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Dynamic analysis of the civil structures such as bridges, towers and buildings is required for their design and maintenance. Modal analysis is a powerful tool to conduct some part of dynamic analysis in determination of the modal parameter in terms of natural frequencies, damping factors and mode shapes. However, excitation of these structures is usually difficult and sometimes impossible. As these structures are usually excited by ambient forces such as wind, this idea is suggested that the structure is modeled considering the natural forces as the inputs.However, the ambient forces are unknown and have a complicated nature to be measured. An alternative approach is using the operational modal analysis concepts in which only the responses are measured and the modal parameter are extracted. In this article Frequency Domain Decomposition (FDD) method is used for identification of the modal parameter of a clamped-clamped beam and the results are compared with those of the FEM. The operational modal analysis is conducted on a type of a bridge under ambient forces in a real test and the results are compared with those of the conventional Modal testing. The results confirm the method for engineering applications.

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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.

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Operational modal analysis (OMA), as a branch of the system identification, plays a very important and practical role in determining the dynamic characteristics of the structures. In the operational approach that is implemented based on the ambient vibration test, the ambient and operation loads are considered as the excitation source of the structure. In the present research, an integrative method composed of frequency domain decomposition (FDD) and wavelet transform (WT) called FDD-WT is proposed in order to identify the natural frequencies and damping ratios of an arch concrete dam. Furthermore, the wavelet transform of the seismic responses is also calculated in order to validate and compare the results. For this purpose, the time and frequency position of the system modes during the different earthquakes is evaluated using the time-frequency representation obtained from wavelet transform. In this paper, Pacoima arch concrete dam located in California, US is selected as the case study and the seismic records related to 1994 Northridge, 2001 San Fernando and 2008 Chino Hills earthquakes are also used to evaluate the dynamic characteristics and structural health monitoring during the period between 1994 to 2008. Investigation of changes in the natural frequencies of the structure indicates that the dam had taken serious damage during 1994 Northridge earthquake (about the fourth second), while the vibrations of the concrete structure has been almost linear during the first 4 seconds of the earthquake and also in 2001 and 2008 earthquakes.