Bridge Structural Health Monitoring Based on Physics-Informed Neural Networks: Research Advances and Review
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摘要:
桥梁结构健康监测（BSHM）在保障桥梁安全运营和延长服役寿命方面具有重要意义. 然而，传统的物理驱动和数据驱动BSHM方法在复杂运营环境、噪声干扰、数据不完备以及模型不确定性等因素影响下，其监测精度与工程适用性往往受到制约. 近年来，物理信息神经网络（PINNs）及广义的物理信息机器学习（PIML）方法发展迅速，为克服传统BSHM方法的局限性提供了新的思路与技术手段. PINNs核心思想是将物理控制方程和边界条件等物理先验知识，显式或隐式地嵌入深度神经网络，从而引导模型在数据学习的同时满足物理一致性并提升泛化性能. 系统梳理PINNs/PIML的理论基础，并对特征空间物理增强、物理模型数据增强、物理知情网络正则化及物理引导网络架构设计等典型物理嵌入策略的优缺点进行比较分析；围绕BSHM中的结构行为建模、参数识别、信号分解与重构以及损伤检测与识别等典型任务，系统总结PINNs在桥梁结构健康监测领域的最新研究进展；讨论基于PINNs的BSHM在实际工程应用中面临的主要挑战与潜在发展方向. 随着深度学习方法与物理建模策略的不断融合，PINNs有望成为桥梁智能运维中的重要技术手段，为提升桥梁状态评估能力和运维决策水平提供支撑.
Abstract:Bridge structural health monitoring (BSHM) plays a critical role in ensuring the safe operation and extending the service life of bridges. However, the monitoring accuracy and engineering applicability of conventional physics-driven and data-driven BSHM methods are often constrained under the influence of complex operational environments, noise interference, data incompleteness, and model uncertainties. In recent years, physics-informed neural networks (PINNs) and generalized physics-informed machine learning (PIML) methods have developed rapidly, providing new ideas and technical means to overcome the limitations of traditional BSHM methods. The core idea of PINNs is to explicitly or implicitly embed physical prior knowledge, such as physical governing equations and boundary conditions, into deep neural networks, thereby guiding the model to satisfy physical consistency while learning data and improving generalization performance. The theoretical foundations of PINNs/PIML were systematically reviewed, and the advantages and disadvantages of typical physics-embedding strategies, including physical enhancement of feature spaces, physical model data augmentation, physics-informed network regularization, and physics-guided network architecture design, were comparatively analyzed. Focusing on typical tasks in BSHM, such as structural behavior modeling, parameter identification, signal decomposition and reconstruction, as well as damage detection and identification, the latest research advances of PINNs in the field of BSHM were systematically summarized. The main challenges and potential development directions faced by PINNs-based BSHM in practical engineering applications were discussed. With the continuous integration of deep learning methods and physical modeling strategies, PINNs are expected to become an important technical means in intelligent bridge operation and maintenance, providing support for improving bridge condition assessment capabilities and operation and maintenance decision-making levels.
