{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T17:44:17Z","timestamp":1762623857349,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,3,23]],"date-time":"2017-03-23T00:00:00Z","timestamp":1490227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51475339"],"award-info":[{"award-number":["51475339"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei province","doi-asserted-by":"publisher","award":["2016CFA042"],"award-info":[{"award-number":["2016CFA042"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology","award":["ZR201603"],"award-info":[{"award-number":["ZR201603"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Mechanical vibration signal mapped into a high-dimensional space tends to exhibit a special distribution and movement characteristics, which can further reveal the dynamic behavior of the original time series. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, the tensor decomposition algorithm has broad application prospects in signal processing. High-dimensional tensor can be obtained from a one-dimensional vibration signal by using phase space reconstruction, which is called the tensorization of data. As a new signal decomposition method, tensor-based singular spectrum algorithm (TSSA) fully combines the advantages of phase space reconstruction and tensor decomposition. However, TSSA has some problems, mainly in estimating the rank of tensor and selecting the optimal reconstruction tensor. In this paper, the improved TSSA algorithm based on convex-optimization and permutation entropy (PE) is proposed. Firstly, aiming to accurately estimate the rank of tensor decomposition, this paper presents a convex optimization algorithm using non-convex penalty functions based on singular value decomposition (SVD). Then, PE is employed to evaluate the desired tensor and improve the denoising performance. In order to verify the effectiveness of proposed algorithm, both numerical simulation and experimental bearing failure data are analyzed.<\/jats:p>","DOI":"10.3390\/e19040139","type":"journal-article","created":{"date-parts":[[2017,3,23]],"date-time":"2017-03-23T11:47:59Z","timestamp":1490269679000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Tensor Singular Spectrum Decomposition Algorithm Based on Permutation Entropy for Rolling Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"19","author":[{"given":"Cancan","family":"Yi","sequence":"first","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Lv","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1840-1043","authenticated-orcid":false,"given":"Mao","family":"Ge","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han","family":"Xiao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xun","family":"Yu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology (Wuhan University of Science and Technology), Ministry of Education, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering (Wuhan University of Science and Technology), Wuhan 430081, China"},{"name":"Department of Mechanical Engineering, New York Institute of Technology, Old Westbury, NY 11568, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1080\/02664763.2014.1001728","article-title":"Wavelet and short-time Fourier transform comparison-based analysis of myoelectric signals","volume":"42","author":"Veer","year":"2015","journal-title":"Ournal Appl. 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