Comments on 'High-dimensional model representation for structural reliability analysis' by R. Chowdhury, B. N. Rao and A. M. Prasad, Communications in Numerical Methods in Engineering 2009; 25:301-337
The authors of the paper published in Commun. Numer. Methods Eng. (2009; 25:301–337) have claimed to present a new computational tool entailing high‐dimensional model representation for structural reliability analysis. This letter demonstrates that the underlying reliability method already exists an...
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| Veröffentlicht in: | International journal for numerical methods in biomedical engineering Jg. 27; H. 10; S. 1652 - 1659 |
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| Abstract | The authors of the paper published in Commun. Numer. Methods Eng. (2009; 25:301–337) have claimed to present a new computational tool entailing high‐dimensional model representation for structural reliability analysis. This letter demonstrates that the underlying reliability method already exists and was originally developed in the Xu and Rahman paper, published in Probabilist. Eng. Mech. (2005; 20:239–250). The authors do not acknowledge the contribution of Xu and Rahman and convey the impression that they are developing the method for the very first time. Instead, the authors have reinvented the wheel. Copyright © 2010 John Wiley & Sons, Ltd. |
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| AbstractList | The authors of the paper published in Commun. Numer. Methods Eng. (2009; 25:301–337) have claimed to present a new computational tool entailing high‐dimensional model representation for structural reliability analysis. This letter demonstrates that the underlying reliability method already exists and was originally developed in the Xu and Rahman paper, published in Probabilist. Eng. Mech. (2005; 20:239–250). The authors do not acknowledge the contribution of Xu and Rahman and convey the impression that they are developing the method for the very first time. Instead, the authors have reinvented the wheel. Copyright © 2010 John Wiley & Sons, Ltd. The authors of the paper published in Commun. Numer. Methods Eng. (2009; 25:301-337) have claimed to present a new computational tool entailing high-dimensional model representation for structural reliability analysis. This letter demonstrates that the underlying reliability method already exists and was originally developed in the Xu and Rahman paper, published in Probabilist. Eng. Mech. (2005; 20:239-250). The authors do not acknowledge the contribution of Xu and Rahman and convey the impression that they are developing the method for the very first time. Instead, the authors have reinvented the wheel. |
| Author | Xu, H. Rahman, S. |
| Author_xml | – sequence: 1 givenname: S. surname: Rahman fullname: Rahman, S. organization: College of Engineering, The University of Iowa, Iowa City, IA 52242, U.S.A – sequence: 2 givenname: H. surname: Xu fullname: Xu, H. organization: AREVA NP Inc., Lynchburg, VA 24501, U.S.A |
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| Cites_doi | 10.1002/nme.1135 10.1137/S0036142997974001 10.1016/j.engfracmech.2006.04.010 10.1214/aos/1176345462 10.1016/S0951-8320(02)00229-6 10.1214/aoms/1177730196 10.1002/nme.1973 10.1016/j.probengmech.2006.05.004 10.1023/A:1019188517934 10.1016/j.probengmech.2005.05.005 10.1016/S0045-7949(02)00069-X 10.2307/2288201 10.1002/cnm.1118 10.1137/S0036142994261439 10.1137/S0036142994277468 |
