# ESTIMATION OF RADIATIVE PARAMETERS IN PARTICIPATING MEDIA USING SHUFFLED FROG LEAPING ALGORITHM

## Main Article Content

## Abstract

The transient radiative transfer in one–dimensional homogeneous media with ultra–short Gaussian pulse laser irradiated was investigation by the finite volume method. The concept of optimal detection distance was proposed. The radiation characteristic was studied thoroughly. Afterwards, a memetic meta-heuristic shuffled frog leaping algorithm (SFL) was introduced to inverse transient radiative problems. It is demonstrated that the extinction coefficient and scattering albedo can be retrieved accurately even with noisy data in a homogeneous absorbing and isotropic scattering plane–parallel slab. Finally, a technique was proposed to accelerate the inverse process by reducing the searching space of the radiative parameters.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2151>. Date accessed: 14 dec. 2017. doi: https://doi.org/10.2298/TSCI150814146R.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Kato, A., Watanabe, M., Morgenroth, J., Gomez, C., Field tree measurement using terrestrial laser for radar remote sensing, Asia–Pacific Conference on Synthetic Aperture Radar (APSAR) IEEE, Tsukuba, 2013, pp. 119–121

[3] Bhowmik, A., Repaka, R., Mishra, S. C., Mitra, K., Analysis of radiative signals from normal and malignant human skins subjected to a short-pulse laser, International Journal of Heat and Mass Transfer, 68(2014), pp. 278–294

[4] Singh, R., Das, K., Mishra, S. C., Laser-induced hyperthermia of nanoshell mediated vascularized tissue–A numerical study. Journal of thermal biology, 44(2014), pp. 55–62

[5] Guo, Z., Kumar, S., Three–dimensional discrete ordinates method in transient radiative transfer, Journal of Thermophysics and Heat Transfer, 16(2002), 3, pp. 289–296

[6] Sakami, M., Mitra, K., Hsu, P. F., Analysis of light pulse transport through two–dimensional scattering and absorbing media’, Journal of Quantitative Spectroscopy and Radiative Transfer, 73(2002), 2, pp. 169–179

[7] Liu, L. H., Ruan, L. M., Tan, H. P., On the discrete ordinates method for radiative heat transfer in anisotropically scattering media, International Journal of Heat and Mass Transfer, 45(2002), 15, pp. 3259–3262

[8] Chai, J. C., One–dimensional transient radiation heat transfer modeling using a finite–volume method, Numerical Heat Transfer B, 44(2003), 2, pp. 187–208

[9] Chai, J. C., Hsu, P. F., Lam, Y. C., Three–dimensional transient radiative transfer modeling using the finite volume method Journal of Quantitative Spectroscopy and Radiative Transfer, 2004, 86(2004), 3, pp. 299–313

[10] Mishra, S. C., Chug, P., Kumar, P., Mitra, K., Development and comparison of the DTM, the DOM and the FVM formulations for the short–pulse laser transport through a participating medium, International Journal of Heat and Mass Transfer, 49(2006), 11–12, pp. 1820–1832

[11] Wu, C. Y., Propagation of scattered radiation in a participating planar medium with pulse irradiation, Journal of Quantitative Spectroscopy and Radiative Transfer, 64(2000), 5, pp. 537–548

[12] Ruan, L. M., An, W., Tan, H. P., Transient radiative transfer of ultra–short pulse in two–dimensional inhomogeneous media, Journal of Engineering Thermophysics, 28(2007), 6, pp. 998–1000

[13] Ruan, L. M., An, W., Tan, H. P., Qi, H., Least–Squares Finite Element Method for multidimensional radiative heat transfer in absorbing and scattering medium, Numerical Heat Transfer, Part A,. 51(2007), 7, pp. 657–677

[14] Hsu, P. F., Effects of multiple scattering and reflective boundary on the transient radiative transfer process, International Journal of Thermal Sciences, 40(2001), 6, pp. 539–549

[15] An, W., Ruan, L. M., Qi, H., Inverse radiation problem in one–dimensional slab by time–resolved reflected and transmitted signals, Journal of Quantitative Spectroscopy and Radiative Transfer, 107(2007), 1, pp. 47–60

[16] Salinas, C. T., Inverse radiation analysis in two–dimensional gray media using the discrete ordinates method with a multidimensional scheme, International Journal of Thermal Sciences, 49(2010), 2, pp. 302–310

[17] Moré, J. J., The Levenberg-Marquardt algorithm: implementation and theory, Springer, Berlin Heidelberg, Germany, 1978

[18] Budil, D. E., Lee, S., Saxena, S., Freed, J. H., Nonlinear-least-squares analysis of slow-motion EPR spectra in one and two dimensions using a modified Levenberg–Marquardt algorithm. Journal of Magnetic Resonance, Series A, 120(1996), 2, pp. 155–189.

