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Volumn 41, Issue 3, 2010, Pages 335-349

A new sparse grid based method for uncertainty propagation

Author keywords

High dimension; Most probable point; Reliability analysis; Robust design; Sparse grid; Uncertainty propagation; Variate interaction

Indexed keywords

HIGH DIMENSIONS; MOST PROBABLE POINT; ROBUST DESIGNS; SPARSE GRID; UNCERTAINTY PROPAGATION; VARIATE INTERACTION;

EID: 78649636082     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-009-0441-x     Document Type: Article
Times cited : (129)

References (35)
  • 1
    • 0034381734 scopus 로고    scopus 로고
    • High dimensional polynomial interpolation on sparse grids
    • Barthelmann V, Novak E, Ritter K (2000) High dimensional polynomial interpolation on sparse grids. Adv Comput Math 12:273-288
    • (2000) Adv Comput Math 12 , pp. 273-288
    • Barthelmann, V.1    Novak, E.2    Ritter, K.3
  • 2
    • 13644277357 scopus 로고    scopus 로고
    • Towards a better understanding of modeling feasibility robustness in engineering design
    • Du X, Chen W (2000) Towards a better understanding of modeling feasibility robustness in engineering design. JMech Des 122:385-394
    • (2000) JMech Des , vol.122 , pp. 385-394
    • Du, X.1    Chen, W.2
  • 3
    • 0002872544 scopus 로고    scopus 로고
    • A most probable point-based method for efficient uncertainty analysis
    • Du X, Chen W (2001) A most probable point-based method for efficient uncertainty analysis. J Design Manuf Autom 4:47-66
    • (2001) J Design Manuf Autom , vol.4 , pp. 47-66
    • Du, X.1    Chen, W.2
  • 4
    • 4344654014 scopus 로고    scopus 로고
    • Sequential optimization and reliability assessment method for efficient probabilistic design
    • Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. ASME JMech Des 126(2):225-233
    • (2004) ASME JMech Des , vol.126 , Issue.2 , pp. 225-233
    • Du, X.1    Chen, W.2
  • 5
    • 4344568641 scopus 로고    scopus 로고
    • An integrated framework for optimization under uncertainty using inverse reliability strategy
    • Du X, Sudjianto A, Chen W (2004) An integrated framework for optimization under uncertainty using inverse reliability strategy. J Mech Des 126:562-570
    • (2004) J Mech Des , vol.126 , pp. 562-570
    • Du, X.1    Sudjianto, A.2    Chen, W.3
  • 6
    • 0242440688 scopus 로고    scopus 로고
    • Numerical integration using sparse grids
    • Gerstner T, GriebelM(1998) Numerical integration using sparse grids. Number Algorithms 18:209-232
    • (1998) Number Algorithms , vol.18 , pp. 209-232
    • Gerstner, T.1    Griebel, M.2
  • 7
    • 0141991028 scopus 로고    scopus 로고
    • Dimension-adaptive tensor-product quadrature
    • Gerstner T, Griebel M (2003) Dimension-adaptive tensor-product quadrature. Computing 71:65-87
    • (2003) Computing , vol.71 , pp. 65-87
    • Gerstner, T.1    Griebel, M.2
  • 8
    • 10944263187 scopus 로고    scopus 로고
    • Application of Kriging method to structural reliability problems
    • Irfan K (2005) Application of Kriging method to structural reliability problems. Struct Saf 27:133-151
    • (2005) Struct Saf , vol.27 , pp. 133-151
    • Irfan, K.1
  • 11
    • 33750032168 scopus 로고    scopus 로고
    • PhD dissertation Institut für Angewandte Analysis und Numerische Simulation Universität Stuttgart
    • Klimke A (2006b) Uncertainty modeling using fuzzy arithmetic and sparse grids. PhD dissertation, Institut für Angewandte Analysis und Numerische Simulation Universität Stuttgart
    • (2006) Uncertainty Modeling Using Fuzzy Arithmetic and Sparse Grids
    • Klimke, A.1
  • 12
    • 33745213726 scopus 로고    scopus 로고
    • Piecewise multilinear hierarchical sparse grid interpolation in MATLAB
    • Klimke A, Wohlmuth B (2005a) Piecewise multilinear hierarchical sparse grid interpolation in MATLAB. ACM Trans Math Softw 31:561-579
    • (2005) ACM Trans Math Softw , vol.31 , pp. 561-579
    • Klimke, A.1    Wohlmuth, B.2
  • 13
    • 21744460436 scopus 로고    scopus 로고
    • Computing expensive multivariate functions of fuzzy numbers using sparse grids
    • DOI 10.1016/j.fss.2005.02.017, PII S0165011405000904
