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Sensitivity based reduced approaches for structural reliability analysis. (English) Zbl 1202.90093

Summary: In the reliability analysis of a complex engineering structures a very large number of system parameters can be considered to be random variables. The difficulty in computing the failure probability increases rapidly with the number of variables. In this paper, a few methods are proposed whereby the number of variables can be reduced without compromising the accuracy of the reliability calculation. Based on the sensitivity of the failure surface, three new reduction methods, namely (a) gradient iteration method, (b) dominant gradient method, and (c) relative importance variable method, have been proposed. Numerical examples are provided to illustrate the proposed methods.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
90C31 Sensitivity, stability, parametric optimization
90C59 Approximation methods and heuristics in mathematical programming

References:

[1] Adhikari S 2004 Reliability analysis using parabolic failure surface approximation. J. Eng. Mech. ASCE 130: 1407–1427 · doi:10.1061/(ASCE)0733-9399(2004)130:12(1407)
[2] Adhikari S 2005 Asymptotic distribution method for structural reliability analysis in high dimensions. Proceedings of the Royal Society of London, Series-A 461: 3141–3158 · Zbl 1206.74014 · doi:10.1098/rspa.2005.1504
[3] Adhikari S, Manohar C S 1999 Dynamic analysis of framed structures with statistical uncertainties. Int. J. Numerical Methods in Eng. 44: 1157–1178 · Zbl 0928.74041 · doi:10.1002/(SICI)1097-0207(19990320)44:8<1157::AID-NME549>3.0.CO;2-5
[4] Adhikari S, Manohar C S 2000 Transient dynamics of stochastically parametered beams. J. Eng. Mech. ASCE 126: 1131–1140 · doi:10.1061/(ASCE)0733-9399(2000)126:11(1131)
[5] Augusti G, Baratta A, Casciati F 1984 Probabilistic Methods in Structural Engineering (London, UK: Chapman and Hall) · Zbl 0562.73078
[6] Bucher C G 1988 Adaptive sampling – an iterative fast Monte Carlo procedure. Structural Safety 5: 119–126 · doi:10.1016/0167-4730(88)90020-3
[7] Bucher C G, Bourgund U 1990 A fast and efficient response surface approach for structural reliability problem. Structural Safety 7: 57–66 · doi:10.1016/0167-4730(90)90012-E
[8] Cai G Q, Elishakoff I 1994 Refined second-order reliability analysis. Structural Safety 14: 267–276 · doi:10.1016/0167-4730(94)90015-9
[9] Chapman O J, Crossland A D 1995 Neural networks in probabilistic structural mechanics, 317–330. Probabilistic structural mechanics handbook (New York, USA: Chapman & Hall)
[10] Deng L, Ghosn M, Shao S 2005 Development of a shredding genetic algorithm for structural reliability. Structural Safety 27: 113–131 · doi:10.1016/j.strusafe.2004.06.002
[11] Der-Kiureghian A, Lin H Z, Hwang S J 1987 Second-order reliability approximations. J. Eng. Mech. ASCE 113: 1208–1225 · doi:10.1061/(ASCE)0733-9399(1987)113:8(1208)
[12] Der-Kiureghian A, Stefano M D 1991 Efficient algorithm for second order reliability analysis. J. Eng. Mech. ASCE 117: 2904–2923 · doi:10.1061/(ASCE)0733-9399(1991)117:12(2904)
[13] Ditlevsen O, Madsen H O 1996 Structural Reliability Methods (Chichester, West Sussex, England: John Wiley and Sons Ltd)
