Page 27 - 《爆炸与冲击》2025年第5期

第 45 卷 柏劲松，等： 端到端机器学习代理模型构建及其在爆轰驱动问题中的应用 第 5 期

0 0
Simulation data
−0.2 h=0 mm h=1 mm −0.2 Simulation data
−0.4 h=2 mm h=3 mm −0.4 h=0 mm h=1 mm
h=3 mm
h=5 mm
h=2 mm
h=4 mm
−0.6 −0.6 h=4 mm h=5 mm
v/(km·s −1 ) −0.8 v/(km·s −1 ) −0.8
−1.0
−1.0
−1.2
Surrogate output
−1.4
−1.4 −1.2 h=0 mm h=1 mm
−1.6 −1.6 h=2 mm h=3 mm
−1.8 −1.8 h=4 mm h=5 mm
0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 24
t/μs Magnification t/μs Magnification
−1.2 −1.2
Simulation data Simulation data
h=0 mm h=1 mm −1.3 h=0 mm h=1 mm
h=2 mm h=3 mm h=2 mm h=3 mm
−1.4 h=4 mm h=5 mm −1.4 h=4 mm h=5 mm
v/(km·s −1 ) −1.6 v/(km·s −1 ) −1.5

−1.6
−1.7 Surrogate output
h=0 mm h=1 mm
−1.8 −1.8 h=2 mm h=3 mm
h=4 mm h=5 mm
−1.9
12 14 16 18 20 22 24 12 14 16 18 20 22 24
t/μs t/μs

(a) P 1 (a) P 1
1.5 2.5

1.2 2.0

v/(km·s −1 ) 0.9 Simulation data v/(km·s −1 ) 1.5 Simulation
data
0.6
h=0 mm
h=2 mm h=1 mm 1.0 h=0 mm
h=3 mm
h=1 mm
h=4 mm h=5 mm Surrogate output h=2 mm
0.3 0.5 h=0 mm h=1 mm h=3 mm
h=2 mm h=3 mm h=4 mm
h=4 mm h=5 mm h=5 mm
0 0
12 14 16 18 20 22 24 12 14 16 18 20 22 24
t/μs t/μs
(b) P 2
(b) P 2
图 7 P 1 和 P 2 处模拟的速度剖面 图 8 训练点上速度代理模型和数值模拟的计算结果比较
Fig. 7 Numerical simulated velocity profiles Fig. 8 Results calculated by the speed surrogate model at the
training points and the numerical simulation result
at P 1 and P 2

表 2 训练点上速度剖面代理模型计算的相对误差
Table 2 Relative errors of velocity surrogate model calculation at training points

相对误差/% 相对误差/%
h/mm h/mm
P 1 P 2 P 1 P 2
0 0.003 4 0.004 0 3 0.005 7 0.001 4
1 0.007 8 0.009 4 4 0.002 7 0.009 4
2 0.006 3 0.003 6 5 0.003 5 0.006 7

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