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图1所示多层胶接结构样件从上至下是由聚甲基丙烯酰亚胺(Polymethylacrylimide,PMI)、上胶层、缓冲垫、下胶层及金属基体经过胶接技术[10]得到的。实验采用的反射式THz-TDS系统的飞秒激光器为锁模钛蓝宝石飞秒激光器,产生的光脉冲中心波长为810 nm,重复频率为80 MHz,脉宽为100 fs,系统的时间分辨率为0.1 ps,快速扫描范围为160 ps,对待测的样件进行逐点扫描,扫描步距为0.5 mm,探测器焦距为76.2 mm,有效焦深为±4.8 mm,以胶层信号的最佳信噪比为依据,调整样件在最佳焦深范围处。THz波经PMI、上胶层、缓冲垫、下胶层,最后到达多层胶接结构样件的金属基体表面,THz波在不同介质表面产生的反射信号被THz探测器接收。THz波在不同介质中传播时,在不同介质分界面时产生反射回波,根据先后通过介质的顺序不同,返回的太赫兹时域信号也会携带胶层信息,THz探测器会依据THz波在通过不同材料到达THz探测器时间的先后,接收不同介质层的反射脉冲,得到太赫兹时域信号[11]。由于检测样件的胶层厚度与探测器接收信号的时间延迟有关,设时间延迟为
$\Delta t$ ,胶层厚度为$l$ ,则有$\Delta t = 2 nl/c$ 。式中:$n$ 为介质折射率,$c$ 为光速(c = 299792458 m/s)。图1中$\Delta {t_{{\rm{up}}}}$ 和$\Delta {t_{{\rm{down}}}}$ 分别表示上胶层和下胶层的时间延迟,可计算检测样件的上/下胶层厚度。图 1 THz信号在多层胶接结构样件传播过程
Figure 1. Propagation process of THz signal in multilayer bonded structure sample
图1中
$E(\omega )$ 为太赫兹发射器射出太赫兹脉冲信号电场强度,四层介质材料的厚度分别为${l_1}$ ,${l_2}$ ,${l_3}$ 和${l_4}$ ,第一层介质PMI材料上表面返回的太赫兹脉冲信号电场强度记为${E_{01}}(\omega )$ ,下表面返回的太赫兹脉冲信号电场强度记为${E_{12}}(\omega )$ ,第二层介质上胶层下表面返回的太赫兹脉冲信号电场强度记为${E_{23}}(\omega )$ ,第三层介质缓冲垫下表面返回的太赫兹脉冲信号电场强度记为${E_{32}}(\omega )$ ,第四层介质下胶层下表面返回的太赫兹脉冲信号电场强度记为${E_{24}}(\omega )$ 。太赫兹接收器收到的太赫兹时域信号$E(t)$ 为${E_{01}}(\omega )$ 、${E_{12}}(\omega )$ 、${E_{23}}(\omega )$ 、${E_{32}}(\omega )$ 及${E_{24}}(\omega )$ 之和的傅里叶逆变换,即:$$ E(t) = {\mathcal{F}^{ - 1}}\left[ {{E_{01}}(\omega ) + {E_{12}}(\omega ) + {E_{23}}(\omega ) + {E_{32}}(\omega ) + {E_{24}}(\omega )} \right] $$ (1) 式中:
${\mathcal{F}^{ - 1}}$ 为傅里叶逆变换。通过THz-TDS系统检测样件可得到具有
$N$ 个采样点的太赫兹时域信号,记为THz信号,如图2所示,图中纵坐标Amplitude/a.u.表示THz接收器接收的信号振幅大小,横坐标Time/ps表示THz接收器采集信号的时间,单位为ps。THz波在PMI与上胶层界面反射得到的波峰记为特征峰1,其对应时间位置记为${T_{{\rm{up1}}}}$ ,上胶层与缓冲垫界面反射得到的波谷记为特征谷2,其对应时间位置记为${T_{{\rm{up2}}}}$ ;缓冲垫与下胶层界面反射得到的波峰记为特征峰3,其对应时间位置记为${T_{{\rm{low1}}}}$ ;下胶层与基体界面反射得到的波峰记为特征峰4,其对应时间位置记为${T_{{\rm{low2}}}}$ 。用点框将THz信号一部分时间区间划分为4个区域,框位置不固定。可以看到THz信号的4个特征峰/谷的峰/谷值是某段时域内的最值,最值点一般也是极值点,故计算THz信号的极值点,然后通过对比获得最值,进而可确定THz信号有效特征区域。分析THz信号的时域特征,如图3所示,虚线框内表示THz信号的有效特征信息所在区域,即信号的4个特征峰/谷所在时域区间,定义为有效特征区域,第一个有效特征峰对应时间位置[12]记为