[14] Faravelli L 1989 Response-surface approach for reliability analysis. J. Eng. Mech. ASCE 115:2763–2781 · doi:10.1061/(ASCE)0733-9399(1989)115:12(2763)
[15] Fiessler B, Neumann H J, Rackwitz R 1979 Quadratic limit states in structural reliability. J. Eng. Mech. Division, Proceedings of the ASCE 105: 661–676
[16] Ghanem R, Spanos P 1991 Stochastic Finite Elements: A Spectral Approach (New York, USA: Springer-Verlag) · Zbl 0722.73080
[17] Grandhi R V, Wang L P 1999 Higher-order failure probability calculation using nonlinear approximations. Computer Methods in Applied Mechanics and Engineering 168: 185–206 · Zbl 0955.74058 · doi:10.1016/S0045-7825(98)00140-6
[18] Gupta S, Manohar C S 2004a An improved response surface method for the determination of failure probability and importance measures. Structural Safety 26: 123–139 · doi:10.1016/S0167-4730(03)00021-3
[19] Gupta S, Manohar C S 2004b Improved response surface method for time variant reliability analysis of nonlinear random structures under nonstationary excitations. Structural Safety 36: 267–280 · Zbl 1157.74309
[20] Haldar A, Mahadevan S 2000 Reliability Assessment Using Stochastic Finite Element Analysis (New York, USA: John Wiley and Sons)
[21] Hasofer A M, Lind N C 1974 Exact and invariant second moment code format. J. Eng. Mech. Division, Proceedings of the ASCE 100: 111–121
[22] Haukaas T, Kiureghian A D 2005 Parameter sensitivity and importance measures in nonlinear finite element reliability analysis. J. Eng. Mech. ASCE 131: 1013–1026 · doi:10.1061/(ASCE)0733-9399(2005)131:10(1013)
[23] Haukaas T, Kiureghian A D 2006 Strategies for finding the design point in nonlinear finite element reliability analysis. Probabilistic Eng. Mech. 21: 133–147 · doi:10.1016/j.probengmech.2005.07.005
[24] Hohenbichler M, Rackwitz R 1988 Improvement of second-order reliability estimates by importance sampling. J. Eng. Mech. ASCE 14: 2195–2199 · doi:10.1061/(ASCE)0733-9399(1988)114:12(2195)
[25] Hong H P 1999 Simple approximations for improving second-order reliability estimates. J. Eng. Mech. ASCE 125: 592–595 · doi:10.1061/(ASCE)0733-9399(1999)125:5(592)
[26] Hurtado J E 2002 Analysis of one-dimensional stochastic finite elements using neural networks. Probabilistic Eng. Mech. 17: 35–44 · doi:10.1016/S0266-8920(01)00011-X
[27] Kleiber M, Hien T D 1992 The Stochastic Finite Element Method (Chichester: John Wiley) · Zbl 0902.73004
[28] Koutsourelakis P S 2004 Reliability of structures in high dimensions, Part II: Theoretical validation. Probabilistic Eng. Mech. 19: 426–433
[29] Koutsourelakis P S, Pradlwarter H J, Schuëller G I 2004 Reliability of structures in high dimensions, Part I: Algorithms and applications. Probabilistic Eng. Mech. 19: 419–427 · doi:10.1016/j.probengmech.2004.05.002
[30] Köylüoǧglu H U, Nielsen S R K 1994 New approximations for SORM integrals. Structural Safety 13:235–246 · doi:10.1016/0167-4730(94)90031-0
[31] Madsen H O 1988 Omission sensitivity factors. Structural Safety 5: 35–45 · doi:10.1016/0167-4730(88)90004-5
[32] Madsen H O, Krenk S, Lind N C 1986 Methods of Structural Safety (Englewood Cliffs, NJ 07632: Prentice-Hall Inc.)
