演化功率谱解耦及其工程应用

摘要

为提高非平稳过程的模拟效率，简化非平稳激励下的结构响应分析，将演化功率谱解耦为一系列时间系数与小波函数傅里叶变换模平方乘积之和，即把一般非平稳过程分解为若干个均匀调制非平稳过程之和，并将其应用于非平稳随机过程模拟和结构随机响应分析。研究结果表明：演化功率谱近似解耦具有较高的精度；演化功率谱解耦后，快速傅里叶变换算法一般可使非平稳随机过程的模拟效率提高数十倍，且模拟样本时程的自相关函数估计值与目标值非常吻合；非平稳激励下的结构响应分析得以简化，且与目标值相比，计算结果的误差很小。%In order to improve the simulation efficiency of nonstationary processes and simplify the structural response analysis under nonstationary excitations, evolutionary power spectral density (EPSD)was approximately decoupled into the linear summation of products of the squared modulus of Fourier transform of wavelet function at different scales and associated time coefficients,i. e. ,a generally modulated nonstationary process was transformed into the summation of a number of uniformly modulated nonstationary processes. The decoupled EPSD was applied to engineering fields,including the simulation of nonstationary processes and the stochastic response analysis of structures. The research results show that the decoupled EPSD has a satisfactory accuracy. The simulation efficiency of nonstationary stochastic processes is generally improved for dozens of times by using the fast Fourier transform (FFT). The estimated autocorrelation function of simulated samples agrees very well with the target function. The stochastic response analysis of structures is simplified, and the calculated responses using the proposed method have small errors compared with the targets.