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| References | Rabitz H, Alis O. General foundations of high-dimensional model representations. Journal of Mathematical Chemistry 1999; 25:197-233. Hickernell FJ. Quadrature error bounds with applications to lattice rules. SIAM Journal of Numerical Analysis 1996; 33:1995-2016. Efron B, Stein C. The Jackknife estimate of variance. The Annals of Statistics 1981; 9:586-596. Hoeffding W. A class of statistics with asymptotically normal distributions. Annals of Mathematical Statistics 1948; 19:293-325. Xu H, Rahman S. A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics. International Journal for Numerical Methods in Engineering 2004; 61:1992-2019. Sobol IM. Multidimensional Quadrature Formulas and Haar functions. Nauka: Moscow, 1969 (in Russian). Takemura A. Tensor analysis of ANOVA decomposition. Journal of American Statistical Association 1983; 78:894-900. Xu H, Rahman S. Decomposition methods for structural reliability analysis. Probabilistic Engineering Mechanics 2005; 20:239-250. Rahman S. Stochastic dynamic systems with complex-valued eigensolutions. International Journal for Numerical Methods in Engineering 2007; 71:963-986. Owen AB. Monte Carlo variance of scrambled net quadrature. SIAM Journal of Numerical Analysis 1997; 34:1884-1910. Chowdhury R, Rao BN, Prasad AM. High-dimensional model representation for structural reliability analysis. Communications in Numerical Methods in Engineering 2009; 25:301-337. Sobol IM. Theorems and examples on high dimensional model representations. Reliability Engineering and System Safety 2003; 79:187-193. Wei D, Rahman S. Structural reliability analysis by univariate decomposition and numerical integration. Probabilistic Engineering Mechanics 2007; 22:27-38. Owen AB. The dimension distribution and quadrature test functions. Statistica Sinica 2003; 13:1-17. Penmetsa R, Grandhi R. Efficient estimation of structural reliability for problems with uncertain intervals. Computers and Structures 2002; 80:1103-1112. Corrected printing of Sections 3-6 in SIAM Journal on Numerical Analysis 1997; 34: 853-866. Rahman S. A dimensional decomposition method for stochastic fracture mechanics. Engineering Fracture Mechanics 2006; 73:2093-2109. 2009; 25 2004; 61 2006; 73 1997; 34 1999; 25 1948; 19 2003; 13 2003; 79 2005; 20 1981; 9 2007; 71 1996 1997; 33 34 2002; 80 2007; 22 1969 1983; 78 Takemura (10.1002/cnm.1381-BIB11|cit12) 1983; 78 (10.1002/cnm.1381-BIB9.2|cit10) 1997; 34 Efron (10.1002/cnm.1381-BIB7|cit7) 1981; 9 Xu (10.1002/cnm.1381-BIB2|cit2) 2005; 20 Sobol (10.1002/cnm.1381-BIB5|cit5) 1969 Penmetsa (10.1002/cnm.1381-BIB16|cit17) 2002; 80 Xu (10.1002/cnm.1381-BIB12|cit13) 2004; 61 Owen (10.1002/cnm.1381-BIB8|cit8) 1997; 34 Rahman (10.1002/cnm.1381-BIB14|cit15) 2007; 71 Hoeffding (10.1002/cnm.1381-BIB3|cit3) 1948; 19 Hickernell (10.1002/cnm.1381-BIB9|cit9) 1996; 33 Rahman (10.1002/cnm.1381-BIB13|cit14) 2006; 73 Sobol (10.1002/cnm.1381-BIB6|cit6) 2003; 79 Wei (10.1002/cnm.1381-BIB15|cit16) 2007; 22 Rabitz (10.1002/cnm.1381-BIB10|cit11) 1999; 25 Owen (10.1002/cnm.1381-BIB4|cit4) 2003; 13 Chowdhury (10.1002/cnm.1381-BIB1|cit1) 2009; 25 |
| References_xml | – reference: Efron B, Stein C. The Jackknife estimate of variance. The Annals of Statistics 1981; 9:586-596. – reference: Owen AB. Monte Carlo variance of scrambled net quadrature. SIAM Journal of Numerical Analysis 1997; 34:1884-1910. – reference: Xu H, Rahman S. Decomposition methods for structural reliability analysis. Probabilistic Engineering Mechanics 2005; 20:239-250. – reference: Hoeffding W. A class of statistics with asymptotically normal distributions. Annals of Mathematical Statistics 1948; 19:293-325. – reference: Wei D, Rahman S. Structural reliability analysis by univariate decomposition and numerical integration. Probabilistic Engineering Mechanics 2007; 22:27-38. – reference: Sobol IM. Theorems and examples on high dimensional model representations. Reliability Engineering and System Safety 2003; 79:187-193. – reference: Rabitz H, Alis O. General foundations of high-dimensional model representations. Journal of Mathematical Chemistry 1999; 25:197-233. – reference: Corrected printing of Sections 3-6 in SIAM Journal on Numerical Analysis 1997; 34: 853-866. – reference: Rahman S. Stochastic dynamic systems with complex-valued eigensolutions. International