NGBoost-Naïve Bayes collaborative deep learning for structural safety evaluation of bridges

In structural safety evaluation, machine learning (ML) based methods often exhibit strong data-fitting capabilities but struggle to effectively handle uncertainties in structural response data. Fortunately, Bayesian deep learning (BDL) algorithms can address this drawback by integrating the Bayesian theory with ML algorithms, thereby unifying perception and inference tasks within a single framework. For this purpose, a BDL framework has been proposed combining natural gradient boosting (NGBoost) and the Naïve Bayes theory. The NGBoost serves as the perception component, capturing correlations between deflections at various measurement locations of a healthy structure, while the Shapley Additive Explanation (SHAP) is employed to enhance interpretability. During the training process, the optimal hyperparameters of the NGBoost is objectively determined through Bayesian optimization (BO). The predicted probability distributions of these deflections are treated as hinge variables. By applying the triple standard deviation principle, a structural safety interval is defined to identify scenarios requiring further evaluation. The task-specific component, based on the Naïve Bayes theory, is then utilized to evaluate the structural condition. A bridge benchmark model was used to verify the safety assessment performance under the limited training samples. In addition, a continuous box-girder bridge was employed to further validate the effectiveness of the proposed structural condition indicator. As the structural degradation increased, the condition indicator accurately reflected the degradation variation.