${T_{{\rm{up}}}}$ ,最后一个有效特征峰对应时间位置记为${T_{{\rm{low}}}}$ ,则有效特征区域对应时间区间为$\left[ {{T_{{\rm{up}}}},{T_{{\rm{low}}}}} \right]$ 。特征区域内还包含了THz信号上/下层飞行时间[13],特征峰1对应时间位置${T_{{\rm{up1}}}}$ 与特征谷2对应时间位置${T_{{\rm{up2}}}}$ 的差值为上层飞行时间$\Delta {t_{{\rm{up}}}}$ ,特征峰3对应时间位置${T_{{\rm{low1}}}}$ 与特征峰4对应时间位置${T_{{\rm{low2}}}}$ 差值为下层飞行时间$\Delta {t_{{\rm{low}}}}$ ,飞行时间是计算多层胶接结构样件上/下胶层厚度的重要参数。THz-TDS系统的时间分辨率为0.1 ps,THz信号的有效特征区域内采样点的数量
${N_1} = 10×({T_{{\rm{low}}}} - {T_{{\rm{up}}}}) +$ 1,框线外无效特征区域,此区域采样点数量为${N_2} = N - {N_1}$ 。如图3所示,经过统计分析,THz信号上层飞行时间为10.9 ps,下层飞行时间为12.4 ps,有效特征区域内采样点数量为335,无效特征区域采样点数量为1265,无效特征区域的采样点数量占据了总采样点数量的79.06%,可见THz中的无效信息不仅占据极大存储空间,更降低了数据处理效率,增加了数据计算时间,故在不影响信号有效信息的前提下,对THz信号进行稀疏,减少无效特征并提高数据处理效率,对于THz-TDS检测的数据处理工作是十分必要且有意义的。
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记采样点为
$n$ 的THz信号为$X$ ,采样时间$T$ ,由于THz-TDS系统检测样件时等时间间隔采样,记时间间隔为$\Delta T$ 。将信号$X$ 一阶梯度定义为$J$ ,表达式为:$$ J(i) = \frac{{X(i + 1) - X(i)}}{{\Delta T}}\text{,}i = 1,2, \cdots ,n - 1 $$ (2) 由公式(2)可得二阶梯度,定义为
$N$ ,$$ {J_2}(j) = \frac{{J(j + 1) - J(j)}}{{\Delta T}}\text{,} j = 1,2, \cdots ,n - 2 $$ (3) 可利用二阶梯度搜索
$X$ 的极值点,极小值数量记为${n_1}$ ,极大值数量记为${n_2}$ ,提取THz信号的特征峰,确定上层特征峰和下层特征峰对应时间位置,即${T_{{\rm{up}}1}}$ 、${T_{{\rm{up2}}}}$ 、${T_{{\rm{low1}}}}$ 和${T_{{\rm{low2}}}}$ ,其中${T_{{\rm{up}}1}} = {T_{{\rm{up}}}}$ 和${T_{{\rm{low2}}}} = {T_{{\rm{low}}}}$ ,进而提取有效特征区域$\left[ {{T_{{\rm{up1}}}},{T_{{\rm{low2}}}}} \right]$ 。 -
将原THz信号
${T_{{\rm{up1}}}}$ 与${T_{{\rm{up2}}}}$ 的差值记为上层飞行时间$\Delta {t_{{\rm{up1}}}}$ ,稀疏THz信号${T_{{\rm{up1}} - s}}$ 与${T_{{\rm{up2}} - s}}$ 的差值记为上层飞行时间$\Delta {t_{{\rm{up2}}}}$ 。文中利用THz信号的时域特征自适应确定阈值稀疏信号,以稀疏前后THz信号上层飞行时间误差为限制条件,假设检测样件THz信号的飞行时间能够接受的最大误差为0.05,稀疏前后误差$e$ 表示为$e = \left| {\Delta {t_{{\rm{up2}}}} - \Delta {t_{{\rm{up1}}}}} \right|$ 。文中基于梯度阈值的太赫兹时域信号自适应稀疏算法步骤如下:Step 1: 输入:采样点为
$N$ 的THz信号$X$ ,设置有效特征区域初始阈值${\tau _0} = \dfrac{{{n_1} + {n_2}}}{{10×({T_l} - {T_u})}}$ ,无效特征区域初始阈值${\eta _0} = \dfrac{{{n_1} + {n_2}}}{{N - ({n_1} + {n_2})}}$ ,阈值精度为0.01;Step 2: 通过阈值
$\tau $ 对THz信号有效特征区域稀疏,稀疏THz信号记为$Y$ ,采样点数量记为${M_1}$ ,提取稀疏后THz信号的${T_{{\rm{up1}} - s}}$ 与${T_{{\rm{up2}} - s}}$ ;Step 3: 计算
$e = \left| {\Delta {t_{{\rm{up2}}}} - \Delta {t_{{\rm{up1}}}}} \right|$ ;Step 4: 若
$0 \leqslant e \lt 0.05$ ,则尝试调小阈值${\tau _{j + 1}} = {\tau _j} - 0.01$ ,${\tau _j} \ne 0$ ,$j$ 为迭代次数,返回Step 2,若误差仍满足$0 \leqslant e \lt 0.05$ 则继续调整,直至$e = 0.05$ 迭代停止,取此次迭代的阈值为最佳稀疏阈值$\tau $ ,转至Step 6;Step 5: 若
