Damage identification attracts wide attention and in-depth research in numerous engineering fields for its paramount importance for systems safety and operational assessment. Among the proposed techniques, structural vibration-based ones are increasingly considered. There are two main reasons behind this progression: a practical motivation, related to the aptitude of dynamic tests in capturing the real behaviour of structural systems,^1,2 and a technological reason, related to the reduction of costs and the miniaturisation of the electronic acquisition devices.³ Vibration-based structural health monitoring systems are nowadays widespread, for both new and existing structural systems, and dynamic structural damage identification is a new target of a wide scientific community.⁴ However, this task is intrinsically more complicated than the ‘mere’ structural identification one, since it calls for extracting damage-sensitive features over time from periodically spaced response measurements. Mathematical models derived from physical basis are used for modelling mechanical systems, often resorting to output-only modal parameter estimation methods^5,6; alternatively, data-driven models describing the systems input–output relation are adopted. A trade-off between the two approaches is based on the combination of both, physical insights and experimental data. As reported in the comprehensive reviews published in the last two decades,^7–9 the variety of proposed identification strategies are devised to detect, localise, quantify damage and, ultimately, to estimate the remaining service life of the structure. These goals are pursued by relying on different quantities, i.e. physical properties (mass, stiffness, damping), modal properties (natural frequencies, mode shapes, modal damping) and structural response signal features (e.g. Fourier, Wavelet or Hilbert transform). In essence, all the identification strategies aim at extracting reliable signs for early diagnosis of structural damage from the least amount of data. For most real structural systems, direct measurement of global physical properties and their variations, possibly ascribable to damage, is unfeasible; therefore, local, albeit numerous, dynamic response quantities are usually relied upon. Modal property-based approaches seek after dynamic response alteration due to damage, which is usually expected to cause a change in stiffness. Predictive models and physically sound interpretations can be provided by these approaches. However, some difficulties may arise, such as the need to rely on accurate structural modelling and to select proper response signals, not to mention the lack of solution uniqueness of the inverse problem. Differently, signal processing-based techniques seek after signals changes, in time and frequency, between undamaged and damaged states. Direct evidence of signals alteration can be readily detected; however, its physical interpretation is often cumbersome.

中文翻译：

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基于正交经验模态分解的伪模态结构破坏指数

损伤识别以其对系统安全和运行评估的最重要意义，在众多工程领域引起了广泛的关注和深入的研究。在提出的技术中，越来越多地考虑基于结构振动的技术。这一进展背后的主要原因有两个：与动态测试在捕获结构系统实际行为中的能力有关的实际动机^1,2，以及与降低成本和电子采购小型化有关的技术原因。设备。³对于新的和现有的结构系统，如今，基于振动的结构健康监测系统已经广泛使用，动态结构损坏的识别是广泛科学界的新目标。⁴然而，此任务本质上比“单纯的”结构识别要复杂，因为它要求随着时间的推移从周期性间隔的响应测量中提取对损伤敏感的特征。从物理基础得出的数学模型用于机械系统建模，通常采用仅输出模态参数估计方法^5,6；或者，采用描述系统输入输出关系的数据驱动模型。两种方法之间的权衡基于物理洞察力和实验数据两者的结合。正如过去二十年来发表的综合评论中所报告的，^7-9设计了各种建议的识别策略来检测，定位，量化损坏，并最终估计结构的剩余使用寿命。这些目标是通过依靠不同的数量来实现的，即物理特性（质量，刚度，阻尼），模态特性（固有频率，模态，模态阻尼）和结构响应信号特征（例如傅立叶，小波或希尔伯特变换）。从本质上讲，所有识别策略都旨在从最少的数据中提取可靠的迹象，以便对结构损坏进行早期诊断。对于大多数实际的结构系统，直接测量可能会造成损坏的全球物理特性及其变化是不可行的；因此，通常依靠局部的动态响应量，尽管数量众多。基于模态特性的方法追求的是由于损坏而引起的动态响应变化，通常希望引起刚度的变化。这些方法可以提供预测模型和物理上合理的解释。但是，可能会出现一些困难，例如需要依赖准确的结构建模并选择适当的响应信号，更不用说缺少反问题的唯一性。不同的是，基于信号处理的技术会寻找信号在未损坏状态和损坏状态之间的时间和频率变化。信号改变的直接证据很容易被发现；但是，其物理解释通常很麻烦。这些方法可以提供预测模型和物理上合理的解释。但是，可能会出现一些困难，例如需要依赖准确的结构建模并选择适当的响应信号，更不用说缺少反问题的唯一性。不同的是，基于信号处理的技术会寻找信号在未损坏状态和损坏状态之间的时间和频率变化。信号改变的直接证据很容易被发现；但是，其物理解释通常很麻烦。这些方法可以提供预测模型和物理上合理的解释。但是，可能会出现一些困难，例如需要依赖准确的结构建模并选择适当的响应信号，更不用说缺少反问题的唯一性。不同的是，基于信号处理的技术会寻找信号在未损坏状态和损坏状态之间的时间和频率变化。信号改变的直接证据很容易被发现；但是，其物理解释通常很麻烦。基于信号处理的技术寻求信号在未损坏和损坏状态之间的时间和频率变化。信号改变的直接证据很容易被发现；但是，其物理解释通常很麻烦。基于信号处理的技术寻求信号在未损坏和损坏状态之间的时间和频率变化。信号改变的直接证据很容易被发现；但是，其物理解释通常很麻烦。