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Implications of High-Dimensional Geometry for Structural Reliability Analysis and a Novel Linear Response Surface Method Based on SVM

Umberto Alibrandi

Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore

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Amir Alani

School of Computing and Technology, University of West London, 8th Floor, Villiers House, Ealing Broadway, London W52PA, UK

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, and

C. G. Koh

Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore

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https://doi.org/10.1142/S0219876215400162Cited by:13 (Source: Crossref)

Abstract

The geometry of high-dimensional spaces is very different from low dimensional spaces and possesses some counter-intuitive features. It is shown that, for high dimensions, the sampling points fall far away from the origin and concentrate within an intersection between a very thin shell and a suitable equatorial slab. The well-known First-Order Reliability Method (FORM), originally formulated for low dimensions, may work well in many engineering problems of high dimension. But it is not able to reveal the level of achieved accuracy. Considering the features of high-dimensional geometry, a novel linear response surface based on Support Vector Method (SVM) is proposed for structural reliability problems of high dimension. The method is shown to outperform FORM for structural reliability problems of high dimension in terms of robustness and accuracy.

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References

U. Alibrandi, An alternative linear response surface improving FORM solution for stochastic dynamic analysis, Reliability and Optimization of Structural Systems, IFIP WG 7.5 Working Conf. (2012) pp. 237–244. Google Scholar
U. Alibrandi , Reliab. Eng. Syst. Saf. 26 , 44 ( 2014 ) . Crossref, Web of Science, Google Scholar
U. Alibrandi and A. Der Kiureghian , Probab. Eng. Mech. 28 , 2 ( 2012 ) . Crossref, Web of Science, Google Scholar
U. Alibrandi, N. Impollonia and G. Ricciardi, Comput. Methods Appl. Mech. Eng. 199(12), 450 (2010). Crossref, Web of Science, Google Scholar
Alibrandi, U., Ma, C. Y. and Koh, C. G. [2013] "A linear response surface based on SVM for structural reliability analysis," in APCOM and ISCM, http://www.sci-cn-tech.com/apcom2013/APCOM2013-proceedings/PDF_Fullpaper/1432.pdf (Last accessed 10 March 2015) . Google Scholar
U. Alibrandi and G. Ricciardi , Bounds of the probability of collapse of rigid-plastic structures by means of stochastic limit analysis , 9th Int. Conf. Structural Safety and Reliability ( 2005 ) . Google Scholar
U. Alibrandi and G. Ricciardi, Int. J. Numer. Methods Eng. 73(6), 747 (2008). Crossref, Web of Science, Google Scholar
U. Alibrandi and G. Ricciardi, Structural Reliabilty Analysis solved through a SVM-based response surface, ICASP 2011, The 11th Int. Conf. Applications of Statistics and Probability in Civil Engineering (2011) pp. 2697–2703. Google Scholar
S. K. Au and J. L. Beck , Probab. Eng. Mech. 16 , 263 ( 2001 ) . Crossref, Web of Science, Google Scholar
J.-M. Bourinet , F. Deheeger and M. Lemaire , Struct. Saf. 33 , 343 ( 2011 ) . Crossref, Web of Science, Google Scholar
S. Boyd and L. Vandenberghe , Convex Optimization ( Cambridge University Press , Cambridge , 2004 ) . Crossref, Google Scholar
K. Breitung, J. Eng. Mech. 110(3), 357 (1984). Crossref, Web of Science, Google Scholar
