Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals
Signal analysis is a fundamental field in engineering and data science, focused on the study of signal representation, transformation, and manipulation. The accurate estimation of harmonic vibration components and their associated parameters in vibrating mechanical systems presents significant chall...
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2025-01-01
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| author | Eduardo Esquivel-Cruz Francisco Beltran-Carbajal Ivan Rivas-Cambero José Humberto Arroyo-Núñez Ruben Tapia-Olvera Daniel Guillen |
| author_facet | Eduardo Esquivel-Cruz Francisco Beltran-Carbajal Ivan Rivas-Cambero José Humberto Arroyo-Núñez Ruben Tapia-Olvera Daniel Guillen |
| author_sort | Eduardo Esquivel-Cruz |
| collection | DOAJ |
| description | Signal analysis is a fundamental field in engineering and data science, focused on the study of signal representation, transformation, and manipulation. The accurate estimation of harmonic vibration components and their associated parameters in vibrating mechanical systems presents significant challenges in the presence of very similar frequencies and mode mixing. In this context, a hybrid strategy to estimate harmonic vibration modes in weakly damped, multi-degree-of-freedom vibrating mechanical systems by combining Empirical Mode Decomposition and Variational Mode Decomposition is described. In this way, this hybrid approach leverages the detection of mode mixing based on the analysis of intrinsic mode functions through Empirical Mode Decomposition to determine the number of components to be estimated and thus provide greater information for Variational Mode Decomposition. The computational time and dependency on a predefined number of modes are significantly reduced by providing crucial information about the approximate number of vibratory components, enabling a more precise estimation with Variational Mode Decomposition. This hybrid strategy is employed to compute unknown natural frequencies of vibrating systems using output measurement signals. The algorithm for this hybrid strategy is presented, along with a comparison to conventional techniques such as Empirical Mode Decomposition, Variational Mode Decomposition, and the Fast Fourier Transform. Through several case studies involving multi-degree-of-freedom vibrating systems, the superior and satisfactory performance of the hybrid method is demonstrated. Additionally, the advantages of the hybrid approach in terms of computational efficiency and accuracy in signal decomposition are highlighted. |
| format | Article |
| id | doaj-art-3d71e6373a8a4a8f8f71561b3843e145 |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-3d71e6373a8a4a8f8f71561b3843e1452025-01-24T13:17:31ZengMDPI AGAlgorithms1999-48932025-01-011812510.3390/a18010025Hybrid Empirical and Variational Mode Decomposition of Vibratory SignalsEduardo Esquivel-Cruz0Francisco Beltran-Carbajal1Ivan Rivas-Cambero2José Humberto Arroyo-Núñez3Ruben Tapia-Olvera4Daniel Guillen5Departamento de Investigación y Posgrado, Universidad Politécnica de Tulancingo, Tulancingo de Bravo 43629, MexicoDepartamento de Energía, Unidad Azcapotzalco, Universidad Autónoma Metropolitana, Azcapotzalco, Ciudad de Mexico 02200, MexicoDepartamento de Investigación y Posgrado, Universidad Politécnica de Tulancingo, Tulancingo de Bravo 43629, MexicoDepartamento de Investigación y Posgrado, Universidad Politécnica de Tulancingo, Tulancingo de Bravo 43629, MexicoDepartamento de Energía Eléctrica, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, MexicoEscuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Monterrey 64849, MexicoSignal analysis is a fundamental field in engineering and data science, focused on the study of signal representation, transformation, and manipulation. The accurate estimation of harmonic vibration components and their associated parameters in vibrating mechanical systems presents significant challenges in the presence of very similar frequencies and mode mixing. In this context, a hybrid strategy to estimate harmonic vibration modes in weakly damped, multi-degree-of-freedom vibrating mechanical systems by combining Empirical Mode Decomposition and Variational Mode Decomposition is described. In this way, this hybrid approach leverages the detection of mode mixing based on the analysis of intrinsic mode functions through Empirical Mode Decomposition to determine the number of components to be estimated and thus provide greater information for Variational Mode Decomposition. The computational time and dependency on a predefined number of modes are significantly reduced by providing crucial information about the approximate number of vibratory components, enabling a more precise estimation with Variational Mode Decomposition. This hybrid strategy is employed to compute unknown natural frequencies of vibrating systems using output measurement signals. The algorithm for this hybrid strategy is presented, along with a comparison to conventional techniques such as Empirical Mode Decomposition, Variational Mode Decomposition, and the Fast Fourier Transform. Through several case studies involving multi-degree-of-freedom vibrating systems, the superior and satisfactory performance of the hybrid method is demonstrated. Additionally, the advantages of the hybrid approach in terms of computational efficiency and accuracy in signal decomposition are highlighted.https://www.mdpi.com/1999-4893/18/1/25intrinsic mode functionsHilbert–Huang transformhybrid strategyvariational mode decompositionvibratory components |
| spellingShingle | Eduardo Esquivel-Cruz Francisco Beltran-Carbajal Ivan Rivas-Cambero José Humberto Arroyo-Núñez Ruben Tapia-Olvera Daniel Guillen Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals Algorithms intrinsic mode functions Hilbert–Huang transform hybrid strategy variational mode decomposition vibratory components |
| title | Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals |
| title_full | Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals |
| title_fullStr | Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals |
| title_full_unstemmed | Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals |
| title_short | Hybrid Empirical and Variational Mode Decomposition of Vibratory Signals |
| title_sort | hybrid empirical and variational mode decomposition of vibratory signals |
| topic | intrinsic mode functions Hilbert–Huang transform hybrid strategy variational mode decomposition vibratory components |
| url | https://www.mdpi.com/1999-4893/18/1/25 |
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