Modeling and diagnosis of structural systems through sparse dynamic graphical models

• SHM systems which treat each sensor individually have reduced sensitivity to damage.
• Jointly modeling all sensors allows for detection of structural inconsistencies.
• Structural knowledge can be built in to better improve estimation and scalability.
• Graphical models can be used to isolate and locate damage within the structure.

Since their introduction into the structural health monitoring field, time-domain statistical models have been applied with considerable success. Current approaches still have several flaws, however, as they typically ignore the structure of the system, using individual sensor data for modeling and diagnosis. This paper introduces a Bayesian framework containing much of the previous work with autoregressive models as a special case. In addition, the framework allows for natural inclusion of structural knowledge through the form of prior distributions on the model parameters. Acknowledging the need for computational efficiency, we extend the framework through the use of decomposable graphical models, exploiting sparsity in the system to give models that are simple to fit and understand. This sparsity can be specified from knowledge of the system, from the data itself, or through a combination of the two. Using both simulated and real data, we demonstrate the capability of the model to capture the dynamics of the system and to provide clear indications of structural change and damage. We also demonstrate how learning the sparsity in the system gives insight into the structure׳s physical properties.