以物理引導生成式 AI 發展高擬真結構模型更新與反應預測方法

Abstract

有限元素模型 (Finite Element Model, FEM) 作為在以振動數據為主的結構健康監測 ( Structural Health Monitoring, SHM ) 中的數位孿生核心，卻常因傳統更新後仍殘存的差異，以及高品質量測資料長期匱乏而難以發揮效能。本研究提出殘差導向之有限元素模型更新框架，利用深度神經網路顯式學習模擬與量測反應之間的固有差異，並將預測殘差嵌入全新的目標函數，再以迭代式最佳化演算法最小化該目標。在柱的勁度折減係數更新中，單參數更新之相對誤差可達 0.70 %，多參數更新之相對誤差為 0.48 %，較傳統方法降低 0.10 %，且在實務高雜訊情境下優勢更為明顯。實驗驗證顯示，本方法能準確辨識所有預設損傷情境；於 40 維參數更新中，分別較基線方法提升準確率 0.9 %、精確率 2.1 %、召回率 16.6 %、F1 分數 4.5 %、平衡準確率 7.2 %。然而，深度學習模型仰賴充足且平衡的結構反應資料，現地量測的結構反應多以健康狀態為主，損傷資料嚴重不足，限制了以殘差為主之有限元素模型更新的潛力。為緩解資料稀缺，本研究進一步提出物理導向條件式生成框架 (Structural Response Diffusion, SRD)。SRD 結合自編碼器重建結構反應、編碼結構配置與損傷狀態的圖神經網路，以及條件化潛在擴散模型，可在圖、外力與時間嵌入條件下，將高斯雜訊去噪生成全長加速度訊號。於資料稀缺且類別失衡之模擬測試中，SRD 所生成之樣本將最少樣本類別的 F1 分數在數值驗證中自 1.9% 提升至 65.4%，並於實驗驗證自 31.8% 提升至 44.8%，同時增進整體指標表現。生成訊號的 KL 散度 ( KL divergence) 低於 0.1，且在降維空間與真實資料高度重疊，驗證其分佈的高度相似性。綜合而言，兩項框架構成閉環SHM 作業流程，SRD 提供符合物理條件的合成資料以強化殘差網路訓練，經校準的 FEM 則作為精準數位孿生以支援預測與決策。此協同機制提供一個可擴展的方法以實現更可靠的基礎設施監測。

Finite element models (FEMs) serve as the digital twins at the heart of vibration-based structural health monitoring (SHM). However, their effectiveness is hindered by inherent discrepancies that persist after conventional updating and by the chronic scarcity of high-quality response measurements. In this study, a residual‐based finite element model updating (FEMU) framework is developed in which a deep neural network explicitly learns the inherent discrepancy between simulated and measured responses. By embedding the learned residual into a new objective and minimizing it with iterative optimizers, our FEMU framework achieves a 0.70 % relative error for single-parameter updates and 0.48 % relative error for multi-parameter column stiffness reduction factor estimation. The framework reduces the relative error by 0.10% compared to conventional approaches, with the advantage widening as measurement noise grows in a real-world scenario. Experimental tests confirm that the proposed method accurately identifies all predefined damage scenarios. In a 40-parameter update, it outperforms the baseline by 0.9%, 2.1%, 16.6%, 4.5%, 7.2% in accuracy, precision, recall, F1 score, balanced accuracy, respectively. However, the full potential of our residual-based FEMU is constrained by a familiar bottleneck: deep learning (DL) models require abundant, well-balanced structural response data, whereas civil structures rarely generate large datasets, and most available vibrations correspond to healthy states, leaving damaged conditions severely underrepresented. To alleviate data scarcity, a physics-guided conditional generative framework, Structural Response Diffusion (SRD), is introduced. SRD combines an autoencoder for structural response reconstruction, a graph neural network-based encoder that encodes structural configuration and damage state, and a latent diffusion model that denoises Gaussian noise into full-length acceleration traces conditioned on graph, force, and temporal embeddings. In the simulated test under data scarcity and class imbalance, the synthetic responses augment the most underrepresented damage class, lifting its F1 score from 1.9% to 65.4% in numerical validation and from 31.8% to 44.8% in experimental validation, while improving the overall performance in both phases. Generated signals exhibit low KL divergence (< 0.1) and strong overlap with real data in the reduced space, confirming distributional similarity. Together, the two frameworks form a closed-loop SHM pipeline. SRD supplies physics-consistent data to train the residual network robustly, and the calibrated FEM provides an accurate digital twin for forecasting and decision support. This synergy provides a scalable approach to more reliable monitoring of civil infrastructure.