Fast maximum-likelihood identification of modal parameters with uncertainty intervals: A modal model-based formulation

El-Kafafy, Mahmoud; Troyer, Tim De; Peeters, Bart; Guillaume, Patrick

doi:10.1016/j.ymssp.2013.01.013

Cited by 36 publications

(38 citation statements)

References 6 publications

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“…Also, we like to be able to obtain different estimates of G x or B T G x B in different frequency bands. We solve this problem by generalizing equation (5) to the case where the modal participation vectors are frequency dependent γ n � γ n (ω):…”

Section: Estimating the Modal Participation From The Response Cf Matrmentioning

confidence: 99%

“…e exact complex modal participation vectors are then calculated according to equation (5), and the exact real modal participation vectors are calculated according to equations (27) and (33). A full band estimate of C is found according to equation (45), i.e, by using numerical integration of the response SD matrix over the Nyquist band and subsequently by estimating the modal participation for all five modes using equations (35) and (37).…”

Section: Estimation Using the Exact Sd Matrixmentioning

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: Estimating the Modal Participation From The Response Cf Matrmentioning

confidence: 99%

Section: Estimation Using the Exact Sd Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modal Participation Estimated from the Response Correlation Matrix

Brincker

Amador

Juul

et al. 2019

Shock and Vibration

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“…In a correlation-based clustering algorithm, it is desirable to form a set of basis vectors which exhibits a noticeable degree of consistency with such randomly appearing modal vectors. 2 If is a matrix whose columns , , … , span a -dimensional subspace, . Then, is -invariant if and only if there exists a matrix that satisfies .…”

Section: Complementary Subspace Correlation Analysismentioning

confidence: 99%

Automated modal parameter estimation using correlation analysis and bootstrap sampling

Yaghoubi

Vakilzadeh

Abrahamsson

2018

Mechanical Systems and Signal Processing

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The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods have been developed to automate this procedure. The common approach is to identify models with different orders and cluster similar modes together. However, most proposed methods based on this approach suffer from high-dimensional optimization problems in either the estimation or clustering step. To overcome this problem, this study presents an algorithm for autonomous modal parameter estimation in which the only required optimization is performed in a three-dimensional space. To this end, a subspace-based identification method is employed for the estimation and a non-iterative correlation-based method is used for the clustering. This clustering is at the heart of the paper. The keys to success are correlation metrics that are able to treat the problems of spatial eigenvector aliasing and nonunique eigenvectors of coalescent modes simultaneously. The algorithm commences by the identification of an excessively high-order model from frequency response function test data. The high number of modes of this model provide bases for two subspaces: one for likely physical modes of the tested system and one for its complement dubbed the subspace of noise modes. By employing the bootstrap resampling technique, several subsets are generated from the same basic dataset and for each of them a model is identified to form a set of models. Then, by correlation analysis with the two aforementioned subspaces, highly correlated modes of these models which appear repeatedly are clustered together and the noise modes are collected in a so-called Trashbox cluster. Stray noise modes attracted to the mode clusters are trimmed away in a second step by correlation analysis. The final step of the algorithm is a fuzzy c-means clustering procedure applied to a three-dimensional feature space to assign a degree of physicalness to each cluster. The proposed algorithm is applied to two case studies: one with synthetic data and one with real test data obtained from a hammer impact test. The results indicate that the algorithm successfully clusters similar modes and gives a reasonable quantification of the extent to which each cluster is physical.

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“…It is verified that, under these circumstances, the algorithm is not so robust and tends to underestimate the damping ratios. 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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Fast maximum-likelihood identification of modal parameters with uncertainty intervals: A modal model-based formulation

Cited by 36 publications

References 6 publications

Modal Participation Estimated from the Response Correlation Matrix

Modal Participation Estimated from the Response Correlation Matrix

Automated modal parameter estimation using correlation analysis and bootstrap sampling

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

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