| 随机过程的第二类随机谐和函数表达 |
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| 引用本文： | 孙伟玲,陈建兵,李杰. 随机过程的第二类随机谐和函数表达[J]. 同济大学学报(自然科学版), 2011, 39(10): 1413-1419. DOI: 10.3969/j.issn.0253-374x.2011.10.001 |
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| 作者姓名： | 孙伟玲 陈建兵 李杰 |
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| 作者单位： | 同济大学土木工程学院,上海200092;同济大学土木工程防灾国家重点实验室,上海 200092 |
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| 基金项目： | 国家“八六三”高技术研究发展计划（10872148、90715033）;国家863计划（编号2008AA05Z413） |
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| 摘 要： | 发展了随机过程的第二类随机谐和函数表达并研究了其性质.证明当随机频率与相位服从独立均匀分布而幅值由频率与目标功率谱密度决定时,随机谐和函数过程的功率谱密度函数精确地等于目标功率谱密度函数.研究第二类随机谐和函数过程的渐进正态性,讨论趋向正态分布的速率,并采用Pearson分布研究1维概率密度函数的性质.研究表明,第二类...
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| 关 键 词： | 第二类随机谐和函数 功率谱密度 相关函数 平稳过程 非线性 |
| 收稿时间： | 2010-07-28 |
| 修稿时间： | 2011-07-12 |
Stochastic Harmonic Functions of Second Kind for Spectral Representations |
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| SUN Weiling,CHEN Jianbing and LI Jie. Stochastic Harmonic Functions of Second Kind for Spectral Representations[J]. Journal of Tongji University(Natural Science), 2011, 39(10): 1413-1419. DOI: 10.3969/j.issn.0253-374x.2011.10.001 |
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| Authors: | SUN Weiling CHEN Jianbing LI Jie |
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| Affiliation: | College of Civil Engineering, Tongji University, Shanghai 200092,China;State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;College of Civil Engineering, Tongji University, Shanghai 200092,China;State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;College of Civil Engineering, Tongji University, Shanghai 200092,China;State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China |
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| Abstract: | The stochastic harmonic function of the second kind is proposed for representations of stochastic processes.It is firstly proved that,as long as the random phase angles and random circular frequencies are independent and uniformly distributed whereas the amplitudes are related to the target power spectral density function in a specified way,the power spectral density of the process represented by the stochastic harmonic function of the second kind is identical to the target power spectral density.Then,it is... |
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| Keywords: | stochastic harmonic function of the second kind power spectral density function covariance function stationary process nonlinearity |
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