Vanvinckenroye, H., Andrianne, T., Denoël, V.: First passage time as an analysis tool in experimental wind engineering. J. Wind Eng. Ind. Aerodyn. 177, 366–375 (2018)
Tominaga, Y., Stathopoulos, T.: CFD simulation of near-field pollutant dispersion in the urban environment: a review of current modeling techniques. Atmos. Environ. 79, 716–730 (2013)
Andrianne, T., de Ville de Goyet, V.: Mitigation of the torsional flutter phenomenon of bridge deck section during a lifting phase. In: 8th International Colloquium on Bluff Body Aerodynamics and Applications, Northeastern University, Boston, Massachusetts, USA (2016)
Schuss, Z.: Theory and Applications of Stochastic Processes, Vol. 170 of Applied Mathematical Sciences. Springer, New York (2010)
Preumont, A.: Random Vibration and Spectral Analysis. Kluwer Academic Publishers, Dordrecht (1994)
Bergman, L.A., Heinrich, J.C.: On the moments of time to first passage of the linear oscillator. Earthq. Eng. Struct. Dyn. 9(3), 197–204 (1981)
Vanvinckenroye, H., Denoël, V.: Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations. J. Sound Vib. 406, 328–345 (2017)
Vanvinckenroye, H., Denoël, V.: Second-order moment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations. J. Sound Vib. 427, 178–187 (2018)
Lin, Y.K.Y.-K.: Probabilistic Theory of Structural Dynamics. R.E. Krieger Pub. Co, Malabar (1976)
Crandall, S.: First-crossing probabilities of the linear oscillator. J. Sound Vib. 12(3), 285–299 (1970)
Yang, J., Shinozuka, M.: First-passage time problem. J. Acoust. Soc. Am. 47(1B), 393–394 (1970)
Oksendal, B.: Stochastic Differential Equations: An Introduction with Applications-Fifth Edition, pp. 1–5 (2003)
Kovaleva, A.: An exact solution of the first-exit time problem for a class of structural systems. Probab. Eng. Mech. 24(3), 463–466 (2009)
Naess, A., Gaidai, O.: Monte Carlo methods for estimating the extreme response of dynamical systems. J. Eng. Mech. 134(8), 628–636 (2008)
Au, S.-K., Wang, Y.: Engineering risk assessment and design with subset simulation (2014)
Grigoriu, M.: Stochastic Calculus: Applications in Science and Engineering. Springer, Birkhäuser (2002)
Kougioumtzoglou, I.A., Zhang, Y., Beer, M.: Softening Duffing Oscillator Reliability assessment subject to evolutionary stochastic excitation. ASCE-ASME J. Risk Uncertain. Eng. Syst. Part A Civ. Eng. 2(2), C4015001 (2016)
Vanmarcke, E.H.: On the distribution of the first-passage time for normal stationary random processes. J. Appl. Mech. 42(1), 215 (1975)
Náprstek, J., Král, R.: Evolutionary analysis of Fokker–Planck equation using multi-dimensional Finite Element Method. Procedia Eng. 199, 735–740 (2017)
Coleman, J.J.: Reliability of aircraft structures in resisting chance failure. Oper. Res. 7(5), 639–645 (1959)
Kougioumtzoglou, I.A., Spanos, P.D.: Stochastic response analysis of the softening Duffing oscillator and ship capsizing probability determination via a numerical path integral approach. Probab. Eng. Mech. 35, 67–74 (2014)
Zhang, Y., Kougioumtzoglou, I.A.: Nonlinear oscillator stochastic response and survival probability determination via the Wiener path integral. ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B Mech. Eng. 1(2), 021005 (2015)
Spanos, P.D., Kougioumtzoglou, I.A.: Galerkin scheme based determination of first-passage probability of nonlinear system response. Struct. Infrastruct. Eng. 10(10), 1285–1294 (2014)
Yurchenko, D., Mo, E., Naess, A.: Reliability of strongly nonlinear single degree of freedom dynamic systems by the path integration method. J. Appl. Mech. 75(6), 061016 (2008)
Li, J., Chen, J.: Stochastic Dynamics of Structures. Wiley, New York (2009)
Kougioumtzoglou, I., Spanos, P.: An approximate approach for nonlinear system response determination under evolutionary stochastic excitation. Curr. Sci. 97, 1203–1211 (2009)
Lin, Y., Cai, G.: Some thoughts on averaging techniques in stochastic dynamics. Probab. Eng. Mech. 15(1), 7–14 (2000)
Red-Horse, J., Spanos, P.: A generalization to stochastic averaging in random vibration. Int. J Non-Linear Mech. 27(1), 85–101 (1992)
Roberts, J.J., Spanos, P.P.: Stochastic averaging: an approximate method of solving random vibration problems. Int. J. Non-Linear Mech. 21(2), 111–134 (1986)
Zhu, W.Q.: Stochastic averaging methods in random vibration. Appl. Mech. Rev. 41(5), 189 (1988)
Proppe, C., Pradlwarter, H., Schuëller, G.: Equivalent linearization and Monte Carlo simulation in stochastic dynamics. Probab. Eng. Mech. 18(1), 1–15 (2003)
Socha, L.: Linearization Methods for Stochastic Dynamic Systems, pp. 1–5. Springer, Berlin (2008)
Roberts, J.B., Spanos, P.D.: Random Vibration and Statistical Linearization. Dover Publications, Mineola (2003)
Spanos, P.-T.D.: Numerics for common first-passage problem. J. Eng. Mech. Div. 108(5), 864–882 (1982)
Spanos, P.D., Di Matteo, A., Cheng, Y., Pirrotta, A., Li, J.: Galerkin scheme-based determination of survival probability of oscillators with fractional derivative elements. J. Appl. Mech. 83(12), 121003 (2016)
Di Matteo, A., Spanos, P.D., Pirrotta, A.: Approximate survival probability determination of hysteretic systems with fractional derivative elements. Probab. Eng. Mech. 54, 138–146 (2018)
Spanos, P., Solomos, G.P.: Barrier crossing due to transient excitation. J. Eng. Mech. 110(1), 20–36 (1984)
Canor, T., Caracoglia, L., Denoël, V.: Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization. Probab. Eng. Mech. 46, 1–17 (2016)
Luo, A.C.J., Huang, J.: Analytical period-3 motions to chaos in a hardening Duffing oscillator. Nonlinear Dyn. 73(3), 1905–1932 (2013)
Xu, Y., Li, Y., Liu, D., Jia, W., Huang, H.: Responses of Duffing oscillator with fractional damping and random phase. Nonlinear Dyn. 74(3), 745–753 (2013)
Spanos, P.D., Red-Horse, J.R.: Nonstationary solution in nonlinear random vibration. J. Eng. Mech. 114(11), 1929–1943 (1988)
Spanos, P.D., Kougioumtzoglou, I.A., dos Santos, K.R.M., Beck, A.T.: Stochastic averaging of nonlinear oscillators: Hilbert transform perspective. J. Eng. Mech. 144(2), 04017173 (2018)
Primožič, T.: Estimating expected first passage times using multilevel Monte Carlo algorithm, M.Sc. in Mathematical and Computational Finance University
Chunbiao, G., Bohou, X.: First-passage time of quasi-non-integrable-Hamiltonian system. Acta Mechanica Sinica 16(2), 183–192 (2000)
Liang, J., Chaudhuri, S.R., Shinozuka, M.: Simulation of nonstationary stochastic processes by spectral representation. J. Eng. Mech. 133(6), 616–627 (2007)
