Fast prediction of blast loading for three-dimensional urban building clusters based on Bayesian deep active learning

To address the high cost and low sample efficiency of deep learning-based blast loading prediction in urban environments, a Bayesian deep active learning (BDAL) method is proposed. The objective is to significantly reduce the dependency on large-scale, high-fidelity numerical simulation data while maintaining prediction accuracy and providing reliable uncertainty quantification. A three-dimensional typical urban building cluster consisting of a 3×3 regular array of cuboid buildings was constructed. A seven-dimensional parameter space was defined, including explosive charge equivalence (1000, 2000, 3000 kT), detonation distance (1000, 2000, 3000 m), building length (10, 20, 30 m), building width (20, 40 m), building height (75, 100 m), street length (50, 75, 100 m), and street width (50, 75 m). A full factorial experimental design was employed, generating 648 parameter combinations. For each combination, the open-source computational fluid dynamics (CFD) software blastFoam was used to perform three-dimensional numerical simulations of blast wave propagation. The background mesh size was set to 30 m based on grid sensitivity analysis, and adaptive mesh refinement (AMR) with local refinement level 2 and dynamic refinement level 1 was applied to capture shock wave details. Peak overpressure values were recorded at 12 points of interest (POIs) in the building cluster, resulting in a dataset of 7776 samples. A BDAL framework was then developed. Bayesian inference was integrated into a deep neural network to enable probabilistic modeling of parameters. Monte Carlo (MC) dropout was adopted as an approximate variational inference method to estimate predictive uncertainty. An uncertainty-driven active sampling strategy was designed: the predictive variance of each unlabeled sample was computed via 30 stochastic forward passes with dropout enabled. Samples with variance exceeding 85% of the maximum variance were selected as candidates, and the top 28 cases (336 samples) with the highest variance were chosen in each active learning cycle. These selected samples were labeled by the blastFoam simulator and added to the training set. The model was retrained iteratively until the relative improvement in mean absolute percentage error (MAPE) fell below 1% or the labeled set reached the full training size. On a test set of 780 unseen samples (65 cases), the proposed BDAL method achieved an MAPE of 13.1% and an R² of 0.972 for peak overpressure prediction. The 95% prediction interval covered the true values in 85.9% of the cases, with a normalized mean prediction interval width (NMPIW) of 0.026. Single-point prediction response time was below 20 ms, representing a speedup of more than 10⁵ compared to high-fidelity numerical simulations. Compared to passive deep learning models trained on the full dataset, the BDAL method required only about 50% of labeled data to reach comparable prediction accuracy. In a comparative experiment with 50% training data, BDAL achieved a MAPE of 17.2%, while a conventional fully connected neural network (FCNN) and a three-dimensional direction-encoded Bayesian neural network (3D-DeBNN) gave MAPEs of 52.9% and 22.6%, respectively. The proposed Bayesian deep active learning method enables efficient and low-cost blast loading prediction in typical regularized urban environments. It effectively reduces the dependency on large-scale numerical simulation data, maintains high prediction accuracy and reliable uncertainty quantification, and meanwhile achieves millisecond-level inference speed. The method shows strong potential for disaster prevention and mitigation applications, such as pre-disaster anti-blast design and post-disaster emergency response.