Fatigue damage detection in beam-like structures under random loading: a multi-stage energy dissipation-based approach using logistic regression, bagging trees, and GRU neural networks

• Two-Step Methodology: The study proposes a two-stage approach for fatigue damage identification in beams—first locating damage using logistic regression and then classifying damage severity using Bagging Decision Trees (BDT) and Gated Recurrent Units (GRU). • Use of Energy Dissipation Features: Dynamic features based on energy dissipation, which are sensitive to stiffness loss, are used as input data for both damage location and severity assessment. • Performance of First Stage: Logistic regression successfully detects damage locations, especially at point P5 (AUC 0.990, 95.7 % accuracy). • Comparison of Second-Stage Models: BDT performs well in detecting hidden damage (e.g., 0.98 recall at P4), making it suitable for critical cases, while GRU provides more balanced, consistent results across all points, indicating better generalization. Additionally, GRUs struggle with detecting subtle anomalies, resulting in slightly lower accuracy than BDTs. This study proposes a two-step damage identification methodology for assessing fatigue damage in beam structures, effectively integrating machine learning and deep learning techniques. The method leverages dynamic features extracted from the energy dissipation, an indicator highly sensitive to stiffness loss and fatigue damage. In the first step, a logistic regression model is employed to pinpoint the location of damage. This model takes a vector of correlation coefficients, derived from the energy dissipation function of individual beam elements, as its input, enabling an accurate classification of damaged areas. The second step focuses on quantifying the severity of the damage at the identified location. To achieve this, two models are developed and compared: a traditional Bagging Decision Tree and a Gated Recurrent Unit (GRU), a type of recurrent neural network. Both models are trained on the energy dissipation data. While the Bagging Decision Tree achieved a higher overall accuracy, the GRU model demonstrated a more balanced and consistent performance across key metrics such as precision and recall. The results confirm the efficacy of the proposed two-step approach in detecting and quantifying fatigue damage, highlighting the significant potential of deep learning techniques in the field of Structural Health Monitoring (SHM) and providing a powerful, stable diagnostic tool for structural engineering applications.