結合不同延遲之相空間吸引子與深度學習應用於沖刷深度預測

Abstract

近年來，氣候變遷使得沖刷的議題愈顯重要，增加跨河橋梁遭受基礎沖刷的頻率。為確保橋梁安全，本研究開發一種結合相空間吸引子與卷積神經網路的數據驅動方法，以即時監測與預測橋梁基礎沖刷深度。在相空間吸引子的重建中，本研究透過時間延遲法重構相空間吸引子，以提取橋梁結構在不同沖刷狀態下的動態特徵；而在沖刷深度的預測中，則利用卷積神經網路自提取特徵的優勢，將前述動態特徵以灰階影像圖的方式進行分類與判讀。 本研究先使用時間延遲法，利用相空間吸引子的概念描述沖刷橋梁的動態特徵，基於Takens嵌入定理將單顆速度或加速度計的歷時訊號重構沖刷橋梁的高維吸引子。其次，將重建的高維吸引子轉換成二維灰階影像，利用卷積神經網路識別以獲得沖刷深度。在時間延遲法中，本研究配合適當參數，將感測器收集到的速度與加速度時間序列轉換為吸引子矩陣，並生成灰階影像圖作為卷積神經網路模型的輸入。模型訓練過程中，本研究探討了不同感測器位置（橋柱頂部、中部、底部）對沖刷深度預測的影響，並比較平均交互資訊與Menger曲率法在吸引子矩陣中，延遲參數選取上的適用性。 本研究的測試結果驗證了將動態系統理論與深度學習技術應用於橋梁沖刷監測的可行性，測試結果也同時表明，在沖刷深度較淺時，本研究提出的深度學習方法可比傳統基於振動頻率改變量迴歸公式的方法更準確的預測沖刷深度。

In recent years, climate change has made the issue of scour increasingly significant, raising the frequency of the foundation scour affecting cross-river bridges. To ensure the safety of bridge, this study develops a data-driven method that integrates phase space attractors and convolutional neural networks (CNNs) for real-time monitoring and prediction of scour depths of bridge foundations. In the reconstruction of phase space attractors, this study employs the time delay method, extracting the dynamic features of bridge structures under different scour conditions. For scour depth prediction, CNNs are utilized for their ability to automatically extract features, classifying and interpreting the previously extracted dynamic features through grayscale images. Firstly, this study applies the time delay method, leveraging the concept of phase space attractors to describe the dynamic characteristics of scoured bridges. Based on Takens’ embedding theorem, the time history signals from a single velocity or acceleration sensor are reconstructed into a high-dimensional attractor which represents scoured bridges. Then, the reconstructed high-dimensional attractor is transformed into a two-dimensional grayscale image, subsequently analyzed using CNNs to determine the scour depth. In the time delay method, appropriate parameters are selected to convert the velocity and acceleration time series collected by sensors into attractor matrices, which are then used to generate grayscale images as inputs for the CNN model. During model training, this study examines the impact of different sensor placements (top, middle, and bottom of the bridge pier) on scour depth prediction and compares the applicability of Average Mutual Information (AMI) and Menger Curvature methods in selecting delay parameters for attractor matrices. The results validate the feasibility of applying dynamical system theory and deep learning techniques to bridge scour monitoring. The tests also demonstrate that for the cases when the scour is not severe, the proposed deep learning method achieves more accurate scour depth predictions than conventional vibration-based methods relying on the regression of modal frequency changes.