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CN110726538B - Transverse crack feature recognition and extraction method for stepped cylindrical shaft elastic wave signal - Google Patents

Transverse crack feature recognition and extraction method for stepped cylindrical shaft elastic wave signal Download PDF

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CN110726538B
CN110726538B CN201910911211.3A CN201910911211A CN110726538B CN 110726538 B CN110726538 B CN 110726538B CN 201910911211 A CN201910911211 A CN 201910911211A CN 110726538 B CN110726538 B CN 110726538B
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cylindrical shaft
stepped cylindrical
transverse
elastic wave
crack
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CN110726538A (en
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魏义敏
史敏捷
陈文华
潘骏
李彤
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

本发明公开了阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法。现有转轴弹性波信号的分析方法在特征提取时，受到倍频信号干扰。本发明对所采集的被测试阶梯状圆柱轴两端的弹性波信号分别进行滤波后，利用EMD、EEMD或CEEMD方法分别分解成为多个IMF分量和残差信号，接着将倍频分量从分解后的信号中减去，然后将横向裂纹阻带的中心频率以及带宽与时间分布的关系特性作为裂纹的特征参量，与特征数据库进行分析匹配，得到横向裂纹的位置和深度信息。本发明将弹性波信号中的倍频成分进行了分解和去除，克服了在对弹性波波成分能量进行分析时，倍频信号干扰大的问题，使得最终的横向裂纹的分析结果更加准确。

Figure 201910911211

The invention discloses a method for identifying and extracting transverse crack characteristics of a stepped cylindrical shaft elastic wave signal. The existing method for analyzing the elastic wave signal of the rotating shaft is disturbed by the frequency-doubling signal during feature extraction. After filtering the collected elastic wave signals at both ends of the stepped cylindrical shaft to be tested, the invention decomposes them into a plurality of IMF components and residual signals by means of EMD, EEMD or CEEMD respectively, and then divides the frequency-doubling components from the decomposed signals into multiple IMF components and residual signals. The signal is subtracted from the signal, and then the center frequency of the transverse crack stopband and the relationship between the bandwidth and the time distribution are used as the characteristic parameters of the crack, which are analyzed and matched with the characteristic database to obtain the position and depth information of the transverse crack. The invention decomposes and removes the frequency-doubling component in the elastic wave signal, overcomes the problem of large interference of the frequency-doubling signal when analyzing the energy of the elastic wave component, and makes the analysis result of the final transverse crack more accurate.

Figure 201910911211

Description

Transverse crack characteristic identification and extraction method of stepped cylindrical shaft elastic wave signal
Technical Field
The invention belongs to the field of signal processing and crack nondestructive testing, and particularly relates to a transverse crack characteristic identification and extraction method of a stepped cylindrical shaft elastic wave signal.
Background
During the operation of a rotating shaft of a rotating machine, fatigue cracks are easily generated under the action of complex external loads, and the expansion of the fatigue cracks can cause serious breakage accidents and even great damage to lives and properties of people. Vibrations of the shaft during operation propagate therein in the form of elastic waves. The propagation characteristic of the elastic wave in the rotating shaft is influenced by various factors such as the geometric dimension of the rotating shaft, the physical properties of materials and the like, and when the rotating shaft has defects such as cracks, the propagation characteristic of the elastic wave is influenced, and the cracks can be researched through analysis of the propagation characteristic of the elastic wave, so that the purpose of crack detection is finally achieved.
The operating environment of the main shaft of the rotary machine is complex, and the obtained elastic wave signal has the characteristics of large background noise interference, instability and nonlinearity. In addition, when the rotating shaft runs by the power frequency signal Xf, due to the reasons of misalignment, oil film vortex and the like, frequency multiplication signals of 0.5Xf, 1Xf, 2Xf and the like can appear, and the signals are also coupled in the elastic wave signals. The elastic wave signal can be generally considered to be transmitted into the rotating shaft from one end (input end) of the rotating shaft and transmitted out of the rotating shaft from the other end (output end). Generally, a signal of an elastic wave may be subjected to spectrum analysis (FFT) or short-time fourier transform (STFT), and propagation characteristics of the elastic wave are compared by changes in energy distribution (spectrum distribution) at an input end and an output end of the elastic wave, so as to achieve the purpose of identifying a transverse crack. In the conventional method, when the spectrum analysis is performed, the characteristics of the crack signal cannot be accurately identified in the spectrum analysis due to the interference of the frequency-multiplied signals such as 0.5Xf, 1Xf and 2 Xf.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a transverse crack characteristic identification and extraction method of a stepped cylindrical shaft elastic wave signal, which mainly solves the problem that the conventional method is interfered by a frequency doubling signal during characteristic extraction.
