Probability Function Estimation of Rock Random Variables Using Chebyshev Orthogonal Polynomial

Abstract:

The Chebyshev orthogonal polynomial with sample moments (the origin moments) were used to approximate the probability density function (PDF) or cumulative distribution function (CDF) of variable (CPA method). Three examples from observed datas of uniaxial compressive strength of a kind of hard rock were presented for illustrative purposes. The results show the PDF or CDF of rock variables can be accurately derived from CPA method with sample moments. The relative errors of estimation by CPA method is much smaller than that of TDF method (PDF fitted by some standard theoretical distributions). It is suggested that the presented method can be used in stochastic reliability analysis of rock engineering.

• Periodical: Applied Mechanics and Materials (Volumes 351-352)
• Pages: 1673-1676
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.351-352.1673
• Online since: August 2013
• Authors: Feng Qiang Gong, Shang Qian Hou, Ting Yu Wu
• Keywords: Chebyshev Orthogonal Polynomial, Cumulative Density Function, Origin Moment, Probabilistic Density Function, Rock Random Variables

References

[1] J. Deng, X.B. Li, G.S. Gu: Int. J. Rock Mech. Min. Sci. Vol. 41(2004), p.1.

[2] G.K. Er: Struct Saf. Vol. 20(1998), p.25.

[3] X.B. Li, F.Q. Gong: Struct Saf. Vol. 31(2009), p.335.

[4] C.A. Kennedy, W.C. Lennox: Probabilist Eng Mech. Vol. 15(2000), p.371.

[5] A. Bultheel, A. Cuyt, W. Van Assche, M. Van Barel, B: : J Comput Appl Math. Vol. 179(2005), p.57.

[6] G. W. Collins: Fundamental numerical methods and data analysis（New York, 2003）.

[7] B. KOŠŤÁĸ, H.U. Bielensiein: Int. J. Rock Mech. Min. Sci. Vol. 8(1971), p.501.

[8] S. T. Quek, C. F. Leung: Int. J. Rock Mech. Min. Sci. Vol. 32(1995), p.617.