$e \gt 0.05$ ,则需要调大阈值${\tau _{j + 1}} = {\tau _j} + 0.01$ ,返回Step 2,直至满足误差$e = 0.05$ ,则停止,此次迭代的阈值为最佳稀疏阈值$\tau $ ,转至Step 6;Step 6: 通过阈值
$\eta $ 稀疏THz信号无效特征区域,稀疏后采样点数量记为${M_2}$ ;Step 7: 恢复THz信号,记为
$\hat X $ ,依据误差分析判断信号是否失真;Step 8: 若信号未失真,尝试调小阈值
${\eta _{k + 1}} = {\eta _k} - 0.01$ ,$\eta_k \neq 0$ ,K为迭代次数,返回步骤6,若下一次迭代信号失真,则此次迭代的阈值为无效区域最佳稀疏阈值$\eta $ ,转至Step 10;Step 9: 若信号失真,调整阈值
${\eta _{k + 1}} = {\eta _k} + 0.01$ ,返回步骤6,直至信号恢复停止迭代,此次迭代阈值为最佳稀疏阈值$\eta $ ,转至Step 10;Step 10: 输出:恢复 THz信号
$\hat X $ 。 -
将THz信号划分为若干区间,通过高斯函数[14]分区间拟合恢复THz信号,恢复信号记为
$\mathop X\limits^ \wedge$ ,$\mathop X\limits^ \wedge = ({{\mathop x \limits^ \wedge}_1 },{{\mathop x \limits^ \wedge}_2 }, \cdots ,{{\mathop x \limits^ \wedge}_i }, \cdots ,{{\mathop x \limits^ \wedge}_m })$ ,$i = 1,2, \cdots ,m$ ,高斯拟合函数可以表示为:$$ {g_i} = f({{\mathop x \limits^ \wedge}_i }) = {a_i}\exp ( - {(({{\mathop x \limits^ \wedge}_i } - {b_i})/{c_i})^2}) $$ (4) 式中:
${a_i}$ ,${b_i}$ ,${c_i}$ 为高斯函数在分段区间的拟合系数,分别表示高斯信号的峰高、峰位置和半宽度。多层胶接结构的THz信号拟合过程存在多个高斯峰叠加的情况,如图4所示,某段时域的THz信号在高斯拟合时至少需要3个高斯峰进行叠加。多高斯函数表达式为:
$$ g = f(\mathop x \limits^ \wedge) = \sum\limits_{i = 1}^{i=k} {{a_i}\exp ( - {{(({\mathop x \limits^ \wedge}_i - {b_i})/{c_i})}^2})} $$ (5) 式中:k为THz信号高斯峰的总数。不考虑多高斯拟合信号过程存在的误差,根据最小二乘法结合梯度下降法[15]求解高斯函数的拟合系数,算法的迭代格式为:
$$ {{\mathop x \limits^ \wedge}_{k+1} } = {P_\Omega }({t_k} - {\delta _k}\nabla f({{\mathop x \limits^ \wedge}_k})) $$ (6) 式中:
${\delta _k} \gt 0$ 为步长;$\nabla f({{\mathop x \limits^ \wedge}_k})$ 为THz信号${\mathop X \limits^ \wedge} $ 的梯度;${P_\Omega }( \cdot )$ 为点${\mathop x \limits^ \wedge}_k $ 到THz信号时间域$\varOmega $ 的投影;$k$ 为迭代次数。 -
文中设计制作一块60 mm×60 mm×27 mm 的多层胶接结构样件,其中PMI材料厚度为20 mm,缓冲垫厚度为3 mm,金属基体的厚度为 2 mm,上胶层与下胶层材料厚度均为 1 mm,然后在上、下胶层的四边利用抽膜法[16]模拟约 0.3 mm 厚度空气隙的脱粘缺陷,得到带有预制脱粘缺陷的多层胶接结构样件,如图5所示,图5(b)圆圈圈出部分是空气隙。通过反射式THz-TDS系统分别对制备完成的实验样件进行检测,信号采样时间间隔为0.1 ps,时间窗口为160 ps。将检测的THz信号分为正常信号与缺陷信号两种,分别记为信号A、信号B。
图 5 (a)正常多层胶接结构样件及THz-TDS检测信号;(b)脱粘缺陷实验样件及THz-TDS检测信号
Figure 5. (a) Normal multilayer bonding structure sample and THz-TDS detection signal; (b) Debonding defect test sample and THz-TDS detection signal