In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:
the invention comprises the following steps:
(1) the method comprises the steps that a three-way acceleration sensor or a three-way displacement sensor is respectively arranged at two ends of a tested stepped cylindrical shaft, when the tested stepped cylindrical shaft rotates, signals at two ends of the tested stepped cylindrical shaft are collected, and three signals at each end are combined into an elastic wave signal.
(2) And filtering the acquired elastic wave signals at two ends of the tested stepped cylindrical shaft by using a high-pass filter to filter white noise.
(3) And (3) decomposing the signals at two ends of the tested stepped cylindrical shaft filtered in the step (2) into a plurality of IMF components and residual signals respectively by using an EMD (empirical mode decomposition), EEMD (empirical mode decomposition) or CEEMD (empirical mode decomposition) method.
(4) And (3) subtracting the signals: calculating the power frequency Xf of the tested stepped cylindrical shaft by using FFT; analyzing the frequency of all IMFs in the step (3), if the frequency of the IMF component falls within the range of 0.44-0.5, 0.9-1.1, 1.9-2.1, 2.9-3.1, 3.9-4.1 or 4.9-5.1 times of the power frequency Xf of the tested step-shaped cylindrical shaft, subtracting the IMF component from the decomposed signal in the step (3), reserving the residual IMF component and residual error signals, and respectively obtaining residual signals X at the input end and the output end of the tested step-shaped cylindrical shaftres,inAnd Xres,out。
(5) Extracting crack characteristic parameters: first the residual signal Xres,inAnd Xres,outNormalization processing is carried out, and the flow of the normalization processing is as follows: obtaining Xres,inAnd Xres,outData value x with the largest absolute value of the two signalsmax(ii) a ② respectively mixing Xres,inAnd Xres,inDivided by xmaxTo obtain
Figure BDA0002214759470000021
And
Figure BDA0002214759470000022
and then using FFT pairs
Figure BDA0002214759470000023
And
Figure BDA0002214759470000024
performing comparative analysis to obtain a spectrum distribution contrast diagram, and obtaining the spectrum distribution contrast diagram by using an STFT method
Figure BDA0002214759470000025
And
Figure BDA0002214759470000026
time-frequency domain distribution of the signal is compared with a graph. Then, using the spectrum distribution contrast map, will
Figure BDA0002214759470000027
And
Figure BDA0002214759470000028
the amplitudes of the signals at the same frequency are compared and
Figure BDA0002214759470000029
the amplitude of the signal being higher than
Figure BDA00022147594700000210
Comparing the frequency range of which the signal amplitude is 1.05 times with the frequency domain resolution of the STFT, and if the frequency range is larger than the frequency domain resolution of the STFT, defining the frequency range as a stop band; and finally, judging whether the stop band exists or not, if not, returning to the step (2) to continue detection, if so, combining the time distribution contrast diagram of the frequency domain distribution, further determining the time distribution of the center frequency of the stop band and the bandwidth, taking the relationship characteristics of the center frequency of the stop band and the bandwidth and the time distribution as characteristic parameters of the crack, and executing the step (6).
(6) Identification of transverse cracks: and analyzing and matching the characteristic parameters of the transverse cracks with the characteristic database to obtain the position and depth information of the transverse cracks.
Further, the high-pass filter is a digital filter with a pass frequency of [2, + ∞).
Further, in the decomposition process of the step (3), an end effect processing method is adopted for end effect processing.
Further, the end effect processing method is an ISBM extension method, a mirror image extension method or a parallel extension method.
