Population-based structural health monitoring (PBSHM) aims to share valuable information among members of a population, such as normal- and damage-condition data, to improve inferences regarding the health states of the members. Even when the population is comprised of nominally-identical structures, benign variations among the members will exist as a result of slight differences in material properties, geometry, boundary conditions, or environmental effects (e.g., temperature changes). These discrepancies can affect modal properties and present as changes in the characteristics of the resonance peaks of the frequency response function (FRF). Many SHM strategies depend on monitoring the dynamic properties of structures, so benign variations can be challenging for the practical implementation of these systems. Another common challenge with vibration-based SHM is data loss, which may result from transmission issues, sensor failure, a sample-rate mismatch between sensors, and other causes. Missing data in the time domain will result in decreased resolution in the frequency domain, which can impair dynamic characterisation. The hierarchical Bayesian approach provides a useful modelling structure for PBSHM, because statistical distributions at the population and individual (or domain) level are learnt simultaneously to bolster statistical strength among the parameters. As a result, variance is reduced among the parameter estimates, particularly when data are limited. In this paper, combined probabilistic FRF models are developed for a small population of nominally-identical helicopter blades under varying temperature conditions, using a hierarchical Bayesian structure. These models address critical challenges in SHM, by accommodating benign variations that present as differences in the underlying dynamics, while also considering (and utilising), the similarities among the blades.

翻译：基于群体的结构健康监测（PBSHM）旨在共享群体成员间的有价值信息（如正常与损伤状态数据），以改进对成员健康状态的推断。即使群体由名义上相同的结构组成，材料属性、几何形状、边界条件或环境效应（如温度变化）的细微差异仍会导致良性变异。这些差异会影响模态特性，并表现为频率响应函数共振峰特征的变化。许多结构健康监测策略依赖于监测结构的动态特性，因此良性变异可能对这些系统的实际实施构成挑战。基于振动的结构健康监测中另一个常见问题是数据丢失——这可能源于传输故障、传感器失效、传感器间采样率不匹配等原因。时域数据缺失将导致频域分辨率下降，进而影响动态特性表征。分层贝叶斯方法为群体结构健康监测提供了有效的建模框架，因为其能同时学习群体和个体（或域）层的统计分布以增强参数间的统计强度，从而减少参数估计的方差，尤其在数据有限时效果显著。本文针对小规模名义相同直升机叶片群体在变温条件下的情况，采用分层贝叶斯结构开发了联合概率频率响应函数模型。这些模型通过包容表现为底层动力学差异的良性变异，同时考虑（并利用）叶片间的相似性，解决了结构健康监测中的关键挑战。