TY  - JOUR
AU  - Li, Wei
AU  - Chen, Lincong
AU  - Trišović, Nataša
AU  - Cvetković, Aleksandar
AU  - Zhao, Junfeng
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3932
AB  - In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge wealdy to an Ito differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - International Journal of Non-Linear Mechanics
T1  - First passage of stochastic fractional derivative systems with power-form restoring force
EP  - 88
SP  - 83
VL  - 71
DO  - 10.1016/j.ijnonlinmec.2015.02.002
ER  - 

@article{
author = "Li, Wei and Chen, Lincong and Trišović, Nataša and Cvetković, Aleksandar and Zhao, Junfeng",
year = "2015",
abstract = "In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge wealdy to an Ito differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "International Journal of Non-Linear Mechanics",
title = "First passage of stochastic fractional derivative systems with power-form restoring force",
pages = "88-83",
volume = "71",
doi = "10.1016/j.ijnonlinmec.2015.02.002"
}

Li, W., Chen, L., Trišović, N., Cvetković, A.,& Zhao, J.. (2015). First passage of stochastic fractional derivative systems with power-form restoring force. in International Journal of Non-Linear Mechanics
Pergamon-Elsevier Science Ltd, Oxford., 71, 83-88.
https://doi.org/10.1016/j.ijnonlinmec.2015.02.002

Li W, Chen L, Trišović N, Cvetković A, Zhao J. First passage of stochastic fractional derivative systems with power-form restoring force. in International Journal of Non-Linear Mechanics. 2015;71:83-88.
doi:10.1016/j.ijnonlinmec.2015.02.002 .

Li, Wei, Chen, Lincong, Trišović, Nataša, Cvetković, Aleksandar, Zhao, Junfeng, "First passage of stochastic fractional derivative systems with power-form restoring force" in International Journal of Non-Linear Mechanics, 71 (2015):83-88,
https://doi.org/10.1016/j.ijnonlinmec.2015.02.002 . .

TY  - JOUR
AU  - Li, Wei
AU  - Chen, Lincong
AU  - Trišović, Nataša
AU  - Cvetković, Aleksandar
AU  - Zhao, Junfeng
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2197
AB  - In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge wealdy to an Ito differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - International Journal of Non-Linear Mechanics
T1  - First passage of stochastic fractional derivative systems with power-form restoring force
EP  - 88
SP  - 83
VL  - 71
DO  - 10.1016/j.ijnonlinmec.2015.02.002
ER  - 

@article{
author = "Li, Wei and Chen, Lincong and Trišović, Nataša and Cvetković, Aleksandar and Zhao, Junfeng",
year = "2015",
abstract = "In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge wealdy to an Ito differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "International Journal of Non-Linear Mechanics",
title = "First passage of stochastic fractional derivative systems with power-form restoring force",
pages = "88-83",
volume = "71",
doi = "10.1016/j.ijnonlinmec.2015.02.002"
}

Li, W., Chen, L., Trišović, N., Cvetković, A.,& Zhao, J.. (2015). First passage of stochastic fractional derivative systems with power-form restoring force. in International Journal of Non-Linear Mechanics
Pergamon-Elsevier Science Ltd, Oxford., 71, 83-88.
https://doi.org/10.1016/j.ijnonlinmec.2015.02.002

Li W, Chen L, Trišović N, Cvetković A, Zhao J. First passage of stochastic fractional derivative systems with power-form restoring force. in International Journal of Non-Linear Mechanics. 2015;71:83-88.
doi:10.1016/j.ijnonlinmec.2015.02.002 .

Li, Wei, Chen, Lincong, Trišović, Nataša, Cvetković, Aleksandar, Zhao, Junfeng, "First passage of stochastic fractional derivative systems with power-form restoring force" in International Journal of Non-Linear Mechanics, 71 (2015):83-88,
https://doi.org/10.1016/j.ijnonlinmec.2015.02.002 . .