Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy
Dynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising an...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-02-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/20/3/152 |
| _version_ | 1811213016707891200 |
|---|---|
| author | Zhang Dang Yong Lv Yourong Li Cancan Yi |
| author_facet | Zhang Dang Yong Lv Yourong Li Cancan Yi |
| author_sort | Zhang Dang |
| collection | DOAJ |
| description | Dynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising and feature extraction algorithm for multi-component coupled noisy mechanical signals is proposed based on the standard DMD algorithm, which provides a new method solving the two intractable problems above. Firstly, a sparse optimization method of non-convex penalty function is adopted to determine the optimal dimensionality reduction space in the process of DMD, obtaining a series of optimal DMD modes. Then, multiscale permutation entropy calculation is performed to calculate the complexity of each DMD mode. Modes corresponding to the noise components are discarded by threshold technology, and we reconstruct the modes whose entropies are smaller than a threshold to recover the signal. By applying the algorithm to rolling bearing simulation signals and comparing with the result of wavelet transform, the effectiveness of the proposed method can be verified. Finally, the proposed method is applied to the experimental rolling bearing signals. Results demonstrated that the proposed approach has a good application prospect in noise reduction and fault feature extraction. |
| first_indexed | 2024-04-12T05:40:13Z |
| format | Article |
| id | doaj.art-aa8a42783a6b4b4aa847008244be571f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-12T05:40:13Z |
| publishDate | 2018-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-aa8a42783a6b4b4aa847008244be571f2022-12-22T03:45:42ZengMDPI AGEntropy1099-43002018-02-0120315210.3390/e20030152e20030152Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation EntropyZhang Dang0Yong Lv1Yourong Li2Cancan Yi3Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, ChinaKey Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, ChinaKey Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, ChinaKey Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, ChinaDynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising and feature extraction algorithm for multi-component coupled noisy mechanical signals is proposed based on the standard DMD algorithm, which provides a new method solving the two intractable problems above. Firstly, a sparse optimization method of non-convex penalty function is adopted to determine the optimal dimensionality reduction space in the process of DMD, obtaining a series of optimal DMD modes. Then, multiscale permutation entropy calculation is performed to calculate the complexity of each DMD mode. Modes corresponding to the noise components are discarded by threshold technology, and we reconstruct the modes whose entropies are smaller than a threshold to recover the signal. By applying the algorithm to rolling bearing simulation signals and comparing with the result of wavelet transform, the effectiveness of the proposed method can be verified. Finally, the proposed method is applied to the experimental rolling bearing signals. Results demonstrated that the proposed approach has a good application prospect in noise reduction and fault feature extraction.http://www.mdpi.com/1099-4300/20/3/152dynamic mode decompositionsparse optimizationnon-convex regularizationmultiscale permutation entropyfeature extraction |
| spellingShingle | Zhang Dang Yong Lv Yourong Li Cancan Yi Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy Entropy dynamic mode decomposition sparse optimization non-convex regularization multiscale permutation entropy feature extraction |
| title | Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy |
| title_full | Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy |
| title_fullStr | Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy |
| title_full_unstemmed | Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy |
| title_short | Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy |
| title_sort | optimized dynamic mode decomposition via non convex regularization and multiscale permutation entropy |
| topic | dynamic mode decomposition sparse optimization non-convex regularization multiscale permutation entropy feature extraction |
| url | http://www.mdpi.com/1099-4300/20/3/152 |
| work_keys_str_mv | AT zhangdang optimizeddynamicmodedecompositionvianonconvexregularizationandmultiscalepermutationentropy AT yonglv optimizeddynamicmodedecompositionvianonconvexregularizationandmultiscalepermutationentropy AT yourongli optimizeddynamicmodedecompositionvianonconvexregularizationandmultiscalepermutationentropy AT cancanyi optimizeddynamicmodedecompositionvianonconvexregularizationandmultiscalepermutationentropy |