Development and Verification of Two-step Spectrum Unfolding Code
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摘要: 为解决预置谱未知的解谱问题，本文首次提出一种广义神经网络（GRNN）算法和迭代算法结合进行的两步解谱法，自主开发了GRNN解谱和迭代法解谱程序，并对2套程序进行分别验证和整体验证。首先用中国实验快堆（CEFR）的活化法实验数据进行分别验证，结果表明：GRNN的解谱结果与理论谱相比，在中子能量大于0.1 MeV时，最大偏差为10.36%，迭代法的解谱结果与最小二乘法的解谱结果最大偏差为9.15%，计算的单核反应率与实验值最大相对偏差为11.71%，符合较好；且与无准确预置谱的迭代法解谱结果相比，GRNN解谱精度更高。最后用俄罗斯碳化硼辐照数据进行整体验证，结果表明：在快中子区域，两步解谱法的结果与有预置谱的迭代法解谱结果最大偏差为11.42%。因此，采用两步解谱法解决预置谱未知的解谱问题是可行的，误差也在可以接受的范围内。本文提出的新型解谱法可为新型堆的解谱提供新的思路，并针对未知预置谱的解谱试验具有一定的参考价值。
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关键词:
- 两步解谱法 /
- 广义神经网络（GRNN） /
- 迭代法 /
- 预置谱
Abstract: To address the challenge of unknown preset spectra, this paper introduces a two-step spectrum unfolding method that combines the generalized regression neural network (GRNN) and the iterative algorithm. We have independently developed the spectrum unfolding codes for GRNN and iteration and conducted separate and comprehensive validations of the codes. Initially, we utilized activation method data from the Chinese Experimental Fast Reactor (CEFR) to validate the codes. The results indicated that at neutron energies greater than 0.1 MeV, the GRNN results deviated by a maximum of 10.36% from the theoretical spectra. The iterative method’s results deviated by a maximum of 9.15% compared to those obtained using the least squares method. The calculated single nuclear reaction rates showed a maximum relative deviation of 11.71% from the experimental values, indicating good agreement. Furthermore, the GRNN method demonstrated higher accuracy compared to the iterative method without accurate pre-set spectra. Finally, comprehensive validation was performed using Russian boron carbide irradiation data, revealing a maximum deviation of 11.42% in the fast neutron region between the two-step method and the iterative method with pre-set spectra. Therefore, employing a "two-step spectrum unfolding method" to address the challenge of unknown pre-set spectra is feasible, with errors remaining within acceptable limits. The innovative spectrum unfolding method introduced in this paper offers fresh perspectives for the spectrum unfolding of new reactors and offers significant reference value for experiments with unknown pre-set spectra. -
图 1 两步解谱法的基本思想
Figure 1. The Basic Idea of Solving Spectrum by Two-step Spectrum Unfolding Method
图 7 GRNN解谱结果与计算值对比
Figure 7. Comparison between GRNN Spectrum Unfolding Results and Calculated Values
图 8 GRNN解谱结果与无预置谱解谱结果对比
Figure 8. Comparison of the Results of GRNN and Non-preset Spectrum Unfolding
表 1 CEFR 2-2 组件中平面6个反应道的反应率
Table 1. Reaction Rate of 6 Reaction Channels in CEFR 2-2 Assembly Plane
序号 核反应 单核反应率/s 1 238U(n,f) 5.60×10−14 2 64Zn(n,p)64Cu 5.15×10−15 3 54Fe(n,p)54Mn 1.01×10−14 4 46Ti(n,p)46Sc 1.27×10−15 5 45Sc(n,γ)46Sc 9.70×10−15 6 235U(n,f) 7.87×10−13 
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表 2 调整谱与预置谱的中子通量密度及偏差
Table 2. Deviation of Neutron Flux Density Between Adjustment Spectrum and Preset Spectrum
中子通量密度 预置谱 调整谱 相对偏差/% 总中子通量密度/(cm−2·s−1) 5.12×1011 5.32×1011 4.27 快中子通量密度/(cm−2·s−1) 4.32×1011 4.52×1011 4.81
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表 3 调整谱与实验测量的单核反应率偏差
Table 3. Deviation of Mononuclear Reaction Rate Between Adjustment Spectrum and Experimental Measurement
核反应 测量单核反应率/s 调整谱计算
单核反应率/s相对偏差/% 238U(n,f) 5.60×10−14 4.94×10−14 −11.71 64Zn(n,p)64Cu 5.15×10−15 5.04×10−15 −2.06 54Fe(n,p)54Mn 1.01×10−14 9.99×10−15 −1.39 46Ti(n,p)46Sc 1.27×10−15 1.32×10−15 4.48 45Sc(n,γ)46Sc 9.70×10−15 1.00×10−14 3.46 235U(n,f) 7.87×10−13 7.08×10−13 −10.03
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表 4 测量得到的探测箔单核反应率
Table 4. Measured Mononuclear Reaction Rate of Foils
距堆芯中心标高/mm 封盒代号 核反应率/s 93Nb(n,n') 93Nb(n,γ) 54Fe(n,p) 46Ti(n,p) 63Cu(n,α) +275（位置1） 7 1.670×10−11 — 3.786×10−12 4.408×10−13 — 8 1.847×10−11 1.869×10−10 4.293×10−12 5.421×10−13 2.378×10−14 9 1.644×10−11 — 3.892×10−12 4.622×10−13 2.050×10−14 –200（位置2） 4 5.199×10−11 — 1.508×10−11 1.741×10−12 8.764×10−14 5 6.396×10−11 2.346×10−10 2.006×10−11 2.704×10−12 11.441×10−14 6 5.388×10−11 — 1.666×10−11 2.097×10−12 8.997×10−14 –500（位置3） 1 4.213×10−12 — 6.155×10−13 7.119×10−14 3.442×10−15 2 4.419×10−12 1.669×10−10 6.823×10−13 8.308×10−14 3.715×10−15 3 4.119×10−12 — 6.102×10−13 7.138×10−14 3.379×10−15
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表 5 GRNN 重构谱计算结果
Table 5. Calculation Results of GRNN Reconstruction Spectrum
解谱位置 MSE 迭代次数 计算时间/s 位置1 9.78×10−5 1280 2.6 位置2 9.79×10−5 1280 2.5 位置3 1.014×10−4 1280 2.6
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