Multipenalty and composed merit functions in Tikhonov-type regularization applied to atmospheric source identification problems

Authors

DOI:

https://doi.org/10.5902/2179460X86857

Keywords:

Inverse problems, Tikhonov-type regularization, Multipenalt, Composed merit functions

Abstract

We propose a technique to simplify the minimization of the objective function arising in Tikhonov-type regularization when there are multiple observations, like multiphysics identification problems, and multiple penalty terms. It breaks the original problem into two or more minimizations that are performed sequentially and recursively. In this preliminary work, we consider the case of two minimization steps. We apply the estimation technique to the identification of pollutant emission sources in the atmosphere, considering the data from the Copenhagen experiment.

Downloads

Download data is not yet available.

Author Biographies

Roseane Alves de Souza Albani, Universidade do Estado do Rio de Janeiro

Holds a degree in Mathematics from the Federal University of Rio de Janeiro - UFRJ (2006), a Master's degree (2010) and a PhD (2014) in Mechanical Engineering from the Alberto Luís Coimbra Institute of Graduate Studies and Research in Engineering (PEM/COPPE/UFRJ), Postdoctoral Degree from the Department of Physics and Astronomy of the University of Bologna (Italy), Postdoctoral Degree from the Department of Mechanical Engineering of the Federal University of Santa Catarina - UFSC Postdoctoral fellow at the Computational Modeling Program of the Polytechnic Institute of the State University of Rio de Janeiro - UERJ. His areas of interest and expertise are atmospheric dispersion and flow modeling, computational fluid dynamics and micrometeorology. 

Vinícius Viana Luiz Albani, Universidade Federal de Santa Catarina

Adjunct Professor at the Department of Mathematics at the Federal University of Santa Catarina and Coordinator of the Laboratory of Mathematical Modeling in Applied Sciences (LAMMCA) at the same institution. His areas of interest are Inverse Problems, Mathematical Modeling, and Mathematical Methods in Finance.

Antônio José da Silva Neto, Universidade do Estado do Rio de Janeiro

Ph.D. in Mechanical Engineering (North Carolina State University, 1993). Professor at IPRJ/UERJ (Adjunct Professor 1997-2012, Associate Professor 2012-2013, Full Professor 2013- ). Full member of the National Academy of Engineering (2017- ). He has been a Scientist of Our State (FAPERJ) since 2002. He has been a Proscientist at UERJ (Internal Competition) since 1997. He works in the area of Mechanical Engineering, with emphasis on Heat Transfer, and in Applied and Computational Mathematics, with emphasis on Numerical Methods.

References

Albani, R. & Albani, V. (2020). An Accurate Strategy to Retrieve Multiple Source Emissions in the Atmosphere. Atmospheric Environment, 233, 117579.

Albani, R, Albani, V, & Silva Neto, A. (2020). Source characterization of airborne pollutant emissions by hybrid metaheuristic/gradient-based optimization techniques. Environ Pollut., 267, 115618.

Albani, V, De Cezaro, A. & Zubelli, J. (2016). On the Choice of the Tikhonov Regularization Parameter and the Discretization Level: A Discrepancy-Based Strategy. Inverse Probl. Imaging, 10(1), 1–25.

Albani, V, De Cezaro, A, & Zubelli, J. (2017). Convex Regularization of Local Volatility Estimation. Int. J. Theor. Appl. Finance, 20(1), 1750006.

Albani, V. & Zubelli, J. (2020). A Splitting Strategy for the Calibration of Jump-Diffusion Models. Finance and Stochastics, 24, 677–722.

Anzengruber, S. & Ramlau, R. (2010). Morozov’s discrepancy principle for Tikhonov-type functionals with nonlinear operators. Inverse Problems, 26 (2).

Arya, S. P. (2001). Introduction to Micrometeorology. Academic Press.

Gryning, S. E. (1981). Elevated source SF6 - tracer dispersion experiments in the Copenhagen area. Technical report, Risø-R-446, Risø

Nacional Laboratory, 187 pp.

Gryning, S. E. & Lyck, E. (1984). Atmospheric Dispersion from Elevated Sources in Urban Area: Comparison Between Tracer and Experiments and the Model Calculations. J. Climate Appl. Meteor., 23, 651–660.

Gryning, S. E. & Lyck, E. (2002). The Copenhagen tracer experiments: Reporting of measurements. Technical Report 1054, Technical University from Denmark, Denmark. Forskningscenter Risoe.

Hughes, T., Franca, L., and Hulbert, G. (1989). A new Finite Element Formulation for Computational Fluid Dynamics: VIII. The Galerkin/Least-Square Method for AdvectiveDiffusive Equations. Comput. Methods Appl. Mech. Engrg., 73, 173–189.

Morozov, V. (1966). On the solution of functional equations by the method of regularization. Dokl. Math., 7, 414–417.

Scherzer, O, Grasmair, M, Grossauer, H, Haltmeier, M, & Lenzen, F. (2008). Variational Methods in Imaging, volume 167 of Applied Mathematical Sciences. Springer, New York.

Ulke, A. G. (2000). New turbulent parameterization for a dispersion model in the atmospheric boundary layer. Atmos. Environ., 34, 1029–1042.

Vogel, C. (2002). Computational methods for inverse problems, volume 23. SIAM.

Downloads

Published

2024-11-04

How to Cite

Albani, R. A. de S., Albani, V. V. L., & Silva Neto, A. J. da. (2024). Multipenalty and composed merit functions in Tikhonov-type regularization applied to atmospheric source identification problems. Ciência E Natura, 46(esp. 1), e86857. https://doi.org/10.5902/2179460X86857

Issue

Section

Special Edition 1

Most read articles by the same author(s)