{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:34:43Z","timestamp":1759970083626,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,5]],"date-time":"2025-01-05T00:00:00Z","timestamp":1736035200000},"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>With the rapid expansion of urban subway networks, vibrations induced by subway operations have become an increasingly significant concern for nearby structures. To assess the influence of subway-induced vibrations on nearby structures, it is essential to predict the vibration effects accurately prior to the construction of the subway system. By combining an improved Long Short-Term Memory (LSTM) model with a spectral analysis, this paper proposes a hybrid method to enhance the accuracy and efficiency of predicting structural vibrations induced by subway operations. The improved LSTM model is composed of BiLSTM, an attention mechanism, and the DBO algorithm. The symmetry inherent in the vibration propagation paths and the structural layouts of subway systems is leveraged to improve the feature extraction and modeling accuracy. Additionally, the hybrid method utilizes the symmetric properties of vibration signals in the spectral domain to enhance prediction robustness and efficiency. Then, the hybrid method is utilized to rapidly achieve highly accurate vibration responses induced by subway operations. The verification results demonstrate the following: (1) The improved LSTM model enhances the ability to recognize patterns in time-series vibration data, leading to improved model convergence and generalization. The improved LSTM mode has a significant improvement in prediction accuracy compared to the standard LSTM network. For numerical simulation and real-world measured signals, values of R2 increased by 3% and 49.37%. (2) The proposed hybrid method significantly reduces computational time while ensuring results consistent with those obtained from the time-history analysis method. Applying the proposed hybrid method for data augmentation enhances the accuracy of the spectral analysis. The hybrid method achieves an improvement of 7% for the prediction accuracy.<\/jats:p>","DOI":"10.3390\/sym17010075","type":"journal-article","created":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T10:40:52Z","timestamp":1736160052000},"page":"75","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Prediction of Structural Vibration Induced by Subway Operations Using Hybrid Method Based on Improved LSTM and Spectral Analysis"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaolin","family":"Liu","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoyuan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7946-1245","authenticated-orcid":false,"given":"Xijun","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Transportation, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xu, D., Zhao, Y., Liu, H., and Zhu, H. 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