{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:28:23Z","timestamp":1760059703214,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T00:00:00Z","timestamp":1751846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study addresses the long-standing difficulty of predicting the remaining useful life (RUL) of rolling bearings from highly non-stationary vibration signals by proposing WaveAtten, a symmetry-aware deep learning framework. First, mirror-symmetric and bi-orthogonal Daubechies wavelet filters are applied to decompose each raw signal into multi-scale approximation\/detail pairs, explicitly preserving the left\u2013right symmetry that characterizes periodic mechanical responses while isolating asymmetric transient faults. Next, a bidirectional sparse-attention module reinforces this structural symmetry by selecting query\u2013key pairs in a forward\/backward balanced fashion, allowing the network to weight homologous spectral patterns and suppress non-symmetric noise. Finally, the symmetry-enhanced features\u2014augmented with temperature and other auxiliary sensor data\u2014are fed into a long short-term memory (LSTM) network that models the symmetric progression of degradation over time. Experiments on the IEEE PHM2012 bearing dataset showed that WaveAtten achieved superior mean squared error, mean absolute error, and R2 scores compared with both classical signal-processing pipelines and state-of-the-art deep models, while ablation revealed a 6\u20138% performance drop when the symmetry-oriented components were removed. By systematically exploiting the intrinsic symmetry of vibration phenomena, WaveAtten offers a robust and efficient route to RUL prediction, paving the way for intelligent, condition-based maintenance of industrial machinery.<\/jats:p>","DOI":"10.3390\/sym17071078","type":"journal-article","created":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T04:43:37Z","timestamp":1751863417000},"page":"1078","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["WaveAtten: A Symmetry-Aware Sparse-Attention Framework for Non-Stationary Vibration Signal Processing"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2915-4402","authenticated-orcid":false,"given":"Xingyu","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7771","DOI":"10.1109\/TII.2022.3206339","article-title":"Optimized random forest model for remaining useful life prediction of experimental bearings","volume":"19","author":"Alfarizi","year":"2023","journal-title":"IEEE Trans. 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