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Polymer bonded explosive (PBX) is a kind of composite material with highly filled molding explosive particles (normally more than 95%) and a small quantity of binders (less than 5%). The effective detection of internal cracks in PBX is of great significance in evaluating structural integrity and safety reliability. Ultrasonic phased array detection and imaging methods show great advantages and potential in detecting crack defects. But acoustic test results indicate that the PBX has unique characteristics with low longitudinal wave velocity (～3000 m·s–1) and strong attenuation (attenuation coefficient ～400 dB·m–1 for 2.5 MHz ultrasound). When the defect is imaged by traditional ultrasonic total focusing method (TFM), the structural noises at the boundaries between particles lead to low signal-to-noise ratio (SNR) in the FMC signals and strong background noise in reconstructed image, which will disturb the detection of cracks. To realize the high SNR imaging of crack defects in PBX, an ultrasonic imaging algorithm based on baseband nonlinear synthetic focusing (BB-NSF) is proposed. By utilizing the spatial coherence of the received signals in full matrix capture (FMC) data, the pixel intensity at defect position can be enhanced while the background noise can be drastically weakened. The delay rule of the algorithm is modified according to the characteristics of PBX surface configuration. In this way, the high SNR imaging of crack defects with different orientations of PBX surface configuration is realized, and the quality of the reconstructed images is compared and evaluated quantitatively. Meanwhile, the base band transformation in calculation process optimization could significantly reduce calculation burden and increase imaging efficiency. Experimental results show that the proposed algorithm can effectively suppress background noise and significantly improve the ability to detect the PBX cracks. The effective suppression to background noise makes the defect more highlighting and distinguished easily. For the BB-NSF algorithm, spatial coherence coefficient p is a crucial parameter used for dynamically regulating the SNR of reconstructed image. When p value is more than 2.0, the SNR of the ultrasonic reconstructed image of PBX crack defect is improved by more than 10 dB compared with that of the traditional linear synthetic focusing imaging. With the increase of p value, the SNR is further improved, while the calculation efficiency for a single image is almost kept stable. Moreover, the increase of SNR to some extent will improve the far-field detect capability. Besides, with the BB-NSF algorithm, flexible transducer inhibits different imaging characteristics of for cracks with different orientations and depths in curved PBX specimens. For defects with large orientation angle and buried depth, the tip, root and shape of cracks can be completely present. For defects with small orientation angle and buried depth, part of shape and contour features will be lost. In conclusion, the BB-NSF algorithm shows the advantage of high SNR and calculation efficiency in imaging PBX cracks, and exhibits great application prospect in imaging internal defects of other strongly attenuated composites. -
Keywords:
- polymer bonded explosives /
- crack defect /
- ultrasonic phased array /
- baseband nonlinear synthesis focusing algorithm
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Dong H S, Zhou F F 1989 Performance of High-energy Explosives and Related Substances (Beijing: Science Press) pp20–32 (in Chinese)
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图 1 BB-NSF算法示意图
Figure 1. Block diagram of BB-NSF algorithm.
图 2 合成聚焦成像示意图
Figure 2. Schematic diagram of synthetic focusing imaging.
图 3 曲面试件后处理成像算法延迟时间计算原理图
Figure 3. Schematic diagram of the time delay calculation of the post-processing imaging algorithm for curved workpiece.
图 4 颗粒复合材料PBX的裂纹缺陷几何模型示意图
Figure 4. Geometric model of PBX workpiece with cracks.
图 5 柔性换能器在不同检测位置时缺陷的仿真成像结果 (a)—(d) 缺陷A; (e) 缺陷B; (f) 缺陷C
Figure 5. Simulated images of (a)−(d) crack A, (e) crack B and (f) crack C with flexible transducers moving along surface.
图 6 (a) TFM图像和(b) BB-NSF图像缺陷区域的像素峰值、背景噪声区域内像素强度的均方根; (c) TFM和BB-NSF缺陷的信噪比指标
Figure 6. Pixel peak of the defect area and the root mean square of the pixel intensity in the background noise area of (a) TFM image and (b) BB-NSF image, respectively. (c) Comparison of SNR indictors for TFM and BB-NSF images.
图 7 实验装置 (a) 采用柔性换能器检测的PBX试件; (b) 16阵元柔性超声换能器PMUT
Figure 7. Experimental setup: (a) PBX workpiece with flexible transducers; (b) the flexible ultrasonic transducer of PMUT with 16 array elements.
图 8 不同算法对PBX缺陷的成像结果对比 (a) 未延时修正TFM; (b) 延时修正后TFM; (c) F-DMAS; (d) BB-NSF算法; (e) 利用延时修正后BB-NSF算法重构的全场图像
Figure 8. Comparison of cracks image with TFM algorithm: (a) Without time delay correction; (b) with time delay correction; (c) F-DMAS; (d) BB-NSF; (e) the reconstructed image of cracks A, B and C with BB-NSF algorithm.
图 9 T = 6, R = 8时域信号 (a) 缺陷A; (b) 缺陷B; (c) 缺陷C
Figure 9. Time domain signal transmitted by the sixth array element and received by the eighth array element for defect (a) A, (b) B and (c) C, respectively.
图 10 不同p值时BB-NSF算法的成像信噪比和计算效率
Figure 10. Calculated SNR and consuming time of BB-NSF algorithm with different p values.
表 1 超声换能器阵列和预制缺陷埋深参数
Table 1. Parameters of flexible transducers and prefabricated cracks.
换能器参数 取值 缺陷 裂尖埋深值/mm 阵元个数 16 缺陷A 16 阵元中心距/mm 1.5 缺陷B 23 中心频率/MHz 2.5 缺陷C 24 
DownLoad: CSV
表 2 不同算法的PBX裂纹缺陷实测信噪比和计算效率对比
Table 2. Experimental comparison of SNR and consuming time for conventional and proposed algorithms.
