This paper derives a formula to determine the minimum detectable damage based on ambient vibration data. It is a key element to analyze which damage scenarios can be detected before a monitoring system is installed. For the analysis, vibration data from the reference structure as well as a finite element model are required. Minimum detectability is defined by adopting a code-based reliability concept that considers the probability of detection and the probability of false alarms. The results demonstrate that the minimum detectable damage depends on three elements: the uncertainty of the damage-sensitive feature (which decreases with increasing measurement duration), its sensitivity towards model-based design parameters, and the reliability requirements regarding the damage diagnosis results. The theory is developed for the stochastic subspace-based damage detection method but can be applied to any damage-sensitive feature provided its sensitivities and statistical properties can be characterized. For proof of concept, the minimum detectable change in stiffness and mass of a pin-supported beam are analyzed in a numerical and experimental study, respectively. The predictions with the developed approach appear to be accurate and robust to noise effects for both simulated and real data.

本文推导了一个公式，用于根据环境振动数据确定最小可检测的损坏。这是分析在安装监控系统之前可以检测到哪些损坏情况的关键要素。为了进行分析，需要参考结构的振动数据以及有限元模型。最低可检测性是通过采用基于代码的可靠性概念来定义的，该概念考虑了检测的概率和错误警报的概率。结果表明，可检测到的最小损坏取决于三个因素：损坏敏感特征的不确定性（随着测量持续​​时间的增加而降低），对基于模型的设计参数的敏感度以及关于损坏诊断结果的可靠性要求。该理论是为基于随机子空间的损伤检测方法而开发的，但是只要可以表征其敏感性和统计特性，它就可以应用于任何对损伤敏感的特征。为了进行概念验证，分别在数值研究和实验研究中分析了销支撑梁的刚度和质量的最小可检测变化。使用已开发方法的预测对于模拟和实际数据的噪声影响似乎都是准确且可靠的。