图6实线为样件胶层正常所检测到的THz信号,即信号A。图6虚线为样件胶层存在缺陷部分检测得到的THz信号,即信号B,图中椭圆圈出的部分为缺陷表征,分别表示的是上层缺陷和下层缺陷,与信号A对比,特征峰1与特征谷2之间突然出现幅值明显增大的特征谷5和特征峰6;特征峰3与特征峰4提前出现,时间位置减小,且特征峰3与特征峰4之间的特征谷7幅值绝对值明显增大。
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如图7所示,预制缺陷样件的下胶层正常信号A与缺陷信号B,基于二阶梯度提取信号A和信号B的4个特征峰/谷,特征峰/谷的峰/谷值对应时间位置如表1所示。基于梯度阈值的太赫兹时域信号自适应稀疏算法稀疏化处理信号A和信号B,并通过多高斯函数恢复信号。图7中虚线为原始信号;带“·”标记的实线为稀疏信号,“·”表示稀疏点;实线为多高斯函数恢复信号,恢复信号与原始信号时间序列长度一致。
表 1 信号A与信号B特征峰峰值对应时间位置
Table 1. Time position corresponding to characteristic peak-to-peak values of signal A and signal B
THz signal ${T_{{\rm{up1}}} }$/ps ${T_{{\rm{up2}}} }$/ps ${T_{{\rm{low1}}} }$/ps ${T_{{\rm{low2}}} }$/ps Signal A 57.2 67.9 78.7 89.6 Signal B 57.6 67.4 78.2 87.8 从表1可知,图7缺陷信号B特征峰1出现时间比正常信号A延迟了0.4 ps,信号B特征谷2比信号A时间提前了0.5 ps,信号B特征峰3比信号A提前了0.5 ps,信号B特征峰4提前了1.4 ps。基于THz信号的特征峰对应时间位置可确定信号A和信号B有效特征区域分别为[57.2 ps, 89.6 ps],[57.6 ps, 87.8 ps]。基于自适应阈值稀疏THz信号,设置最大允许误差为0.05,表2为图7信号A和信号B有效特征区域和无效特征区域的稀疏阈值
$\tau $ 和$\eta $ 。由表2可知,信号A的有效特征区域稀疏阈值为0.42,无效特征区域稀疏阈值为0.07;信号B有效特征区域稀疏阈值为0.33,无效特征区域稀疏阈值为0.09。稀疏阈值的值越小,信号越稀疏,在保证信号不失真且保留有效特征峰/谷的前提下,得到图7所示稀疏信号。图7(a)中的信号A稀疏后采样点数量为224,图7(b)中的信号B稀疏后采样点数量为216,与原始信号相比可以发现信号A与信号B的无效信息大幅度减少,并且保留了信号的4个有效特征峰,这对于提高数据处理的效率具有极大意义。
表 2 信号A与信号B的稀疏阈值
Table 2. Sparse threshold of signal A and signal B
THz signal $\tau $ $\eta $ Original data number Sparse data number Signal A 0.42 0.07 1 600 224 Signal B 0.33 0.09 1 600 216 图7所示的原始THz信号与恢复THz信号之间存在微小偏差,是由稀疏造成的,计算稀疏信号的幅值误差,如图8所示。
图 8 (a) 恢复信号A幅值误差;(b) 恢复信号B幅值误差
Figure 8. (a) Amplitude error of recovered signal A; (b) Amplitude error of recovered signal B
图8(a)信号A稀疏后幅值误差最大值约为0.003 8,4个有效特征峰/谷的幅值误差最大值约为3.56 e-5;图8(b)为信号B稀疏后幅值误差最大值约为0.005 8,4个有效特征峰/谷的幅值误差最大值约为2.37 e-5。在误差允许的范围内,THz信号经阈值稀疏,不仅保留了信号有效特征峰/谷,还减少了无效特征信息,实现了THz信号的有效压缩。
文中通过压缩率[17](Compression Ratio,CR)、相对均方根误差[18](Relative Root Mean Squared Error,RMSE)及相关系数[19]3项指标评价DCT、PCA、K-SVD算法与文中算法4种算法的压缩性能。
压缩率是评价压缩效果的重要指标,能较准确地反应信号稀疏程度。用
$CR$ 表示,计算公式为:$$ CR = \frac{{N - M}}{N} \times 100 {\text{%}} $$ (7) 式中:
$N$ 为原THz信号采样点数量;$M$ 为稀疏后THz信号的采样点数量。$CR$ 越大,压缩率越高,表示信号越稀疏。相对均方根误差与相关系数是衡量压缩算法的重要指标。分别记作
