitivity analysis and propagation of uncertainty for the simulation of vehicle pass-by noise. Appl. Acoust. 149, 85–98 (2019). Elsevier. https://doi.org/10.1016/j.apacoust.2019.01.026
Hesstvedt, E., Hov, Ø., Isaksen, I.A.: Quasi-steady-state approximations in air pollution modeling: comparison of two numerical schemes for oxidant prediction. Int. J. Chem. Kinet. 10, 971–994 (1978)
Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of nonlinear models. Reliab. Eng. Syst. Saf. 52, 1–17 (1996)
Karaivanova, A.: Stochastic numerical methods and simulations (2012)
Kuipers, L., Niederreiter, H.: [1974], Uniform distribution of sequences, p. 129,158. Dover Publications (2005). ISBN 0-486-45019-8, Zbl 0281.10001
Marchuk, G.I.: Mathematical modeling for the problem of the environment. In: Studies in Mathematics and Applications, North-Holland, Amsterdam, vol. 16 (1985)
Ostromsky, T., Dimov, I.T., Georgieva, R., Zlatev, Z.: Air pollution modelling, sensitivity analysis and parallel implementation. Int. J. Environ. Pollut. 46(1/2), 83–96 (2011)
Ostromsky, T., Dimov, I.T., Georgieva, R., Zlatev, Z.: Parallel computation of sensitivity analysis data for the Danish Eulerian model, In: Proceedings of the 8th International Conference LSSC’11, 6–10 Oct 2011 Sozopol Bulgaria, LNCS, 7116, pp. 301–309. Springer (2012)
Ostromsky, T., Dimov, I.T., Marinov, P., Georgieva, R., Zlatev, Z.: Advanced sensitivity analysis of the Danish Eulerian model in parallel and grid environment. In: Proceedings of the Third International Conference AMiTaNS’11, 20–25 June 2011 Albena Bulgaria, AIP Conference Proceedings, vol. 1404, pp. 225–232 (2011)
Poryazov, S.: A suitable unit of sensitivity in telecommunications. TELECOM, 13–14.10.2011. Sofia. ISSN 1314–2690, 165–172 (2011)
Saltelli, A., Chan, K., Scott, M.: Sensitivity Analysis. Probability and Statistics Series, Wiley and Sons publishers (2000)
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis. The Primer, Wiley (2008)
Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M.: Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Halsted Press, New York (2004)
Sloan, I.H., Kachoyan, P.J.: SIAM J. Numer. Anal. 24, 116–128 (1987)
I.H. Sloan and S. Joe, Lattice methods for multiple Integration, (Oxford University Press 1994)
Sobol’, I.M.: Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp. 1, 407–414 (1993)
Sobol’, I.M.: Sensitivity estimates for nonlinear mathematical models. Matem. Model. 2(1), 112–118 (1990)
Sobol’, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55(1–3), 271–280 (2001)
Sobol’, I.M.: Theorem and examples on high dimensional model representation. Reliab. Eng. Syst. Saf. 79, 187–193 (2003)
Sobol, I.M., Myshetskaya, E.: Monte Carlo estimators for small sensitivity indices. Monte Carlo Methods Appl. 13(5–6), 455–465 (2007)
Sobol, I.M., Tarantola, S., Gatelli, D., Kucherenko, S., Mauntz, W.: Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliab. Eng. Syst. Saf. 92, 957–960 (2007)
Wang, Y., Hickernell, F.J.: An historical overview of lattice point sets (2002)
van der Corput, J.G.: Verteilungsfunktionen (Erste Mitteilung) (PDF). In: Proceedings of the Koninklijke Akademie van Wetenschappen te Amsterdam (in German), vol. 38, pp. 813–821 (1935). Zbl 0012.34705
Veleva, E., Georgiev, I.R.: Seasonality of the levels of particulate matter PM10 air pollutant in the city of Ruse, Bulgaria. In: AIP Conference Proceedings, vol. 2302, no. 1, p. 030006. AIP Publishing LLC (2020)
Wang, Y., Hickernell, F.J.: An historical overview of lattice point sets.. In: Monte Carlo and Quasi-Monte Carlo Methods 2000, Proceedings of a Conference held at Hong Kong Baptist University, China (2000)
Zheleva, I., Georgiev, I., Filipova, M., Menseidov, D.: Mathematical modeling of the heat transfer during pyrolysis process used for end-of-life tires treatment. In: AIP Conference Proceedings, vol. 1895, no. 1, p. 030008. AIP Publishing LLC (2017)
Zlatev, Z.: Computer Treatment of Large Air Pollution Models. KLUWER Academic Publishers, Dorsrecht-Boston-London (1995)
Zlatev, Z., Dimov, I.T.: Computational and Numerical Challenges in Environmental Modelling. Elsevier, Amsterdam (2006)
Zlatev, Z., Dimov, I., Georgiev, K.: Three-dimensional version of the Danish Eulerian model. Zeitschrift für Angewandte Mathematik und Mechanik 76(S4), 473–476 (1996)
Acknowledgements
Venelin Todorov is supported by the by the Bulgarian National Science Fund under Project DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Problems” and by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)”, contract No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria. The work is also supported by Young Scientists Project KP-06-M32/2—17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics” and by Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” funded by National Science Fund—Bulgaria. Barcelona Supercompputing Centre (BSC) is kindly acknowledged too for granting us access and computer time on their most powerful supercomputer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Todorov, V., Dimov, I., Ostromsky, T., Zlatev, Z., Georgieva, R., Poryazov, S. (2022). Optimized Quasi-Monte Carlo Methods Based on Van der Corput Sequence for Sensitivity Analysis in Air Pollution Modelling. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-82397-9_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-82396-2
Online ISBN: 978-3-030-82397-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)