C. Bucher , Probab. Eng. Mech. 24 , 504 ( 2009 ) . Crossref, Web of Science, Google Scholar
C. Bucher and U. Burgound , Struct. Saf. 7 , 57 ( 1990 ) . Crossref, Web of Science, Google Scholar
C. Bucher and T. Most , Probab. Eng. Mech. 23 , 154 ( 2008 ) . Crossref, Web of Science, Google Scholar
C. J. C. Burges , Data Min. Knowl. Discov. 2 , 121 ( 1998 ) . Crossref, Web of Science, Google Scholar
A. Der Kiureghian , Probab. Eng. Mech. 15 , 81 ( 2000 ) . Crossref, Web of Science, Google Scholar
A. Der Kiureghian , H.-Z. Lin and S.-J. Hwang , J. Eng. Mech. 113 , 1208 ( 1987 ) . Crossref, Web of Science, Google Scholar
O. Ditlevsen and H. O. Madsen , Structural Reliability Methods ( Wiley , Chichester , 1999 ) . Google Scholar
L. Faravelli , J. Eng. Mech. 115 , 2763 ( 1989 ) . Crossref, Web of Science, Google Scholar
B. Fiessler, H. J. Neumann and R. Rackwitz, J. Eng. Mech. Div. 105(4), 661 (1979). Crossref, Web of Science, Google Scholar
J. E. Hurtado , Struct. Saf. 26 , 271 ( 2004 ) . Crossref, Web of Science, Google Scholar
J. E. Hurtado , Struct. Saf. 29 , 2 ( 2007 ) . Crossref, Web of Science, Google Scholar
J. E. Hurtado , Probab. Eng. Mech. 29 , 16 ( 2012 ) . Crossref, Web of Science, Google Scholar
J. E. Hurtado and D. A. Alvarez , J. Struct. Eng. 129 , 1141 ( 2003 ) . Crossref, Web of Science, Google Scholar
J. E. Hurtado and D. A. Alvarez , Probab. Eng. Mech. 25 , 26 ( 2010 ) . Crossref, Web of Science, Google Scholar
L. S. Katafygiotis and K. M. Zuev , Probab. Eng. Mech. 23 , 208 ( 2008 ) . Crossref, Web of Science, Google Scholar
S.-H. Kim and S.-W. Na , Struct. Saf. 19 , 3 ( 1997 ) . Crossref, Web of Science, Google Scholar
H. Koo , A. Der Kiureghian and K. Fujimura , Probab. Eng. Mech. 20 , 136 ( 2005 ) . Crossref, Web of Science, Google Scholar
L. D. Lutes and S. Sarkani , Random Vibrations: Analysis of Structural and Mechanical Systems ( Elsevier , Burlington , 2004 ) . Google Scholar
H. O. Madsen , S. Krenk and N. C. Lind , Methods of Structural Safety ( Prentice-Hall , Englewood Cliffs, NJ , 1986 ) . Google Scholar
R. E. Melchers , Structural Reliability, Analysis and Prediction ( Wiley and Sons , New York , 1999 ) . Google Scholar
T. Most and C. Bucher , Adaptive response surface approach using artificial neural networks and moving least squares , Proc. 17th Int. Conf. Application of Computer Science and Mathematics in Architecture and Civil Engineering , eds. K. Gurlebeck and C. Konke ( Bauhaus-University Weimar , 2006 ) . Google Scholar
H. J. Pradlwarter et al. , Struct. Saf. 29 , 208 ( 2007 ) . Crossref, Web of Science, Google Scholar
M. R. Rajashekhar and B. R. Ellingwood , Struct. Saf. 12 , 205 ( 1993 ) . Crossref, Web of Science, Google Scholar
Rice, S. O. [1957] "Mathematical analysis of random noise," in Selected Papers on Noise and Stochastic Processes (Dover Publications Inc., New York) . Google Scholar
L. Tvedt , Section on Structural Reliability ( A/S Vertas Research , Hovik, Norway , 1984 ) . Google Scholar
L. Tvedt , Section on Structural Reliability ( A/S Vertas Research , Hovik, Norway , 1985 ) . Google Scholar
M. A. Valdebenito , H. J. Pradlwarter and G. I. Schuëller , Struct. Saf. 32 , 101 ( 2010 ) . Crossref, Web of Science, Google Scholar
V. Vapnik , The Nature of Statistical Learning Theory ( Springer-Verlag , New York , 1995 ) . Crossref, Google Scholar
Y. Zheng and P. K. Das , Eng. Struct. 22 , 544 ( 2000 ) . Crossref, Web of Science, Google Scholar