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Erschienen in: Structural and Multidisciplinary Optimization 4/2018

26.10.2017 | RESEARCH PAPER

A two-step methodology to apply low-discrepancy sequences in reliability assessment of structural dynamic systems

verfasst von: Jun Xu, Ding Wang

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 4/2018

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Abstract

This study introduces various low-discrepancy sequences and then develops a new methodology for reliability assessment for structural dynamic systems. In this methodology, a two-step algorithm is first proposed, in which the most uniformly scattered point set among the low-discrepancy sequences is selected according to the centered L2-discrepancy (CL2 discrepancy) and then rearranged to minimize the generalized F-discrepancy (GF discrepancy). After that, the developed point set is incorporated into the maximum entropy method to capture the fractional moments for deriving the extreme value distribution for reliability assessment of structural dynamic systems. Numerical examples are investigated, where the results are compared with those obtained from Monte Carlo simulations, demonstrating the accuracy and efficiency of the proposed methodology.
Literatur
Zurück zum Zitat Au S, Beck J (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J Eng Mech 129(8):901–917 CrossRef Au S, Beck J (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J Eng Mech 129(8):901–917 CrossRef
Zurück zum Zitat Brandimarte P (2014) Low-Discrepancy Sequences . Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics, pp 379–401 Brandimarte P (2014) Low-Discrepancy Sequences . Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics, pp 379–401
Zurück zum Zitat Bratley P, Fox BL (1988) Algorithm 659: implementing Sobol's quasirandom sequence generator. ACM Trans Math Softw (TOMS) 14(1):88–100 CrossRefMATH Bratley P, Fox BL (1988) Algorithm 659: implementing Sobol's quasirandom sequence generator. ACM Trans Math Softw (TOMS) 14(1):88–100 CrossRefMATH
Zurück zum Zitat Chen JB, Li J (2007) The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Struct Saf 29(2):77–93 CrossRef Chen JB, Li J (2007) The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Struct Saf 29(2):77–93 CrossRef
Zurück zum Zitat Chen JB, Ghanem R, Li J (2009) Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures. Probabilist Eng Mech 24(1):27–42 CrossRef Chen JB, Ghanem R, Li J (2009) Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures. Probabilist Eng Mech 24(1):27–42 CrossRef
Zurück zum Zitat Chen J, Yang J, Li J (2016) A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters. Struct Saf 59:20–31 CrossRef Chen J, Yang J, Li J (2016) A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters. Struct Saf 59:20–31 CrossRef
Zurück zum Zitat Conway JH, Sloane NJA (2013) Sphere packings, lattices and groups, vol 290. Springer Science & Business Media, Berlin MATH Conway JH, Sloane NJA (2013) Sphere packings, lattices and groups, vol 290. Springer Science & Business Media, Berlin MATH
Zurück zum Zitat Dai H, Wang W (2009) Application of low-discrepancy sampling method in structural reliability analysis. Struct Saf 31(1):55–64 CrossRef Dai H, Wang W (2009) Application of low-discrepancy sampling method in structural reliability analysis. Struct Saf 31(1):55–64 CrossRef
Zurück zum Zitat Dick J, Pillichshammer F (2010) Digital nets and sequences: discrepancy theory and quasi–Monte Carlo integration. Cambridge University Press, Cambridge CrossRefMATH Dick J, Pillichshammer F (2010) Digital nets and sequences: discrepancy theory and quasi–Monte Carlo integration. Cambridge University Press, Cambridge CrossRefMATH
Zurück zum Zitat Goller B, Pradlwarter HJ, Schuller GI (2013) Reliability assessment in structural dynamics. J Sound Vib 332(10):2488–2499 CrossRef Goller B, Pradlwarter HJ, Schuller GI (2013) Reliability assessment in structural dynamics. J Sound Vib 332(10):2488–2499 CrossRef
