基于结构感知变分光流法的BOS冲击波超压非接触式测量

周志刚; 王长利; 吴郑浩; 肖昌炎; 柯明; 张鑫; 钱秉文

doi:10.11883/bzycj-2025-0269

基于结构感知变分光流法的BOS冲击波超压非接触式测量

doi: 10.11883/bzycj-2025-0269

1.
湖南大学电气与信息工程学院，湖南长沙 410082
2.
西北核技术研究所，陕西西安 710024

详细信息

作者简介:
周志刚（2000－　），男，博士研究生，zhigangzhou@hnu.edu.cn

通讯作者:
王长利（1980－　），男，博士研究生，研究员，wangchangli@nint.ac.cn

中图分类号: O348.1
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- 被引次数: 0
出版历程
- 收稿日期: 2025-08-18
- 修回日期: 2025-10-23
- 网络出版日期: 2025-11-04

Non-contact measurement of BOS shock wave overpressure based on structure-aware variational optical flow method

1.
College of Electrical and Information Engineering, Hunan University, Changsha 410082, Hunan, China
2.
Northwest Institute of Nuclear Technology, Xi'an 710024, Shaanxi, China

摘要

摘要: 背景纹影（background-oriented schlieren，BOS）技术因其非接触与高时空分辨率的优势，已成为爆炸力学外场试验的重要测量手段，但受强光干扰、产物散射及冲击波信号微弱且形态复杂等因素影响，BOS图像中波阵面的自动精确提取十分困难。为此，提出了一种结构感知加权变分光流方法（structure-aware weighted variational optical flow，SAW-VF），用于对冲击波的高速瞬态位移场进行鲁棒量化，其核心是最小化一个针对性构建的能量泛函：首先，在数据保真项中融合一阶光度与二阶Hessian矩阵不变性约束，从而显著增强对冲击波线状局部几何特征的敏感性；其次，引入由归一化互相关（normalized cross-correlation，NCC）驱动的空间自适应加权机制，能够动态抑制严重畸变区域对估计结果的负面影响；然后，采用受佩罗娜-马利克（perona-malik）扩散启发的各向异性正则项，以有效保护冲击波锋锐的运动边界。为了以应对大位移运动，整个优化过程嵌入由粗至精的高斯金字塔框架中。在此基础上，进一步构建了物理模型驱动的波阵面拟合方法，通过最大内点集优化与冲击波动力学约束精确提取波阵面。最终，通过基于几何标定与时间序列估计冲击波半径及传播速度，结合兰金-雨贡纽（rankine-hugoniot）理论实现非接触式超压定量测量。在TNT爆炸试验中，该方法测量结果与压力传感器数据的相对误差为0.93%~9.85%，验证了其在冲击波非侵入式超压测量中的有效性与准确性。
- 背景纹影 /
- 冲击波 /
- 变分光流 /
- 超压测量 /
- 波阵面提取 /
- 非接触式测量
Abstract: Background-oriented schlieren (BOS) imaging, owing to its non-contact nature and high spatiotemporal resolution, has become an important measurement technique in field experiments of explosion mechanics. However, due to strong illumination interference, scattering from detonation products, and the inherently weak and morphologically complex shockwave signature, automatic and accurate extraction of the shock front from BOS images remains highly challenging. To address this issue, we propose a structure-aware weighted variational optical flow method (SAW-VF) for robust quantification of the high-speed transient displacement field of shockwaves. The proposed approach minimizes a purpose-designed energy functional. Specifically, the data fidelity term combines a first-order photometric constraint with a second-order Hessian-invariance constraint, substantially enhancing sensitivity to the local line-like geometric features of shock fronts. In addition, a spatially adaptive weighting mechanism driven by normalized cross-correlation (NCC) is introduced to dynamically suppress the adverse influence of severely distorted regions on the estimation. Moreover, an anisotropic regularization term inspired by Perona-Malik diffusion is employed to effectively preserve the sharp motion boundaries of the shock front. To cope with large displacements, the optimization is embedded in a coarse-to-fine Gaussian pyramid framework. Building upon the estimated displacement field, we further develop a physics model–driven shock-front fitting method, in which the shock front is accurately extracted via maximum-inlier-set optimization coupled with shockwave dynamical constraints. Finally, the shock radius and propagation velocity are estimated using geometric calibration and temporal information, and the overpressure is quantitatively determined in a non-contact manner based on the Rankine-Hugoniot theory. In TNT explosion experiments, the proposed method achieves a relative error of 0.93%—9.85% with respect to pressure sensor measurements, demonstrating its effectiveness and accuracy for non-intrusive overpressure measurement of shockwaves.
- BOS /
- shock wave /
- variational optical flow /
- overpressure measurement /
- wavefront extraction /
- non-contact measurement

