Rapid seismic vulnerability assessment using closed-form damage index equations obtained via explainable machine learning

In the early stages of seismic vulnerability assessment for a large number of structures, Seismic Damage Indices (SDIs) are computed to quantify the overall damage state. The Maximum Interstory Drift Ratio (MIDR) is widely employed, yet it is conventionally evaluated through computationally intensive nonlinear time history analyses (NTHAs). Machine Learning (ML) algorithms have been previously employed for this task, but their lack of interpretability limits their adoption into practice. This research effort aims to bridge this gap, by developing analytical equations to estimate MIDR, which approximate the behavior of a fully trained ML model. This task was carried out by employing the SHapley Additive exPlanations (SHAP) methodology, which is commonly utilized as a valid explainability tool. A Light Gradient Boosting Machine model was initially trained, which achieved very high accuracy. Subsequently, analytical terms were fitted to the SHAP values of each feature. The final equations, obtained via the so-called “SHAP additive property”, reached comparable high performance levels, with the underlying ML model. Furthermore, they correctly classified the damage state, especially for the “Heavy” and “Slight” damage classes. The overall results are promising, and they indicate the potential applicability of the proposed methodology in real life cases.