Zurück zum Zitat Halton JH (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer Math 2(1):84–90 MathSciNetCrossRefMATH Halton JH (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer Math 2(1):84–90 MathSciNetCrossRefMATH
Zurück zum Zitat Harald N (1992) Random number generation and quasi-Monte Carlo methods. Society for lndustrial and Applied Mathematics, Philadelphia MATH Harald N (1992) Random number generation and quasi-Monte Carlo methods. Society for lndustrial and Applied Mathematics, Philadelphia MATH
Zurück zum Zitat Hess S, Polak J (2003) An alternative method to the scrambled Halton sequence for removing correlation between standard Halton sequences in high dimensions. Plant Cell, 15(3):760-770. Hess S, Polak J (2003) An alternative method to the scrambled Halton sequence for removing correlation between standard Halton sequences in high dimensions. Plant Cell, 15(3):760-770.
Zurück zum Zitat Hickernell F, Wang X (2002) The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension. Math Comput 71(240):1641–1661 MathSciNetCrossRefMATH Hickernell F, Wang X (2002) The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension. Math Comput 71(240):1641–1661 MathSciNetCrossRefMATH
Zurück zum Zitat Hu Z, Du X (2013) A sampling approach to extreme value distribution for time-dependent reliability analysis. J Mech Des 135(7):071003 CrossRef Hu Z, Du X (2013) A sampling approach to extreme value distribution for time-dependent reliability analysis. J Mech Des 135(7):071003 CrossRef
Zurück zum Zitat Hu Z, Du X (2015a) First order reliability method for time-variant problems using series expansions. Struct Multidiscip Optim 51(1):1–21 MathSciNetCrossRef Hu Z, Du X (2015a) First order reliability method for time-variant problems using series expansions. Struct Multidiscip Optim 51(1):1–21 MathSciNetCrossRef
Zurück zum Zitat Hu Z, Du X (2015b) Mixed efficient global optimization for time-dependent reliability analysis. J Mech Des 137(5):051401 CrossRef Hu Z, Du X (2015b) Mixed efficient global optimization for time-dependent reliability analysis. J Mech Des 137(5):051401 CrossRef
Zurück zum Zitat Hua L-K, Wang Y (2012) Applications of number theory to numerical analysis. Springer Science & Business Media, Berlin Hua L-K, Wang Y (2012) Applications of number theory to numerical analysis. Springer Science & Business Media, Berlin
Zurück zum Zitat Hua LK, Yuan W (1981) Applications of number theory to numerical analysis. Springer, Berlin MATH Hua LK, Yuan W (1981) Applications of number theory to numerical analysis. Springer, Berlin MATH
Zurück zum Zitat Iourtchenko DV, Mo E, Naess A (2006) Response probability density functions of strongly non-linear systems by the path integration method. Int J Non Linear Mech 41(5):693–705 MathSciNetCrossRefMATH Iourtchenko DV, Mo E, Naess A (2006) Response probability density functions of strongly non-linear systems by the path integration method. Int J Non Linear Mech 41(5):693–705 MathSciNetCrossRefMATH
Zurück zum Zitat Joe S, Kuo FY (2003) Remark on algorithm 659: implementing Sobol's quasirandom sequence generator. ACM Trans Math Softw (TOMS) 29(1):49–57 MathSciNetCrossRefMATH Joe S, Kuo FY (2003) Remark on algorithm 659: implementing Sobol's quasirandom sequence generator. ACM Trans Math Softw (TOMS) 29(1):49–57 MathSciNetCrossRefMATH
Zurück zum Zitat Joe S, Kuo FY (2008) Notes on generating Sobol sequences. Technical report, University of New South Wales. Joe S, Kuo FY (2008) Notes on generating Sobol sequences. Technical report, University of New South Wales.
Zurück zum Zitat Kapur JN, Kesavan HK (1992) Entropy optimization principles with applications. Academic Pr, Cambridge CrossRefMATH Kapur JN, Kesavan HK (1992) Entropy optimization principles with applications. Academic Pr, Cambridge CrossRefMATH
Zurück zum Zitat Kocis L, Whiten WJ (1997) Computational investigations of low-discrepancy sequences. ACM Trans Math Softw (TOMS) 23(2):266–294 CrossRefMATH Kocis L, Whiten WJ (1997) Computational investigations of low-discrepancy sequences. ACM Trans Math Softw (TOMS) 23(2):266–294 CrossRefMATH
