摘要
中子深度剖面(NDP)分析技术是一种无损检测方法,能够同时测量样品中目标核素的浓度与空间信息,已被广泛应用于锂电池、半导体等产业.在NDP分析过程中,由测量能谱反演出目标核素浓度的分布信息是关键步骤.目前NDP测量反演中常用的算法为最大似然期望最大化(MLEM)算法.针对MLEM算法计算结果易陷入局部最优解的情况,本文提出了粒子群(PSO)与MLEM混合(PSO-MLEM)算法,并通过动态加速因子提高了算法的收敛速度与计算精度.应用PSO-MLEM算法、PSO算法、MLEM算法、奇异值分解求解最小二乘(SVDLS)算法对锂电池中6Li的NDP模拟能谱进行反演,并对反演计算结果进行了评价.结果表明:对比PSO算法,PSO-MLEM算法的收敛效率与计算精度明显提升;对比MLEM算法,PSO-MLEM算法的全局寻优能力有效提升了反演精度,避免了局部最优解的影响;对比SVDLS算法,PSO-MLEM算法的反演精度明显提升.
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 pres-ent,the common NDP spectrum unfolding algorithm is the maximum likelihood expecta-tion 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 decom-position 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.
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