西南交通大学学报
西南交通大學學報
서남교통대학학보
JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY
2015年
2期
319-324,330
,共7页
彭留留%黄国庆%马存明%苏延文
彭留留%黃國慶%馬存明%囌延文
팽류류%황국경%마존명%소연문
演化功率谱%小波%非平稳过程模拟%快速傅里叶变换%随机响应分析
縯化功率譜%小波%非平穩過程模擬%快速傅裏葉變換%隨機響應分析
연화공솔보%소파%비평은과정모의%쾌속부리협변환%수궤향응분석
evolutionary power spectral density%wavelet%simulation of nonstationary process%fast Fourier transform%random response analysis
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。
為提高非平穩過程的模擬效率,簡化非平穩激勵下的結構響應分析,將縯化功率譜解耦為一繫列時間繫數與小波函數傅裏葉變換模平方乘積之和,即把一般非平穩過程分解為若榦箇均勻調製非平穩過程之和,併將其應用于非平穩隨機過程模擬和結構隨機響應分析。研究結果錶明:縯化功率譜近似解耦具有較高的精度;縯化功率譜解耦後,快速傅裏葉變換算法一般可使非平穩隨機過程的模擬效率提高數十倍,且模擬樣本時程的自相關函數估計值與目標值非常吻閤;非平穩激勵下的結構響應分析得以簡化,且與目標值相比,計算結果的誤差很小。
위제고비평은과정적모의효솔,간화비평은격려하적결구향응분석,장연화공솔보해우위일계렬시간계수여소파함수부리협변환모평방승적지화,즉파일반비평은과정분해위약간개균균조제비평은과정지화,병장기응용우비평은수궤과정모의화결구수궤향응분석。연구결과표명:연화공솔보근사해우구유교고적정도;연화공솔보해우후,쾌속부리협변환산법일반가사비평은수궤과정적모의효솔제고수십배,차모의양본시정적자상관함수고계치여목표치비상문합;비평은격려하적결구향응분석득이간화,차여목표치상비,계산결과적오차흔소。
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.