圖深度學習於非線性歷時分析及結構斷面設計最佳化之應用

Abstract

近年來，隨著人工智慧領域的發展，機器學習、深度學習技術逐漸被使用在結構工程的領域中，包括此研究主要探討的兩個主題：結構分析及結構斷面設計。然而，過去以機器學習預測結構分析及最佳化斷面設計的研究仍有諸多限制，例如結構系統規模、對不同結構之泛用性、結構分析之預測目標反應、無法基於歷時分析設計斷面等。因此，本研究提出一系列基於圖神經網路 (graph neural network) 之深度學習方法，對現有以機器學習預測結構分析和最佳化斷面方法所遇之瓶頸進行改善。 在將鋼結構以圖 (graph) 資料結構表示後，本研究基於此表示法進行了三項結構工程之研究。第一項研究透過一訊息傳遞層 (message-passing layer) 數量會隨著輸入結構樓層數改變之圖神經網路，對結構在受到外施載重下靜力分析之結構反應進行預測。第二項研究透過結合圖神經網路與長短期記憶模型 (long short-term memory network) 預測不同幾何形狀之結構在不同地震下之非線性歷時反應。第三項研究結合圖神經網路及強化學習 (reinforcement learning) ，以持續縮減斷面尺寸之方式對結構之斷面設計進行最佳化，並融入第二項研究中所預測之非線性歷時反應，作為斷面設計時檢核之條件，以得到在不同強度考慮情況下最佳化之設計。 數值結果驗證了此基於圖神經網路方法之可行性。在第一項研究中，靜力分析之位移、剪力、彎矩預測皆達到99\%之相對準確率，且模型在更高、未看過之結構也有96\%之準確率。在第二項研究中，模型在非線動力分析之加速度、速度、位移、彎矩、剪力歷時預測皆能達到0.90之決定係數 ($R^2$)，而在峰值預測更達到0.95。在最後第三項研究中，模型在70\%以上不同幾何形狀之鋼結構中，得到之設計會比90\%經由抽樣產生之設計更好，且多考慮歷時分析時，產生之斷面設計有更好的耐震能力。

In recent years, machine learning and deep learning techniques have gradually been applied in the field of structural engineering. However, previous studies in the machine-learning-based prediction of structural analysis and section design optimization have encountered various limitations, such as scalability issues, lack of generality across different structures, limitations in predicting target responses in structural analysis, and the inability to incorporate nonlinear response-history analysis in section design. To address these limitations, this research proposes a series of deep learning methods based on graph neural networks to improve the prediction of structural analysis and section design optimization and overcome the existing bottlenecks. This study investigates three areas of structural engineering using the graph representation of steel structures. The first study focuses on predicting the structural response under external loads using a graph neural network with a dynamic number of message-passing layers. The second study combines graph neural networks with long short-term memory models to predict the nonlinear response-history responses of structures under earthquakes. The third study integrates graph neural networks and reinforcement learning to optimize section design by iteratively reducing section sizes and incorporating the predicted nonlinear response-history responses from the second study as design constraints. The numerical results confirm the feasibility of the graph neural network approach used in this study. In the first study, the relative accuracy of predicting displacements, shear forces, and bending moments in static analysis reached 99\%, with a 96\% accuracy rate even for unseen structures. In the second study, the model achieved determination coefficients ($R^2$) of 0.90 for predicting accelerations, velocities, displacements, bending moments, and shear forces in nonlinear dynamic analysis, and a peak prediction accuracy of 0.95. In the final study, over 90\% of the model's section designs outperformed over 70\% of the designs sampled from the input space. Furthermore, when incorporating the additional consideration of response-history analysis, the generated section designs demonstrated improved seismic performance.