### 用逐步扩阶双递推时域法识别线性振动系统复模态参数

1. 南京航空学院
• 收稿日期:1985-04-23 修回日期:1900-01-01 出版日期:1986-04-25 发布日期:1986-04-25

### THE DOUBLE-RECURRENCE METHOD FOR THE IDENTIFICATION OF COMPLEX MODEL PARAMETERS OF A LINEAR VIBRATION SYSTEM

Bao Yimin, Zhou Chuanrong

1. Nanjing Aeronautical Institute
• Received:1985-04-23 Revised:1900-01-01 Online:1986-04-25 Published:1986-04-25

Abstract: This paper proposes a method to identify complex model parameters of a linear vibration system with viscous damping by use of the free decay response of the system. The identification procedure uses experimental data of a vibration system to fit the free-response expression {x （ t ）}=,where. {n （t）} is noise vector which may be fitted with several complex exponential functions. The fitting is treated as a linearproblem in two steps--first, to determine i and then {Pi}. To identifythe complex frequency parameters i, the expression of free-response function is changed into a model of an autoregressive equation and a polynomial equation. The double-recurrence method （DRM） which refers to the recurrence of least-square and the recurrence of gradually increasing the order of fitting model is proposed as a technique for the identification of the model parameters. Firstly the coefficients{ 9 }of auto-regressive equation are estimated by using the recurrence of the least-square （formula （12）） and the recurrence of gradually increasing the order of fitting modal (formula （l9）21) and then the roots bi of the polynomial equation （Eq. （5）） are extracted so that the parameters i are obtained. By making use of the DRM, the difficulty of determining order of the fitting model is avoided, the CPU time and main storage are greatly reduced and the selection of initial values is unifield compared with the least square method which directly deals with the expression of free-response. In determining {Pi}, the recurrence formula （26） for the least squ- are is derived. Computer-simulated experiments have been done for proving the feasibility of the DRM under various conditions including:1 ) the effect of various noise/signalratios on the results of identifications; 2 ) the ability of DRM to identify model parameters of a complex vibration system with closely spaced modes. In addition, parameter identification of the frame of a cross-country car has been conducted and some results are presented in this paper. Several aspects of applications of DRM are also discussed.