High spatial resolution modal identification of a stadium suspension roof: Assessment of the estimates uncertainty and of modal contributions

Diord, Sandro; Magalhães, Filipe; Cunha, Álvaro

doi:10.1016/j.engstruct.2016.12.060

Cited by 18 publications

(12 citation statements)

References 17 publications

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“…where (•) H denotes the conjugate transpose (Hermitian) of a complex matrix. In [4], it is proposed to estimate the modal participation vectors, γ n , either in the time domain fitting the empirical CF function matrices to the theoretical solutions (2) and (6) or in the frequency domain by fitting the empirical SD matrices to the similar theoretical solution for the SD matrix of the response,…”

Section: Theorymentioning

confidence: 99%

“…Furthermore, we will formulate a simple way to estimate the modal participation vectors from the correlation matrix, and finally we will illustrate how this information can be used to synthesize the SD matrix in case of random response data. can now be calculated in two different ways using equations (2) and (6), C + � R(0 + ) and C � R(0 ), we will start showing that the two different ways of calculation leads to the same result. From the bottom part of equation 2, we have…”

Section: Theorymentioning

confidence: 99%

“…Taking origin in the top part of equation 2instead of equation 6and using the definition of the modal participation matrix given by equation (19) leads to satisfaction of the equation C − � 2π(BΓ T + B * Γ H ), which is the version of equation 18corresponding to the top part of equation (6).…”

Section: Theorymentioning

confidence: 99%

“…Another fact that justifies the necessity of estimating the modal participation factors is that it is always a good idea to synthesize the CF and/or the SD function from the estimated modal parameters in order to check the accuracy of these estimates. Furthermore, the state-of-art modal parameter estimation techniques such as those based on maximum likelihood [5] can only be used to estimate/optimize the modal parameters if a good guess of the poles, mode shapes, and modal participation factors are known a priori as discussed, for instance, in [6].…”

Section: Introductionmentioning

confidence: 99%

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Modal Participation Estimated from the Response Correlation Matrix

Brincker

Amador

Juul

et al. 2019

Shock and Vibration

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In this paper, we are considering the case of estimating the modal participation vectors from the operating response of a structure. Normally, this is done using a fitting technique either in the time domain using the correlation function matrix or in the frequency domain using the spectral density matrix. In this paper, a more simple approach is proposed based on estimating the modal participation from the correlation matrix of the operating responses. For the case of general damping, it is shown how the response correlation matrix is formed by the mode shape matrix and two transformation matrices T1 and T1 that contain information about the modal parameters, the generalized modal masses, and the input load spectral density matrix Gx. For the case of real mode shapes, it is shown how the response correlation matrix can be given a simple analytical form where the corresponding real modal participation vectors can be obtained in a simple way. Finally, it is shown how the real version of the modal participation vectors can be used to synthesize empirical spectral density functions.

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modal Participation Estimated from the Response Correlation Matrix

Brincker

Amador

Juul

et al. 2019

Shock and Vibration

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“…This new variant of the algorithm consists of a 2-step approach which was developed to address these issues [14]. In fact, this approach consists of a combination of two different estimators, for example, the pLSCF and the poly-reference Maximum Likelihood Estimator in Modal Model formulation (pMLE-MM) [12,[14][15][16][17] used in a final step of the identification process to increase the precision of the estimates provided by pLSCF as well as to compute the uncertainties bounds on the estimated modal parameters.…”

Section: Introductionmentioning

confidence: 99%

A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model

et al. 2019

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Recently, a lot of efforts have been devoted to developing more precise Modal Parameter Estimation (MPE) techniques. This is explained by the necessity in civil, mechanical and aerospace engineering of obtaining accurate estimates for the modal parameters of the tested structures, as well as of determining reliable confidence intervals for these estimates. The Non-linear Least Squares (NLS) identification techniques based on Maximum Likelihood (ML) have been increasingly used in modal analysis to improve precision of estimates provided by the Least Squares (LS) based estimators when they are not accurate enough. Apart from providing more accurate estimates, the main advantage of the ML estimators, with regard to their LS counterparts, is that they allow for taking into account not only the measured Frequency Response Functions (FRFs) but also the noise information during the parametric identification process and, therefore, provide the modal parameters estimates together with their uncertainties bounds. In this paper, a new derivation of a Maximum Likelihood Estimator formulated in Pole-residue Modal Model (MLE-PMM) is presented. The proposed formulation is meant to be used in combination with the Least Squares Frequency Domain (LSCF) to improve the precision of the modal parameter estimates and compute their confidence intervals. Aiming at demonstrating the efficiency of the proposed approach, it is applied to two simulated examples in the final part of the paper.

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