\شماره٪٪۱
Chen, G. and Yang, D. ``Direct probability integral method
for stochastic response analysis of static and dynamic structural
systems'', {\it Comput. Methods Appl. Mech. Eng}, {\bf 357},
p. 112612 (2019).
\شماره٪٪۲
Dodwell, T.J., Kynaston, S., Butler, R. and et al.
``Multilevel monte carlo simulations of
composite structures with uncertain manufacturing defects'', {\it Probabilistic
Eng. Mech}, {\bf 63}, p. 103116 (2021).
\شماره٪٪۳
Yun, W., Lu, Z., Wang, L. and et al. ``Error-based
stopping criterion for the combined adaptive Kriging and importance
sampling method for reliability analysis'', {\it Probabilistic Eng.
Mech}, {\bf 65}, p. 103131 (2021).
\شماره٪٪۴
Guo, Q., Liu, Y., Chen, B. and et al. ``An active learning
Kriging model combined with directional importance sampling method
for efficient reliability analysis'', {\it Probabilistic Eng. Mech}, {\bf 60},
p. 103054 (2020).
\شماره٪٪۵
Xu, Z., Cao, J., Zhang, G. and et al. ``Active learning
accelerated Monte-Carlo simulation based on the modified K-nearest
neighbors algorithm and its application to reliability estimations'', Def
Technol (In Press) (2022).
\شماره٪٪۶
Betz, W., Papaioannou, I. and Straub, D. ``Bayesian post-processing
of monte carlo simulation in reliability analysis'', {\it Reliab. Eng.
Syst. Saf}, {\bf 227}, p. 108731 (2022).
\شماره٪٪۷
Xiao, S. and Nowak, W. ``Reliability sensitivity analysis based
on a two-stage Markov chain Monte Carlo simulation'', {\it Aerosp.
Sci. Technol}, {\bf 130}, p. 107938 (2022).
\شماره٪٪۸
Rahgozar, N., Pouraminian, M. and Rahgozar, N. ``Reliability-based
seismic assessment of controlled rocking steel cores'', {\it J. Build.
Eng}, {\bf 44}, p. 102623 (2021).
\شماره٪٪۹
Pouraminian, M. and Ekranejad, H. ``Reliability analysis of
concrete arch dam under stage construction and hydrostatic pressure
by MCS and RS methods'', {\it Sharif J. Civ. Eng}, {\bf 37.2}(3.2-3), pp.
135-145 (2021).
\شماره٪٪۱۰
Bjerager, P. ``Probability integration by directional simulation'', {\it J.
Eng. Mech}, {\bf 114}(8), pp. 1285-1302 (1988).
\شماره٪٪۱۱
Engelund, S. and Rackwitz, R. ``A benchmark study on importance
sampling techniques in structural reliability'', {\it Struct. Saf}, {\bf
12}(4),
pp. 255-276 (1993).
\شماره٪٪۱۲
Hsu, W.C. and Ching, J. ``Evaluating small failure probabilities
of multiple limit states by parallel subset simulation'', {\it Probabilistic
Eng. Mech}, {\bf 25}(3), pp. 291-304 (2010).
\شماره٪٪۱۳
Au, S.-K. and Beck, J.L. ``Estimation of small failure probabilities
in high dimensions by subset simulation'', {\it Probabilistic Eng.
Mech}, {\bf 16}(4), pp. 263-277 (2001).
\شماره٪٪۱۴
Breitung, K. ``40 years FORM: Some new aspects'', {\it Probabilistic
Eng. Mech}, 42, pp. 71-77 (2015).
\شماره٪٪۱۵
Xiang, Y. and Liu, Y. ``Application of inverse first-order
reliability method for probabilistic fatigue life prediction'',
{\it Probabilistic
Eng. Mech}, {\bf 26}(2), pp. 148-156 (2015).
\شماره٪٪۱۶
Zhao, Y.G., Zhang, X.Y. and Lu, ZH. ``Complete monotonic
expression of the fourth-moment normal transformation for structural
reliability'', {\it Comput. Struct}, {\bf 196}, pp. 186-199 (2018).
\شماره٪٪۱۷
Lutes, L.D. and Winterstein, S.R. ``A dynamic inverse FORM
method: Design contours for load combination problems'', {\it Probabilistic
Eng. Mech}, {\bf 44}, pp. 118-127 (2016).
\شماره٪٪۱۸
Hasofer, A.M. and Lind, N.C. ``Exact and invariant second-moment
code format'', {\it J. Eng. Mech. Div}, {\bf 100}(1), pp. 111-121 (1974).
\شماره٪٪۱۹
Rackwitz, R. and Flessler, B. ``Structural reliability under
combined random load sequences'', {\it Comput. Struct}, {\bf
9}(5), pp. 489-494
(1978).
\شماره٪٪۲۰
Zhang, Y. and Kiureghian, A. ``Two improved algorithms for
reliability analysis'', Reliab. Optim. Struct. Syst., Boston,
MA: Springer US, pp. 297-304 (1995).
\شماره٪٪۲۱
Santos, S.R., Matioli, L.C. and Beck, A.T. ``New optimization
algorithms for structural reliability analysis'', {\it C - Comput.
Model Eng. Sci}, {\bf 83}, pp. 23-55 (2012).
\شماره٪٪۲۲
Roudak, M.A., Shayanfar, M.A. and Karamloo, M. ``Improvement
in first-order reliability method using an adaptive chaos control
factor'', {\it Structures}, {\bf 16}, pp. 150-156 (2018).