DownLoad: CSV
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[1] 董海山, 周芬芬 1989 高能炸药及相关物性能 (北京: 科学出版社) 第20—32页
Dong H S, Zhou F F 1989 Performance of High-energy Explosives and Related Substances (Beijing: Science Press) pp20–32 (in Chinese)
[2] 范航, 何冠松, 杨志剑, 聂福德, 陈鹏万 2019 物理学报 68 106201
Google Scholar
Fan H, He G S, Yang Z J, Nie F D, Chen P W 2019 Acta Phys. Sin. 68 106201
Google Scholar
[3] Yang Z F, Tian Y, Li W B, Zhou H Q, Zhang W B, Li J M 2017 Materials 10 660
Google Scholar
[4] 宗和厚, 张伟斌, 肖丽, 周海强, 杨占锋 2016 含能材料 24 166
Google Scholar
Zong H H, Zhang W B, Xiao L, Zhou H Q, Yang Z F 2016 Chin. J. Energ. Mater. 24 166
Google Scholar
[5] 江畅, 杨占锋, 李卫彬, 张伟斌, 田勇 2020 含能材料 28 749
Google Scholar
Jiang C, Yang Z F, Li W B, Zhang W B, Tian Y 2020 Chin. J. Energ. Mater. 28 749
Google Scholar
[6] Drinkwater B W, Wilcox P D 2006 NDT & E Int. 39 525
Google Scholar
[7] Li W, Zhou Z, Li Y 2019 Ultrasonics 96 75
Google Scholar
[8] Holmes C, Drinkwater B W, Wilcox P D 2005 NDT & E Int. 38 701
Google Scholar
[9] Peng C Y, Peng S, Wang Z X, Zhang J 2019 Far East NDT New Technology & Application Forum Qingdao, China, June 24–27, 2019 p11
[10] Wilcox P D, Holmes C, Drinkwater B W 2007 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54 1541
Google Scholar
[11] Zhang J, Drinkwater B W, Wilcox P D, Hunter A J 2010 NDT & E Int. 43 123
Google Scholar
[12] 张海燕, 宋佳昕, 任燕, 朱琦, 马雪芬 2021 物理学报 70 114301
Google Scholar
Zhang H Y, Song J X, Ren Y, Zhu Q, Ma X F 2021 Acta Phys. Sin. 70 114301
Google Scholar
[13] Nakahata K, Tokumasu S, Sakai A, Iwata Y, Ohira K, Ogura Y 2016 NDT & E Int. 82 13
Google Scholar
[14] Pan Q, Xu X, Xu L, Jia Y, Liu X, Xiao D, Chang M 2019 IEEE International Conference on Mechatronics and Automation Tianjin, China, August 4–7, 2019 p2041
[15] 李萌, 徐尧, 肖盼, 张伟斌, 李丽, 蔡文路, 周海强, 陈振茂 2020 含能材料 29 29
Google Scholar
Li M, Xu Y, Xiao P, Zhang W B, Li L, Cai W L, Zhou H Q, Chen Z M 2020 Chin. J. Energ. Mater. 29 29
Google Scholar
[16] Jeon S, Park E Y, Choi W, Managuli R, Jong Lee K, Kim C 2019 Photoacoustics 15 100136
Google Scholar
[17] Mozaffarzadeh M, Mahloojifar A, Periyasamy V, Pramanik M, Orooji M 2018 IEEE J. Sel. Top. Quantum Electron. 25 1
Google Scholar
[18] Yang G, Amidi E, Zhu Q 2021 Biomed. Opt. Express 12 2250
Google Scholar
[19] Mozaffarzadeh M, Mahloojifar A, Orooji M 2017 Iranian Conference on Electrical Engineering Tehran, Iran, May 2–4, 2017 p65
[20] Matrone G, Savoia A S, Caliano G, Magenes G 2015 IEEE Trans. Med. Imaging 34 940
Google Scholar
[21] Matrone G, Savoia A S, Caliano G, Magenes G 2017 Ultrasonics 75 216
Google Scholar
[22] Matrone G, Ramalli A, Savoia A S, Tortoli P, Magenes G 2016 IEEE Trans. Med. Imaging 36 478
Google Scholar
[23] Luo L, Tan Y, Li J, Zhang Y, Gao X 2022 NDT & E Int. 127 102601
Google Scholar
[24] Teng D, Liu L, Xiang Y, Xuan F Z 2022 Ultrasonics 128 106881
Google Scholar
[25] Yu L, Song Y, Li X 2022 NDT & E Int. 130 102660
Google Scholar
[26] Shen C C 2020 Biomed. Signal Process. 60 101964
Google Scholar
[27] Shen C C 2021 Ultrasonics 96 165
Google Scholar
[28] Kozai R, Okubo K, Tagawa N, Irie T, Yoshizawa M 2019 IEEE International Ultrasonics Symposium Glasgow, UK, October 6–9, 2019 p320
[29] Ji W, Liu L, Xing Z, Zhang D, Wang Y, Chen L, Chen Y, Sun X, Du Y 2021 IEEE Trans Ultrason. Ferroelectr. Freq. Control 68 1380
Google Scholar
[30] 周正干, 彭地, 李洋, 胡宏伟 2015 机械工程学报 51 1
Google Scholar
Zhou Z G, Peng D, Li Y, Hu H W 2015 Chin. J. Mech. Eng. 51 1
Google Scholar
[31] Mozaffarzadeh M, Yan Y, Mehrmohammadi M, Makkiabadi B 2018 J. Biomed. Opt. 23 026005
Google Scholar
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