$RMSE$ 和$r$ ,多高斯拟合THz信号$\hat{X}=\left(\hat{x}_1, \hat{x}_2, \cdots, \hat{x}_n\right)$ 与原信号$X = ({x_1},{x_2}, \cdots ,{x_n})$ 的$RMSE$ 和$r$ 计算公式为:$$ R M S E=\sqrt{\frac{ \displaystyle \sum\limits_{i=1}^N\left(x_i-\hat{x_i}\right)^2}{ \displaystyle \sum\limits_{i=1}^N x_i^2}} \times 100 {\text{%}} $$ (8) $$ r=\frac{E\left(X × \hat{X}-E(X × \hat{X})\right)}{\sqrt{D(X)} × \sqrt{D(\hat{X})}} $$ (9) 式中:
$E(X)$ 为信号的数学期望;$D(X)$ 为数学方差。$RMSE$ 越小,则表明算法恢复信号与原信号相位差越小;$r$ 越高,恢复信号与原信号相关度越高。利用DCT、PCA、K-SVD算法与文中算法分别对THz-TDS系统检测制备的多层胶接结构样件的检测数据进行压缩,图9为4种算法压缩性能的对比。
如图9所示,THz信号经过4种算法压缩,文中算法压缩率最高,较DCT提高了59%,较PCA提高了75%,较K-SVD算法提高了26%。虽然文中算法相比其他3种算法相对均方根误差的值较高,但误差低于2%,且4种算法的相关系数均超过了0.97,均呈高度相关。
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通过对THz-TDS系统检测预制脱粘缺陷的多层胶接结构样件,分别对其THz信号的飞行时间,峰峰值及峰谷值成像[20],得到124 pixel×128 pixel大小的图像,图像的每一个像素点均对应一组1600个采样点的THz信号,其中,峰峰值图像与峰谷值图像表示THz接收器接收的反射信号强度,表征材料的反射性能,如图10所示,缺陷样件的图像部分区域呈现颜色突变,该区域为样件缺陷区域。利用文中算法稀疏恢复THz信号的飞行时间图像,峰峰值图像和峰谷值图像如图11所示。图10~11中(a)~(d)为缺陷样件的THz信号上、下层飞行时间图像,上层峰峰值图像和下层峰谷值图像,可以看到(c)~(d)中虚线框内明显的上、下层缺陷区域,分别标记为1、2、3、4。
图 10 原始信号的THz图像。(a)上层飞行时间图像;(b)下层飞行时间图像;(c)上层峰峰值图像;(d)下层峰谷值图像
Figure 10. THz images of the original signal. (a) Upper flight time image; (b) Lower flight time image; (c) Upper peak-to-peak image; (d) Lower peak-to-veally image
稀疏恢复信号的THz图像与原信号的THz图像存在微小偏差,利用二值化进行图像分割[21],识别缺陷样件THz图像的缺陷区域,分别计算1、2、3、4个缺陷区域面积,将稀疏恢复信号的THz信号缺陷区域的面积与原始信号的THz图像对应区域面积比值记为
$\;\rho $ :$$ \rho = \frac{{{S_{{\rm{re}}{{\rm{cov}}} {\rm{er}}}}}}{{{S_{{\rm{det}} {\rm{ect}}}}}} $$ (10) 式中:
${S_{{\rm{re}}{{\rm{cov}}} {\rm{er}}}}$ 为稀疏恢复信号的THz图像某个缺陷区域面积大小;${S_{{\rm{det}} {\rm{ect}}}}$ 为THz-TDS系统检测信号的THz图像对应缺陷区域面积大小。计算结果如表3所示。由表3可以看到,THz图像上层的缺陷区域1和4面积稀疏后变大,表明有少部分正常信号被错误识别为缺陷信号,而区域3的面积变小,则部分缺陷信号未识别,THz图像上层缺陷区域面积最大偏差为0.05;同理,THz图像下层的缺陷区域1面积变大,表明部分信号错误识别,区域3面积变小,则部分缺陷信号未识别,THz图像下层缺陷区域面积最大偏差为0.03。结果表明,经文中算法稀疏恢复的THz图像,虽然缺陷区域会存在微小偏差,但并不影响对样件中缺陷区域的识别,保证了缺陷识别精度。
由图10~11可以看到,经文中算法稀疏恢复信号的THz图像与原信号的THz图像对比,减少了大量的无效特征,提高了图像清晰度,不影响样件缺陷区域的识别。
图 11 稀疏恢复信号的THz图像。 (a)上层飞行时间图像;(b)下层飞行时间图像;(c)上层峰峰值图像;(d)下层峰谷值图像
Figure 11. THz images of sparse recovery signal. (a) Upper flight time image; (b) Lower flight time image; (c) Upper peak-to-peak image; (d) Lower peak-to-veally image
