Naess Arvid
Faculty of Civil Engineering, The Norwegian Institute of Technology, Rich. Birkelands vci la, N-7034 Trondheim, Norway.
J Res Natl Inst Stand Technol. 1994 Jul-Aug;99(4):465-474. doi: 10.6028/jres.099.044.
This paper studies the applicability of the path integral solution technique for estimating extreme response of nonlinear dynamic oscillators whose equations of motion can be modelled by the use of Itô stochastic differential equations. The state vector process associated with such a model is generally a diffusion process, and the probability density function of the state vector thus satisfies the Fokker-Planck-Kolmogorov equation. It is shown that the path integral solution technique combined with an appropriate numerical scheme constitutes a powerful method for solving the Fokker-Planck Kolmogorov equation with natural boundary conditions. With the calculated probability density function of the state vector in hand, one can proceed to calculate the required quantities for estimating extreme response. The proposed method distinguishes itself by remarkably high accuracy and numerical robustness. These features are highlighted by application to example studies of nonlinear oscillators excited by white noise.
本文研究路径积分求解技术在估计非线性动力振荡器极端响应方面的适用性，其运动方程可通过伊藤随机微分方程进行建模。与该模型相关的状态向量过程通常是一个扩散过程，因此状态向量的概率密度函数满足福克 - 普朗克 - 柯尔莫哥洛夫方程。结果表明，路径积分求解技术与适当的数值格式相结合，构成了一种求解具有自然边界条件的福克 - 普朗克 - 柯尔莫哥洛夫方程的强大方法。有了计算出的状态向量概率密度函数，就可以着手计算估计极端响应所需的量。所提出的方法以极高的精度和数值稳健性脱颖而出。通过应用于白噪声激励的非线性振荡器的实例研究，突出了这些特性。
