First passage of stochastic fractional derivative systems with power-form restoring force
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.
Keywords:
Stochastic averaging method / Power-form restoring force / Fractional derivative / First-passage failureSource:
International Journal of Non-Linear Mechanics, 2015, 71, 83-88Publisher:
- Pergamon-Elsevier Science Ltd, Oxford
Funding / projects:
- National Natural Science Foundation of China [11302157, 11202155]
- National Natural Science Foundation of Fujian Province [2014J01014]
- Fundamental Research Funds for the Central Universities [K5051370008]
- Chinese-Serbian Science and Technology Cooperation [2-14]
- Program for New Century Excellent Talents in University [NCET-10-0665]
Note:
- Peer reviewed version of the paper: https://machinery.mas.bg.ac.rs/handle/123456789/3932
Related info:
DOI: 10.1016/j.ijnonlinmec.2015.02.002
ISSN: 0020-7462
WoS: 000351962000010
Scopus: 2-s2.0-84925855755
Collections
Institution/Community
Mašinski fakultetTY - 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 . .