On the use of Gaussian Process Regression of transmissibility functions for loosening detection in bolted structures under excitation level variations

Bolted joints are widely used in industrial structures, but they require regular inspections to prevent failures such as bolt loosening. Conventional inspections are costly and time-consuming, as they involve manual checks and downtime. Therefore, indirect detection of loosening is a major challenge, further complicated by variability and nonlinear effects. This paper proposes a damage detection approach that avoids feature extraction by using the raw frequency response signal. A Gaussian Process Regression (GPR) model is directly trained on transmissibility functions to build a baseline model in the frequency domain. A GPR-based damage index is then formulated to detect outliers relative to this baseline. To improve sensitivity, a Global Sensitivity Analysis (GSA) with Sobol’s indices is applied as a feature selection method, identifying frequency ranges most affected by loosening. The paper also extends the GPR-based model to a three-dimensional formulation that captures the evolution of nonlinear behavior as input levels increase. In this way, the GPR-based damage index can distinguish different motion regimes and separate changes caused by nonlinear regime transitions from those caused by loosening. In summary, with proper feature selection, the proposed probabilistic frameworks reliably detect bolt loosening while minimizing false diagnoses in a clear way. • Efficient monitoring methods for bolted joints are required to reduce reliance on costly manual inspections. • Gaussian Process Regression (GPR) is trained directly on transmissibility functions, thereby eliminating the need for feature extraction. • A GPR-based damage index identifies loosening by detecting outliers relative to a healthy baseline. • Sobol-based GSA identifies frequency ranges most sensitive to loosening. • 3D GPR captures nonlinear effects, improving sensitivity and reducing false alarms.