金属圆棒超声螺旋扫查检测的合成孔径成像技术

图1 Cartesian坐标系下超声合成孔径成像技术(SAFT)原理图

Fig.1 Schematic diagram of SAFT imaging in cartesian coordinate system (SAFT—synthetic aperture focusing technology; x and z—location for object point by lateral distance and depth, L—effective length of synthetic aperture, $β$ _0.5—diffusion angle of sound beam, 1…i…n—position of each probe, $S_{1}$ … $S_{i}$ … $S_{n}$ —detection signal at each probe position, M and M ′—measured size of defect A before and after SAFT processing, respectively)

(a) linear scanning mode

(b) signal set corresponding to each detection position

但在检测金属棒材时，由于常采用螺旋扫查方式，故经典的SAFT方法需要进行改造。假定用直径为D、焦距为F的水浸聚焦探头检测圆棒，使焦点位于棒表面，以 $Δ φ (r a d)$ 步距角对半径为R的圆棒进行螺旋扫查。

如图2所示，工件中声束可视为焦点前变窄的入射声束的反向扩展，因此可将探头的焦点设为SAFT重建过程的虚拟孔径^[24]。由于焦点位于耦合剂和试样之间的异质界面，因此在计算虚拟源的孔径角 $θ^{'}$ 时必须考虑折射效应。声束入射角和半孔径角分别为：

\frac{θ}{2} = a r c t a n (\frac{D}{2 F})

(2)

\frac{θ^{'}}{2} = a r c s i n (s i n (\frac{θ}{2}) ∙ \frac{C_{2}}{C_{1}})

(3)

图2

图2 圆棒在极坐标系下SAFT (pSAFT)成像原理图

Fig.2 Schematics of SAFT in polar coordinate system (pSAFT) imaging of round bar (R—cross section radius of round bar, r—radius of inscribed circle of sound beam, $θ$ —twice the incident angle of sound beam, $θ$ '—aperture angle of virtual source, $φ_{1}$ … $φ_{i}$ … $φ_{n}$ —circumferential scanning angle, $γ$ and $γ$ '—synthetic aperture radian for virtual inspection aperture near and far away object A respectively, $ρ$ and $α$ —location for defect in polar system by polar radius and angle respectively, $d$ —distance from virtual aperture position to object point)

(a) surrounding-scan-mode, object B in the ‘r’ zone

(b) scope of virtual inspection aperture for object A (scanning at $d < R$ side)

(d) object B signal set corresponding to each scanning angle

(e) object A signal set corresponding to each scanning angle

(f) circular section tomograph

式中， $C_{1}$ 表示水中声速， $C_{2}$ 表示试样内声速，θ表示2倍声束入射角。

令虚拟孔径位置至目标点的距离为d，当目标点B位于心部r区内时，会被所有扫查位置探头声场所覆盖(如图2a所示)，因此，所有扫查角度下信号都将参与SFAT创建，即有效合成孔径弧度(SAR)为2 $π$ ；当目标点A位于棒表面之下近表面区即r区外时，会被如图2b所示各扫查角下的声场所覆盖(此时 $d < R$ )，也会被如图2c所示各扫查角下的声场所覆盖(此时 $d > R$ )。这2种目标点的信号集分别如图2d和e所示。r区内外分界线可用如图2a中半径为r的虚线圆表示。即

r = R s i n (\frac{θ^{'}}{2})

(4)

建立如图3所示的极坐标系，当目标点A( $ρ$ , $α$ )位于近场侧时( $r < ρ < R$ ) ( $ρ$ 和 $α$ 分别为A点的极径和极角)，其SAR为 $γ$ 。根据图3a的几何关系可得：

γ = 2 a r c s i n (\frac{r}{ρ}) - θ^{'}

(5)

