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<p>In Beidou navigation satellite system (BDS) deformation monitoring applications, achieving 2 mm horizontal and 5 mm vertical monitoring accuracy typically requires continuous 24-h observations. This pre-requisite results in only 365 or 366 deformation values per year, which is generally considered as a small sample size. However, existing artificial intelligence-based deformation prediction methods have limited capability to extract deformation features from small sample data, leading to low prediction accuracy. To address this issue, this study proposes a novel BDS deformation prediction method considering both global and local features. Firstly, data preparation. To ensure that the model can effectively capture data features, BDS deformation samples for model training are extracted from the raw coordinate time series using a sliding window. Secondly, model design. A Transformer-BiLSTM (Bi-directional Long Short-Term Memory) fusion prediction model is developed, where the Transformer network is designed to capture long-term global deformation features, and the BiLSTM network to extract bi-directional short-term local features. A dense neural network is sequentially added to adjust weights of extracted global and local features. Thirdly, model training. The Tree-structured Parzen Estimator algorithm is introduced to search the optimal model hyper-parameter combination. Subsequently, the optimal fusion prediction model is obtained based on the determined hyper-parameter combination and 80% BDS deformation samples in the data preparation stage. The proposed model is evaluated based on a BDS deformation application of 43 monitoring stations in the year of 2023. Numerical results show that: (1) the prediction accuracies by the proposed model can achieve 2.50 and 3.19 mm in the horizontal and vertical directions, respectively. (2) Compared to the classic LSTM and Transformer models, the proposed fusion model improves the prediction accuracy by 6.3/6.5% and 8.3/10.9% in horizontal/vertical directions, respectively. These results validate both the effectiveness and the superiority of the proposed prediction method for BDS deformation prediction applications with small sample data. In conclusion, the proposed method improves the prediction accuracy with respect to classic methods, offering a novel solution for deformation prediction with small sample data and a promising approach for engineering safety early warning.</p>

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A novel BDS deformation prediction method considering both global and local features for small sample data

  • 期刊论文

  • 发表日期：

    2025年9月27日

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  • Junbo Shi,
  • Cheng Hou,
  • Chenhao Ouyang,
  • Jiming Guo,
  • Jingui Zou

摘要

In Beidou navigation satellite system (BDS) deformation monitoring applications, achieving 2 mm horizontal and 5 mm vertical monitoring accuracy typically requires continuous 24-h observations. This pre-requisite results in only 365 or 366 deformation values per year, which is generally considered as a small sample size. However, existing artificial intelligence-based deformation prediction methods have limited capability to extract deformation features from small sample data, leading to low prediction accuracy. To address this issue, this study proposes a novel BDS deformation prediction method considering both global and local features. Firstly, data preparation. To ensure that the model can effectively capture data features, BDS deformation samples for model training are extracted from the raw coordinate time series using a sliding window. Secondly, model design. A Transformer-BiLSTM (Bi-directional Long Short-Term Memory) fusion prediction model is developed, where the Transformer network is designed to capture long-term global deformation features, and the BiLSTM network to extract bi-directional short-term local features. A dense neural network is sequentially added to adjust weights of extracted global and local features. Thirdly, model training. The Tree-structured Parzen Estimator algorithm is introduced to search the optimal model hyper-parameter combination. Subsequently, the optimal fusion prediction model is obtained based on the determined hyper-parameter combination and 80% BDS deformation samples in the data preparation stage. The proposed model is evaluated based on a BDS deformation application of 43 monitoring stations in the year of 2023. Numerical results show that: (1) the prediction accuracies by the proposed model can achieve 2.50 and 3.19 mm in the horizontal and vertical directions, respectively. (2) Compared to the classic LSTM and Transformer models, the proposed fusion model improves the prediction accuracy by 6.3/6.5% and 8.3/10.9% in horizontal/vertical directions, respectively. These results validate both the effectiveness and the superiority of the proposed prediction method for BDS deformation prediction applications with small sample data. In conclusion, the proposed method improves the prediction accuracy with respect to classic methods, offering a novel solution for deformation prediction with small sample data and a promising approach for engineering safety early warning.