Further, in the step (6), a feature database is pre-established, and the relationship characteristics of the central frequency of the transverse crack stop band and the bandwidth and the time distribution of the transverse crack stop band are respectively determined for a plurality of axial transverse cracks and a plurality of depth values of each position transverse crack when the feature database is established. The determination process of the characteristics of the central frequency and the bandwidth of the transverse crack stop band in relation to the time distribution is as follows: and (3) selecting a stepped cylindrical shaft without transverse cracks, processing the transverse cracks with preset positions and depths on the stepped cylindrical shaft in advance, and then executing the steps (1) to (5) without executing the step (6), so as to determine the central frequency of the transverse crack stop band and the relation characteristics of the bandwidth and the time distribution.
Further, in the step (6), if the relation between the transverse crack stop band width and the time distribution is inconsistent with the characteristic database, selecting the positions of the two transverse cracks with the minimum difference value with the transverse crack stop band width in the characteristic database to obtain a middle value as the position of the transverse crack, and taking the average value of the depth values of the two transverse cracks with the minimum difference value with the transverse crack stop band width as the depth value of the transverse crack.
The invention has the following beneficial effects:
according to the method, the EMD, EEMD or CEEMD method is adopted to decompose and remove the frequency doubling component in the elastic wave signal, so that the problem of large interference of the frequency doubling signal when the energy of the elastic wave component is analyzed is solved, and the final analysis result of the transverse crack is more accurate.
Drawings
FIG. 1 is a flow chart of the operation of the present invention;
fig. 2 is a detailed view of the operation flow in fig. 1.
Detailed Description
In order that those skilled in the art can better understand the present invention, the following technical solutions are further described with reference to the accompanying drawings and examples.
As shown in fig. 1 and 2, the transverse crack feature identification and extraction method of the stepped cylindrical axis elastic wave signal includes the following steps:
(1) the method comprises the steps of respectively arranging a three-way acceleration sensor or a three-way displacement sensor at two ends of a tested stepped cylindrical shaft, acquiring signals (vibration acceleration or vibration amplitude) at two ends of the tested stepped cylindrical shaft, and synthesizing three signals at each end into an elastic wave signal. Elastic waves are input from one end of the tested stepped cylindrical shaft, and are output from the other end of the tested stepped cylindrical shaft; the elastic wave signal with large vibration energy corresponds to the input end of the tested stepped cylindrical shaft, and the elastic wave signal with small vibration energy corresponds to the output end of the tested stepped cylindrical shaft. In this embodiment, the elastic wave signals at the two ends of the tested stepped cylindrical shaft are subjected to spectrum analysis to determine the magnitude of the vibration energy, and the vibration energy is considered to be large when the frequency band is wide and the amplitude is large.
(2) And filtering the acquired elastic wave signals at two ends of the tested stepped cylindrical shaft by using a high-pass filter to filter white noise. The high pass filter employed in this embodiment is a digital filter with a pass frequency of [2, + ∞).
(3) Decomposing the signals at two ends of the tested stepped cylindrical shaft filtered in the step (2) into a plurality of IMF components and residual signals respectively by using an EMD (empirical mode decomposition), EEMD (empirical mode decomposition) or CEEMD (empirical mode decomposition) method; in the decomposition process, an endpoint effect processing method is adopted for endpoint effect processing; the end effect processing method is ISBM extension method, mirror image extension method or parallel extension method.