表 3 上、下层THz信号图像缺陷区域面积比
Table 3. Area ratio of defect regions in upper and lower THz signal images
Defect region 1 Defect region 2 Defect region 3 Defect region 4 Upper 1.01 1.00 0.96 1.05 Lower 1.03 1.00 0.99 1.00 -
实验所用CPU为2.4 GHz,内存空间为16 GB,通过算法压缩后数据计算时间与数据存储空间表征算法效率,图12为DCT、PCA、K-SVD算法及文中算法压缩后数据计算时间和存储空间的对比结果。
由图12可以看到,文中算法压缩的数据计算时间最短,仅需0.25 s,占用存储空间最少,仅占0.0149 GB空间,相比其他算法缩短了大约80%的时间,减小了大约95%空间占用,极大地提高了数据处理效率。
Adaptive sparse algorithm for terahertz time domain signals based on gradient threshold
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摘要: 胶接结构广泛应用于航空航天等国防领域,但在工艺制作及使用过程可能会产生胶接界面脱粘缺陷和损伤,由于太赫兹无损检测技术对非金属材料良好的穿透性能,已被广泛应用于复合材料的无损检测中,太赫兹无损检测技术在多层胶接结构样件胶层内部缺陷的无损检测方面具有较大优势。利用反射式太赫兹时域光谱系统检测多层胶接结构样件,得到的具有样件内部材料信息的太赫兹时域信号,但信号中还包含了大量的冗余特征和噪声等无效信息,这些无效信息大大降低了信号处理和分析效率。针对这一问题,文中提出了基于二阶梯度法提取太赫兹时域信号有效特征,以飞行时间误差为限制条件基于信号的时域特征自适应确定阈值,稀疏太赫兹时域信号,减少信号中冗余无效信息,实现太赫兹时域信号的有效压缩。然后,通过二值化图像分割识别多高斯恢复信号和太赫兹时域光谱系统检测信号的太赫兹图像缺陷区域。最后,制备具有脱粘缺陷的多层胶接结构样件,开展太赫兹无损检测实验。结果表明:文中算法的数据压缩率达到了81%,相比传统压缩算法离散余弦变换提高了59%,相比主成分分析算法提高了75%,相比K-SVD字典学习算法提高了26%,缩短了约80%的数据计算时间,减小了约95%数据存储空间占用,且缺陷识别偏差不超过0.05。文中算法极大地提高了数据处理和分析效率,保证了缺陷识别的精度。Abstract:
Objective Bonding structure is widely used in aviation, aerospace, national defense and other fields. But during service, the bond interface may appear disbonding defects or damage, seriously reducing the bearing capacity of the structure and affecting the structure safety. Terahertz nondestructive testing technology is widely used in the nondestructive test of composite materials. Terahertz time-domain spectroscopy technology can effectively realize the nondestructive test and identification of internal defects of multilayer adhesives. However, the terahertz detection signal carries a large number of invalid redundant features, noise and other invalid information. With the gradual increase of detection data, the redundant and invalid information in the data, and the workload of data processing are also increasing. A large amount of invalid information not only consumes a lot of data processing and analysis time, but also brings great interference to the subsequent signal analysis work such as defect