Research on PSO and MLEM Hybrid Algorithm for NDP Spectrum Unfolding

Abstract

Neutron depth profiling (NDP) is a non-destructive analysis method which is widely used in lithium batteries, semiconductors, and other complex and high-precision industries. The NDP spectrum is the second particles of the interaction between neutrons and target nuclides, and then the content and spatial information of the target nuclides in the measured samples are obtained by unfolding the NDP spectrum. At present, the common NDP spectrum unfolding algorithm is the maximum likelihood expectation maximization (MLEM) algorithm. But in some case, the MLEM algorithm falls into the local optimal solution. In this paper, a hybrid PSO-MLEM algorithm by taking advantages of the wide search range of PSO (particle swarm optimization) and the fast convergence speed of MLEM was proposed. In the PSO-MLEM algorithm, the dynamic acceleration factor was used to balance the local optimal and the global optimal on the particle displacement in each iteration, which improved the convergence speed and the accuracy of the algorithm. The PSO-MLEM algorithm was applied to unfold the NDP spectra of lithium batteries with 0, 5, and 10 hours of charging and discharging, which were simulated by Geant4 tool. The unfolding results of PSO-MLEM algorithm were compared to the results of PSO algorithm, MLEM algorithm and singular value decomposition solving least squares (SVDLS) algorithm. The correlation coefficients of the unfolding result by PSO-MLEM algorithm and the reference distributions are 0.993, 0.984, and 0.946, respectively, and the relative average errors are 14.46%, 9.84%, and 9.41%. Compared with PSO algorithm, the convergence speed of PSO-MLEM algorithm is improved from 800 times to 100 times, and the relative error is reduced from about 50% to about 10%. To the MLEM algorithm, the PSO-MLEM algorithm improves the global optimization capability and avoids the problem of local optimal solution caused by the influence of the initial value of the MLEM algorithm, especially with the result of 0 hour. The SVDLS algorithm is worked well in unfolding NDP spectra except the NDP spectrum of lithium battery at 0 hour. Compared to result of SVDLS algorithm, the PSO-MLEM algorithm has better convergence properties and is numerically stable.

Keywords

• neutron depth profiling analysis
• particle swarm optimization algorithm
• maximum likelihood expectation maximization algorithm
• lithium battery