# Blast Loading Prediction of Complex Structures Based on Bayesian Deep Active Learning
## 3 Blast Loading Prediction Method Based on BDAL
### Uncertainty-Based Active Learning  
The dataset \(D\) containing all \(M\) samples was divided into labeled sample set \(B\) and unlabeled sample set \(U\). Here, dataset \(B=\{X,Y\}\) contained \(K\) labeled samples \(X=\{\mathbf{x}_{i}\}_{i=1}^{K}\), and each sample carries its corresponding label \(Y=\{y_{i}\}_{i=1}^{K}\). Dataset \(U\) contained \(L\) unlabeled samples \(\hat{X}=\{\hat{\mathbf{x}}_{i}\}_{i=1}^{L}\), and each sample has no corresponding label. The core problem of active learning is to select high-quality samples from the unlabeled sample set \(U\) based on specific selection criteria [39]. In a BDL model trained using the MC dropout approximate inference method, the variance of the prediction distribution can be used to quantify the uncertainty of the prediction results. A higher variance represents a wider probability distribution range, indicating a larger deviation between the predicted results of the model and the true value. Thus, the predicted results of the model have a higher uncertainty [39]. In this study, the uncertainty of model prediction was used as the sample-selection criterion for active learning. When the uncertainty of a sample's blast loading prediction is relatively high, it indicates that the model has limited knowledge of the region in the feature space. By obtaining the sample's label and incorporating it into the model's training, the model can explore regions with sparse knowledge of blast loading prediction, thus improving training efficiency. Specifically, the unlabeled sample \(\hat{X}\) in \(U\) is predicted based on the trained BDL model, and the uncertainty of the result is quantified. The sample \(\mathbf{x}^{*}\) with the greatest uncertainty is selected from the sample, and the corresponding blast loading label is obtained using the numerical simulation test for the sample. This is added to the labeled sample set \(B\), and the BDL model is retrained based on \(B\). With each iteration, the prediction performance of the BDL model is gradually improved. The construction process for the BDAL model based on the uncertainty selection strategy can be summarized as follows:  
Step 1: Record the prediction accuracy of the benchmark model. All 360 datasets were divided into a training set and a test set at a ratio of 9:1. The constructed BDL model was trained on all samples of the training set, and its blast loading prediction performance on the test set was marked as \(a\). Step 2: Labeled sample set initialization and BDAL network initialization. In total, 36 groups of examples from the original training set were randomly selected to form labeled sample set \(B\) (with each sample point marked by its corresponding peak overpressure). The remaining 288 groups constituted unlabeled sample set \(U\) (where each sample point only included its corresponding scene parameter characteristics without the peak overpressure label). The new BDL model was trained on the labeled sample set \(B\), and its performance was evaluated on the test set. Step 3: Select unlabeled samples based on the uncertain selection strategy. The BDL model trained on the labeled sample set \(B\) was used to predict the blast loading of each sample in the unlabeled sample set \(U\), and the variance of the predicted peak overpressure of each unlabeled sample was obtained. The average variance of multiple prediction results was used as the uncertainty quantization result of the sample point. According to the results of uncertainty quantization, 36 groups of samples with the greatest uncertainty in \(U\) were selected, and their corresponding peak overpressure labels were obtained. Step 4: Update the labeled sample set and retrain the Bayesian deep learning model. The newly labeled samples in step 3 were added to labeled sample set \(B\), and the BDL model was retrained based on the updated labeled sample set. Step 5: Model prediction performance evaluation. The BDL model's performance on the test set was evaluated.