## 4 Conclusions  
This paper introduced a model for predicting temperature time series, providing a reliable basis for adjusting the elevation of bridge construction sites. The model integrates advanced machine learning techniques, utilizing convolutional neural network (CNN) layers for initial feature extraction and bidirectional long short-term memory (Bi-LSTM) layers to capture temporal dependencies. An attention mechanism enhances the model's focus during training, allowing it to concentrate on the most relevant parts of the sequence.  
The model's parameters, including the number of LSTM units, dropout rate, and learning rate, were optimized using the CPO algorithm. Experimental results demonstrate that the proposed model outperformed six other models when evaluated on real data from  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Statistic** & **15.0\% Level** & **10.0\% Level** & **5.0\% Level** & **2.5\% Level** & **1.0\% Level** \\ \hline
**BiLSTM** & 0.347 & Normal & Normal & Normal & Normal & Normal \\
**BiLSTM-Attention** & 0.245 & Normal & Normal & Normal & Normal & Normal \\
**Transformer** & 0.232 & Normal & Normal & Normal & Normal & Normal \\
**GRU** & 0.871 & Not Normal & Not Normal & Not Normal & Normal & Normal \\
**CNN-BiLSTM-Attention** & 0.410 & Normal & Normal & Normal & Normal & Normal \\
**Our Model** & 0.280 & Normal & Normal & Normal & Normal & Normal \\ \hline \hline \end{tabular}
\end{table}
Table 6: The Anderson–Darling normality test results for the six models.  
Figure 15: Testing data on different models.  
temperature measurement points on the Xuefeng Lake Bridge. Its low sensitivity to data variations enables it to adapt well to different data environments. The model achieved good prediction accuracy and robustness and eliminated the need for manual network parameter tuning, significantly enhancing its practical value in engineering applications. By applying this model to analyze and predict the collected data, the construction or maintenance plans of the bridge can be adjusted in a timely manner. Overall, the model's ability to accurately predict temperature sequences and its ease of use make it a valuable tool for bridge construction and other engineering applications requiring precise temperature forecasting.  
Although this model has shown great potential in practical engineering applications, there is still room for improvement and expansion. Future work can focus on the following areas: first--further optimizing the algorithm to enhance the model's adaptability to different types of bridges and variable environmental conditions and second--exploring the optimization of more hyperparameters to achieve superior performance.  
Conceptualization, Y.G. and F.G.; Methodology, Y.G., J.W., and F.G.; Software, J.W.; Validation, Y.G.; Formal Analysis, J.W., W.Y., and L.Y.; Investigation, W.Y., L.Y., and F.G.; Resources, W.Y., L.Y., and F.G.; Data Curation, J.W., W.Y., and L.Y.; Writing--Original Draft Preparation, J.W.; Writing--Review and Editing, Y.G.; Visualization, J.W.; Supervision, Y.G.; Project Administration, W.Y. and F.G.; Funding Acquisition, W.Y. and L.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the construction monitoring and technological support unit of the Malukou Zishui Bridge (No: H738012038).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Authors [PERSON] and [PERSON] were employed by the company CCCC Second Harbor Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.