噪声与振动控制2019，Vol.39Issue(3)：40-43,4.DOI:10.3969/j.issn.1006-1355.2019.03.008
随机动力学响应的高斯相关过程模拟
Gaussian Correlation Process Simulation of Stochastic Dynamic Responses
摘要
Abstract
The dynamic response is an important criterion to evaluate system vibration state and performance and control the system. The conventional stochastic response analysis is hampered by the system complexity and uncertainty and the measurement difficulty of random excitations. Thus, new methods for direct random process probability modeling and statistics analysis based on system response observation need to be studied and developed. Recently, the random process probability modeling, probability evaluation and system state prediction of uncertainty system model developed in artificial intelligence and data processing technology have provided different approaches for the probability analysis of dynamic response. Especially, the Gaussian correlation process with better applicability and mathematical expression has provided a complete theoretical method. Therefore, this paper proposes a direct method for the random process probability modeling and statistics analysis of dynamic system response and presents a preliminary research. Based on the statistics characteristics of dynamic system response to Gaussian white noise excitation, Gaussian random process characteristics of the system response, response correlation in time domain and exponential reduction of response covariance are analyzed. Then, the probability modeling and statistics analysis method of Gaussian correlation process is given. It includes response covariance calculation, Gaussian process covariance and kernel function fitting, probability modeling of Gaussian correlation process, direct response sample production and statistics evaluation. The basic expressions of Bayesian update and system state prediction of Gaussian correlation process are also given. Numerical results illustrate the feasibility and availability of the proposed probability modeling and statistics analysis method of Gaussian correlation process.关键词
振动与波/随机响应/高斯过程/统计特性Key words
vibration and wave/ stochastic response/ Gaussian process/ statistical characteristics分类
数理科学引用本文复制引用
张巍,应祖光..随机动力学响应的高斯相关过程模拟[J].噪声与振动控制,2019,39(3):40-43,4.基金项目
国家自然科学基金重点资助项目(51535009) （51535009）