    • Klimke A, Wohlmuth B (2005b) Computing expensive multivariate functions of fuzzy numbers using sparse grids. Fuzzy Sets Syst 154:432-453 (Pubitemid 40940832)
    • (2005) Fuzzy Sets and Systems , vol.154 , Issue.3 , pp. 432-453
    • Klimke, A.1    Wohlmuth, B.2
  • 14
    • 56449100211 scopus 로고    scopus 로고
    • A comparative study of uncertainty propagation methods for black-box type functions
    • Lee SH, Chen W (2008) A comparative study of uncertainty propagation methods for black-box type functions. Struct Multidiscipl Optim 37:239-253
    • (2008) Struct Multidiscipl Optim , vol.37 , pp. 239-253
    • Lee, S.H.1    Chen, W.2
  • 15
    • 33751332312 scopus 로고    scopus 로고
    • Alternative methods for reliabilitybased robust design optimization including dimension reduction method
    • Philadelphia, PA, 10-13 September 2006
    • Lee I, Choi KK, Du L (2006) Alternative methods for reliabilitybased robust design optimization including dimension reduction method. In: 32nd ASME design automation conference, Philadelphia, PA, 10-13 September 2006
    • (2006) 32nd ASME design automation conference
    • Lee, I.1    Choi, K.K.2    Du, L.3
  • 16
    • 42949123972 scopus 로고    scopus 로고
    • Dimension reduction method for reliability-based robust design optimization
    • DOI 10.1016/j.compstruc.2007.05.020, PII S0045794907001897
    • Lee I, Choi KK, Du L, Gorsich D (2008a) Dimension reduction method for reliability-based robust design optimization. Comput Struct 86:1550-1562 (Pubitemid 351609089)
    • (2008) Computers and Structures , vol.86 , Issue.13-14 , pp. 1550-1562
    • Lee, I.1    Choi, K.K.2    Du, L.3    Gorsich, D.4
  • 17
    • 54849408991 scopus 로고    scopus 로고
    • Inverse analysis method using MPP-based dimension reduction for reliabilitybased design optimization of nonlinear and multi-dimensional systems
    • Lee I, Choi KK, Du L, Gorsich D (2008b) Inverse analysis method using MPP-based dimension reduction for reliabilitybased design optimization of nonlinear and multi-dimensional systems. Comput Methods Appl Math 198:14-27
    • (2008) Comput Methods Appl Math , vol.198 , pp. 14-27
    • Lee, I.1    Choi, K.K.2    Du, L.3    Gorsich, D.4
  • 18
    • 0033666117 scopus 로고    scopus 로고
    • Directional methods for structural reliability analysis
    • Nie J, Ellingwood BR (2000) Directional methods for structural reliability analysis. Struct Saf 22:233-249
    • (2000) Struct Saf , vol.22 , pp. 233-249
    • Nie, J.1    Ellingwood, B.R.2
  • 19
    • 0030524566 scopus 로고    scopus 로고
    • High dimensional integration of smooth functions over cubes
    • Novak E, Ritter K (1996) High dimensional integration of smooth functions over cubes. J Numer Math 75:79-97 (Pubitemid 126343480)
    • (1996) Numerische Mathematik , vol.75 , Issue.1 , pp. 79-97
    • Novak, E.1    Ritter, K.2
  • 20
    • 0033238933 scopus 로고    scopus 로고
    • Simple cubature formulas with high polynomial exactness
    • Novak E, Ritter K (1999) Simple cubature formulas with high polynomial exactness. Constr Approx 15:499-522
    • (1999) Constr Approx , vol.15 , pp. 499-522
    • Novak, E.1    Ritter, K.2
  • 21
    • 0035743192 scopus 로고    scopus 로고
    • Reliability analysis-a review and some perspective
    • DOI 10.1016/S0167-4730(02)00009-7, PII S0167473002000097, Papers presented at the 8th American Society of Civil Engineers Joint Conference on Probabilistic Methods and Structural Reliability
    • Rackwitz R (2001) Reliability analysis-a review and some perspectives. Struct Saf 23:365-395 (Pubitemid 34696460)
    • (2001) Structural Safety , vol.23 , Issue.4 , pp. 365-395
    • Rackwitz, R.1
  • 22
    • 33644872201 scopus 로고    scopus 로고
    • A univariate approximation at most probable point for higher-order reliability analysis
    • DOI 10.1016/j.ijsolstr.2005.05.053, PII S0020768305003355
    • Rahman S, Wei D (2006) A univariate approximation at most probable point for higher-order reliability analysis. Int J Solids Struct 43:2820-2839 (Pubitemid 43374688)
    • (2006) International Journal of Solids and Structures , vol.43 , Issue.9 , pp. 2820-2839
    • Rahman, S.1    Wei, D.2
  • 23
    • 4644360462 scopus 로고    scopus 로고
    • A univariate dimension-reduction method for multidimensional integration in stochastic mechanics