(4) And (3) subtracting the signals: calculating the power frequency Xf of the tested stepped cylindrical shaft by using FFT; analyzing the frequencies of all IMFs in the step (3), if the frequency of a certain IMF component falls within the range of 0.44-0.5, 0.9-1.1, 1.9-2.1, 2.9-3.1, 3.9-4.1 or 4.9-5.1 times of the power frequency Xf of the tested step-shaped cylindrical shaft, subtracting the IMF component from the decomposed signal in the step (3), reserving the residual IMF component and residual error signals, and respectively obtaining residual signals X at the input end and the output end of the tested step-shaped cylindrical shaftres,inAnd Xres,out。
(5) Extracting crack characteristic parameters: the residual signal Xres,inAnd Xres,outNormalization processing is carried out, and the flow of the normalization processing is as follows: obtaining Xres,inAnd Xres,outData value x with the largest absolute value of the two signalsmax(ii) a ② respectively mixing Xres,inAnd Xres,inDivided by xmaxTo obtain
Figure BDA0002214759470000041
And
Figure BDA0002214759470000042
and then using FFT pairs
Figure BDA0002214759470000043
And
Figure BDA0002214759470000044
performing comparative analysis to obtain a spectrum distribution contrast diagram, and obtaining the spectrum distribution contrast diagram by using an STFT method
Figure BDA0002214759470000045
And
Figure BDA0002214759470000046
time-frequency domain distribution of the signal is compared with a graph. Then, using the spectrum distribution contrast map, will
Figure BDA0002214759470000047
And
Figure BDA0002214759470000048
the amplitudes of the signals at the same frequency are compared and
Figure BDA0002214759470000049
the amplitude of the signal being higher than
Figure BDA00022147594700000410
Comparing the frequency range of which the signal amplitude is 1.05 times with the frequency domain resolution of the STFT, and if the frequency range is larger than the frequency domain resolution of the STFT, defining the frequency range as a stop band; finally, judging whether a stop band exists or not, if not, returning to the step (2) for continuous detection, if so, combining the time distribution contrast diagram of the frequency domain distribution, further determining the central frequency of the stop band and the time distribution of the bandwidth, taking the central frequency of the stop band and the relation characteristic of the bandwidth and the time distribution as the characteristic parameters of the crack, and executingAnd (6) carrying out a step.
When the stepped cylindrical shaft has no crack, the energy loss is very small when the elastic wave is transmitted on the stepped cylindrical shaft because the cross section of each shaft section is unchanged, and the residual signal X at the input end isres,inCan be approximately equivalent to the residual signal X of the output terminalres,outTherefore, when the stop band exists in the step (5),
Figure BDA00022147594700000411
and
Figure BDA00022147594700000412
the signal comparison can be regarded as the comparison of the elastic wave signal at the output end of the stepped cylindrical shaft without the crack and the elastic wave signal at the input end of the stepped cylindrical shaft with the crack on the premise of the same elastic wave signal.
(6) Identification of transverse cracks: and analyzing and matching the characteristic parameters of the transverse cracks with the characteristic database to obtain the position and depth information of the transverse cracks.
Further, in the step (6), a feature database is pre-established, and when the feature database is established, the relationship characteristics of the central frequency and the bandwidth of the transverse crack stop band and the time distribution need to be respectively determined for a plurality of axial transverse cracks and a plurality of depth values of each axial transverse crack, and the position distribution of the transverse cracks needs to ensure a certain concentration along the axial direction, and the depth value distribution also needs to ensure a certain concentration. The determination process of the characteristics of the central frequency and the bandwidth of the transverse crack stop band in relation to the time distribution is as follows: and (3) selecting a stepped cylindrical shaft without transverse cracks, processing the transverse cracks with preset positions and depths on the stepped cylindrical shaft in advance, and then executing the steps (1) to (5) without executing the step (6), so as to determine the central frequency of the transverse crack stop band and the relation characteristics of the bandwidth and the time distribution.
Further, in the step (6), if the relation between the transverse crack stop band width and the time distribution is inconsistent with the characteristic database, selecting the positions of the two transverse cracks with the minimum difference value with the transverse crack stop band width in the characteristic database to obtain a middle value as the position of the transverse crack, and taking the average value of the depth values of the two transverse cracks with the minimum difference value with the transverse crack stop band width as the depth value of the transverse crack.

