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

For the estimation of blast loading on complex structures, traditional numerical simulation methods were computationally intensive, while rapid estimation methods based on neural networks could only provide point estimates without offering confidence intervals for the results. To achieve fast and reliable estimation of blast loading on complex structures during explosions, Bayesian theory was integrated with deep learning to develop a Bayesian deep learning approach for rapid estimation of blast loading on complex structures. The approach initially utilized open-source numerical simulation software to generate a dataset of blast loading on 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 numerical simulation accuracy verification. On this foundation, 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 uncertainty quantification precision. Additionally, an error decomposition of the estimation results was conducted, analyzing model performance based on target parameters and scaled distance. The results indicate that the proposed method achieved an estimation error of approximately 12.2% on the test set, with a confidence interval covering over 81.6% of true values, and the estimation time for a single sample point did not exceed 20 milliseconds. This method enables fast and accurate estimation of blast loading on complex structures while providing confidence information for the estimation results, representing a novel approach for achieving rapid and reliable estimation of blast loading on complex structures.