求解线性单自由度复合随机系统的改进算法

An Improved Solution About Linear Single Degree of Freedom Compound Stochastic System

摘要:

考虑到空间随机场与随机过程的相互独立性,对常用的摄动虚拟激励法进行改进,直接得到随机反应的均值和方差.以前的研究得到的随机反应方差是随机变量的函数,从而需要求反应方差的均值和反应方差的方差.单自由度复合随机系统的计算结果表明,改进的摄动虚拟激励法的计算结果更合理.与常规摄动虚拟法得到的反应方差要由可靠度确定不同,改进摄动虚拟激励法得到的随机反应方差不再需要由可靠度确定,这更符合统计规律,事实上方差只是对统计数据的离散程度的表示,与可靠度无关.

Abstract:

By taking the independence of space stochastic field and random process into consideration,the conventional perturbation pseudo excitation method(PPEM) is improved and mean or variation of stochastic response can be directly obtained.During the previous researches,the independence was neglected,and so stochastic response variation was function of stochastic variables.As a result,means and variations of response variation had to be solved.Computational results of single degree of freedom(SDOF) compound stochastic system reveal that the improved PPEM is more reasonable.Being different from the fact that the response variation of stochastic system based on the conventional perturbation pseudo excitation method is decided by reliability,response variation based on the improved perturbation pseudo excitation method is not decided by reliability,which is in conformity with the statistic regularity.In fact,variation describes only the divergence of random data and is independent of reliability.