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图 2 PINNs中SHM各方向的可解释性描述
Figure 2. Descriptions of interpretability in various SHM domains within PINNs
图 4 基于特征空间物理增强的物理约束嵌入流程
Figure 4. Physical constraint embedding process based on physical enhancement of feature space
图 5 物理知情网络正则化一般架构
Figure 5. General architecture of physics-informed network regularization
图 6 基于物理模型数据增强的物理约束嵌入流程
Figure 6. Physical constraint embedding process based on physical model data augmentation
表 1 结构行为建模与正反问题求解的PINNs相关研究统计
Table 1. Statistics of PINNs-related studies for structural behavior modeling and positive and negative problem solving
文献来源 物理信息类型 嵌入方式 应用场景 Zhang 等[106] 运动微分方程 + Bouc-Wen 模型 ② 非线性结构动力系统的小样本建模与响应预测 Zhang 等[109] 热膨胀效应 + 结构长周期演化趋势 ① 环境变异条件下斜拉桥桥面位移预测 Li 等[108] Euler-Bernoulli 梁偏微分运动方程 ② 非线性梁结构参数求解 Li 等[110] 结构线性状态空间方程 ③ 四自由度框架与悬臂梁的动力响应预测 Meethal 等[107] 静力平衡 ③ 高层建筑风效应不确定性量化 Oh 等[111] 状态空间方程 ③ 梁结构动力响应预测和荷载识别 Guo 等[112] 数值积分时间步进器 ③ + ④ 非线性结构地震响应预测 Kapoor 等[113] Euler-Bernoulli 梁偏微分运动方程 ② 弹性地基梁结构动力学模拟 Kapoo r等[114] Euler-Bernoulli 梁与 Timoshenko 梁的无量
纲运动方程② 单梁与双梁结构动力学模拟与参数求解 Liang 等[115] 结构运动频域方程 ② 移动荷载下的梁动力响应预测和参数求解 Xing 等[116] 四阶龙格-库塔方程与梯度方程 ① + ④ 桥梁结构地震响应预测 Al-adly 等[117] 薄板挠曲控制方程 ② 结构静力学建模与响应预测 Zhang 等[118] 位移、转角连续及力的平衡方程 ② 连续结构系统状态参数估计 Chen 等[119] Koopman 算子线性化 ③ + ④ 多自由度系统动力学建模 Li 等[120] 连续时间状态空间方程 ① + ④ 受迫振动系统的动力响应分析与预测 Li 等[121] 运动微分方程 ① + ④ 混合结构的地震响应建模与实时动力分析 Jeon 等[122] Euler-Bernoulli 梁偏微分运动方程 ③ 复杂大型桥梁结构动力响应预测 Söyleyici 等[123] Euler-Bernoulli 梁偏微分运动方程 ② 梁结构横向振动响应预测 Xiong 等[124] 弹性力学势能变分原理 ② + ③ 结构弹性力学建模与响应预测 注：嵌入方式 ①～④ 分别代表特征空间物理增强、物理知情网络正则化、物理模型数据增强和物理引导网络架构设计. 
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表 2 结构响应分解与重构的PINNs相关研究统计
Table 2. Statistics of PINNs-related studies for structural response decomposition and reconstruction
文献来源 物理信息类型 嵌入方式 应用场景 Zhang 等[129] 运动微分方程 ② 结构地震响应预测与易损性评估 Ni 等[77] 状态变量间的导数关系 ② + ④ 桥梁结构的交通荷载位移重构 Lai 等[130] 基于有限元模型的物理振型与模态解耦 ① + ④ 结构全场响应重建 Baddoo 等[131] 满足矩阵的物理流形 ④ 多域复杂动力系统的响应重构 Fan 等[132] 响应信号的空间位置关联性 ④ 超高建筑缺失响应的时序重构与全场预测 Li 等[127] 基于有限元模型的冲激响应矩阵 ② + ④ 结构全场响应重构 Xu 等[128] 状态变量间的导数关系 ② + ④ 板梁组合结构的动态响应预测及全场动静态位移重构 Liu 等[133] 功率谱密度的一致性、信号高阶统计矩