图3

图3 极坐标系下合成孔径弧度(SAR)推导示意图

Fig.3 Schematics about synthetic aperture radian (SAR) derivation in polar coordinate ( $ψ$ —intermediate variable used to calculate $γ$ and $γ'$ , is the sum of half aperture angle of the virtual source and half of the SAR)

(a) for scanning at $d < R$ side (b) for scanning at $d > R$ side

目标点A还可从图2c所示远场侧被探测到，根据图3b的几何关系可得远场侧探测时的SAR为 $γ^{'}$ ：

γ' = 2 a r c s i n (\frac{r}{ρ}) + θ^{'}

(6)

根据极坐标系下两点间的距离公式，各扫查位置 $P (R, φ_{k})$ 相对于目标点A( $ρ$ , $α$ )进行SAFT的信号延迟时间 $τ_{k i}$ 为：

τ_{k i} = \frac{2 [\sqrt[]{R^{2} + ρ^{2} - 2 R ρ c o s (α - φ_{k})} - (R - ρ)]}{C_{2}}

(7)

因此，极坐标系下的合成孔径(pSAFT)聚焦成像公式为：

\{\begin{matrix} S_{p S A F T} (ρ, α) = \frac{\sum_{k = 1}^{N} S_{k} (t - τ_{k i})}{N} (ρ \leq r) (8 - 1) \\ S_{p S A F T} (ρ, α) = \frac{\sum_{k = 1}^{M_{1}} S_{k} (t - τ_{k i})}{M_{1}} (ρ > r, d < R) (8 - 2) \\ S_{p S A F T} (ρ, α) = \frac{\sum_{k = 1}^{M_{2}} S_{k} (t + τ_{k i})}{M_{2}} (ρ > r, d > R) (8 - 3) \end{matrix}

(8)

式中， $N = \frac{2 π}{Δ φ} + 1$ ， $M_{1} = \frac{γ}{Δ φ} + 1$ ， $M_{2} = \frac{γ^{'}}{Δ φ} + 1$ 。式(8)的实质就是利用实际扩散声场的检测信号 $S_{k} (t)$ 将之转化为在目标点的以虚拟聚焦声场得到的检测信号 $S_{p S A F T} (ρ, α)$ ，即通过聚焦原理提高圆棒内缺陷定位准确率和分辨率。

1.2 ST-SAFT成像

螺旋扫查一周后将得到数据集 $S_{φ} (t)$ ， $φ \in 0 ~ 2 π$ 。进行pSAFT处理的第一步是根据探头参数和式(3)计算工件表面的半孔径角；并根据式(4)计算能被所有位置声束覆盖的内接圆半径r。

第二步是对圆棒内所有点A( $ρ$ , $α$ ) (其中 $ρ \in 0 ~ R, α \in 0 ~ 2 π$ )以适当的成像分辨率 $Δ x$ (如每像素代表0.1 mm)分别将 $S_{φ} (t)$ 按式(8)进行合成聚焦计算，当 $ρ \leq r$ 时按式(8- 1)计算，当 $ρ > r$ 时按式(8- 2)和(8-3)计算，从而得到数据矩阵 S_p(i, j)，i表示径向从0到R以 $Δ x$ 的计数，j表示周向从0到 $2 π$ 以 $Δ φ$ 的计数。

第三步将极坐标数据矩阵进行坐标变换以显示圆截面断层扫描图，可如图2f所示，坐标变换公式为：

\{\begin{matrix} x = ρ c o s (α) \\ y = ρ s i n (α) \end{matrix}

(9)

注意到当 $ρ$ 很小时，可以以数倍的 $Δ φ$ 进行计算，从而减少计算量和提高成像速率。基于上述思想，还可进一步改进算法以提高成像质量和成像速率。

2 实验设备和试样

2.1 实验设备和检测参数

超声成像实验设备如图4所示，由机械设备和超声检测电子设备组成。Y轴电机用于调整探头对准圆棒的母线，Z轴电机用于调整探头相对于圆棒的焦点位置，X轴电机使探头沿圆棒轴线移动，U轴电机驱动圆棒旋转移动，从而实现对圆棒的环绕式螺旋超声扫查检测。

