基于非线性方程组和优化建模的实验数据重构方法  

Experimental data reconstruction method based on nonlinear equation system and optimized modeling

作　　者：郝玉洁 郭子萱[2] 胡兵[1] 唐昌兵 王浩煜 辛勇[2] HAO Yu-Jie;GUOZi-Xuan;HU Bing;TANG Chang-Bing;WANG Hao-Yu;XIN Yong(School of Mathematics,Sichuan University,Chengdu 610064,China;Science and Technology on Reactor System Design Technology Laboratory,Nuclear Power Institute of China,Chengdu 610000,China)

机构地区：[1]四川大学数学学院,成都610064 [2]中国核动力研究设计院核反应堆系统设计技术重点实验室,成都610000

出　　处：《四川大学学报（自然科学版）》2021年第6期9-14,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11971336)。

摘　　要：针对离散测量γ射线计数过程中的实验数据重构问题,本文首先建立了正向计算的矩阵模型,将重构问题转化为求解不定的非线性方程组的数学问题,然后分别基于优化目标函数和Lagrange乘子法建立了两种重构模型,进而求解最优解.数值算例表明,两种重构模型都能获得比探测值更接近于真实值的重构结果,第二种模型的重构结果比第一种更加精确,而且允许直接把探测值作为迭代初值.This paper discusses the reconstruction of experimental data of discrete measurement of γ-ray counting. By establishing the matrix model for the forward direction computation of experimental data, we transform this engineering problem into a mathematical problem of solving indefinite nonlinear equations. Then we present two reconstruction models respectively based on the optimization objective function and the Lagrange multiplier method to find the optimal solution. Numerical experiments show that both reconstruction models can obtain closer results to the true value than the detection value, while the reconstruction results of the second model is more accurate than the first one. Moreover, the second reconstruction model allows directly using the experimental data as the initial value of the iterative solver.

关 键 词：非线性方程组 最优化 LAGRANGE乘子法 重构 

分 类 号：O242.2[理学—计算数学]