HTML全文

图 1 斜条纹背景板

Figure 1. Diagonal-striped background target

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图 2 高速相机与防护板实物图

Figure 2. Photograph of the high-speed camera and protective plate

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图 3 BOS测量系统现场布置图

Figure 3. Field layout of the BOS measurement system

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图 4 冲击波成像几何模型图

Figure 4. Geometric model of shock-wave imaging

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图 5 不同方法拟合曲线的像素误差曲线

Figure 5. Pixel error curves of fitted wavefronts using different methods

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图 6 不同方法处理结果对比

Figure 6. Comparison of results obtained by different methods

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图 7 样例1不同方法对比结果

Figure 7. aaa

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图 8 样例2不同方法对比结果

Figure 8. aaa

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图 9 SWPM-CFA拟合算法结果图

Figure 9. Results of the SWPM-CFA fitting algorithm

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图 10 压电式压力传感器布置图

Figure 10. Layout of piezoelectric pressure sensors

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图 11 冲击波测得半径及误差界随时间变化曲线

Figure 11. Measured shock-wave radius with upper and lower error bounds versus time

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图 12 冲击波测得超压及误差界随时间变化曲线

Figure 12. Measured shock-wave overpressure with upper and lower error bounds versus time

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图 13 冲击波测得超压随半径变化曲线及对比结果

Figure 13. Radial variation of the measured shock-wave overpressure and comparison results

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表 1 不同方法与 SAW-VF 的评价指标对比

Table 1. Comparison of evaluation metrics for different methods

方法	平均绝对误差/pixels	均方误差/pixels
FDM	5.8271	35.1475
CCM	4.9899	26.2430
FB-OF	9.3556	104.7900
HS-OF	12.6970	184.1961
SWA-VF	1.5536	4.7066

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表 2 不同方法与SWPM-CFA的评价指标对比

Table 2. Comparison of evaluation metrics between various methods and the SWPM-CFA method

方法	平均绝对误差/pixels	均方误差/pixels	$\mathrm{R}^2$
LSM	5.72	8.28	0.86
NSWPM-CFA	3.2	3.0	0.90
SWPM-CFA(Ours)	2.95	2.20	0.94

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表 3 0.85 kg TNT 当量条件下本方法测量结果误差统计

Table 3. Relative errors of the proposed method for a 0.85 kg TNT equivalent charge

距离/m	压力传感器测量值/MPa	经验公式预测值/MPa	本文方法测量值/MPa	相对误差/%
3	0.0936	0.0717	0.0844	9.85 (PSV) 17.71 (EFP)
4	0.0504	0.0427	0.0474	5.69 (PSV) 11.01(EFP)
5	0.0299	0.0290	0.0304	1.75 (PSV) 4.83 (EFP)

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表 4 1.2 kg TNT 当量条件下本方法测量结果误差统计

Table 4. Relative errors of the proposed method for a 1.2 kg TNT equivalent charge

距离/m	压力传感器测量值/MPa	经验公式预测值/MPa	本文方法测量值/MPa	相对误差/%
3	0.1190	0.0895	0.1087	8.68 (PSV) 21.45 (EFP)
4	0.0637	0.0521	0.0618	2.76 (PSV) 18.62 (EFP)
5	0.0414	0.0355	0.0396	4.32 (PSV) 11.55 (EFP)
6	0.0276	0.0262	0.0279	0.93(PSV) 6.49 (EFP)
7	0.0199	0.0207	0.0202	1.59 (PSV) 2.42 (EFP)

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