k_eff Rapid Prediction Method of Array Nuclear Material Storage Based on γ Monitoring

The paper focuses on the research of rapidly predicting the k_eff value of array nuclear material storage to ensure nuclear criticality safety. In nuclear material warehouses, the storage of nuclear materials in an array form makes the k_eff value directly related to the safety status. However, existing criticality calculation software fails to provide timely k_eff values when there are changes in geometric positions and quantities during storage and transportation. To address this issue, a γ-detector array corresponding to the storage model was established for data monitoring. A uranium solution storage model was designed, with 9 iron boxes arranged in a 3×3 matrix on a 30 cm thick concrete layer. The dimensions of the solution barrels and iron boxes were determined, and the k_eff value of the model was calculated. The BP neural network, which consisted of an input layer, a hidden layer, and an output layer, was utilized. Neurons in the network received input signals and generate outputs through weight and activation function operations. The backpropagation algorithm was used for training, and the gradient descent method was employed to optimize the weights. A loss function was defined to evaluate the performance of the network, and an empirical formula was used to determine the number of nodes in the hidden layer. A dataset was created by generating 950 models with different storage box arrangements and calculating their k_eff values and γ fluxes. After removing duplicate data, 916 models were obtained. These were divided into a learning set and a test set in a 7∶3 ratio, and the data were standardized using the Z-score method. A BP neural network with 9 inputs and 1 output was designed, with 5 nodes in the hidden layer. The activation function was set as Relu, the optimization function as Adam, the loss function as MSE, the learning rate as 0.01, and the maximum number of training epochs as 500. The training results were analyzed, and the mean square error curve was plotted to evaluate the effectiveness of the model. A measurement bench was built, consisting of a computer, instruments, and detectors. The consistency between the detectors and the storage boxes was verified. Different storage box arrangement schemes were designed, and the detection data were obtained by averaging the measurements over 30 minutes. The prediction values of the neural network were compared with the k_eff values calculated by MCNP, and the errors were calculated to evaluate the performance of the model. In conclusion, based on the array storage model dataset, through data processing and neural network training, a high-precision BP neural network model is constructed, which can predict the k_eff value in real time. In the experiment, it can effectively evaluate the nuclear criticality safety and is in good agreement with the theoretical values, providing a new approach for the safety monitoring of nuclear material warehouses.