MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION UNDER AMBIENT EXCITATION

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. A theory of cross correlation functions is developed in this paper that the cross correlation functions can be expressed as summations of decaying sinusoids as the impulse response functions under white noise excitation. Each decaying sinusoid has a damped natural frequency and a damping ratio that is identical to that of a corresponding structural mode. So cross correlation functions can be applied to some classical modal analysis method instead of the impulse response functions under ambient excitation. The Complex Exponential Method and Eigensystem Realization Algorithm with cross correlation functions are applied to a cantilever beam. The modal properties of the beam from both of these methods are compared with those from peak picking of power spectral density under white noise excitation. The results show that the proposed method in this paper is feasible exactly. The modal analysis method with cross correlation functions opens up a new path of modal analysis under unknown excitation.