[33] Mahadevan S, Raghothamachar P 2000 Adaptive simulation for system reliability analysis of large structures. Computer and Structures 77: 725–734 · doi:10.1016/S0045-7949(00)00013-4
[34] Mahadevan S, Shi P 2001 Multiple linearization method for nonlinear reliability analysis. J. Eng. Mech.-ASCE 127: 1165–1173 · doi:10.1061/(ASCE)0733-9399(2001)127:11(1165)
[35] Manohar C S, Adhikari S 1998a Dynamic stiffness of randomly parametered beams. Probabilistic Eng. Mech. 13: 39–51 · doi:10.1016/S0266-8920(97)00006-4
[36] Manohar C S, Adhikari S 1998b Statistical analysis of vibration energy flow in randomly parametered trusses. J. Sound and Vib. 217: 43–74 · doi:10.1006/jsvi.1998.1744
[37] Manohar C S, Gupta S 2003 Modelling and evaluation of structural reliability: Current status and future directions. In K S Jagadish, R N Iyengar (eds.), Research reviews in structural engineering, Golden Jubilee Publications of Department of Civil Engineering, Indian Institute of Science, Bangalore (University Press)
[38] Matthies H G, Brenner C E, Bucher C G, Soares C G 1997 Uncertainties in probabilistic numerical analysis of structures and solids – Stochastic finite elements. Structural Safety 19: 283–336 · doi:10.1016/S0167-4730(97)00013-1
[39] Melchers R E 1999 Structural Reliability Analysis and Prediction. 2nd edition (Chichester, West Sussex, England: John Wiley and Sons Ltd)
[40] Penmetsa R, Grandhi R 2002a Efficient estimation of structural reliability for problems with uncertain intervals. Computers and Structures 80: 1103–1112 · doi:10.1016/S0045-7949(02)00069-X
[41] Penmetsa R, Grandhi R 2002b Structural system reliability quantification using multipoint function approximations. AIAA J. 40: 2526–2531 · doi:10.2514/2.1597
[42] Penmetsa R C, Grandhi R V 2003 Adaptation of fast Fourier transformations to estimate structural failure probability. Finite Elements in Analysis and Design 39: 473–485 · doi:10.1016/S0168-874X(02)00104-X
[43] Polidori D C, Beck J L, Papadimitriou C 1999 New approximations for reliability integrals. J. Eng. Mech. ASCE 125: 466–475 · doi:10.1061/(ASCE)0733-9399(1999)125:4(466)
[44] Rackwitz R, Fiessler B 1978 Structural reliability under combined random load sequences. J. Computers and Structures 9: 489–494 · Zbl 0402.73071 · doi:10.1016/0045-7949(78)90046-9
[45] Rosenblatt M 1952 Remarks on a multivariate transformation. The Annals of Mathematical Statistics 23: 470–472 · Zbl 0047.13104 · doi:10.1214/aoms/1177729394
[46] Schuëller G I, Pradlwarter H J, Koutsourelakis P S 2004 A critical appraisal of reliability estimation procedures for high dimensions. Probabilistic Eng. Mech. 19: 465–477
[47] Schuëller G I, Stix R 1987 A critical appraisal of methods to determine failure probabilities. Structural Safety 4: 293–309 · doi:10.1016/0167-4730(87)90004-X
[48] Shao S, Murotsu Y 1999 Approach to failure mode analysis of large structures. Probabilistic Eng. Mech. 14: 169–177 · doi:10.1016/S0266-8920(98)00028-9
[49] Sudret B, Der-Kiureghian A 2000 Stochastic Finite Element Methods and Reliability. Technical Report UCB/SEMM-2000/08, Department of Civil and Environmental Engineering, University of California, Berkeley
[50] Thoft-Christensen P, Baker M J 1982 Structural Reliability Theory and its Applications (Berlin, Germany: Springer-Verlag) · Zbl 0495.73078
[51] Tichy M 1993 Applied Methods of Structural Reliability (Dordrecht, The Netherlands: Kluwer Academic Publishers) · Zbl 0842.00007
[52] Tvedt L 1990 Distribution of quadratic forms in normal space: application to structural reliability. J. Eng. Mech. ASCE 116: 1183–1197 · doi:10.1061/(ASCE)0733-9399(1990)116:6(1183)
[53] Wang L P, Grandhi R V 1996 Safety index calculation using intervening variables for structural reliability analysis. Computer and Structures 59: 1139–1148 · Zbl 0919.73193 · doi:10.1016/0045-7949(96)00291-X
[54] Zhao Y G, Ono T 1999a New approximations for SORM: Part 1. J. Eng. Mech. ASCE 125: 79–85 · doi:10.1061/(ASCE)0733-9399(1999)125:1(79)
[55] Zhao Y G, Ono T 1999b New approximations for SORM: Part 2. J. Eng. Mech. ASCE 125: 86–93 · doi:10.1061/(ASCE)0733-9399(1999)125:1(86)
[56] Zona A, Barbato M, Conte J P 2005 Finite element response sensitivity analysis of steel-concrete composite beams with deformable shear connection. J. Eng. Mech. ASCE 131: 1126–1139 · doi:10.1061/(ASCE)0733-9399(2005)131:11(1126)
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