\شماره٪٪۲۳
Meng, Z., Li, G., Yang, D. and et al. ``A new directional
stability transformation method of chaos control for first order
reliability analysis'', {\it Struct. Multidiscip. Optim}, {\bf
55}, pp. 601-612
(2017).
\شماره٪٪۲۴
Gong, J.-XX and Yi, P. ``A robust iterative algorithm for
structural reliability analysis'', {\it Struct. Multidiscip. Optim}, {\bf
43}(4),
pp. 519-527 (2011).
\شماره٪٪۲۵
Keshtegar, B. ``A hybrid conjugate finite-step length method
for robust and efficient reliability analysis'', {\it Appl. Math. Model},
{\bf 45},
pp. 226-237 (2017).
\شماره٪٪۲۶
Wang, X., Zhao, W., Chen, Y. and et al. ``A first order reliability
method based on hybrid conjugate approach with adaptive Barzilai-Borwein
steps'', {\it Comput. Methods Appl. Mech. Eng}, {\bf 401}, 115670 (2022).
\شماره٪٪۲۷
Liu, P.L. and Der Kiureghian, A. ``Optimization algorithms
for structural reliability'', {\it Struct. Saf},
{\bf 9}(3), pp. 161-177 (1991).
\شماره٪٪۲۸
Lalee, M., Nocedal, J. and Plantenga, T. ``On the implementation
of an algorithm for large-scale equality constrained optimization'', {\it SIAM
J. Optim}, {\bf 8}(3), pp. 682-706 (1998).
\شماره٪٪۲۹
Schittkowski, K. ``A robust implementation of a sequential
quadratic programming algorithm with successive error restoration'', {\it
Optim.
Lett}, {\bf 5}, pp. 283-296 (2011).
\شماره٪٪۳۰
Byrd, R.H., Hribar, M.E. and Nocedal, J. ``An interior point
algorithm for large-scale nonlinear programming'', {\it SIAM J. Optim},
{\bf 9}(4),
pp. 877-900 (1999).
\شماره٪٪۳۱
Schittkowski, K. ``The nonlinear programming method of Wilson,
Han, and powell with an augmented Lagrangian type line search
function - Part 2: An efficient implementation with linear least
squares subproblems'', {\it Numer. Math}, {\bf 38}, pp. 115-127 (1982).
\شماره٪٪۳۲
Kraft, D. ``A software package for sequential quadratic programming'',
Koln, 88 (1988).
\شماره٪٪۳۳
Lawson, C.L., Lawson, C.L. and Hanson, R.J. ``Solving least
squares problems'', Prentice-Hall (1974).
\شماره٪٪۳۴
Rashki, M. ``Structural reliability reformulation'', {\it Struct.
Saf}, {\bf 88}, p. 102006 (2021).
\شماره٪٪۳۵
Kang, S.B., Park, J.W. and Lee, I. ``Accuracy improvement
of the most probable point-based dimension reduction method using
the hessian matrix'', {\it Int. J. Numer. Methods Eng}, {\bf 111}(3), pp.
203-217 (2017).
\شماره٪٪۳۶
Yang, M., Zhang, D. and Han, X. ``New efficient and robust
method for structural reliability analysis and its application
in reliability-based design optimization'', {\it Comput. Methods Appl.
Mech. Eng}, {\bf 366}, p. 113018 (2020).
\شماره٪٪۳۷
Roudak, M.A. and Karamloo, M. ``Establishment of non-negative
constraint method as a robust and efficient first-order reliability
method'', {\it Appl. Math. Model}, {\bf 68}, pp. 281-305 (2019).
\شماره٪٪۳۸
Jiang, C., Han, S., Ji, M. and et al. ``A new method to
solve the structural reliability index based on homotopy analysis'', {\it Acta
Mech}, {\bf 226}, pp. 1067-1083 (2015).
\شماره٪٪۳۹
Zhao, Y.-G. and Ono, T. ``New point estimates for probability
moments'', {\it J. Eng. Mech}, {\bf 126}, pp. 433-436 (2000).
\شماره٪٪۴۰
Huang, P., Huang, H.Z. and Huang, T. ``A novel algorithm
for structural reliability analysis based on finite step length
and Armijo line search'', {\it Appl. Sci}, {\bf 9}(12), p. 2546 (2019).
\شماره٪٪۴۱
Roudak, M.A., Shayanfar, M.A., Barkhordari, M.A. and et al.
``A robust approximation method for nonlinear cases of structural
reliability analysis'', {\it Int. J. Mech. Sci}, {\bf 133}, pp. 11-20 (2017).
\شماره٪٪۴۲
Gong, J., Yi, P. and Zhao, N. ``Non-gradient-based algorithm
for structural reliability analysis'', {\it J. Eng. Mech}, {\bf
140}(6), 04014029
(2014).
\شماره٪٪۴۳
Liu, B. and Xie, L. ``An improved structural reliability
analysis method based on local approximation and
parallelization'', {\it Mathematics},
{\bf 8}(2),
p. 209 (2020).
\شماره٪٪۴۴
Bichon, B.J., Eldred, M.S., Swiler, L.P. and et al.
``Efficient global reliability analysis for nonlinear
implicit performance functions'', {\it AIAA J}, {\bf 46}(10), pp. 2459-2468
(2008).
\شماره٪٪۴۵
Keshtegar, B. and Chakraborty, S. ``A hybrid self-adaptive
conjugate first order reliability method for robust structural
reliability analysis'', {\it Appl. Math. Model}, {\bf 53}, pp. 319-332 (2018).
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