图4

图4 实验设备

Fig.4 Photo of experimental equipment (a) and schematic diagram of spiral scanning for a bar (b)

实验采用45#热轧态圆钢棒(直径为65 mm，高35 mm)，声速为5900 m/s；采用晶片直径13 mm的5 MHz水浸聚焦探头，焦距为55 mm；探头声束垂直于被检试样表面入射，水距为55 mm；采样频率为50 MHz。沿轴向扫查20 mm，螺距1 mm，周向步距角为1°。

2.2 人工试样设计

为考察ST-SAFT的成像分辨率，选取上述圆钢设计了人工缺陷试样。共设计有11个横孔，孔深25 mm，试样实物图及各横孔在其端面的位置分布如图5a和b及表1所示。

图5

图5 钢制试样示意图

Fig.5 Schematic diagram of steel specimen (ϕ—diameter of the specimen)

(a) transverse-hole artificial defect sample (b) polar diagram of each transverse hole position

表1 人工缺陷位置及尺寸测量

Table 1 Location and size measurement of artificial defects

Hole	Defect size			Defect position
Hole	number	ϕ / mm			ρ / mm			α / (º)
	Design value	Measured value	Absolute error	Design value	Measured value	Absolute error	Design value	Measured value	Absolute error
1#	2.0	2.0	0	10.0	11.1	1.1	51	53	2
2#	2.0	2.0	0	10.0	10.8	0.8	74	72	2
3#	2.0	2.0	0	22.5	23.1	0.6	141	141	0
4#	2.0	2.0	0	22.5	23.8	1.3	151	151	0
5#	2.0	2.0	0	22.5	23.5	1.0	164	165	1
6#	1.0	1.4	0.4	22.5	23.7	1.2	235	234	1
7#	1.5	1.8	0.3	22.5	24.2	1.7	244	243	1
8#	2.0	2.0	0	22.5	24.6	2.1	254	255	1
9#	2.0	2.0	0	18.5	20.3	1.8	274	274	0
10#	2.0	1.8	0.2	14.5	15.9	1.4	294	295	1
11#	2.0	2.0	0	10.5	11.5	1.0	314	314	0

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其中1#~2#和10#~11#的ϕ2横孔都位于 $r$ 区以内，1#~2#用于考察 $r$ 区内的周向分辨率；3#~5#用于考察不同周向间距的分辨率；6#~8#用于考察不同尺寸缺陷的分辨率；9#~11#用于考察跨 $r$ 区的径向分辨率。

3 检测结果及分析

3.1 ST-SAFT处理前后的成像图对比

将检测一周得到的各扫查角度位置的超声回波信号采样记录下来，然后将此原始数据进行B扫成像如图6a所示，通过将采样时间转化为试样内深度，并进行简单坐标变换可得到此截面的扫查成像结果如图6b所示。从图6a可看出，1#~2#、3#~5#和6#~8#缺陷难以区分开来，而从图6b则可区分开1#和2#，这说明不同的成像方式分辨缺陷的能力是不同的，截面成像方式更优，但不进行SAFT处理仍然不能反映缺陷的真实分布状况。

图6

图6 某一周扫查结果成像图

Fig.6 Imaging charts of scanning results in a circle

(a) B-scan image (b) cross-sectional image with raw data

将该原始数据按前述ST-SAFT法进行处理后缺陷径向深度位置的周向展开图和截面成像图如图7a和b所示。对比图5和图7b，可见ST-SAFT处理后的截面断层扫描图能够很直观地反映缺陷状况。

