圖神經網路於線性靜力分析之應用

Linear Static Analysis with Graph Neural Networks

周遠同(Yuan-Tung Chou) ； 黎光曜(Kuang-Yao Li) ； 郭柏志(Po-Chih Kuo) ； 張慰慈(Wei-Tze Chang) ； 黃尹男(Yin-Nan Huang) ； 陳俊杉(Chuin-Shan Chen)

《結構工程》 37卷4期 (2022/12) Pp. 27-40

https://doi.org/10.6849/SE.202212_37(4).0002

摘要

結構設計是朝向最佳化的迭代過程，目前多依賴結構工程師過往的經驗結合結構分析的結果完成。結構最佳化設計需反覆進行結構分析，如何加速結構分析則是重要的突破關鍵。本研究使用深度學習模型作為線性靜力分析之代理模型，提供快速即時且精準之結構反應預測。因著結構物之空間幾何關係與圖資料結構之間之相似性，本研究將結構物表達成圖，並以圖神經網路模型去學習結構物所受之外力與結構物反應之間的關係。在透過由結構軟體所生成包含隨機樓層數、跨數、樑柱長度，以及隨機大小的側向外施載重之結構分析資料集訓練後，圖神經網路模型不僅顯示了其在預測位移以及力具有良好之表現，模型也具有很好之泛化能力，能夠預測在訓練時從未接觸過的、更高的結構物。在特徵重要性分析中也顯示模型所學習到之特徵具有一定之物理意義。

並列摘要

Structural design is an iterative process for optimum selection, which relies on structural analysis results and experience from structural engineers. Since iterative structural analysis is a necessary for getting a good design, accelerating structural analysis is an important task. In this work, we adopt deep learning approaches as a surrogate model for linear static analysis, which provides fast and accurate structural response prediction. Based on the similarity between the structure's topology and graph data structure, we represent structures as graphs and leverage graph neural networks (GNNs) to learn the relationship between given external forces and corresponding structural responses. The GNN model is trained with random-generated structures, including random story number, span number, beam-column length, and value of external forces. The results show that the GNN model has good performance on displacement and force predictions and excellent generalizability on unseen, taller structures. In addition, it is shown that based on the analysis of feature importance, the GNN model can extract important physical attributes from the input features.

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