    • Rahman S, Xu H (2004) A univariate dimension-reduction method for multidimensional integration in stochastic mechanics. Probab Eng Mech 19:393-408
    • (2004) Probab Eng Mech , vol.19 , pp. 393-408
    • Rahman, S.1    Xu, H.2
  • 24
    • 0000301907 scopus 로고
    • Remarks on a multivariate transformation
    • Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23:470-472
    • (1952) Ann Math Stat , vol.23 , pp. 470-472
    • Rosenblatt, M.1
  • 25
    • 0037051278 scopus 로고    scopus 로고
    • Efficient statistical tolerance analysis for general distributions using three-point information
    • DOI 10.1080/00207540110095709
    • Seo HS, Kwak BM (2002) Efficient statistical tolerance analysis for general distributions using three-point information. Int J Prod Res 40:931-944 (Pubitemid 34593806)
    • (2002) International Journal of Production Research , vol.40 , Issue.4 , pp. 931-944
    • Seo, H.S.1    Kwak, B.M.2
  • 26
    • 0001048297 scopus 로고
    • Quadrature and interpolation formulas for tensor products of certain classes of functions
    • Smolyak SA (1963) Quadrature and interpolation formulas for tensor products of certain classes of functions. Sov Math, Dokl 4:240-243
    • (1963) Sov Math, Dokl , vol.4 , pp. 240-243
    • Smolyak, S.A.1
  • 27
    • 46649113146 scopus 로고    scopus 로고
    • Stochastic sparse-grid collocation algorithm (SSCA) for periodic steadystate analysis of nonlinear system with process variations
    • Tao J, Zeng X, Cai W, Su Y, Zhou D, Chiang C (2007) Stochastic sparse-grid collocation algorithm (SSCA) for periodic steadystate analysis of nonlinear system with process variations. In: Proc ASPDAC 5A-5, Jan 2007, pp 474-479
    • (2007) Proc ASPDAC 5A-5, Jan 2007 , pp. 474-479
    • Tao, J.1    Zeng, X.2    Cai, W.3    Su, Y.4    Zhou, D.5    Chiang, C.6
  • 28
    • 85072478513 scopus 로고    scopus 로고
    • Reliability assessment using discriminative sampling and metamodeling
    • Wang G,Wang L, Shan Q (2005) Reliability assessment using discriminative sampling and metamodeling. SAE Transact 114:291-300
    • (2005) SAE Transact , vol.114 , pp. 291-300
    • Wang, G.1    Wang, L.2    Shan, Q.3
  • 29
    • 0028483881 scopus 로고
    • Computational methods for efficient structural reliability and reliability sensitivity analysis
    • Wu Y (1994) Computational methods for efficient structural reliability and reliability sensitivity analysis. AIAA J 32:1717-1723
    • (1994) AIAA J , vol.32 , pp. 1717-1723
    • Wu, Y.1
  • 30
    • 33646577797 scopus 로고    scopus 로고
    • High order collocation method for differential equations with
    • random inputs
    • Xiu D, Hesthaven J (2005) High order collocation method for differential equations with random inputs. SIAM J Sci Comput 27:1118-1139
    • (2005) SIAM J Sci Comput , vol.27 , pp. 1118-1139
    • Xiu, D.1    Hesthaven, J.2
  • 31
    • 10244251553 scopus 로고    scopus 로고
    • A generalized dimension-reduction method for multidimensional integration in stochastic mechanics
    • DOI 10.1002/nme.1135
    • Xu H, Rahman S (2004) A generalized dimension-reduction method for multidimensional integration in stochastic mechanics. Int J Numer Methods Eng 61:1992-2019 (Pubitemid 39622519)
    • (2004) International Journal for Numerical Methods in Engineering , vol.61 , Issue.12 , pp. 1992-2019
    • Xu, H.1    Rahman, S.2
  • 32
    • 23844454565 scopus 로고    scopus 로고
    • Decomposition methods for structural reliability analysis
    • DOI 10.1016/j.probengmech.2005.05.005, PII S026689200500010X
    • Xu H, Rahman S (2005) Decomposition methods for structural reliability analysis. Probab Eng Mech 20:239-250 (Pubitemid 41145456)
    • (2005) Probabilistic Engineering Mechanics , vol.20 , Issue.3 , pp. 239-250
    • Xu, H.1    Rahman, S.2
  • 34
    • 55849096638 scopus 로고    scopus 로고
    • Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis
    • Youn B, Xi Z, Wang P (2008) Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis. Struct Multidiscipl Optim 37:13-28
    • (2008) Struct Multidiscipl Optim , vol.37 , pp. 13-28
    • Youn, B.1    Xi, Z.2    Wang, P.3


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