Fast detection method for radionuclides based on Sequential Bayesian approach

Linjian WAN; Xuan ZHANG; Chunlei ZHANG; Jianwei HUANG; Jiacheng LIU; Xiaole ZHANG; Dehong LI; Zhijun YANG

doi:10.11889/j.0253-3219.2025.hjs.48.240190

NUCLEAR TECHNIQUES, Volume. 48, Issue 1, 010404(2025)

Fast detection method for radionuclides based on Sequential Bayesian approach

Linjian WAN^1,2, Xuan ZHANG², Chunlei ZHANG^1、*, Jianwei HUANG^2、**, Jiacheng LIU³, Xiaole ZHANG², Dehong LI², and Zhijun YANG²

Author Affiliations

¹College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China

²Institute of Ionizing Radiation Metrology, National Institute of Metrology, Beijing 100013, China

³Nuclear and Radiation Safety Center, Ministry of Ecology and Environment, Beijing 102400, China

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Figures & Tables(20)

Fig. 1. Diagram of time events sequence of ray ${\vec{ξ}}_{i}$ (a) Distribution of ${\vec{ξ}}_{i}$ , (b) Normalized histogram of $Δ t_{i}$

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Fig. 2. Snapshots of background measurement (a) Low background radiation environment, (b) Natural background radiation environment

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Fig. 3. Snapshot of a standard set of point sources

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Fig. 4. Process flowchart of sequential Bayesian fast radionuclide detection

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Fig. 5. Variations of decision function $P_{0}^{ϑ}$ versus time in low background radiation environment (color online)(a) No false alarm occurred, (b) False alarm occurred

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Fig. 6. Variations of decision function $P_{0}^{ϑ}$ versus time in natural background radiation environment (color online)(a) No false alarm occurred, (b) False alarm occurred

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Fig. 7. Results of 100 experiments under no sources conditions in two types of background radiation environment (color online)(a) Detection time, (b) Number of detected samples

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Fig. 8. Variations of decision function $P_{0}^{ϑ}$ with time(a) Low background radiation environment, (b) Natural background radiation environment

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Fig. 9. Average detection time $\bar{T}$ (a) Versus full-spectrum net count rate, (b) Versus signal-to-noise ratio

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Fig. 10. Average number of detected samples $\bar{N}$ (a) Versus full-spectrum net count rate, (b) Versus signal-to-noise ratio

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Fig. 11. Δt_th versus τ_min under the condition of $B_{Δ t}^{ϑ} \equiv 1$

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Fig. 12. Variations of average detection time $\bar{T}$ of the background with parameter τ_min

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Fig. 13. Variations of η_min obtained by experimental measurements and theoretical calculations with parameter τ_min(color online)

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Fig. 14. Variations of false alarm rate α_exp of experimental measurement with parameters α and β

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Fig. 15. Variations of false negative rate β_exp of experimental measurement with parameters α and β

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Table 1. Information of point sources

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Table 1. Information of point sources

核素 Nuclide	编号 No.	相对扩展不确定度U_rel (k=2) Relative expanded uncertainty (k=2)	活度 Activity / Bq	参考日期 Reference date	半衰期 Half life / d
⁶⁰Co	191101	0.024	5.0×10⁴	2020/6/21	1.9×10³
²⁴¹Am	152	0.031	9.5×10³	2020/6/28	1.6×10⁵
¹³⁷Cs	341	0.026	9.5×10³	2020/6/29	1.1×10⁴
¹⁰⁹Cd	364	0.038	9.8×10⁴	2020/7/24	4.6×10²
⁵⁷Co	327	0.033	2.9×10⁴	2020/7/26	2.7×10²
²²Na	386	0.031	5.1×10⁴	2020/7/15	9.5×10²
²¹⁰Pb	Pb1802	0.038	7.6×10³	2020/7/27	8.1×10³
⁸⁸Y	Y200403	0.034	4.6×10⁴	2020/6/30	1.1×10²

Table 2. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

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Table 2. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

全谱净计数率 ${\dot{n}}_{n e t}$ ^a Net count rate of full spectrum ${\dot{n}}_{n e t}$ ^a / s^-1	计数率信噪比η Signal-to-noise ratio of counting rate η / %	做出有效判决 Making effective judgments		全谱净计数率 ${\dot{n}}_{n e t}$ ^a Net count rate of full spectrum ${\dot{n}}_{n e t}$ ^a / s^-1	计数率信噪比η Signal-to-noise ratio of counting rate η / %	做出有效判决 Making effective judgments
	计数率信噪比η Signal-to-noise ratio of counting rate η / %	$\bar{T}$ / s	$\bar{N}$		计数率信噪比η Signal-to-noise ratio of counting rate η / %	$\bar{T}$ / s	$\bar{N}$
32 855	55 405	0.000 8	26	35.57	60.0	0.82	75
2 531	4 269	0.010 1	27	20.54	34.7	1.42	112
825	1 392	0.030 8	28	5.95	10.1	6.92	451
422	712	0.064 5	30	4.84	8.2	8.59	556
150	253	0.167 1	37	4.44 (β_exp=8%)^*b	7.5	10.00	643
79.02	134	0.345 5	48	3.91 (β_exp=9%)^*b	6.6	20.73	1 305

Table 3. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in natural background radiation environment ( ${\dot{n}}_{n o r_b k g} = 165.9 s^{- 1}$ )

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Table 3. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in natural background radiation environment ( ${\dot{n}}_{n o r_b k g} = 165.9 s^{- 1}$ )