Claims (6)

1.阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法，其特征在于：该方法包括以下步骤：1. A method for identifying and extracting transverse crack features of a stepped cylindrical shaft elastic wave signal, characterized in that: the method comprises the following steps: (1)在被测试阶梯状圆柱轴的两端分别设置一个三向加速度传感器或分别设置一个三向位移传感器，被测试阶梯状圆柱轴转动时，采集被测试阶梯状圆柱轴两端的信号，每一端的三个信号合成一个弹性波信号；(1) A three-way acceleration sensor or a three-way displacement sensor are respectively installed at both ends of the stepped cylindrical shaft to be tested. When the stepped cylindrical shaft to be tested rotates, the signals from both ends of the stepped cylindrical shaft to be tested are collected. The three signals at one end are synthesized into an elastic wave signal; (2)利用高通滤波器对所采集的被测试阶梯状圆柱轴两端的弹性波信号分别进行滤波，滤除白噪音；(2) Filtering the collected elastic wave signals at both ends of the stepped cylindrical shaft under test by using a high-pass filter to filter out white noise; (3)利用EMD、EEMD或CEEMD方法将经过步骤(2)滤波后的被测试阶梯状圆柱轴两端信号分别分解成为多个IMF分量和残差信号；(3) using EMD, EEMD or CEEMD method to decompose the signals at both ends of the tested stepped cylindrical shaft after step (2) filtering into a plurality of IMF components and residual signals respectively; (4)信号作减法处理：利用FFT计算被测试阶梯状圆柱轴的工频Xf；分析步骤(3)中所有IMF的频率，若IMF分量的频率落入被测试阶梯状圆柱轴工频Xf的0.44～0.5、0.9～1.1、1.9～2.1、2.9～3.1、3.9～4.1或4.9～5.1倍范围内，则把该IMF分量从步骤(3)分解后的信号中减去，保留剩余的IMF分量和残差信号，分别得到被测试阶梯状圆柱轴输入端和输出端的剩余信号Xres,in和Xres,out；(4) Subtract the signal: use FFT to calculate the power frequency Xf of the stepped cylindrical shaft to be tested; analyze the frequencies of all IMFs in step (3), if the frequency of the IMF component falls within the power frequency Xf of the stepped cylindrical shaft to be tested 0.44～0.5, 0.9～1.1, 1.9～2.1, 2.9～3.1, 3.9～4.1 or 4.9～5.1 times, then subtract the IMF component from the decomposed signal in step (3), and keep the remaining IMF components and residual signal, respectively obtain the residual signals X res,in and X res,out of the input end and output end of the stepped cylindrical shaft to be tested; (5)裂纹特征参量的提取：首先将剩余信号Xres,in和Xres,out作归一化处理，归一化处理的流程为：①获取Xres,in和Xres,out两个信号中绝对值最大的数据值xmax；②分别将Xres,in和Xres,in除以xmax，得到
Figure FDA0002214759460000011
和
Figure FDA0002214759460000012
然后利用FFT对
Figure FDA0002214759460000013
和
Figure FDA0002214759460000014
进行对比分析，得到频谱分布对比图，并利用STFT方法得到
Figure FDA0002214759460000015
和
Figure FDA0002214759460000016
信号的时频域分布对比图；接着，利用频谱分布对比图，将
Figure FDA0002214759460000017
和
Figure FDA0002214759460000018
信号在相同频率下的幅值进行比较，并将
Figure FDA0002214759460000019
信号的幅值高于
Figure FDA00022147594600000110
信号幅值1.05倍的频率范围与STFT的频域分辨率对比，若该频率范围大于STFT的频域分辨率，则该频率范围定义为阻带；最后，判别是否存在阻带，若不存在，回到步骤(2)继续检测，若存在，则结合时频域分布对比图，进一步确定阻带中心频率以及带宽的时间分布，将阻带的中心频率以及带宽与时间分布的关系特性作为裂纹的特征参量，并执行步骤(6)；(5) Extraction of crack characteristic parameters: First, the residual signals X res,in and X res,out are normalized. The normalization process is as follows: ① Obtain two signals of X res,in and X res,out The data value x max with the largest absolute value in the
Figure FDA0002214759460000011
and
Figure FDA0002214759460000012
Then use the FFT to
Figure FDA0002214759460000013
and
Figure FDA0002214759460000014
Carry out comparative analysis to obtain a spectrum distribution comparison diagram, and use the STFT method to obtain
Figure FDA0002214759460000015
and
Figure FDA0002214759460000016
The time-frequency domain distribution comparison diagram of the signal; then, using the spectrum distribution comparison diagram, the
Figure FDA0002214759460000017
and
Figure FDA0002214759460000018
The amplitudes of the signals at the same frequency are compared, and the
Figure FDA0002214759460000019
The amplitude of the signal is higher than
Figure FDA00022147594600000110
