The use of the L-curve method in the inversion of diffusion battery data

Journal of Aerosol Science

Volumn 28, Issue 7, 1997, Pages 1251-1264

  Lloyd, J J ^a   Taylor, C J ^b   Lawson, R S ^a   Shields, R A ^a  

^a MANCHESTER ROYAL INFIRMARY   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CURVE FITTING; ELECTRIC BATTERIES; FUNCTIONS; INVERSE PROBLEMS;

DIFFUSION BATTERY; ERROR ESTIMATION; L CURVE METHOD;

PARTICLE SIZE ANALYSIS;

AEROSOL; ARTICLE; DIFFUSION; MATHEMATICAL MODEL; PARTICLE SIZE; PRIORITY JOURNAL;

EID: 0031258560     PISSN: 00218502     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8502(97)00018-9     Document Type: Article

References (23)

1. Bashurova, V. S., Koutzenogil, K. P., Pusep, A. Y. and Shokhirev, N. V. (1991) Determination of atmospheric aerosol size distribution functions from screen diffusion battery data: mathematical aspects. J. Aerosol Sci. 22, 373-388.
2. Cheng, Y. S., Yeh, H. C. and Brinsko, K. J. (1985) Use of wire screens as a fan model filter. Aerosol Sci. Tech. 4, 165-174.
3. Cooper, D. W. and Spielman, L. A. (1976) Data inversion using nonlinear programming with physical constraints: aerosol size distribution measurement by impactors. Atmos. Envir. 10, 723-729.
4. Crump, J. G. and Seinfeld, J. H. (1982) A new algorithm for inversion of aerosol size distribution data. Aerosol Sci. Tech. 1, 15-34.
5. Gill, P. E., Hammarling, S. J., Murray, W., Saunders, M. A. and Wright, M. H. (1984) User's guide for LSSOL Version 1.0.
6. Hansen, P. C. (1992) Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev. 34, 561-580.
7. Hansen, P. C. and O'Leary, D. P. (1993) The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14, 1487-1503.
8. Lemb, M., Oei, T. H., Eifert, H. and Gunther, B. (1993) Technegas: a study of particle structure, size and distribution. Eur. J. Nucl. Med. 20, 576-579.
9. Lloyd, J. J., Shields, R. A., Taylor, C. J., Lawson, R. S., James. J. M. and Testa, H. J. (1995) Technegas and Pertechnegas particle size distribution. Eur. J. Nucl. Med. 22, 473-476.
10. Lloyd, J. J., Taylor, C. J., Lawson, R. S. and Shields, R. A. (1997) Comparison of local and global optimisation techniques for diffusion battery data analysis. J. Aerosol Sci. 28, 821-831.
11. Lloyd, J. J., Taylor, C. J. and Shields, R. A. (1994) Analysis of diffusion battery data using simulated annealing Aerosols; their generation behaviour and applications. Proc. 8th Annual Conf. of the Aerosol Society, University of York.
12. Maher, E. F. and Laird, N. M. (1985) EM algorithm reconstruction of particle size distributions from diffusion battery data. J. Aerosol Sci. 16, 557-570.
13. Markowski, G. R. (1987) Improving Twomey's algorithm for inversion of aerosol measurement data. Aerosol Sci. Technol. 7, 127-141.
14. Nelder, J. A. and Mead, R. (1965) A simplex method for function minimization. Comput. J. 7, 308-313.
15. Phillips, D. L. (1962) A technique for the numerical solution of certain integral equations of the first kind. J. Assoc. Comput. Mach. 9, 84-97.
16. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Plannery, B. P. (1992) Numerical Recipes in FORTRAN. Cambridge University Press, Cambridge.
17. Ramachandran, G., Johnson, E. W. and Vincent, J. H. (1996) Inversion techniques for personal cascade impactor data. J. Aerosol Sci. 27, 1083-1097.
18. Sinclair, D. and Hoopes, G. S. (1975) A novel form of diffusion battery. Am. Ind. Hyg. Assoc. J. 36, 39-42.
19. Strong, J. C. and Agnew, J. E. (1989) The particle size distribution of Technegas and its influence on regional lung deposition. Nucl. Med. Comm. 10, 425-430.
20. Twomey, S. (1975) Comparison of constrained linear inversion and an iterative nonlinear alogrithm applied to the indirect estimation of particle size distributions. J. Comput. Phys. 18, 188-200.
21. Wahba, G. (1990) Spline Models for Observational Data. Society for Industrial and Applied Mathematics, Philadelphia.
22. Wolfenbarger, J. K. and Seinfield, J. H. (1990) Inversion of aerosol size distribution data. J Aerosol Sci 21, 227-247.
23. Wolfenbarger, W. L. and Seinfeld, J. H. (1991) Regularized solutions to the aerosol data inversion problem. SIAM J. Sci. Stat. Comput. 12, 342-361.