Fast estimation of blast loading in complex structures based on Bayesian deep learning

For the estimation of blast loading in complex structures, traditional numerical simulation methods were computationally intensive whereas rapid estimation methods based on neural networks can only provide estimates at local points without providing confidence intervals for the predicted results. To achieve fast and reliable estimation of the blast loading in complex structures, Bayesian theory was combined with deep learning to develop a Bayesian deep learning approach for rapid estimation of blast loading in complex structures. The approach initially utilized open-source numerical simulation software to generate a dataset of blast loading in complex structures, encompassing a wide range of parameters such as explosion equivalents, locations, and velocities. During this process, mesh sizes that balanced computational accuracy and speed were determined through mesh sensitivity analysis and the verification of the numerical simulation accuracy. Then, the deep learning model was extended into a Bayesian deep learning model based on Bayesian theory. By introducing probability distributions over the weights of the neural network, the model parameters were treated as random variables. Variational Bayesian inference was then employed to efficiently train the model, ensuring the accuracy of rapid blast loading estimation while also equipping the model with the ability to quantify uncertainty. Finally, metrics such as mean absolute percentage error (MAPE), normalized mean prediction interval width (NMPIW) and prediction interval coverage probability (PICP) were adopted to quantitatively assess the model's estimated accuracy and the precision of the uncertainty quantification. Additionally, an error decomposition of the estimation results was conducted to analyze model’s performance based on target parameters and scaled distance. The results indicate that the proposed method achieved an estimation error of 12.2% on the test set, with a confidence interval covering over 81.6% of true values, and less than 20 milliseconds of the estimation time for a single sample point. This method provides a novel approach for fast and accurate estimation of blast loading in complex structures with sufficient confidence for the estimation results.