Linear fit method for modal parameter estimation using the real and imaginary parts of frequency response function (Identification accuracy improvement based on weighted least square method)

Abstract

The experimental modal analysis is widely used to identify the modal parameters: natural frequency, damping characteristics and mode shape, in the structural dynamic analysis. The existing method, however, is not adequate when the damping characteristics is too low. When the resonance frequency is not close to the measured frequencies, it is difficult to identify low damping characteristics due to lack of FRF data around resonance frequency. Thus, the linear fit method which is applicable to systems with very low damping characteristics is proposed in our previous study. In the proposed method, a set of linear functions with respect to the real and imaginary parts of original Frequency Response Function (FRF) is derived by canceling the residue of FRF. Then, the modal parameters are identified by fitting the experimental data to the obtained linear functions using the least-square method. However, there is a technical issue left in the method: the identified parameters are sensitive to the data range applied due to inhomogeneous error distribution. Here, the weighted least-square method is introduced to improve the identification accuracy. That is, smaller weight is assigned to the data with low accuracy, while larger weight is assigned to the data with high accuracy. A series of experiment was conducted to investigate influence of the data range and the difference of the governing equations derived from FRF. The result validates the modified method coupling with the weighted least-square method.

Keywords

• modal analysis
• vibraion testing
• modal properties
• identification method
• single-degree-of-freedom