A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model
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 dete...
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MDPI AG
2019-08-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/9/15/3120 |
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| author | Sandro Amador Mahmoud El-Kafafy Álvaro Cunha Rune Brincker |
| author_facet | Sandro Amador Mahmoud El-Kafafy Álvaro Cunha Rune Brincker |
| author_sort | Sandro Amador |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T00:06:17Z |
| format | Article |
| id | doaj.art-c2801ad1102a44cfb710aa2ff423d858 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-22T00:06:17Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-c2801ad1102a44cfb710aa2ff423d8582022-12-21T18:45:33ZengMDPI AGApplied Sciences2076-34172019-08-01915312010.3390/app9153120app9153120A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal ModelSandro Amador0Mahmoud El-Kafafy1Álvaro Cunha2Rune Brincker3Department of Civil Engineering, Technical University of Denmark (DTU), Building 118, 2800 Kgs. Lyngby, DenmarkDepartment of Mechanical Engineering, Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, BelgiumViBest, Faculty of Engineering, University of Porto (FEUP), R. Dr. Roberto Frias, 4200-465 Porto, PortugalDepartment of Civil Engineering, Technical University of Denmark (DTU), Building 118, 2800 Kgs. Lyngby, DenmarkRecently, 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.https://www.mdpi.com/2076-3417/9/15/3120modal analysissystem identificationmodal identificationmaximum likelihoodfrequency domainconfidence intervalsmodal parameterspole-residue modal model |
| spellingShingle | Sandro Amador Mahmoud El-Kafafy Álvaro Cunha Rune Brincker A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model Applied Sciences modal analysis system identification modal identification maximum likelihood frequency domain confidence intervals modal parameters pole-residue modal model |
| title | A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model |
| title_full | A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model |
| title_fullStr | A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model |
| title_full_unstemmed | A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model |
| title_short | A New Maximum Likelihood Estimator Formulated in Pole-Residue Modal Model |
| title_sort | new maximum likelihood estimator formulated in pole residue modal model |
| topic | modal analysis system identification modal identification maximum likelihood frequency domain confidence intervals modal parameters pole-residue modal model |
| url | https://www.mdpi.com/2076-3417/9/15/3120 |
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