Intelligent optimization method for lead-bismuth reactor based on Kriging surrogate model

Qiong Li; Zijing Liu; Hao Xiao; [in Chinese]; Pengcheng Zhao; Chang Wang; Tao Yu

doi:10.11884/HPLPB202234.210560

High Power Laser and Particle Beams, Volume. 34, Issue 5, 056007(2022)

Intelligent optimization method for lead-bismuth reactor based on Kriging surrogate model

Qiong Li^1,2, Zijing Liu^1,2、*, Hao Xiao¹, [in Chinese]^1,2, Pengcheng Zhao^1,2, Chang Wang¹, and Tao Yu^1,2

Author Affiliations

¹School of Nuclear Science and Technology, University of South China, Hengyang 421001, China

²Hunan Engineering and Technology Research Center for Virtual Nuclear Reactor, University of South China, Hengyang 421001, China

show less

Abstract Get PDF(in Chinese)

Figures & Tables(17)

Fig. 1. Main technical principle of core intelligent optimization method

Download full size

View in Article

Fig. 2. Comparison of two sampling results

Download full size

View in Article

Fig. 3. Flow diagram of SEUMRE spatial search algorithm

Download full size

View in Article

Fig. 4. Realization flowchart of DOPPLER

Download full size

View in Article

Fig. 5. SPARLER-4 structure diagram

Download full size

View in Article

Fig. 6. URANUS structure diagram

Download full size

View in Article

Fig. 7. Comparison of K_eff, burnup predicted by Kriging surrogate model and RMC calculated value

Download full size

View in Article

Fig. 8. Iterative graph of fuel loading optimization for SPALLER-4

Download full size

View in Article

Fig. 9. Comparison of K_eff, burnup predicted by Kriging surrogate model and RMC calculated value

Download full size

View in Article

Fig. 10. Iterative graph of fuel loading optimization for URANUS

Download full size

View in Article

Table 1. Commonly used related functions of Kriging surrogate model and their expressions

View table

View in Article

Table 1. Commonly used related functions of Kriging surrogate model and their expressions

correlation function	expression
exponential function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\exp(-{\theta }_{k}{d}_{k})$
Gaussian function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\exp(-{\theta }_{k}{d}_{k}^{2})$
linear function	$ {R}_{k}\left({\theta }_{k},{d}_{k}\right)=\mathrm{m}\mathrm{a}\mathrm{x}\{\mathrm{0,1}-{\theta }_{k}{d}_{k}\} $
cubic spline function	${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\left\{\begin{array}{l}1-15{\zeta }_{k}+30{\zeta }_{k}^{3},\quad 0\leqslant {\zeta }_{k}\leqslant 0.2\\ 1.25{(1-15{\zeta }_{k})}^{3},\quad 0.2 < {\zeta }_{k} < 1\\ 0,\quad{\zeta }_{k}\geqslant 1,{\zeta }_{k}={\theta }_{k}{d}_{k}\end{array}\right.$

Table 2. Materials used for the design parameters of SPALLER-4 and the interval value of optimization variables

View table

View in Article

Table 2. Materials used for the design parameters of SPALLER-4 and the interval value of optimization variables

design scheme	thermal power/MW	fuel loading/kg	equivalent diameter of active region/cm	height of active area/cm	average volume power density of active region/(W·cm⁻³)	fuel (mass fraction of Pu)/%	coolant and reflector	shielding layer
SPALLER-4	4	577.89	95.4	80	6.99	PuN-ThN (31/48)	²⁰⁸Pb-Bi(90)	B₄C(126)
URANUS	100	17580	97.02	180	19.18	UO₂(9.55/17.09)	²⁰⁸Pb-Bi(27.11 cm)	B₄C(15 cm)

design scheme	solid moderator (thickness/cm)	gate diameter ratio	fuel rod core radius/cm	air gap of fuel rod (thickness/cm)	cladding of fuel rod (thickness/cm)	upper/lower end plug of fuel rod (height/cm)	gas cavity/ spring area of fuel rod (height/cm)	top/bottom insulation of fuel rod (height/cm)
SPALLER-4	BeO (3.5)	1.20	0.60	He (0.015)	TH-9(0.06)	TH-9(3/3)	He(48/14)	He(1/1)
URANUS	—	1.35	0.72	He (0.010)	TH-9(0.06)	TH-9(30/30)	He(130/30)	—