Zurück zum Zitat Kougioumtzoglou IA, Spanos PD (2012) Response and first-passage statistics of nonlinear oscillators via a numerical path integral approach. J Eng Mech 139(9):1207–1217 CrossRef Kougioumtzoglou IA, Spanos PD (2012) Response and first-passage statistics of nonlinear oscillators via a numerical path integral approach. J Eng Mech 139(9):1207–1217 CrossRef
Zurück zum Zitat Li J, Chen JB, Fan WL (2007) The equivalent extreme-value event and evaluation of the structural system reliability. Struct Saf 29(2):112–131 CrossRef Li J, Chen JB, Fan WL (2007) The equivalent extreme-value event and evaluation of the structural system reliability. Struct Saf 29(2):112–131 CrossRef
Zurück zum Zitat Madsen PH, Krenk S (1984) An integral equation method for the first-passage problem in random vibration. J Appl Mech 51(3):674–679 MathSciNetCrossRefMATH Madsen PH, Krenk S (1984) An integral equation method for the first-passage problem in random vibration. J Appl Mech 51(3):674–679 MathSciNetCrossRefMATH
Zurück zum Zitat Mourelatos ZP, Majcher M, Pandey V, Baseski I (2015) Time-dependent reliability analysis using the Total probability theorem. J Mech Des 137(3):031405 CrossRef Mourelatos ZP, Majcher M, Pandey V, Baseski I (2015) Time-dependent reliability analysis using the Total probability theorem. J Mech Des 137(3):031405 CrossRef
Zurück zum Zitat Naess A, Iourtchenko D, Batsevych O (2011) Reliability of systems with randomly varying parameters by the path integration method. Probabilist Eng Mech 26(1):5–9 CrossRefMATH Naess A, Iourtchenko D, Batsevych O (2011) Reliability of systems with randomly varying parameters by the path integration method. Probabilist Eng Mech 26(1):5–9 CrossRefMATH
Zurück zum Zitat Nie J, Ellingwood BR (2004) A new directional simulation method for system reliability. Part I: application of deterministic point sets. Probabilist Eng Mech 19(4):425–436 CrossRef Nie J, Ellingwood BR (2004) A new directional simulation method for system reliability. Part I: application of deterministic point sets. Probabilist Eng Mech 19(4):425–436 CrossRef
Zurück zum Zitat Robinson D, Atcitty C (1999) Comparison of quasi- and pseudo-Monte Carlo sampling for reliability and uncertainty analysis. In: Proceedings of the AIAA probabilistic methods conference, St. Louis, MO. AIAA99-1589. Robinson D, Atcitty C (1999) Comparison of quasi- and pseudo-Monte Carlo sampling for reliability and uncertainty analysis. In: Proceedings of the AIAA probabilistic methods conference, St. Louis, MO. AIAA99-1589.
Zurück zum Zitat Singh A, Mourelatos Z, Nikolaidis E (2011) Time-dependent reliability of random dynamic systems using time-series modeling and importance sampling. SAE Technical Paper Singh A, Mourelatos Z, Nikolaidis E (2011) Time-dependent reliability of random dynamic systems using time-series modeling and importance sampling. SAE Technical Paper
Zurück zum Zitat Song PY, Chen JB (2015) Point selection strategy based on minimizing GL2-discrepancy and its application to multi-dimensional integration. Chin Sci 45:547–558 (in Chinese) Song PY, Chen JB (2015) Point selection strategy based on minimizing GL2-discrepancy and its application to multi-dimensional integration. Chin Sci 45:547–558 (in Chinese)
Zurück zum Zitat Spanos PD, Kougioumtzoglou IA (2014) Survival probability determination of nonlinear oscillators subject to evolutionary stochastic excitation. J Appl Mech 81(5):051016 CrossRef Spanos PD, Kougioumtzoglou IA (2014) Survival probability determination of nonlinear oscillators subject to evolutionary stochastic excitation. J Appl Mech 81(5):051016 CrossRef
Zurück zum Zitat Tont G, Vladareanu L, Munteanu MS, Tont DG (2010) Markov approach of adaptive task assignment for robotic system in non-stationary environments. WSEAS Trans Circuits Syst 9(3):273–282 MATH Tont G, Vladareanu L, Munteanu MS, Tont DG (2010) Markov approach of adaptive task assignment for robotic system in non-stationary environments. WSEAS Trans Circuits Syst 9(3):273–282 MATH