图7

图7 ST-SAFT处理后的成像图

Fig.7 ST-SAFT processed images

(a) circumferential expansion of radial depth position of defect

(b) cross-sectional tomogram after ST-SAFT processing

3.2 ST-SAFT成像的缺陷分辨能力

将图6a的数据以采样深度150~600 pts设置闸门，读取各周向扫查位置信号闸门内的最大幅值得到缺陷的周向分布曲线如图8所示，由于不满足6 dB分辨规则，只能将11个缺陷识别为4个，这在实际检测中会夸大缺陷的尺寸。同样可将ST-SAFT处理后的图7a的数据处理得到缺陷的周向分布曲线，如图9所示，11个缺陷可完全分辨，图9说明图像信噪比高达26 dB。对图7放大进行缺陷边缘识别如图10所示，各显示缺陷尺寸与真实值对比如表1所示。说明以0.2 mm的像素长度测量时，缺陷尺寸测量误差约在2个像素长度单位以内(约0.4 mm)；缺陷位置的极径 $ρ$ 测量误差为0.6~2.1 mm，再以人工缺陷半径进行修正，缺陷的径向定位误差约1 mm；极角 $α$ 的测量误差为1°。因此ST-SAFT的缺陷定量定位能力能满足工程检测需求。

图8

图8 ST-SAFT处理前的分辨率曲线

Fig.8 Resolution curve before ST-SAFT processing

图9

图9 ST-SAFT处理后的分辨率曲线

Fig.9 Resolution curve after ST-SAFT processing

图10

图10 ST-SAFT处理后的成像图

Fig.10 Zoom images processed by ST-SAFT to indicate those holes positions (Herein, $ϕ$ means the measured diameter of transverse hole image)

由图9根据峰值下降6 dB法进行分辨率的计算， $r$ 区的1#~2#的周向分辨率为2.43°；3#~5#不同周向间距的分辨率为2.09°，与方位分辨率理论值 $δ ϕ \approx D_{f} / (2 R) \approx 0.02 r a d$ ^[9] (其中， $D_{f}$ 为焦斑直径)基本相符；6#~8#不同尺寸缺陷的周向分辨率为3.26°。由图10沿径向画出信号分布曲线按-6 dB法，得9#~11#跨 $r$ 区的径向分辨率为0.58 mm，小于人工缺陷尺寸。可见其方位分辨率与深度无关等特性与经典SAFT的优势一致。

3.3 ST-SAFT的成像速度

在2.6 GHz的CPU为Intel®Core™i7的笔记本电脑上，用MATLAB编程，环绕一周扫查后进行一个截面ST-SAFT成像处理的时间大约需250 ms，这意味着ST-SAFT成像速率可与每秒扫查4周的机械扫查速率相匹配。如果采用机器语言(如VC)则成像速率还可提高一倍，若采用FPGA和DSP产品的专用仪器则成像速率更快，可适应每秒扫10周的机械扫查快速实时检测速率。

ST-SAFT在连续检测时的成像方式可如图11的360°展开式的3D成像及切片式成像，也可以如图12的柱状3D成像和连续视频方式的截面成像，从而可对试样内部缺陷的3D分布信息进行综合评价。

图11

图11 ST-SAFT处理后的初始连续成像

Fig.11 Initial serial imaging after ST-SAFT processing

(a) 3D image (b) axial space slice

图12

图12 ST-SAFT处理后的最终连续成像

Fig.12 Final serial imaging after ST-SAFT processing

(a) columnar image (b) axial space section

4 讨论

工程上，金属棒材通常主要用平探头进行纵波检测，常以 $ϕ$ 2.0平底孔作为检测灵敏度，而本实验设计中以 $ϕ$ 2.0和 $ϕ$ 1.0横孔作为检测灵敏度和采用5 MHz水浸聚焦探头，均是以满足高质量要求金属棒材的检测需求为目标的。实验中 $ϕ$ 1.0横孔(大致对应于GB/T 4162—2008中的AAA最高质量等级)在SAFT前后都能可靠检出，虽然未能显示出ST-SAFT在提高灵敏度方面的益处，这是由于本实验的圆钢材料本底噪声小、干扰性随机噪声小和人工缺陷信号较强，但SAFT在成像过程中是对各目标点附近多个信号的合成(见式(8))，它具有平均滤波抑制噪声的作用，理论上可提高信噪比与检测灵敏度。因此ST-SAFT相较于常规棒材超声探伤技术，既可提供缺陷的定量、定位以及其分布状况等更丰富的信息，还能以高信噪比而检测出小缺陷(也有研究^[25]指出：理论上超声检测可检出的最小缺陷尺寸近似为探头中心频率对应的半波长)，一些原来难以探伤的棒材(如粗晶材料和粉末冶金材料)检测难题可尝试用SAFT解决。