Journal for Numerical Methods in Engineering 2007; 71:963-986. – reference: Xu H, Rahman S. A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics. International Journal for Numerical Methods in Engineering 2004; 61:1992-2019. – reference: Sobol IM. Multidimensional Quadrature Formulas and Haar functions. Nauka: Moscow, 1969 (in Russian). – reference: Penmetsa R, Grandhi R. Efficient estimation of structural reliability for problems with uncertain intervals. Computers and Structures 2002; 80:1103-1112. – reference: Chowdhury R, Rao BN, Prasad AM. High-dimensional model representation for structural reliability analysis. Communications in Numerical Methods in Engineering 2009; 25:301-337. – reference: Hickernell FJ. Quadrature error bounds with applications to lattice rules. SIAM Journal of Numerical Analysis 1996; 33:1995-2016. – reference: Takemura A. Tensor analysis of ANOVA decomposition. Journal of American Statistical Association 1983; 78:894-900. – reference: Rahman S. A dimensional decomposition method for stochastic fracture mechanics. Engineering Fracture Mechanics 2006; 73:2093-2109. – reference: Owen AB. The dimension distribution and quadrature test functions. Statistica Sinica 2003; 13:1-17. – volume: 20 start-page: 239 year: 2005 end-page: 250 article-title: Decomposition methods for structural reliability analysis publication-title: Probabilistic Engineering Mechanics – volume: 61 start-page: 1992 year: 2004 end-page: 2019 article-title: A generalized dimension‐reduction method for multi‐dimensional integration in stochastic mechanics publication-title: International Journal for Numerical Methods in Engineering – volume: 33 34 start-page: 1995 853 year: 1996 1997 end-page: 2016 866 article-title: Quadrature error bounds with applications to lattice rules publication-title: SIAM Journal of Numerical Analysis SIAM Journal on Numerical Analysis – volume: 73 start-page: 2093 year: 2006 end-page: 2109 article-title: A dimensional decomposition method for stochastic fracture mechanics publication-title: Engineering Fracture Mechanics – volume: 25 start-page: 301 year: 2009 end-page: 337 article-title: High‐dimensional model representation for structural reliability analysis publication-title: Communications in Numerical Methods in Engineering – volume: 25 start-page: 197 year: 1999 end-page: 233 article-title: General foundations of high‐dimensional model representations publication-title: Journal of Mathematical Chemistry – volume: 71 start-page: 963 year: 2007 end-page: 986 article-title: Stochastic dynamic systems with complex‐valued eigensolutions publication-title: International Journal for Numerical Methods in Engineering – year: 1969 – volume: 78 start-page: 894 year: 1983 end-page: 900 article-title: Tensor analysis of ANOVA decomposition publication-title: Journal of American Statistical Association – volume: 13 start-page: 1 year: 2003 end-page: 17 article-title: The dimension distribution and quadrature test functions publication-title: Statistica Sinica – volume: 22 start-page: 27 year: 2007 end-page: 38 article-title: Structural reliability analysis by univariate decomposition and numerical integration publication-title: Probabilistic Engineering Mechanics – volume: 19 start-page: 293 year: 1948 end-page: 325 article-title: A class of statistics with asymptotically normal distributions publication-title: Annals of Mathematical Statistics – volume: 79 start-page: 187 year: 2003 end-page: 193 article-title: Theorems and examples on high dimensional model representations publication-title: Reliability Engineering and System Safety – volume: 9 start-page: 586 year: 1981 end-page: 596 article-title: The Jackknife estimate of variance publication-title: The Annals of Statistics – volume: 80 start-page: 1103 year: 2002 end-page: 1112 article-title: Efficient estimation of structural reliability for problems with uncertain intervals