一种基于标准正交基的区间过程展开方法  

An interval process expansion method based on standard orthogonal bases

作　　者：何雨轩 李金武 姜潮[1] HE YuXuan;LI JinWu;JIANG Chao(State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle,College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学整车先进设计制造技术全国重点实验室,机械与运载工程学院,长沙410082

出　　处：《中国科学：技术科学》2024年第11期2143-2155,共13页Scientia Sinica(Technologica)

基　　金：国家自然科学基金重点项目(批准号:52235005)和国家自然科学基金青年科学基金项目(批准号:52105253)资助。

摘　　要：相较于传统的随机过程模型,区间过程模型使用有界区间变量表示参数在某一时间点的变动范围,无需获得变量的概率分布情况,参数在整个时间历程中的不确定性由上下两条边界函数描述.区间过程模型为不确定性动力学分析等工程问题的解决提供了一种新的工具.本文提出了一种基于标准正交基的区间过程级数展开方法,以高效地表征动态不确定性参数在时间上的特征.首先,通过相关结构分解将区间过程表示为标准正交基与一组标准区间变量的线性组合形式.其次,提出了区间过程截断级数展开方法以便于实际使用,并对其进行了误差分析.再次,基于截断级数展开形式,提出了一种区间过程的抽样方法,可在时域上对区间过程进行高精度的模拟.最后,对三种具有典型自相关系数函数类型的区间过程进行模拟,验证了本文所提方法的有效性.Compared with traditional stochastic process models that rely on precise probability distributions, the interval process model usesupper and lower boundary functions. This method is adept at describing dynamic or time-varying uncertainty parameters, providing anew tool for solving engineering problems such as uncertainty dynamics analysis. This article proposes an interval process seriesexpansion method that leverages standard orthogonal bases to efficiently characterize the temporal characteristics of dynamicuncertainty parameters. First, we propose a truncated series expansion approach tailored for practical use, coupled with error analysis,to ensure reliability. Second, a sampling method designed for interval processes is introduced. Third, leveraging the truncated seriesexpansion form, we propose a sampling method for interval processes. This method can simulate interval processes with highaccuracy in the time domain. Finally, the effectiveness of the proposed method is verified by simulating three interval processes withtypical types of auto-correlation coefficient functions.

关 键 词：区间过程 正交级数展开 标准正交基 区间过程模拟 

分 类 号：O211.6[理学—概率论与数理统计]