| Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing–Rayleigh–Mathieu system |
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| 基金项目： | The work reported in this paper was supported by the Foundation of ECUST （East China University of Science and Technology） for Outstanding Young Teachers （YH0157105）. |
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| 摘 要： | The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.
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| 关 键 词： | 有色噪音 随机值 可靠性 统计学 |
| 收稿时间： | 2005-02-04 |
Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing-Rayleigh-Mathieu system |
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| Yongjun Wu,Wang Fang. Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing-Rayleigh-Mathieu system[J]. Acta Mechanica Sinica, 2008, 24(5): 575-582. DOI: 10.1007/s10409-008-0140-7 |
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| Authors: | Yongjun Wu Wang Fang |
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| Affiliation: | (1) Institute of Automation, School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China;(2) Hangzhou Yiheng Technologies Co., Ltd, 2F, 28 Wantang Road, Hangzhou, 310013, China |
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| Abstract: | The first-passage statistics of Duffing–Rayleigh–Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation. The work reported in this paper was supported by the Foundation of ECUST (East China University of Science and Technology) for Outstanding Young Teachers (YH0157105). |
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| Keywords: | First-passage Colored noise Stochastic averaging Reliability Monte Carlo simulation |
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