第 47 卷第 7 期 2 0 11 年 4 月
机
械
工
程
学 报
Vo l . 4 7 Apr.
No.7 2 0 11
JOURNAL OF MECHANICAL ENGINEERING
DOI：10.3901/JME.2011.07.090
Taylor 展开的线性时变系统参数辨识及误差分析*
陈恩伟 1, 2 陆益民 1 刘正士 1 王 勇1 龚兴龙 2
(1. 合肥工业大学机械与汽车工程学院 合肥 230009； 2. 中国科学技术大学近 学系 合肥 230027)
摘要：以辨识线性时变系统参数为目的，应用时变参数 Taylor 级数展开后变为定常系数多项式的特点，在利用实测系统响应 数据建立的时变自回归滑动平均模型(Time varying-auto regressive moving average，TV-ARMA)基础上，对线性时变系统参数 辨识方法进行研究。利用最小二乘法获得时变参数的定常待定系数。对输入、输出误差对参数辨识的影响以及算法对误差的 放大作用进行分析，根据误差分析结果，以减少误差及提高效率和精度为目的，提出分段辨识方法以及处理参数边缘不连续 的线性插值技术，提高辨识的效率和精度。在 Matlab 环境下对谐波快变以及线性慢变的时变参数进行辨识以及讨论，提出合 适的分段长度。仿真结果显示，在一定的误差条件下，方法所获得的时变参数的轨迹与理论值比较吻合，所采取的措施具有 较强的抗干扰性和高效性。 关键词：辨识 时变参数 Taylor 展开 输入误差 输出误差 中图分类号：TP272
Parameter Identification and Error Analysis of Linear Time Varying System Based on Taylor Expansion
CHEN Enwei 1, 2 LU Yimin 1 LIU Zhengshi 1 WANG Yong 1 GONG Xinglong 2
(1. School of Mechanical and Automotive Engineering, Hefei University of Technology, Hefei 230009; 2. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027)
Abstract：In order to identify the time-varying parameters in linear system, the property that the time-varying parameters can be changed into time-invariant coefficient polynomials after Taylor expansion is used. The parameter identification method of time varying system is studied based on the time-varying auto regressive moving average (TV-ARMA) model established by using the response data from measured system. The time-invariant coefficients of the time-varying parameters are obtained by the least-square algorithm. The effect of input and output error on parameters identification as well as the amplification of algorithm to error are analyzed. According to error analysis, to reduce errors and improve efficiency and accuracy, the estimation time is divided into small intervals and the above method is used in each interval so as to be less error and more efficiency. The linear interpolation technique is used to solve discontinuity of time-varying parameters in margin of different interval, which improves the precision of identification. The fast varying, such as harmonic changing, parameters and the slow varying, such as linear changing, parameters are identified and analyzed by using the Matlab software and the appropriate segment length is given. Simulation results show that, under certain error condition, the identified time-varying parameters obtained by the method are in good agreement with the theoretical value, and the measures taken have strong anti-interference and high efficiency. Key words：Identification Time-varying parameter Taylor expansion Input error Output error

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