中文摘要：

结构的安全上的 Gaussian 白噪音刺激的效果在现在的纸由于在与两倍潜在的井未击中振荡器的安全的盆的侵蚀被学习。由采用开发得好的随机的 Melnikov 条件和蒙特卡罗方法，各种各样的侵蚀的盆在系统的确定、随机的盒子中被模仿，并且安全的起始的点(RSIP ) 的比率在系统的 Hamiltonian 为各种各样的参数或第一经过的时间定义的某给定的有限领域被介绍。噪音刺激什么时候在系统上被强加，被显示出结构的安全控制变得更困难，并且分数维的盆边界可以也出现系统什么时候仅仅由 Gaussian 白人噪音是激动的。从在给定的有限领域的 RSIP 结果，当系统由泛音或随机的力量是激动的时，在 RSIP 曲线的突然的不连续的降下可以发生，鉴于第一经过的问题，它与惯常的连续的不同。另外，发现价值能甚至与增加增加的那 RSIP 当 Gaussian 白噪音也是在系统的现在时，驾驶外部泛音刺激的振幅有趣。

英文摘要：

The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition and Monte-Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio of safe initial points （RSIP） is presented in some given limited domain defined by the system＇s Hamiltonian for various parameters or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited by harmonic or stochastic forces, which are different from the customary continuous ones in view of the firstpassage problems. In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external harmonic excitation when the Gaussian white noise is also present in the system.