SUPPORT DOMAIN EFFECTS ON SHAPE PARAMETER C IN MAPPING BY RADIAL BASIS FUNCTIONS (RBFs)

Document Type : Original Article

Authors

1 Assistant Professor of Civil Engineering Department, Faculty of Engineering, Zabol University, Zabol, Iran

2 Professor of Civil Engineering Department, Faculty of Engineering, Shiraz University, Shiraz, Iran

Abstract

In many water engineering studies, there is a need to fill lost rain data using mapping tools. In this research this has been done by 5 types of RBFs; the data used were extracted by 3 test functions in which the support domain varied from 0.1 by 0.1 meter net to 0.5 by 0.5 meter net with different numbers of stations in a unit area domain. The c parameter was optimized by cross validation method and the Normalized Mean Square Error (NMSE), Percent Average Estimation Error (PAEE) and Coefficient of determination (R2) were the statistical controlling tools for choosing suitable RBF function type. Compared to other works in literature, this work had a better performance in mapping. It is also shown that the c parameter that optimizes the RBF function is highly dependent on the support domain size; the finer the resolutions of support domain, the better the results achieved. The attribute was also found for an arbitrary station point, Z (0.25, 0.35) to show the model capability for an irregular domain. This work may be compared with meshless methods for further research.

Keywords

References

Borga, M. and Vizzaccaro A. (1997),  "On the interpolation of hydrologic variables: formal equivalence of multiquadratic surface fitting and kriging", Journal of Hydrology, 195, pp.160-171.
Carlson, R.E. and Foley, (1991).  T.A. The parameter R2 in multiquadric interpolation, Comput. Math. Appl. 21, pp. 29–42.
Foley, T.A. (1987). Interpolation and approximation of 3-D and 4-D scattered data, Comput. Math. Appl.13, pp. 711–740.
Foley, T.A. (1991). Near optimal parameter selection for multiquadric interpolation, J. Appl. Sci. Comput.1, pp. 54–69.
 Franke, R. (1982). Scattered data interpolation: tests of some methods, Math. Comp. 38, pp. 181–200.
 Hardy, R.L. (1971). Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res.76, pp.1905–1915.
 Hardy, R.L. (1990), Theory and applications of the multiquadric-biharmonic method, Comput. Math. Appl. 19, pp. 163–208.
 Lyche, T. and Morken, K. (1987). Knot removal for parametric B-spline curves and surfaces, Comput. Aided Geom. Design 4, pp. 217–230.
Magness, A. L. G. and McCuen, R. H. (2004), "Accuracy evaluation of rainfall disaggregation methods", Journal of Hydrologic Engineering, 9(2), pp.71-77.
Myers, D. E. (1994), " Spatial interpolation: an overview", Geoderma, 62, pp. 17-28.
Poggio, T. and Girosi, F. (1990), Networks for approximation and learning, Proceedings of the IEEE 78, pp. 1481–1497.
 Powell, M.J.D. (1990), The theory of radial basis function approximation, Advances in Numerical Analysis, Vol. 2: Wavelets, Subdivision Algorithms and Radial Functions, ed. W. Light pp. 105–210.
Rippa, S. (1999), "An algorithm for selecting a good value for the parameter C in radial basis function interpolation", Advances in Computational Mathematics, 11, pp.193-210.
Shams, S., Abedini M. J. and Asghari K. (2003), "Rainfall disaggregation via artificial neural networks", Fourth Iranian hydraulic conference, Shiraz University, Iran, pp.1-8.
Iran-Water Resources Research
Volume 7, Issue 4
January 2012
Pages 82-94

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History

  • Receive Date: 08 December 2007
  • Accept Date: 18 January 2012

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