identification. To solve this problem, a gradient threshold adaptive sparse compression algorithm is proposed based on time-domain characteristics of terahertz signals with multi-layer adhesive structures. Methods The gradient threshold adaptive sparse model is established. Effective time-domain features of terahertz signals were extracted using the second-order gradient (Fig.3), and the time-domain features of signals were used as constraints to determine the threshold sparse time-domain signals based on the time-domain features of signals, and the terahertz signals were recovered by the multi-Gaussian fitting function (Fig.4). The compression performance of the algorithm was evaluated according to the compression ratio, relative root mean variance and correlation coefficient, and the data processing time and memory occupied space were used to characterize the compression efficiency of the algorithm. Results and Discussions Terahertz detection signals were divided into normal signals and defective signals (Fig.5), and signal characteristic peaks were extracted (Tab.1) to determine effective feature intervals. The maximum allowable error was set as 0.05, and the threshold was determined adaptively. The sparse recovery results of terahertz signals were shown (Fig.7). The reconstruction error of the recovered signal is less than 0.006 (Fig.8). The compression rate of this algorithm reaches 81%, which is 59% higher than that of discrete cosine transform, 75% higher than that of principal component analysis, and 26% higher than that of K-singular value decomposition. The relative root-mean-square error of the algorithm is less than 2%, and the correlation coefficient is greater than 0.97 (Fig.9). Compared with the traditional signal compression algorithm, the data processing time is reduced by 20%. Space utilization is reduced by 95% (Fig.12). This algorithm achieves effective compression of terahertz signal. Combined with terahertz imaging technology and binarized threshold segmentation method, the debonding defects of the sample were identified, and the identification deviation was less than 0.05 (Tab.3). The results