[19] Qi, H., Ruan, L. M., Zhang, H. C., Wang, Y. M., Tan H. P., Inverse radiation analysis of a one–dimensional participating slab by stochastic particle swarm optimizer algorithm, International Journal of Thermal Sciences, 46(2007), 7, pp. 649–661

[20] Ren, Y. T., Qi, H., Chen, Q., Ruan, L. M., Tan, H. P., Simultaneous retrieval of the complex refractive index and particle size distribution, Optics Express, 23(2015), 15, pp. 19328–19337

[21] Zhang, B., Qi, H., Ren, Y. T., Sun, S. C., Ruan, L. M., Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer, International Journal of Heat and Mass Transfer, 66(2013), pp. 507–516

[22] Zhang, B., Qi, H., Sun, S. C., Ruan, L. M., Tan, H. P., A novel hybrid ant colony optimization and particle swarm optimization algorithm for inverse problems of coupled radiative and conductive heat transfer, Thermal Science, 00(2014), pp. 23–23

[23] Kim, K. W., Baek, S. W., Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite difference Newton method, Journal of Quantitative Spectroscopy and Radiative Transfer, 108(2007), 3, pp. 423–439

[24] Eusuff, M. M., Lansey, K. E., Optimization of water distribution network design using the shuffled frog leaping algorithm, Journal of Water Resource Planning and Management, 129(2003) 3, pp. 210–225

[25] Kennedy, J., Eberhart, R., Particle Swarm Optimization, Neural Networks, Proceedings. IEEE International Conference, Perth, Australia, 1995, pp. 1942–1948

[26] Elbeltagiy, E., Hegazyz, T., Griersonz, D., A modified shuffled frog-leaping optimization algorithm: applications to project management, Structure and Infrastructure Engineering: Maintenance, 3(2007), 1, pp. 153–60

[27] Moscato, P., Cotta, C., Mendes A., Memetic algorithms, Springer, Berlin Heidelberg, Germany, 2004

[28] Rahimi-Vahed, A., Mirzaei, A. H., A hybrid multi-objective shuffled frog-leaping algorithm for a mixed-model assembly line sequencing problem. Computers & Industrial Engineering, 53(2007) 4, pp. 642–666

[29] Ebrahimi, J., Hosseinian, S. H., Gharehpetian, G. B., Unit commitment problem solution using shuffled frog leaping algorithm. Power Systems, IEEE Transactions on, 26(2011), 2, pp. 573–581

[30] Pan, Q. K., Wang, L., Gao, L., Li, J. Q., An effective shuffled frog-leaping algorithm for lot-streaming flow shop scheduling problem. The International Journal of Advanced Manufacturing Technology, 52(2011), 5–8, pp. 699–713.

[31] Smith, K. D., Katika, K. M., Pilon, L., Maximum time–resolved hemispherical reflectance of absorbing and isotropically scattering media, Journal of Quantitative Spectroscopy and Radiative Transfer, 104(2007), 3, pp. 384–399

[32] Modest, M. F., Radiative heat transfer, Academic Press, San Diego, USA, 2003

[33] Qi, H., Ren, Y. T., Chen, Q., Ruan, L. M., Fast method of retrieving the asymmetry factor and scattering albedo from the maximum time-resolved reflectance of participating media, Applied Optics, 54(2015), 16, pp. 5234-5242

[34] Guo, Z., Kumar, S., Discrete–ordinates solution of short–pulsed laser transport in two–dimensional turbid media, Applied Optics, 40(2001), 19, pp. 3156–3163

[35] Ruan, L. M., Wang, S. G., Qi, H., Analysis of the characteristics of time–resolved signals for transient Radiative transfer in scattering participating media, Journal of Quantitative Spectroscopy and Radiative Transfer, 111(2010), 16, pp. 2405–2414