Higher-Order Stabilized Perturbation for Recursive Eigen-Decomposition Estimation
| Title: | Higher-Order Stabilized Perturbation for Recursive Eigen-Decomposition Estimation |
|---|---|
| Authors: | Mucchielli, Paul, Bhowmik, Basuraj, Hazra, Budhaditya, Pakrashi, Vikram |
| Source: | Journal of Vibration and Acoustics; December 2020, Vol. 142 Issue: 6 p061010-061010, 1p |
| Abstract: | Eigen-decomposition remains one of the most invaluable tools for signal processing algorithms. Although traditional algorithms based on QR decomposition, Jacobi rotations and block Lanczos tridiagonalization have been proposed to decompose a matrix into its eigenspace, associated computational expense typically hinders their implementation in a real-time framework. In this paper, we study recursive eigen perturbation (EP) of the symmetric eigenvalue problem of higher order (greater than one). Through a higher order perturbation approach, we improve the recently established first-order eigen perturbation (FOP) technique by creating a stabilization process for adapting to ill-conditioned matrices with close eigenvalues. Six algorithms were investigated in this regard: first-order, second-order, third-order, and their stabilized versions. The developed methods were validated and assessed on multiple structural health monitoring (SHM) problems. These were first tested on a five degrees-of-freedom (DOF) linear building model for accurate estimation of mode shapes in an automated framework. The separation of closely spaced modes was then demonstrated on a 3DOF + tuned mass damper (TMD) problem. Practical utility of the methods was probed on the Phase-I ASCE-SHM benchmark problem. The results obtained for real-time mode identification establishes the robustness of the proposed methods for a range of engineering applications. |
| Database: | Supplemental Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Higher-Order Stabilized Perturbation for Recursive Eigen-Decomposition Estimation – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mucchielli%2C+Paul%22">Mucchielli, Paul</searchLink><br /><searchLink fieldCode="AR" term="%22Bhowmik%2C+Basuraj%22">Bhowmik, Basuraj</searchLink><br /><searchLink fieldCode="AR" term="%22Hazra%2C+Budhaditya%22">Hazra, Budhaditya</searchLink><br /><searchLink fieldCode="AR" term="%22Pakrashi%2C+Vikram%22">Pakrashi, Vikram</searchLink> – Name: TitleSource Label: Source Group: Src Data: Journal of Vibration and Acoustics; December 2020, Vol. 142 Issue: 6 p061010-061010, 1p – Name: Abstract Label: Abstract Group: Ab Data: Eigen-decomposition remains one of the most invaluable tools for signal processing algorithms. Although traditional algorithms based on QR decomposition, Jacobi rotations and block Lanczos tridiagonalization have been proposed to decompose a matrix into its eigenspace, associated computational expense typically hinders their implementation in a real-time framework. In this paper, we study recursive eigen perturbation (EP) of the symmetric eigenvalue problem of higher order (greater than one). Through a higher order perturbation approach, we improve the recently established first-order eigen perturbation (FOP) technique by creating a stabilization process for adapting to ill-conditioned matrices with close eigenvalues. Six algorithms were investigated in this regard: first-order, second-order, third-order, and their stabilized versions. The developed methods were validated and assessed on multiple structural health monitoring (SHM) problems. These were first tested on a five degrees-of-freedom (DOF) linear building model for accurate estimation of mode shapes in an automated framework. The separation of closely spaced modes was then demonstrated on a 3DOF + tuned mass damper (TMD) problem. Practical utility of the methods was probed on the Phase-I ASCE-SHM benchmark problem. The results obtained for real-time mode identification establishes the robustness of the proposed methods for a range of engineering applications. |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1115/1.4047302 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: 061010 Titles: – TitleFull: Higher-Order Stabilized Perturbation for Recursive Eigen-Decomposition Estimation Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mucchielli, Paul – PersonEntity: Name: NameFull: Bhowmik, Basuraj – PersonEntity: Name: NameFull: Hazra, Budhaditya – PersonEntity: Name: NameFull: Pakrashi, Vikram IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: December 2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 10489002 – Type: issn-print Value: 15288927 Numbering: – Type: volume Value: 142 – Type: issue Value: 6 Titles: – TitleFull: Journal of Vibration and Acoustics Type: main |
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