Inverse estimation methods of unknown radioactive source for fuel debris search

To identify the distribution of fuel debris remaining in the reactor vessel and/or the containment vessel of Fukushima Daiichi NPS, we focused on the inverse estimation of radioactive source distribution using the measured radiation counts. The Maximum Likelihood-Expectation Maximization (ML-EM) and the Moore-Penrose Matrix Inverse (MPMI) methods are examined. The ML-EM method has been used for the image reconstruction of computed tomography, and the MPMI method is one of the solution methods for simultaneous linear equations with the underdetermined condition. A simple calculation model simulating a containment vessel was constructed including detectors and radiation sources. In an actual situation, a sufficient number of radiation measurement positions would not be available owing to the complexity of structures inside the containment vessel. Thus, the number of radiation measurement points (number of constraints) is smaller than that of radiation source positions. It means that an underdetermined inverse problem should be solved. The detection probability of radiation (neutron or photon) is calculated by the adjoint transport calculation since the detection probability is used as the coupling coefficient between radiation counts at a detector and a radioactive source. The result of estimation using the ML-EM or the MPMI method indicates that the accuracy of estimation depends on the distance between a radiation source and a detector, and measurement positions of radiation count. The ML-EM and the MPMI methods show different prediction accuracy depending on the prediction condition. It is found that reasonable prediction accuracy would be obtained when the detectors are placed at the vicinity of radiation sources of interest.