Table 3. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

View table

View in Article

Table 3. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

contrast group	thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	third-year K_eff			burnup/(MW·d·kg⁻¹)
contrast group	thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
1	4.6555	47.2024	0.2911	112.1659	1.3710	1.0502	1.0503	−0.0154	22.9477	22.7960	0.6654
2	4.8222	45.4101	0.2776	115.2353	1.3773	1.0352	1.0352	0.0006	24.6610	24.4460	0.8794
3	4.9908	48.9315	0.2608	118.1860	1.4117	1.0325	1.0334	−0.0846	26.8646	26.8940	0.1093
4	4.5899	48.8228	0.2117	103.6606	1.3534	1.0164	1.0174	−0.0987	46.3528	46.5440	0.4108
5	4.7828	46.6647	0.2173	116.5918	1.3548	1.0244	1.0234	0.0994	39.1589	39.3960	0.6019

Table 4. Optimization results of SPALLER-4 core design scheme

View table

View in Article

Table 4. Optimization results of SPALLER-4 core design scheme

thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	third-year K_eff			burnup/(MW·d·kg⁻¹)
thickness of solid moderator/cm	mass fraction of Pu in fuel/%	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
4.5732	49.8686	0.2003	100.0818	1.3131	1.0057	1.0052	0.0550	53.7021	53.7990	−0.0018

Table 5. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

View table

View in Article

Table 5. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

contrast group	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	twentieth-year K_eff			burnup/(MW·d·kg⁻¹)
contrast group	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
1	0.7287	164.3119	1.3207	1.0010	1.0018	−0.0809	44.0797	44.4100	−0.7438
2	0.7373	157.4453	1.3208	1.0004	1.0007	−0.0338	45.2746	45.2710	0.0080
3	0.7388	156.9933	1.3211	1.0005	1.0009	−0.0409	45.2266	45.2130	0.0301
4	0.7410	153.9331	1.3205	0.9994	0.9999	−0.0585	43.5830	43.5540	0.0666
5	0.7374	157.4387	1.3203	1.0006	1.0003	0.0297	45.2645	45.2560	0.0187

Table 6. Optimization results of design parameters for URANUS core

View table

View in Article

Table 6. Optimization results of design parameters for URANUS core

URANUS core	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	initial K_eff	twentieth-year K_eff			burnup/(MW·d·kg⁻¹)
URANUS core	fuel rod core radius/cm	height of core active zone/cm	grid diameter ratio	initial K_eff	prediction by KSM	calculation by RMC	relative error/%	prediction by KSM	calculation by RMC	relative error/%
initial	0.7200	180.0000	1.3500	1.0289	—	1.0031	—	—	41.5240	—
optimization	0.7314	155.5838	1.2893	1.0307	1.0007	1.0010	−0.0229	46.5773	46.5530	0.0523

Table 6. [in Chinese]

View table

View in Article

Table 6. [in Chinese]

URANUS core	refueling interval/ EFPY	fuel loading/kg	total mass of core (including reflector)/kg	volume of the active area/m³	average volume power density of the active area/(W·cm⁻³)	total volume of core (including reflector)/m³	maximum temperature of fuel cladding/K	maximum temperature of fuel core/K
initial	20	17580.0925	175459.3633	5.2138	19.1800	8.5734	600.6219	770.3892
optimization	20	15681.0697	155309.9496	4.2697	23.4208	7.1059	604.1702	796.0589

Tools

Get Citation

Copy Citation Text

Qiong Li, Zijing Liu, Hao Xiao, [in Chinese], Pengcheng Zhao, Chang Wang, Tao Yu. Intelligent optimization method for lead-bismuth reactor based on Kriging surrogate model[J]. High Power Laser and Particle Beams, 2022, 34(5): 056007

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Feature Issue on Application Technology of Research Reactor

Received: Dec. 14, 2021

Accepted: --

Published Online: Jun. 2, 2022

The Author Email: Zijing Liu (liuzijing1123@163.com)

DOI:10.11884/HPLPB202234.210560

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Commonly used related functions of Kriging surrogate model and their expressions

Table 1. Commonly used related functions of Kriging surrogate model and their expressions

Table 2. Materials used for the design parameters of SPALLER-4 and the interval value of optimization variables

Table 2. Materials used for the design parameters of SPALLER-4 and the interval value of optimization variables

Table 3. Accuracy verification results of Kriging surrogate model for predicting Keff and burnup

Table 3. Accuracy verification results of Kriging surrogate model for predicting Keff and burnup

Table 4. Optimization results of SPALLER-4 core design scheme

Table 4. Optimization results of SPALLER-4 core design scheme

Table 5. Accuracy verification results of Kriging surrogate model for predicting Keff and burnup

Table 5. Accuracy verification results of Kriging surrogate model for predicting Keff and burnup

Table 6. Optimization results of design parameters for URANUS core

Table 6. Optimization results of design parameters for URANUS core

Table 6. [in Chinese]

Table 6. [in Chinese]

Table 3. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

Table 3. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

Table 5. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup

Table 5. Accuracy verification results of Kriging surrogate model for predicting K_eff and burnup