Interval importance sampling method for finite element-based structural reliability assessment under parameter uncertainties

Der Kiureghian, 2009, Aleatory or epistemic? Does it matter?, Struct Saf, 31, 105, 10.1016/j.strusafe.2008.06.020 Der Kiureghian, 2008, Analysis of structural reliability under parameter uncertainties, Probab Eng Mech, 23, 351, 10.1016/j.probengmech.2007.10.011 Ellingwood, 2009, Quantifying and communicating uncertainty in seismic risk assessment, Struct Saf, 31, 179, 10.1016/j.strusafe.2008.06.001 Reid, 2009, Confidence and risk, Struct Saf, 31, 98, 10.1016/j.strusafe.2008.06.006 Ang, 2006 Ferson S, Kreinovich V, Ginzburg L, Myers DS, Sentz K. Constructing probability boxes and Dempster–Shafer structures. Tech. rep. SAND2002-4015, Sandia National Laboratories; 2003. Baudrit, 2008, Representing parametric probabilistic models tainted with imprecision, Fuzzy Sets Syst, 159, 1913, 10.1016/j.fss.2008.02.013 Limbourg, 2010, Uncertainty analysis using evidence theory-confronting level-1 and level-2 approaches with data availability and computational constraints, Reliab Eng Syst Saf, 95, 550, 10.1016/j.ress.2010.01.005 Walley, 1982, Towards a frequentist theory of upper and lower probability, Ann Stat, 10, 741, 10.1214/aos/1176345868 Walley, 1991 Oberkampf, 2004, Challenge problems: uncertainty in system response given uncertain parameters, Reliab Eng Syst Saf, 85, 11, 10.1016/j.ress.2004.03.002 Ferson, 2004, Summary from the epistemic uncertainty workshop: consensus amid diversity, Reliab Eng Syst Saf, 85, 355, 10.1016/j.ress.2004.03.023 Schweiger, 2005, Reliability analysis in geotechnics with the random set finite element method, Comput Geotech, 32, 422, 10.1016/j.compgeo.2005.07.002 Tonon, 2006, Using random set theory to calculate reliability bounds for a wing structure, Struct Infrastruct Eng, 2, 191, 10.1080/15732470600590689 Adduri, 2007, Bounds on structural system reliability in the presence of interval variables, Comput Struct, 85, 320, 10.1016/j.compstruc.2006.10.012 Oberguggenberger, 2008, Reliability bounds through random sets: non-parametric methods and geotechnical applications, Comput Struct, 86, 1093, 10.1016/j.compstruc.2007.05.040 Zhang, 2010, Interval Monte Carlo methods for structural reliability, Struct Saf, 32, 183, 10.1016/j.strusafe.2010.01.001 Williamson, 1990, Probabilistic arithmetic I: numerical methods for calculating convolutions and dependency bounds, Int J Approx Reason, 4, 89, 10.1016/0888-613X(90)90022-T Alvarez, 2006, On the calculation of the bounds of probability of events using infinite random sets, Int. J. Approx Reason, 43, 241, 10.1016/j.ijar.2006.04.005 Nie, 2005, Finite element-based structural reliability assessment using efficient directional simulation, J Eng Mech, ASCE, 131, 259, 10.1061/(ASCE)0733-9399(2005)131:3(259) Buonopane, 2006, Reliability of steel frames designed with advanced analysis, J Struct Eng, ASCE, 132, 267, 10.1061/(ASCE)0733-9445(2006)132:2(267) Moens, 2005, A survey of non-probabilistic uncertainty treatment in finite element analysis, Comput Methods Appl Mech Eng, 194, 1527, 10.1016/j.cma.2004.03.019 Zhang H. Nondeterministic linear static finite element analysis: an interval approach. PhD thesis, Georgia Institute of Technology, Atlanta, GA, USA; 2005. Koyluoglu, 1995, Interval algebra to deal with pattern loading and structural uncertainty, J Eng Mech, ASCE, 121, 1149, 10.1061/(ASCE)0733-9399(1995)121:11(1149) Dessombz, 2001, Analysis of mechanical systems using interval computations applied to finite elements methods, J Sound Vib, 238, 949, 10.1006/jsvi.2000.3191 Möller, 2004 Muhanna, 2007, Combined axial and bending stiffness in interval finite-element methods, J Struct Eng, ASCE, 133, 1700, 10.1061/(ASCE)0733-9445(2007)133:12(1700) Gao, 2007, Interval finite element analysis using interval factor method, Comput Mech, 39, 709, 10.1007/s00466-006-0055-8 Möller, 2000, Fuzzy structural analysis using level-optimization, Comput Mech, 26, 547, 10.1007/s004660000204 Berleant, 1993, Automatically verified reasoning with both intervals and probability density functions, Interval Comput, 48 Dubois, 1991, Random sets and fuzzy interval analysis, Fuzzy Sets Syst, 42, 87, 10.1016/0165-0114(91)90091-4 Tonon, 2004, Using random set theory to propagate epistemic uncertainty through a mechanical system, Reliab Eng Syst Saf, 85, 169, 10.1016/j.ress.2004.03.010 Zhang, 2012, Structural analysis with probability-boxes, Int J Reliab Saf, 6, 110, 10.1504/IJRS.2012.044292 Dempster, 1967, Upper and lower probabilities induced by a multi-valued mapping, Ann Mater Stat, 38, 325, 10.1214/aoms/1177698950 Au, 1999, A new adaptive importance sampling scheme for reliability calculations, Struct Saf, 21, 135, 10.1016/S0167-4730(99)00014-4 Melchers, 1990, Search-based importance sampling, Struct Saf, 9, 117, 10.1016/0167-4730(90)90003-8 Melchers, 1999 Haldar, 2000 Mazzoni, 2007