DOI QR코드

DOI QR Code

3D reconstruction of two-phase random heterogeneous material from 2D sections: An approach via genetic algorithms

  • Pizzocri, D. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division) ;
  • Genoni, R. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division) ;
  • Antonello, F. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division) ;
  • Barani, T. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division) ;
  • Cappia, F. (Idaho National Laboratory, Characterization and Advanced PIE Division)
  • Received : 2020.10.14
  • Accepted : 2021.03.08
  • Published : 2021.09.25

Abstract

This paper introduces a method to reconstruct the three-dimensional (3D) microstructure of two-phase materials, e.g., porous materials such as highly irradiated nuclear fuel, from two-dimensional (2D) sections via a multi-objective optimization genetic algorithm. The optimization is based on the comparison between the reference and reconstructed 2D sections on specific target properties, i.e., 2D pore number, and mean value and standard deviation of the pore-size distribution. This represents a multi-objective fitness function subject to weaker hypotheses compared to state-of-the-art methods based on n-points correlations, allowing for a broader range of application. The effectiveness of the proposed method is demonstrated on synthetic data and compared with state-of-the-art methods adopting a fitness based on 2D correlations. The method here developed can be used as a cost-effective tool to reconstruct the pore structure in highly irradiated materials using 2D experimental data.

Keywords

Acknowledgement

One of the authors would like to acknowledge financial support from the U.S. Department of Energy (DOE), Office of Nuclear Energy under DOE Idaho Operations Office Contract DE-AC07-051D14517 as part of the Nuclear Science User Facilities (NSUF), Project 17-1091. The authors greatly appreciate the reviewers who have dedicated their considerable time and expertise to this manuscript.

References

  1. C.L.Y. Yeong, S. Torquato, Reconstructing random media. II. Three-dimensional media from two-dimensional cuts, Phys. Rev. E 58 (1998) 224-233, https://doi.org/10.1103/PhysRevE.58.224.
  2. M. Yang, A. Nagarajan, B. Liang, S. Soghrati, New algorithms for virtual reconstruction of heterogeneous microstructures, Comput. Methods Appl. Mech. Eng. 338 (2018) 275-298, https://doi.org/10.1016/j.cma.2018.04.030.
  3. F. Cappia, D. Pizzocri, A. Schubert, P. Van Uffelen, G. Paperini, D. Pellottiero, R. Macian-Juan, V.V. Rondinella, Critical assessment of the pore size distribution in the rim region of high burnup UO2 fuels, J. Nucl. Mater. 480 (2016), https://doi.org/10.1016/j.jnucmat.2016.08.010.
  4. D. Nychka, G. Wahba, S. Goldfarb, T. Pugh, Cross-validated spline methods for the estimation of three-dimensional tumor size distributions from observations on two-dimensional cross sections, J. Am. Stat. Assoc. 79 (1984) 832-846. https://doi.org/10.1080/01621459.1984.10477100
  5. J. Serra, Image Analysis and Mathematical Morphology, 1983.
  6. C.L.Y. Yeong, S. Torquato, Reconstructing random media, Phys. Rev. E. 57 (1998) 495-506, https://doi.org/10.1103/PhysRevE.57.495.
  7. E. Patelli, G. Schueller, On optimization techniques to reconstruct micro-structures of random heterogeneous media, Comput. Mater. Sci. 45 (2009) 536-549, https://doi.org/10.1016/j.commatsci.2008.11.019.
  8. Z. Jiang, W. Chen, C. Burkhart, Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization, J. Microsc. 252 (2013) 135-148, https://doi.org/10.1111/jmi.12077.
  9. Y. Jiao, F.H. Stillinger, S. Torquato, Modeling heterogeneous materials via two-point correlation functions: basic principles, Phys. Rev. E - Stat. Nonlinear Soft Matter Phys. 76 (2007) 1-15, https://doi.org/10.1103/PhysRevE.76.031110.
  10. S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983) 671-680. https://doi.org/10.1126/science.220.4598.671
  11. J. Pearl, Heuristics: Intelligent Search Strategies for Computer Problem Solving, 1984.
  12. J.A. Quiblier, A new three-dimensional modeling technique for studying porous media, J. Colloid Interface Sci. 98 (1984).
  13. A.B. Tarek, A. El-Mihoub, Adrian A. Hopgood, Lars nolle, "hybrid genetic algorithms, A Review 13 (2006) 124-137.
  14. S. Torquato, Random Heterogeneous Materials, Springer New York, New York, NY, 2002, https://doi.org/10.1007/978-1-4757-6355-3.
  15. S. Torquato, Morphology and effective properties of disordered heterogeneous media, Int. J. Solid Struct. 35 (1998) 2385-2406, https://doi.org/10.1016/S0020-7683(97)00142-X.
  16. C. Lantuejoul, Geostatistical Simulation: Models and Algorithms, Springer, 2002.
  17. H. Furutani, S. Katayama, M. Sakamoto, T. Ito, Stochastic analysis of schema distribution in a multiplicative landscape, Artif. Life Robot. 11 (2007), 101-104. 10.1007/s10015-006-0409-5.
  18. Y.A. Zhang, M. Sakamoto, H. Furutani, Effects of population size and mutation rate on results of genetic algorithm, Proc. 4th Int. Conf. Nat. Comput. ICNC 1 (2008) 70-75, https://doi.org/10.1109/ICNC.2008.345.
  19. B.S. Weir, D.L. Hartl, Principles of population genetics, Biometrics 37 (1981) 414, 10.2307/2530432.
  20. M.D. Rintoul, S. Torquato, Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model, J. Phys. Math. Gen. 30 (1997), https://doi.org/10.1088/0305-4470/30/16/005.
  21. E. Limpert, W.A. Stahel, M. Abbt, Log-normal distributions across the sciences: keys and clues, Bioscience 51 (2006) 341, 10.1641/0006-3568(2001)051 [0341:lndats]2.0.co;2.
  22. C. Lantuejoul, Ergodicity and integral range, J. Microsc. 161 (1991) 387-403. https://doi.org/10.1111/j.1365-2818.1991.tb03099.x
  23. R. Genoni, D. Pizzocri, F. Antonello, T. Barani, L. Luzzi, T.R. Pavlov, J.J. Giglio, F. Cappia, Three-dimensional reconstruction from experimental two-dimensional images: application to irradiated metallic fuel, J. Nucl. Mater. (2021), 152843, https://doi.org/10.1016/j.jnucmat.2021.152843.