publication-title: Computers and Structures – volume: 34 start-page: 1884 year: 1997 end-page: 1910 article-title: Monte Carlo variance of scrambled net quadrature publication-title: SIAM Journal of Numerical Analysis – volume: 61 start-page: 1992 year: 2004 ident: 10.1002/cnm.1381-BIB12|cit13 article-title: A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1135 – volume: 34 start-page: 853 year: 1997 ident: 10.1002/cnm.1381-BIB9.2|cit10 publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/S0036142997974001 – volume: 73 start-page: 2093 year: 2006 ident: 10.1002/cnm.1381-BIB13|cit14 article-title: A dimensional decomposition method for stochastic fracture mechanics publication-title: Engineering Fracture Mechanics doi: 10.1016/j.engfracmech.2006.04.010 – volume: 9 start-page: 586 year: 1981 ident: 10.1002/cnm.1381-BIB7|cit7 article-title: The Jackknife estimate of variance publication-title: The Annals of Statistics doi: 10.1214/aos/1176345462 – volume: 79 start-page: 187 year: 2003 ident: 10.1002/cnm.1381-BIB6|cit6 article-title: Theorems and examples on high dimensional model representations publication-title: Reliability Engineering and System Safety doi: 10.1016/S0951-8320(02)00229-6 – volume: 19 start-page: 293 year: 1948 ident: 10.1002/cnm.1381-BIB3|cit3 article-title: A class of statistics with asymptotically normal distributions publication-title: Annals of Mathematical Statistics doi: 10.1214/aoms/1177730196 – volume: 71 start-page: 963 year: 2007 ident: 10.1002/cnm.1381-BIB14|cit15 article-title: Stochastic dynamic systems with complex-valued eigensolutions publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1973 – volume: 22 start-page: 27 year: 2007 ident: 10.1002/cnm.1381-BIB15|cit16 article-title: Structural reliability analysis by univariate decomposition and numerical integration publication-title: Probabilistic Engineering Mechanics doi: 10.1016/j.probengmech.2006.05.004 – volume: 25 start-page: 197 year: 1999 ident: 10.1002/cnm.1381-BIB10|cit11 article-title: General foundations of high-dimensional model representations publication-title: Journal of Mathematical Chemistry doi: 10.1023/A:1019188517934 – volume: 20 start-page: 239 year: 2005 ident: 10.1002/cnm.1381-BIB2|cit2 article-title: Decomposition methods for structural reliability analysis publication-title: Probabilistic Engineering Mechanics doi: 10.1016/j.probengmech.2005.05.005 – volume: 80 start-page: 1103 year: 2002 ident: 10.1002/cnm.1381-BIB16|cit17 article-title: Efficient estimation of structural reliability for problems with uncertain intervals publication-title: Computers and Structures doi: 10.1016/S0045-7949(02)00069-X – volume: 78 start-page: 894 year: 1983 ident: 10.1002/cnm.1381-BIB11|cit12 article-title: Tensor analysis of ANOVA decomposition publication-title: Journal of American Statistical Association doi: 10.2307/2288201 – volume: 25 start-page: 301 year: 2009 ident: 10.1002/cnm.1381-BIB1|cit1 article-title: High-dimensional model representation for structural reliability analysis publication-title: Communications in Numerical Methods in Engineering doi: 10.1002/cnm.1118 – volume: 13 start-page: 1 year: 2003 ident: 10.1002/cnm.1381-BIB4|cit4 article-title: The dimension distribution and quadrature test functions publication-title: Statistica Sinica – volume-title: Multidimensional Quadrature Formulas and Haar functions year: 1969 ident: 10.1002/cnm.1381-BIB5|cit5 – volume: 33 start-page: 1995 year: 1996 ident: 10.1002/cnm.1381-BIB9|cit9 article-title: Quadrature error bounds with applications to lattice rules publication-title: SIAM Journal of Numerical Analysis doi: 10.1137/S0036142994261439 – volume: 34 start-page: 1884 year: 1997 ident: 10.1002/cnm.1381-BIB8|cit8 article-title: Monte Carlo variance of scrambled net quadrature publication-title: SIAM Journal of Numerical Analysis doi: 10.1137/S0036142994277468 |
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