全谱净计数率 ${\dot{n}}_{n e t}$ ^a Net count rate of full spectrum ${\dot{n}}_{n e t}$ ^a / s^-1	计数率信噪比η Signal-to-noise ratio of counting rate η / %	做出有效判决 Making effective judgments		全谱净计数率 ${\dot{n}}_{n e t}$ ^a Net count rate of full spectrum ${\dot{n}}_{n e t}$ ^a / s^-1	计数率信噪比 Signal-to-noise ratio of counting rateη / %	做出有效判决 Making effective judgments
	计数率信噪比η Signal-to-noise ratio of counting rate η / %	检出时间 $\bar{T}$ Detection time $\bar{T}$ / s	检出样本量 $\bar{N}$ Number of detected samples $\bar{N}$		计数率信噪比 Signal-to-noise ratio of counting rateη / %	检出时间 $\bar{T}$ Detection time $\bar{T}$ / s	检出样本量 $\bar{N}$ Number of detected samples $\bar{N}$
35 104	21 160	0.000 8	26	72.81	43.9	0.38	89
7 903	4 764	0.003 2	27	50.96	30.8	0.64	135
1 287	776	0.019 8	30	24.60	14.9	1.36	258
777	469	0.032 9	32	15.50	9.4	2.71	490
381	230	0.071 6	39	10.10	6.1	6.61	1 154
189	114	0.140 3	51	7.21 (β_exp=20%)	4.4	14.14	2 458

Table 4. Experimental and theoretical detection performance corresponding to k=0.85

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Table 4. Experimental and theoretical detection performance corresponding to k=0.85

本底环境

Background environment

实验测量检测灵敏度下限η_{min_exp}

Lower limit of experimental measurement detection sensitivity / %

理论计算检测灵敏度下限η_{min_the}

Lower limit of theoretical detection sensitivity / %

检出时间 $\bar{T}$

Detection time $\bar{T}$ / s

检出样本量 $\bar{N}$

Number of detected samples $\bar{N}$

实验测量漏报率β_exp

Experimental measurement false negative rates β_exp / %

低辐射本底实验室

Low background radiation laboratory

8.2

5.6

8.59

556

自然辐射本底实验室

Natural background radiation laboratory

6.1

5.6

6.61

1 154

Table 5. Effect of parameter τ_min on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

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Table 5. Effect of parameter τ_min on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

k	检测灵敏度理论下限η_{min_the} Lower limit of theoretical detection sensitivity η_{min_the} / %	计数率信噪比η^a Signal-to-noise ratio of counting rate η^a/ %	检出时间 $\bar{T}$ Detection time $\bar{T}$ / s	检出样本量 $\bar{N}$ Number of detected samples $\bar{N}$	计数率信噪比η^a Signal-to-noise ratio of counting rate η^a/ %	检出时间 $\bar{T}$ Detection time $\bar{T}$ / s	检出样本量 $\bar{N}$ Number of detected samples $\bar{N}$
0.8	7.6	55 405	0.000 6	19.0	10.1 (β_exp=3%)^*b	8.73	565
0.8	7.6	2 043	0.015 6	20.0	0 (α_exp=13%)^*c	12.93	767
0.5	27.5	55 405	0.000 2	6.0	24.5 (β_exp=6%)^*b	0.98	76
0.5	27.5	2 043	0.005 0	6.7	0 (α_exp=11%)^*c	1.53	91
0.1	135.1	55 405	0.000 1	2.1	133.3 (β_exp=2%)^*b	0.08	11
0.1	135.1	2 043	0.001 7	2.2	0 (β_exp=6%)^*c	0.22	14
0.01	359.6	55 405	0.000 015	1.1	320.3 (β_exp=3%)^*b	0.04	8
0.01	359.6	2 043	0.001 1	1.2	0 (α_exp=3%)^*c	0.10	6

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Linjian WAN, Xuan ZHANG, Chunlei ZHANG, Jianwei HUANG, Jiacheng LIU, Xiaole ZHANG, Dehong LI, Zhijun YANG. Fast detection method for radionuclides based on Sequential Bayesian approach[J]. NUCLEAR TECHNIQUES, 2025, 48(1): 010404

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Paper Information

Category: NUCLEAR ELECTRONICS AND INSTRUMENTATION

Received: May. 1, 2024

Accepted: --

Published Online: Feb. 26, 2025

The Author Email: ZHANG Chunlei (张春雷), HUANG Jianwei (黄建微)

DOI:10.11889/j.0253-3219.2025.hjs.48.240190

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Information of point sources

Table 1. Information of point sources

Table 2. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in low background radiation environment (n˙low_bkg=59.3 s-1)

Table 2. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in low background radiation environment (n˙low_bkg=59.3 s-1)

Table 3. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in natural background radiation environment (n˙nor_bkg=165.9 s-1)

Table 3. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in natural background radiation environment (n˙nor_bkg=165.9 s-1)

Table 4. Experimental and theoretical detection performance corresponding to k=0.85

Table 4. Experimental and theoretical detection performance corresponding to k=0.85

Table 5. Effect of parameter τmin on detection performance in low background radiation environment (n˙low_bkg=59.3 s-1)

Table 5. Effect of parameter τmin on detection performance in low background radiation environment (n˙low_bkg=59.3 s-1)

Table 2. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

Table 2. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

Table 3. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in natural background radiation environment ( ${\dot{n}}_{n o r_b k g} = 165.9 s^{- 1}$ )

Table 3. Effects of full-spectrum net count rate and signal-to-noise ratio on detection performance in natural background radiation environment ( ${\dot{n}}_{n o r_b k g} = 165.9 s^{- 1}$ )

Table 5. Effect of parameter τ_min on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )

Table 5. Effect of parameter τ_min on detection performance in low background radiation environment ( ${\dot{n}}_{l o w_b k g} = 59.3 s^{- 1}$ )