Multivariate GP-VAR models for robust structural identification under operational variability

While the concept of structural monitoring has been around for a number of decades, it remains under-exploited in practice. A main driver for this shortcoming lies in the difficulty to robustly and autonomously interpret the information that is extracted from dynamic data. This hindrance in properly deciphering the collected information may be attributed to the uncertainty that is inherent in i) the finite set of measured data, ii) the models employed for capturing the manifested dynamics, and more importantly, iii) the susceptibility of these systems to variations in Environmental and Operational Parameters (EOPs). In previous work of the authors, a Gaussian Process (GP) time-series approach has been introduced, which serves as a hierarchical input-output method to account for the influence of EOPs on structural response. This in turn enables a robust structural identification. In this scheme, the short-term dynamics are modeled by means of linear-in-the-parameters time-series models, while EOV dependence - acting on a long-term time scale - is achieved via GP regression of the model coefficients on measured EOPs. This work corresponds to a further advancement on this modeling approach, corresponding to its generalization to the vector response case. Particularly, the problem of global identification here is solved via an Expectation-Maximization algorithm tailored to the GP time-series model structure. Moreover, an EOP-dependent innovations covariance matrix is integrated in the model, which helps to capture variation in the vibration power. The resulting model does not only have the capability to represent the long-term response of a structure under variable EOPs, but also facilitates the enhanced tracking of modal quantities in contrast to traditional operational modal analysis techniques. The proposed approach is exemplified on the identification of the vibration response of a simulated wind turbine blade at different points along the blade axis in the flap-wise direction, under variability of both the acting wind speeds and ambient temperatures.