Computing the modal mass from the state space model in combined experimental–operational modal analysis

Cara, Javier

doi:10.1016/j.jsv.2016.01.043

Cited by 27 publications

(16 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The system identification problem investigated in this work can be defined as the determination of the corresponding system matrices A , B , C , D , Q ,and R (up to within a similarity transformation) using the input and output measurements available for N time steps, { u 1 , u 2 ,…, u N } and { y 1 , y 2 ,…, y N }. From the point of view of modal parameters, natural frequencies and modal damping ratios can be retrieved from the eigenvalues of A , the mode shapes can be evaluated using the eigenvectors of A and the output matrix C , and the modal masses can be computed using the eigenvectors of A and the input matrix B (see Cara for a general overview): •The eigenvalues of A come in complex conjugate pairs, and each pair represents one physical vibration mode. Assuming proportional damping, the j th eigenvalue of A has the form

λ_{j} = \exp ((), z_{j} normalΔ t), z_{j} = - ζ_{j} ω_{j} \pm i ω_{j} \sqrt{1 - ζ_{j}^{2}},

where ω j are the natural frequencies, ζ j are damping ratios, and Δ t is the time step.…”

Section: From the State‐space Model To Modal Parametersmentioning

confidence: 99%

“…These data were used to estimate the modal parameters using the proposed method. First, we needed to decide the order of the state space model, that is, the size of matrix A (this is equivalent to decide how many modal parameters are going to be estimated, because in theory, the number of modal parameters is half of the size of matrix A ). The usual procedure is to estimate the state space model considering different model orders and to compute the modal parameters for each order.…”

Section: Numerical Example: Field Datamentioning

confidence: 99%

See 1 more Smart Citation

Modal identification of structures from input/output data using the expectation-maximization algorithm and uncertainty quantification by mean of the bootstrap

Cara

2018

Struct Control Health Monit

Self Cite

View full text Add to dashboard Cite

Modal testing in civil engineering includes the possibility to apply measured forces in addition to the unmeasured ambient excitation. In these cases, it is necessary to consider mathematical models that account for both excitation sources, what explains the increasing interest in sophisticated system identification methods for modal analysis with input/output data. In this work, the maximum likelihood estimation of the state space model from input/output vibration data is investigated. This model can be estimated using different techniques: Among them, the maximum likelihood method has optimal statistical properties, so modal parameters computed using this approach will be optimum in a statistical point of view. The algorithm considered for maximizing the likelihood is the expectation-maximization algorithm. The quantification of modal parameters uncertainty is addressed using a Monte Carlo type approach called the bootstrap, which is based on resampling the residuals of the estimated model. Finally, the proposed techniques are applied to synthetic data and also to field data recorded on a stress-ribbon footbridge. KEYWORDS bootstrap, combined experimental-operational modal analysis, expectation-maximization algorithm, mass-normalized modal vectors, modal parameters, operational modal analysis with exogenous inputs, state space model, stress-ribbon footbridge Struct Control Health Monit. 2019;26:e2272.wileyonlinelibrary.com/journal/stc

show abstract

λ_{j} = \exp ((), z_{j} normalΔ t), z_{j} = - ζ_{j} ω_{j} \pm i ω_{j} \sqrt{1 - ζ_{j}^{2}},

where ω j are the natural frequencies, ζ j are damping ratios, and Δ t is the time step.…”

Section: From the State‐space Model To Modal Parametersmentioning

confidence: 99%

Section: Numerical Example: Field Datamentioning

confidence: 99%

Modal identification of structures from input/output data using the expectation-maximization algorithm and uncertainty quantification by mean of the bootstrap

Cara

2018

Struct Control Health Monit

Self Cite

View full text Add to dashboard Cite

show abstract

“…This method is based on the excitation of the structure being partly provided by natural en-2 vironmental excitation (e.g. traffic, wind) and partly by one or more actuators providing measured broadband excitation [20,21]. Further techniques couple known dynamic systems (e.g.…”

Section: Introductionmentioning

confidence: 99%

Global scaling of operational modal analysis modes with the OMAH method

Brandt

Berardengo

Manzoni

et al. 2019

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

show abstract

“…Therefore, in the estimation of modal parameters, the mode shapes cannot be mass normalized. However methods for the estimation of the mode shapes scaling factors have been proposed, even for civil buildings [4,5], providing suggestions to overcome this limitation.…”

Section: Introductionmentioning

confidence: 99%

Monitoring of a Strengthened Barrel Vault

Primio¹,

Fiorini²,

Spina³

et al. 2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

View full text Add to dashboard Cite

Structural monitoring and vibration-based identification methods are fundamental tools to help assessing the conditions of the structural state, in particular as it concern the conservation of historical buildings and the support to civil protection strategies. Although a large part of the Italian and European historical heritage is composed by masonry and vaulted structures, in the literature, comparatively few papers are targeted to the study of the dynamic behaviour of vaulted systems. The present work originates by a spontaneous collaboration between the Chieti/Pescara University and the Italian Civil Protection Department and focuses on the study of the dynamic behaviour of a barrel vault of the Bussi Castel located in Province of Pescara. The barrel vault suffered some damage as a consequence of the 2009 L'Aquila earthquake. Environmental vibration tests were carried out both in the damaged state and after repair and strengthening. In either conditions, the modal parameters of the vault were identified using operational modal analysis techniques. The comparison of the dynamic behaviour in the two states clearly indicates an improvement in the seismic behaviour of the consolidated vault. The results confirm the validity of structural monitoring for the evaluation of the effectiveness of the structural conditions of vaulted masonry systems.

show abstract

Computing the modal mass from the state space model in combined experimental–operational modal analysis

Cited by 27 publications

References 23 publications

Modal identification of structures from input/output data using the expectation-maximization algorithm and uncertainty quantification by mean of the bootstrap

Modal identification of structures from input/output data using the expectation-maximization algorithm and uncertainty quantification by mean of the bootstrap

Global scaling of operational modal analysis modes with the OMAH method

Monitoring of a Strengthened Barrel Vault

Contact Info

Product

Resources

About