激励中含有谐波成分时的工况模态参数辨识

摘要

在实际工程中,工况模态分析(operational modal analysis,OMA)方法得到了广泛应用.当激励中含有谐波并且谐波频率靠近系统固有频率时,可以通过添加极点来修改传统OMA算法以提高模态辨识精度.基于自然激励技术(natural excitation technique),推导了添加极点的理论依据.当系统所受的激励中含有谐波成分时,将其响应的相关函数表示为系统受白噪声激励时响应的相关函数与一系列谐波的叠加.基于传统OMA方法进行模态参数辨识时,谐波不会改变原来系统极点的数学表达,但是当谐波频率靠近系统固有频率时会影响OMA算法对系统固有极点的拟合准确性.在谐波频率已知时,通过添加谐波造成的极点,可以有效提高OMA算法对系统固有频率和阻尼比的辨识精度.通过仿真和实验,进一步验证了所提出的理论.%Operational modal analysis (OMA) procedures are efficient techniques to identify the modal parameters of the structures excited by externalexcitations which are assumed to be white noises.In many practical cases,harmonic excitations are often included in the excitations in addition to the white noises.If the harmonic frequencies of the excitations are close to the structural frequencies,the traditional OMA algorithms become invalid.Many modified OMA algorithms,such as modified Ibrahim time domain technique (ITD) and modified eigensystem realization algorithm (ERA),have been proposed to increase the accuracy of modal parametric identification.In these methods,the new poles that correspond to harmonic excitations are added to traditional OMA algorithms.In this paper,based on modified ERA,the theoretical basis of the modified OMA algorithms is derived.The correlation functions of the structural responses are expressed as the superposition of the correlation functions caused by harmonics and those caused by white noises.This means that the involvement of the harmonics does not change the mathematical expression of the system poles.However,when the harmonic frequencies are close to the natural frequencies of the structure,the poles cannot be fitted by the traditional OMA algorithms.By knowing the harmonic frequencies in advance,the modified OMA algorithms significantly improve the accuracy of modal analysis.Finally,the effectiveness of the proposed method is confirmed by simulation and an experiment.