Comparing Static and Dynamic Regression Models for Temperature Compensation in Vibration-Based SHM Systems

Vibration-based structural health monitoring systems consistently assess the condition of structures by monitoring their modal parameters. However, the estimated modal parameters can be influenced by several factors, including environmental and operational variabilities such as temperature fluctuations. Such variations can trigger false alarms, in the healthy state, or can hinder the detection of anomalies when the structure is damaged. To address this issue, temperature compensation techniques are commonly employed to remove the effect of temperature fluctuations from the modal data. One prevalent approach involves developing a regression model based on a database representative of the healthy structure, in which the independent variables are temperatures, while the target variables are the modal parameters. There are two primary categories of regression used for this purpose: static and dynamic. In the static approach, real-time temperature values are used with the corresponding samples of modal parameters. Conversely, the dynamic approach also incorporates past temperature data as independent parameters. This is particularly important due to the time delay in heat transmission from the environment to the structural core. This delay introduces a nonuniform temperature distribution within the structure, influenced by past temperature values. In this study, we will conduct a numerical comparison between static and dynamic compensation techniques. Different regression models and time delays will be considered, with a focus on evaluating the probability of false alarms (PFA) and the probability of damage detection (POD). The results show that the dynamic approach lead to an improved POD.