Zurück zum Zitat van Noortwijk JM, van der Weide JA, Kallen M-J, Pandey MD (2007) Gamma processes and peaks-over-threshold distributions for time-dependent reliability. Reliab Eng Syst Safe 92(12):1651–1658 CrossRef van Noortwijk JM, van der Weide JA, Kallen M-J, Pandey MD (2007) Gamma processes and peaks-over-threshold distributions for time-dependent reliability. Reliab Eng Syst Safe 92(12):1651–1658 CrossRef
Zurück zum Zitat Vanmarcke EH (1975) On the distribution of the first-passage time for normal stationary random processes. J Appl Mech 42(1):215–220 CrossRefMATH Vanmarcke EH (1975) On the distribution of the first-passage time for normal stationary random processes. J Appl Mech 42(1):215–220 CrossRefMATH
Zurück zum Zitat Wang Z, Wang P (2012) Reliability-based product design with time-dependent performance deterioration. Prognostics and Health Management (PHM), 2012 I.E. Conference on, IEEE Wang Z, Wang P (2012) Reliability-based product design with time-dependent performance deterioration. Prognostics and Health Management (PHM), 2012 I.E. Conference on, IEEE
Zurück zum Zitat Wen Y-K (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102(2):249–263 Wen Y-K (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102(2):249–263
Zurück zum Zitat Xu J (2016) A new method for reliability assessment of structural dynamic systems with random parameters. Struct Saf 60:130–143 Xu J (2016) A new method for reliability assessment of structural dynamic systems with random parameters. Struct Saf 60:130–143
Zurück zum Zitat Xu J, Chen JB, Li J (2012) Probability density evolution analysis of engineering structures via cubature points. Comput Mech 50(1):135–156 MathSciNetCrossRefMATH Xu J, Chen JB, Li J (2012) Probability density evolution analysis of engineering structures via cubature points. Comput Mech 50(1):135–156 MathSciNetCrossRefMATH
Zurück zum Zitat Xu J, Zhang W, Sun R (2016) Efficient reliability assessment of structural dynamic systems with unequal weighted quasi-Monte Carlo simulation. Comput Struct 175:37–51 CrossRef Xu J, Zhang W, Sun R (2016) Efficient reliability assessment of structural dynamic systems with unequal weighted quasi-Monte Carlo simulation. Comput Struct 175:37–51 CrossRef
Zurück zum Zitat Xu J, Dang C, Kong F (2017) Efficient reliability analysis of structures with the rotational quasi-symmetric point- and the maximum entropy methods. Mech Syst Signal Process 95:58–76 CrossRef Xu J, Dang C, Kong F (2017) Efficient reliability analysis of structures with the rotational quasi-symmetric point- and the maximum entropy methods. Mech Syst Signal Process 95:58–76 CrossRef
Zurück zum Zitat Zhang X, Pandey MD (2013) Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method. Struct Saf 43:28–40 CrossRef Zhang X, Pandey MD (2013) Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method. Struct Saf 43:28–40 CrossRef
Zurück zum Zitat Zhang H, Dai H, Beer M, Wang W (2013) Structural reliability analysis on the basis of small samples: an interval quasi-Monte Carlo method. Mech Syst Signal Process 37(1):137–151 CrossRef Zhang H, Dai H, Beer M, Wang W (2013) Structural reliability analysis on the basis of small samples: an interval quasi-Monte Carlo method. Mech Syst Signal Process 37(1):137–151 CrossRef
Zurück zum Zitat Zhang X, Pandey MD, Zhang Y (2014) Computationally efficient reliability analysis of mechanisms based on a multiplicative dimensional reduction method. J Mech Des 136(6):061006 CrossRef Zhang X, Pandey MD, Zhang Y (2014) Computationally efficient reliability analysis of mechanisms based on a multiplicative dimensional reduction method. J Mech Des 136(6):061006 CrossRef
Metadaten
Titel
A two-step methodology to apply low-discrepancy sequences in reliability assessment of structural dynamic systems
verfasst von
Jun Xu
Ding Wang
Publikationsdatum
26.10.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 4/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-017-1834-x

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