基于压缩感知理论的中子能谱解谱方法

Neutron Spectrum Unfolding Method Based on Compressed Sensing Theory

准确的中子能谱信息对于核装置的设计和运行具有十分重要的意义,现有解谱方法通常将先验信息作为迭代初值使用,限制了解谱过程多重先验信息的使用。本文针对中子能谱测量中的解谱问题,建立了基于压缩感知理论的中子能谱解谱方法,并应用于几种典型中子能谱的多球谱仪测量和辐照监督管处中子能谱的活化片测量中的中子能谱解谱问题,结果表明:所建立的解谱方法可实现一次解谱中多重先验信息的使用,可有效实现典型中子能谱和反应堆辐照监督管处中子能谱的解谱,解谱结果与标准解吻合良好。另外,由于多重先验信息的使用,使得解谱过程对方程数量的依赖降低,去除^(238)U和^(237)Np等裂变探测器时辐照监督管处中子能谱依然可得到较高精度的求解,为辐照监督项目去除裂变探测器奠定了理论基础。

Accurate information of neutron spectrum is very important for design and operation of nuclear facilities.The current unfolding methods commonly use the prior information as the initial values of the iteration process,which limits implementation of multiple prior information during the unfolding process and accuracies of the unfolding results are difficult to be enhanced.In this paper,a neutron spectrum unfolding method based on compressed sensing theory was proposed.Multiple prior information can be implemented into the unfolding process due to the basic principle of the compressed sensing theory.The proposed method includes two processes,such as the sparse representation process and the sparse reconstruction process.Two kinds of algorithms,the K-SVD algorithm and the online dictionary learning algorithm,were applied for sparse representation.The K-SVD algorithm is efficient and easy to be implemented.However,computation always fail while the singularity of the training matrix increases.The online dictionary learning algorithm uses the stochastic approximation.It assumes the training set as a distribution and processes one sample from the distribution during each iteration.Hence,the online dictionary learning algorithm can effectively avoid the computation failure caused byℓ0ℓ1matrix singularity.Algorithms based on-norm and-norm were applied for sparse reconstruction.ℓ0The-norm based algorithm has the closet meaning to sparsity but lacks the ability of suppressingℓ1noises containing in the measured data.The-norm based algorithm equivalents the sparse reconstruction to the LASSO equation,which has better performance on suppressing noises.The proposed unfolding method was applied to unfolding problems of multi-sphere spectrometer of measuring several typical neutron spectra.The K-SVD algorithm was applied for sparse representationℓ0and the-norm based algorithm was applied for sparse reconstruction.The unfolded spectra agree well with the standard solutions.High accuracies can be obtained with implementation of multiple prior information.Moreover,measured data of multiple activation foils at the irradiation surveillance capsule was also unfolded with the proposed method.To avoid computational failure caused by singularity of the training matrix,the online dictionary learning algorithm was applied for sparse representation.Andℓ1the-norm based algorithm was applied for sparse reconstruction to suppress noises contained in the measured data.The unfolded spectra agree well with the standard solutions.Besides,dependence of the unfolding process on the number of equations is reduced as a result of implementation of multiple prior information,allowing successful unfolding with acceptable accuracies while removing fission detectors such as ^(238)U and ^(237)Np,which lays theoretical foundation for removal of fission detectors in radiation surveillance project.