Output-only damping estimation of structures using enhanced frequency domain decomposition method

Authors
M. Ghalishooyan
M. Abdelghani
Abstract
Modal parameter identification of structures is of significant importance in many fields of civil and mechanical engineering. Output-only modal identification methods have gained great attention of civil engineers community in recent years. The algorithms estimating the dynamic parameters (natural frequencies, mode shape vectors and modal damping ratios) of structures just based on the output responses, became popular as operational modal analysis (OMA) or output-only modal analysis or ambient vibration analysis. In the context of OMA, the force acting on the structure should be stochastic, smooth and broadband and there is no need to measure it. Therefore, these methods are appropriate for identification of huge and complex civil structures. One of the most well-established and popular methods of OMA is frequency domain decomposition (FDD) proposed by Brincker et al. Estimation procedure of FDD is based on singular value decomposition of power spectral density matrix of structure responses. Then, the single degree of freedom spectral bell is obtained using modal assurance criteria (MAC) and transformed to correlation function of corresponded degree of freedom by inverse Fourier transform. Later, Brincker et al. presented the enhanced frequency domain decomposition (EFDD) method to estimate not only modal frequencies (with higher accuracy in the comparison with FDD) and mode shapes, but also modal damping ratios. Despite the high capability of EFDD in frequency and mode shape estimation, it still suffers from some limitations in identifying modal damping ratio. This paper first aims to investigate the modal parameters identification by EFDD and explains its merits and demerits and then proposes in-operation modal appropriation (INOPMA) algorithm for use with EFDD to improve the modal damping estimation. The key idea of INOPMA is to realize that the correlation sequence of the system output (subjected to random input) is the sum of decaying sinusoids with a certain phase shift and therefore it may be considered as an impulse response. The convolution of this correlation sequence with a pure sine wave allows the isolation of the mode at a characteristic frequency which depends on the modal damping ratio. By using a force in quadrature of phase with a sine wave, it is possible to estimate the damping ratio which in turn allows the estimation of the undamped natural frequency. In fact, modal damping ratios are first estimated by INOPMA and natural frequencies are then identified based on damping ratio values. By 70 times simulation of a four-story shear frame, capability of proposed method is validated for damping estimation through EFDD analysis. The results are then compared with the ones derived from the typical EFDD method. Regarding randomness of input force, different results are obtained by each new simulation run. So, the comparison process should be performed based on several numbers of simulations. The number of simulation was adopted in a way that the mean or variance of estimated modal damping ratios converges to a constant value. The relative error (the exact value minus the estimated value over the exact value) and variance of the set of the estimated modal dampings are regarded as comparison indexes. Finally, it is shown that by proposed method, the damping ratios are estimated with much less variance and error.

Keywords

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Modares Civil Engineering journal
Volume 18, Issue 2
July and August 2018
Pages 183-193