show that the algorithm improves the efficiency of data analysis and guarantees the accuracy of defect identification. Conclusions A gradient threshold adaptive sparse algorithm is proposed to solve the problem of terahertz signal feature redundancy and low processing efficiency. The algorithm has the advantages of strong adaptive ability, high compression rate, fast running speed and low complexity. The second order gradient is used to extract the signal feature peak and determine the effective feature region. Then, according to the time-domain characteristics of terahertz signals, sparse thresholds and sparse signals of effective and invalid feature regions are determined. Finally, signals are restored by using multiple Gaussian functions. The compression ratio of the algorithm is greater than 81%, the relative root mean square error is less than 2%, the correlation coefficient is greater than 0.97, and the defect identification error is less than 5%. Compared with the traditional signal compression algorithm, the data computation time is reduced by 20% and the space is reduced by 95%. The algorithm reduces a large number of invalid features and retains effective features, ensuring the accuracy of terahertz image defect recognition. It is suitable for compression of normal terahertz signals and defective terahertz signals with complex redundant characteristic information. -
表 1 信号A与信号B特征峰峰值对应时间位置
Table 1. Time position corresponding to characteristic peak-to-peak values of signal A and signal B
THz signal ${T_{{\rm{up1}}} }$ /ps${T_{{\rm{up2}}} }$ /ps${T_{{\rm{low1}}} }$ /ps${T_{{\rm{low2}}} }$ /psSignal A 57.2 67.9 78.7 89.6 Signal B 57.6 67.4 78.2 87.8 表 2 信号A与信号B的稀疏阈值
Table 2. Sparse threshold of signal A and signal B
THz signal $\tau $ $\eta $ Original data number Sparse data number Signal A 0.42 0.07 1 600 224 Signal B 0.33 0.09 1 600 216 表 3 上、下层THz信号图像缺陷区域面积比
Table 3. Area ratio of defect regions in upper and lower THz signal images
Defect region 1 Defect region 2 Defect region 3 Defect region 4 Upper 1.01 1.00 0.96 1.05 Lower 1.03 1.00 0.99 1.00 -
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