的物理真实性② + ④ 强震激励下建筑结构缺失响应的重构 孙榕徽等[134] DMD 系统矩阵的流形约束 ② 桥梁结构动态监测信号降噪 Eischens 等[135] 状态变量间的导数关系 ① + ④ 地震激励下Duffing振子的响应重构
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表 3 结构参数识别的PINNs相关研究统计
Table 3. Statistics of PINNs-related studies for structural parameter identification
文献来源 物理信息类型 嵌入方式 应用场景 Liu 等[136] 功率谱密度矩阵分解 ③ + ④ 海上风电结构的实时模态参数识别 Guo 等[137] 频率与刚度显式关系 ② + ③ 框架结构的层间刚度识别 Guo 等[138] 频响函数、交叉特征置信准则 ② 大跨度桥梁的索力识别 徐皓等[91] 运动微分方程 ② 大跨度桥梁的索力识别 Mahar 等[139] 运动微分方程 ② + ④ 框架结构的层间刚度及模态频率识别 Mahar 等[140] 运动微分方程、离散状态空间方程 ② 框架结构的参数估计 DE O Teloli 等[141] Euler-Bernoulli 梁偏微分运动方程 ② 悬臂钢梁的物理参数识别 Luo 等[142] 数值积分算法的动力平衡方程算法层编码 ④ 双跨连续梁模型及悬臂梁试验模型的刚度识别 Liu 等[143] 结构冲激响应矩阵 ④ 简支梁模型的移动荷载识别
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表 4 结构损伤检测与识别的PINNs相关研究统计
Table 4. Statistics of PINNs-related studies for structural damage detection and identification
文献来源 物理信息类型 嵌入方式 应用场景 Figueiredo 等[144] 结构刚度与温度的物理关联模型 ① 桥梁结构损伤检测 Das 等[145] 动态模式分解的结构动力特性提取 ① 混凝土裂缝识别与裂缝扩展预测 Zhang 等[146] 有限元模型的结构特征 ① 风机叶片结构损伤识别 Zhang 等[147] 有限元模型的结构动力特征方程 ① 钢桁人行桥梁损伤识别 Feng 等[148] 断裂力学相场模型 ① 结构剩余寿命预测与损伤演化 Goswami 等[149] 控制方程的变分形式 ② 脆性断裂问题中的替代建模与失效预测 Huang 等[150] 有限元模态参数流形对齐 ① 有限监测数据下的结构损伤检测与识别 Hu 等[151] 结构劣化与退化机理的数学物理模型 ① 混凝土桥面板劣化预测与状态评估 Rojas 等[152] 相场偏微分方程 ② 结构材料参数识别与损伤演化分析 Yamaguchi 等[153] 运动微分方程 + Bouc-Wen 模型 ② 震后 RC 桥墩的损伤识别与状态评估 Chen 等[154] 运动微分方程、结构连接关系矩阵 ① + ④ 结构系统响应预测与局部异常/损伤识别 Peng 等[155] 地震响应信号变分模态分解的分量 ④ 震后轨-桥系统的损伤预测与状态评估 Lei 等[156] 模态参数对损伤变量的灵敏度 ② 简支梁桥结构损伤定位与损伤程度量化 Wang 等[90] 运动微分方程 ② 简支梁结构损伤定位与损伤程度量化
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表 5 基于PINNs的BSHM需求和存在的优缺点总结
Table 5. Summary of PINNs-based BSHM requirements and existing advantages and disadvantages
考虑维度 重点需求 优势 局限性 数据需求 数据类型，数据量，数据质量 少样本学习，物理约束补偿，稀疏数据鲁棒性 噪声敏感，高阶导数放大多源异构融合困难 物理信息依赖 物理模型准确性，完备性 控制方程嵌入，物理一致性，可解释性 模型误差敏感，非线性损伤刻画不足 网络架构设计 网络深度，物理嵌入方式 架构灵活，CNN/GNN 扩展架构级物理引导 架构无统一范式，经验依赖强多尺度建模困难 损失函数构造 物理损失-数据损失平衡 物理残差约束，模态/动力学一致性 损失权重调整困难，训练不稳定 计算代价 训练与推理效率 离线预测高效，参数反演能力 训练成本高，自动微分开销大实时性受限 泛化能力 跨工况，跨结构 外推能力增强，跨工况鲁棒性强 结构依赖性强，跨桥泛化有限 工程可实施性 实际监测条件 物理-数据统一框架，工程潜力高 高质量物理模型依赖，应用门槛高
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