Inverse estimation scheme of radioactive source distributions inside building rooms based on monitoring air dose rates using LASSO: Theory and demonstration

Predicting radioactive source distributions inside reactor building rooms based on monitoring air dose rates is one of the most essential steps towards decommissioning of nuclear power plants. However, the attempt is rather a difficult task, because it can be generally mapped onto mathematically ill-posed problem, i.e., information obtained by air dose rate measurements inside the building rooms is generally poor in predicting the contaminated distributions on surface mesh units of structural materials inside the target building rooms. Then, in order to successfully perform the inverse estimations on radioactive source distributions even in such ill-posed conditions, we suggest that a machine learning method, least absolute shrinkage and selection operator (LASSO) minimizing the loss function, ‖CP−Q‖22+λ‖P‖1 is a promising scheme. For the purpose of its feasibility demonstrations in real building rooms, we employ a Monte Carlo simulation code, i.e., Particle and Heavy Ion Transport Systems (PHITS) to make LASSO input as the above matrix C connecting the radioactive source vector P defined on surface meshes of structural materials with the air dose rate vector Q measured at internal positions inside the rooms. We develop a mathematical criterion on the number of monitoring points to correctly predict source distributions based on the theory of Candes and Tao. Then, we confirm that LASSO actually shows extremely high possibility for source distribution reconstructions as far as the number of detection points satisfies our criterion. Besides, we find that source distributions are partly reconstructed even when the number of detections is less than the bound. In addition, we demonstrate that the proposed LASSO scheme is applicable to remote sensing situations as monitoring is permissible only from distant regions like its neighboring rooms. Moreover, we verify that radioactive hot spots can be truly reconstructed in an experiment setup. At last, we examine an influence factor like detector-source distance to enhance the predicting possibility in the inverse estimation. From the above demonstrations, we propose that LASSO scheme is a quite useful way to explore hot spots as seen in damaged nuclear power plants like Fukushima Daiichi nuclear power plants.