Approximation for the First Passage Probability of Systems Under Nonstationary Random Excitation
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摘要: 提出了非平稳Gauss白噪声激励下线性系统条件首次穿越概率的近似解析解.该近似解基于VanMarcke 近似,但是,因为引进了随机过程和界限水平的标准化,VanMarcke 公式中的期望衰减率可由响应的二阶统计矩获得,而不需要知道响应的相关函数或谱密度函数.给出了非平稳激励下线性系统响应的显式二阶统计矩.调制白噪声激励下单自由度线性系统的首次穿越概率分析说明了该方法的精度、效率和应用过程.Abstract: An approximate method is presented for obtaining analytical solutions for the conditional fast passage piubability of systems under modulated white noise excitation, the method is based on VanMarcke's approximation, however, because the normalization of the response was introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered stnrcrures. Explicit solutions for the second-moment statistics of the response were given. The accuracy, efficiency and usage of the proposed method were demonstrated by the fast passage analysis of single-degree-of freedom (SDOF) linear systems under two special types of modulated white noise excitations.
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Key words:
- first passage probability /
- D-type barrier /
- decay rate /
- nonstationary excitation /
- envelope Process
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