Improving the accuracy of SOD for modal parameters estimation of damped systems

Rezaee, Mousa; Yam, Gholamreza Fattahi

doi:10.1007/s00707-014-1279-x

Cited by 3 publications

(5 citation statements)

References 23 publications

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“…Then, the SOD method will give results with considerable errors. Therefore, the arrangement of excitation forces can affect the accuracy of the SOD method, which explains the excitation arrangement effect mentioned in (Rezaee and Yam, 2015).…”

Section: The Covariance Of Modal Responsesmentioning

confidence: 99%

“…Rezaee et al (2013) used SOD to analyze a vehicle vibration excited by time shift non-independent inputs caused by the rough surface of the road. Rezaee et al tried to improve the frequency identification accuracy of using SOD by improving the numerical differentiation method (Rezaee and Yam, 2015). Although they noticed that the system damping, the excitation arrangement form, and the derivative method will affect the identification accuracy of using SOD, the underlying theoretical reasons are not analyzed.…”

Section: Introductionmentioning

confidence: 99%

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Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

Zhi

et al. 2020

Advances in Structural Engineering

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The smooth orthogonal decomposition method (SOD) is an efficient algorithm that can be used to extract modal matrix and frequencies of lightly damped vibrating systems. It uses the covariance matrices of output-only displacement and velocity responses to form a generalized eigenvalues problem (EVP). The mode shape vectors are estimated by the eigenvectors of the EVP. It is stated in this work that the accuracy of the SOD method is mainly affected by the correlation characteristic of modal coordinate responses. For the damped vibration systems, biases will be contained in the results of using the SOD. Therefore, an iterative smooth orthogonal decomposition (ISOD) method is proposed to identify modal parameters of the damped system from the covariance matrices of the displacement, velocity, and acceleration responses. The modal matrix given by the SOD method is updated in each iteration step using a transformation matrix. The transformation matrix can be efficiently computed using a set of analytical formulations. Meanwhile, natural frequencies and damping ratios are obtained by using a simple search method. The performance of the proposed ISOD method is verified by numerical and experimental studies. The results demonstrate that, by considering the correlation of modal responses, the ISOD method can be used to extract accurately the modal information of vibration systems with coupled modes.

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Section: The Covariance Of Modal Responsesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

Zhi

et al. 2020

Advances in Structural Engineering

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“…The vehicle suspension system is modeled as a 7-DOF vibration system as shown in Fig. 5 [16]. The system parameters are presented in Table 3.…”

Section: Applying the Modified Mafvro Methods To A 7-dof Full Car Vehimentioning

confidence: 99%

“…In Ref. [16], some modifications have been made on the traditional SOD algorithm in order to improve the accuracy of SOD for the modal analysis of damped systems. For compensating the mentioned deficiencies, the modal analysis free vibration response only (MAFVRO) method has been introduced for systems which are subjected to initial conditions, and it leads to more accurate results for these sorts of systems [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Development of "modal analysis free vibration response only" method for randomly excited systems

2015

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Modal analysis free vibration response only (MAFVRO) is one of the output-only modal analysis methods which is able to determine the modal parameters of a vibration system by the free vibration responses. However, most of the vibrating systems are subjected to random excitations, and in such cases, the traditional MAFVRO cannot extract the modal parameters. In this study, the traditional MAFVRO method has been developed to randomly excited vibration systems by using some modifications. In order to verify the accuracy of modified MAFVRO, this method is applied to vibration analysis of a cantilever beam and a vehicle suspension system which are subjected to the random white noise excitation. The estimated results are compared with the exact solution obtained from the structural eigenvalue problem. Comparing the results reveals that the developed method can estimate the natural frequencies and mode shapes of a randomly excited system with a good accuracy. In addition, the effect of the measurement noise on the estimated modal parameters is investigated.

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Extended Smooth Orthogonal Decomposition for Modal Analysis

Huang

Wang

et al. 2018

Journal of Vibration and Acoustics

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The smooth orthogonal decomposition (SOD) is an output-only modal analysis method, which has simple structure and gives good results for undamped or lightly damped vibration systems. In the present study, the SOD method is extended to incorporate various measurements that contain the displacement, the velocity, the acceleration, and even the jerk (derivation of the acceleration). Several generalized eigenvalue problems (EVPs) are put forward considering different measurement combinations, and it is proved that all these EVPs can reduce to the eigenvalue problems of the undamped vibration system. These different methods are called extended smooth orthogonal decomposition (ESOD) methods in this paper. For the damped vibration system, the frequencies obtained by different ESOD methods are different from each other. Thus, a cost function is defined and a search algorithm is proposed to find the optimal frequency and damping ratio that can explain these differences. Although the search algorithm is derived for the single-degree-of-freedom (SDOF) vibration systems, it is effective for the multi-degrees-of-freedom (MDOF) vibration system after assuming that the smooth orthogonal coordinates (SOCs) computed by the ESOD methods are approximate to the modal coordinate responses. In order to verify the ESOD methods and the search algorithm, simulations are carried out and the results indicate that all ESOD methods reach correct results for undamped vibration systems and the search algorithm can give accurate frequency and damping ratio for damped systems. In addition, the effects of measurement noises are considered and the results show that the proposed method has anti-noise property to some extent.

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Improving the accuracy of SOD for modal parameters estimation of damped systems

Cited by 3 publications

References 23 publications

Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

Development of "modal analysis free vibration response only" method for randomly excited systems

Extended Smooth Orthogonal Decomposition for Modal Analysis

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