上述ST-SAFT理论及实验是基于探头焦点位于圆棒表面的情况，另外的焦点位置还有3种情况：分别位于：(a) 棒外的水中，(b) 棒表面下和(c) 棒的圆心。基于上述极坐标下pSAFT理论可分别推导出ST-SAFT成像算法。对于情况(a)，r区较大，则会出现大面积过度合成现象，其ST-SAFT成像效果不佳且增加了计算时间而减慢成像速率。对于情况(c)，直接对检测数据进行B扫成像的分辨率要优于图6，但其ST-SAFT处理后的成像效果更佳(与聚焦于表面的图7相近)，成像速率比情况(a)略慢。对于情况(b)，只在焦点区直接B扫成像效果较佳，而经其ST-SAFT处理后的成像效果也与聚焦于表面的图7相近。因此，ST-SAFT相当于对圆棒内各点都是以聚焦的焦点进行检测的，焦点位置的设置对成像效果影响不大，其差别在于算法的复杂度和成像速率。

虽然本实验对象是 $ϕ$ 65圆钢，但ST-SAFT是可满足GB/T 4162等标准要求(圆钢直径范围 $ϕ$ 12~ $ϕ$ 250)的。不过，在进行ST-SAFT成像处理时，应综合考虑被检棒材材质、直径和检测灵敏度及检测效率要求等因素，并据此优化确定探头频率、扫查步进角和分辨率等检测参数与成像参数。

需要注意的是，图7的断层扫描成像图中显示圆棒表层有一定的检测盲区，这是界面波的阻塞效应造成的，需要采用声束斜入射的脉冲回波检测技术加以补充，以检测表面及近表层缺陷。另外，图7中还有缺陷的多次回波所产生的伪像，因此，声束斜入射时的SFAT技术及多次反射的伪像消除技术还需进一步研究。

5 结论

(1) pSAFT具有与Cartesian坐标系下的SAFT一样的优势：即高信噪比、方位分辨率与检测深度无关等，实验的角分辨率可达到其理论值。

(2) ST-SAFT的断层扫描成像方式相比于B扫成像方式更优，能更加直观和准确地反映缺陷的尺寸、位置以及分布状况，以进行缺陷定量、定位和定性评价。

(3) ST-SAFT算法的一个圆截面的成像速率可与棒材螺旋式机械扫查速率相匹配，可满足快速实时检测需求。

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A technique for the application of composite patches for repairing metallic structures has been developed recently. In order to achieve to an effective repair, high-quality patches and bonding should be used. Various ultrasonic testing (UT) techniques, such as pulse-echo, are commonly used to check the patch and bonding. Ultrasonic measurements are associated with some limitations, especially for the multilayered structures, due to the presence of a significant amount of noise in the scan images. In order to enhance the UT images, various processing techniques can be employed. In the present research, different image processing algorithms based on morphology techniques have been adopted to enhance the C-scan images obtained from the ultrasonic measurement of five carbon/epoxy patches bonded to an aluminum plate. Twelve delaminations with various sizes and locations along with three disbond discontinuities were artificially embedded in the five patches. The processed and input images have been quantitatively compared to clarify how useful the utilized morphology processing algorithms can be. According to the comparison results, a morphology-based processing algorithm that is more useful than the others has been introduced.

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