The frequency range of 1.05 times the signal amplitude is compared with the frequency domain resolution of the STFT. If the frequency range is greater than the frequency domain resolution of the STFT, the frequency range is defined as the stop band; finally, it is judged whether there is a stop band. Go back to step (2) to continue the detection. If it exists, then combine the time-frequency domain distribution comparison chart to further determine the stopband center frequency and the time distribution of the bandwidth, and take the center frequency of the stopband and the relationship between the bandwidth and the time distribution as the crack. characteristic parameters, and execute step (6); (6)横向裂纹的识别：通过横向裂纹的特征参量与特征数据库进行分析匹配，得到横向裂纹的位置和深度信息。(6) Identification of transverse cracks: The position and depth information of transverse cracks are obtained by analyzing and matching the characteristic parameters of transverse cracks with the characteristic database. 2.根据权利要求1所述的阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法，其特征在于：所述的高通滤波器为数字滤波器，其通过频率为[2,+∞)。2. The method for identifying and extracting transverse crack features of stepped cylindrical shaft elastic wave signals according to claim 1, characterized in that: the high-pass filter is a digital filter, and its passing frequency is [2,+∞) . 3.根据权利要求1所述的阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法，其特征在于：步骤(3)分解过程中，采用端点效应处理方法进行端点效应处理。3. The transverse crack feature identification and extraction method of the stepped cylindrical shaft elastic wave signal according to claim 1 is characterized in that: in the decomposition process of step (3), an end effect processing method is adopted to carry out end effect processing. 4.根据权利要求3所述的阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法，其特征在于：所述的端点效应处理方法为ISBM延拓法、镜像延拓法或平行延拓法。4. The lateral crack feature identification and extraction method of stepped cylindrical shaft elastic wave signal according to claim 3, is characterized in that: described end effect processing method is ISBM extension method, mirror image extension method or parallel extension Law. 5.根据权利要求1所述的阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法，其特征在于：步骤(6)中，特征数据库预先建立，建立特征数据库时需要对轴向上多个位置横向裂纹以及每个位置横向裂纹的多个深度值分别确定横向裂纹阻带的中心频率和带宽与时间分布的关系特性；横向裂纹阻带的中心频率和带宽与时间分布关系特性的确定过程如下：选取没有横向裂纹的阶梯状圆柱轴，预先在该阶梯状圆柱轴上加工出预设位置和深度的横向裂纹，然后执行步骤(1)～步骤(5)，但不执行步骤(6)，从而确定该横向裂纹阻带的中心频率以及带宽与时间分布的关系特性。5. The lateral crack feature identification and extraction method of the stepped cylindrical shaft elastic wave signal according to claim 1, is characterized in that: in step (6), the feature database is established in advance, and when establishing the feature database, it is necessary to perform multiple analysis on the axial direction. The transverse cracks at each position and the depth values of the transverse cracks at each position respectively determine the relationship between the center frequency and bandwidth of the transverse crack stopband and the time distribution; the process of determining the relationship between the center frequency and bandwidth of the transverse crack stopband and the time distribution As follows: select a stepped cylindrical shaft without transverse cracks, pre-process transverse cracks with preset positions and depths on the stepped cylindrical shaft, and then perform steps (1) to (5), but do not perform step (6) , so as to determine the center frequency of the transverse crack stopband and the relationship between the bandwidth and the time distribution. 6.根据权利要求1所述的阶梯状圆柱轴弹性波信号的横向裂纹特征识别与提取方法，其特征在于：步骤(6)中，若出现横向裂纹阻带带宽与时间分布的关系和特征数据库中不符，则选取特征数据库中与该横向裂纹阻带带宽差值最小的两个横向裂纹的位置求取中间值作为该横向裂纹的位置，且将与该横向裂纹阻带带宽差值最小的两个横向裂纹的深度值均值作为横向裂纹的深度值。6. the lateral crack feature identification and extraction method of stepped cylindrical shaft elastic wave signal according to claim 1, is characterized in that: in step (6), if the relation and characteristic database of transverse crack stopband bandwidth and time distribution occur If it does not match, select the position of the two transverse cracks with the smallest difference in the stop-band bandwidth of the transverse crack in the feature database to obtain the intermediate value as the position of the transverse crack, and the two transverse cracks with the smallest difference in the stop-band bandwidth of the transverse crack will be used. The average value of the depth value of each transverse crack is used as the depth value of transverse crack.
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