Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation

MITSEAS, Ioannis P.;KOUGIOUMTZOGLOU, Ioannis A.;SPANOS, Pol D.;BEER, Michael .
Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation. 
Strojniški vestnik - Journal of Mechanical Engineering, [S.l.], v. 62, n.7-8, p. 440-451, june 2018. 
ISSN 0039-2480.
Available at: <https://www.sv-jme.eu/article/nonlinear-mdof-system-survival-probability-determination-subject-to-evolutionary-stochastic-excitation/>. Date accessed: 04 feb. 2026. 
doi:http://dx.doi.org/10.5545/sv-jme.2016.3752.

Mitseas, I., Kougioumtzoglou, I., Spanos, P., & Beer, M.
(2016).
Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation.
Strojniški vestnik - Journal of Mechanical Engineering, 62(7-8), 440-451.
doi:http://dx.doi.org/10.5545/sv-jme.2016.3752

@article{sv-jmesv-jme.2016.3752,
	author = {Ioannis P. Mitseas and Ioannis A. Kougioumtzoglou and Pol D. Spanos and Michael  Beer},
	title = {Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {62},
	number = {7-8},
	year = {2016},
	keywords = {first-passage problem; nonlinear stochastic dynamics; evolutionary stochastic processes; nonlinear/hysteretic systems; survival probability},
	abstract = {An approximate technique for assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) oscillators. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are determined. Overall, the developed technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF system exhibiting hysteresis following the Bouc-Wen model is included in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the accuracy of the technique.},
	issn = {0039-2480},	pages = {440-451},	doi = {10.5545/sv-jme.2016.3752},
	url = {https://www.sv-jme.eu/article/nonlinear-mdof-system-survival-probability-determination-subject-to-evolutionary-stochastic-excitation/}
}

Mitseas, I.,Kougioumtzoglou, I.,Spanos, P.,Beer, M.
2016 June 62. Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation. Strojniški vestnik - Journal of Mechanical Engineering. [Online] 62:7-8

%A Mitseas, Ioannis P.
%A Kougioumtzoglou, Ioannis A.
%A Spanos, Pol D.
%A Beer, Michael 
%D 2016
%T Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation
%B 2016
%9 first-passage problem; nonlinear stochastic dynamics; evolutionary stochastic processes; nonlinear/hysteretic systems; survival probability
%! Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation
%K first-passage problem; nonlinear stochastic dynamics; evolutionary stochastic processes; nonlinear/hysteretic systems; survival probability
%X An approximate technique for assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) oscillators. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are determined. Overall, the developed technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF system exhibiting hysteresis following the Bouc-Wen model is included in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the accuracy of the technique.
%U https://www.sv-jme.eu/article/nonlinear-mdof-system-survival-probability-determination-subject-to-evolutionary-stochastic-excitation/
%0 Journal Article
%R 10.5545/sv-jme.2016.3752
%& 440
%P 12
%J Strojniški vestnik - Journal of Mechanical Engineering
%V 62
%N 7-8
%@ 0039-2480
%8 2018-06-27
%7 2018-06-27

Mitseas, Ioannis, Ioannis A. Kougioumtzoglou, Pol D. Spanos, & Michael  Beer.
"Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation." Strojniški vestnik - Journal of Mechanical Engineering [Online], 62.7-8 (2016): 440-451. Web.  04 Feb. 2026

TY  - JOUR
AU  - Mitseas, Ioannis P.
AU  - Kougioumtzoglou, Ioannis A.
AU  - Spanos, Pol D.
AU  - Beer, Michael 
PY  - 2016
TI  - Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation
JF  - Strojniški vestnik - Journal of Mechanical Engineering
DO  - 10.5545/sv-jme.2016.3752
KW  - first-passage problem; nonlinear stochastic dynamics; evolutionary stochastic processes; nonlinear/hysteretic systems; survival probability
N2  - An approximate technique for assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) oscillators. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are determined. Overall, the developed technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF system exhibiting hysteresis following the Bouc-Wen model is included in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the accuracy of the technique.
UR  - https://www.sv-jme.eu/article/nonlinear-mdof-system-survival-probability-determination-subject-to-evolutionary-stochastic-excitation/

@article{{sv-jme}{sv-jme.2016.3752},
	author = {Mitseas, I., Kougioumtzoglou, I., Spanos, P., Beer, M.},
	title = {Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {62},
	number = {7-8},
	year = {2016},
	doi = {10.5545/sv-jme.2016.3752},
	url = {https://www.sv-jme.eu/article/nonlinear-mdof-system-survival-probability-determination-subject-to-evolutionary-stochastic-excitation/}
}

TY  - JOUR
AU  - Mitseas, Ioannis P.
AU  - Kougioumtzoglou, Ioannis A.
AU  - Spanos, Pol D.
AU  - Beer, Michael 
PY  - 2018/06/27
TI  - Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation
JF  - Strojniški vestnik - Journal of Mechanical Engineering; Vol 62, No 7-8 (2016): Strojniški vestnik - Journal of Mechanical Engineering
DO  - 10.5545/sv-jme.2016.3752
KW  - first-passage problem, nonlinear stochastic dynamics, evolutionary stochastic processes, nonlinear/hysteretic systems, survival probability
N2  - An approximate technique for assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) oscillators. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are determined. Overall, the developed technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF system exhibiting hysteresis following the Bouc-Wen model is included in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the accuracy of the technique.
UR  - https://www.sv-jme.eu/article/nonlinear-mdof-system-survival-probability-determination-subject-to-evolutionary-stochastic-excitation/

Mitseas, Ioannis, Kougioumtzoglou, Ioannis, Spanos, Pol, AND Beer, Michael.
"Nonlinear MDOF System Survival Probability Determination Subject to Evolutionary Stochastic Excitation" Strojniški vestnik - Journal of Mechanical Engineering [Online], Volume 62 Number 7-8 (27 June 2018)