CN111551630B - Damage non-wave-velocity positioning method based on space-wave-number filter - Google Patents

Damage non-wave-velocity positioning method based on space-wave-number filter Download PDF

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CN111551630B
CN111551630B CN202010325775.1A CN202010325775A CN111551630B CN 111551630 B CN111551630 B CN 111551630B CN 202010325775 A CN202010325775 A CN 202010325775A CN 111551630 B CN111551630 B CN 111551630B
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CN111551630A (en
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刘彬
刘廷章
杭丹
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Air Force Service College of PLA
University of Shanghai for Science and Technology
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Abstract

The invention discloses a damage wave-speed-free positioning method based on a space-wave number filter, and belongs to the technical field of engineering structure health monitoring. Firstly, acquiring a double-frequency damage scattering signal in a structure by using a cross array; then, obtaining wave number-time images of two linear array damage scattering signals in the cross array under each frequency by using a space-wave number filter, and obtaining the wave number and the arrival time of the two linear array damage scattering signals under each frequency; calculating the angle of the damage and the wave speed of Lamb waves by using the wave number of the damage scattering signals; and finally, calculating the damage distance by using the wave speed of the Lamb wave and the arrival time of the damage scattering signal, thereby realizing the damage positioning. The Lamb wave velocity is calculated on line by utilizing the Lamb wave number obtained by the space-wave number filter, and the Lamb wave velocity is not required to be obtained in advance, so that the influence of structural material parameter anisotropy on a damage positioning result is inhibited, and the application range of the damage positioning method of the space-wave number filter is expanded.

Description

Damage non-wave-velocity positioning method based on space-wave-number filter
Technical Field
The invention relates to a damage wave-speed-free positioning method based on a space-wave number filter, and belongs to the technical field of engineering structure health monitoring.
Background
The structure health monitoring technology has important scientific research significance and wide application prospect for preventing major accidents, improving the safety of the structure, reducing economic loss, reducing the maintenance cost of the structure and guaranteeing the construction of major engineering projects. The Lamb wave-based structural health monitoring method has the advantages of high damage monitoring sensitivity, large monitoring range, capability of being applied on line or off line, capability of performing active damage monitoring and passive impact monitoring, capability of monitoring a metal structure and a composite material structure and the like. Therefore, the Lamb wave-based structural health monitoring method is widely researched at home and abroad, and is one of the most promising structural health monitoring technologies at present. The structure monitoring method based on the piezoelectric sensor array and Lamb waves utilizes monitoring information of a plurality of excitation-sensing channels in the piezoelectric sensor array and realizes the visual imaging of the structure by controlling a synthesis mechanism of array signals. The method can effectively optimize the signal-to-noise ratio of the monitoring signal and visually display the health state of the structure, thereby improving the accuracy of damage positioning. The space-wave number filter method based on the piezoelectric sensor array and the Lamb waves can extract incident waves, reflected waves and the like of specific modes in the Lamb waves, reduce aliasing of damage scattering signals and improve the signal-to-noise ratio of the damage scattering signals. The existing damage positioning method based on a cross array and a space-wave number filter realizes 0-360-degree omnibearing online damage imaging independent of Lamb wave number, so that the influence of structural material parameters on damage angle calculation is inhibited. However, in the damage distance calculation process, Lamb wave velocity still needs to be obtained in advance, Lamb wave velocity of complex structures is difficult to obtain accurately, and Lamb wave velocity of composite materials has the characteristic of anisotropy, so that the application of the space-wave number filter damage positioning method in structure health monitoring is severely limited.
Disclosure of Invention
The invention provides a damage non-wave-velocity positioning method based on a space-wave-number filter, which is characterized in that the Lamb wave velocity at the angle is calculated on line by utilizing the Lamb wave number obtained by the space-wave-number filter, and the Lamb wave velocity is not required to be obtained in advance, so that the influence of structural material parameter anisotropy on a damage positioning result is inhibited, and the application range of the damage positioning method of the space-wave-number filter is expanded.
The invention adopts the following technical scheme for solving the technical problems:
a damage non-wave-velocity positioning method based on a space-wave-number filter comprises the following steps:
the method comprises the following steps: acquiring a dual-frequency damage scattering signal;
step two: carrying out space-wave number filtering on the dual-frequency damage scattering signal;
step three: calculating a damage angle;
step four: and calculating the damage distance.
The specific implementation process of the first step is as follows:
a cross array is arranged on the structure, and two linear arrays in the cross array are respectively marked as a linear array I and a linear array II; the two linear arrays are composed of M piezoelectric sensors, and the distance between the central points of two adjacent piezoelectric sensors is delta x; the piezoelectric sensors in the linear array I are sequentially numbered as I-1, I-2, …, I-M, … and I-M, and the piezoelectric sensors in the linear array II are sequentially numbered as II-1, II-2, …, II-M, … and II-M; arranging an active Lamb wave excitation element near the central point of the cross array;
firstly, when the structure is in a healthy state, the excitation elements respectively excite the structure to have a central frequency of omega1And ω2The Lamb wave of the structure is acquired by a cross array and used as a health reference signal H (omega, r-m, t) of the structure, omega is the central frequency of the Lamb wave, r is the serial number of a linear array, m is the serial number of a piezoelectric sensor in the linear array, r-m is a piezoelectric sensor m in the linear array, and t is sampling time;
secondly, after the structure is damaged, the exciting elements respectively excite the center frequency omega in the structure again1And ω2Collecting Lamb wave response signals of the structure by a cross array, and using the Lamb wave response signals as online monitoring signals D (omega, r-m, t) of the structure;
using the health reference signal H (omega, r-m, t) of the structure and the online monitoring signal D (omega, r-m, t) of the structure to extract a damage scattering signal f (omega, r-m, t), as shown in formula (1):
f(ω,r-m,t)＝D(ω,r-m,t)-H(ω,r-m,t) (1)
in the formula: f (omega, r-m, t) is a damage scattering signal of the piezoelectric sensor number m of the linear array number r in the cross array under the omega frequency, D (omega, r-m, t) is an online monitoring signal of the piezoelectric sensor number m of the linear array number r in the cross array under the omega frequency, H (omega, r-m, t) is a health reference signal of the piezoelectric sensor number m of the linear array number r in the cross array under the omega frequency, omega is the central frequency of Lamb waves, r is the serial number of the linear array, r-m is the piezoelectric sensor number m in the linear array number r, and t is sampling time.
The concrete implementation process of the second step is as follows:
first, the wave number filtering interval of the space-wave number filter is set to be delta k, and the wave number filtering range of the space-wave number filter is set to be (-k)s,+ks)，ksSpatial sampling wave number for linear array:
Figure BDA0002463149310000044
in the formula: delta x is the array element spacing of the linear array, and pi is the circumferential rate;
then, a wave number filtered value k, -k is selecteds＜k＜ksAnd respectively carrying out space-wave number filtering on the two linear arrays:
Figure BDA0002463149310000041
in the formula: phir(omega, k, t) is the space-wave number filtering synthesis value of the r number linear array damage scattering signal under the omega frequency when the wave number filtering value is k,
Figure BDA0002463149310000042
for convolution operation, phi (k, r-m) is a space-wave number filtering weight function of the piezoelectric sensor with number m in the linear array with number r, as shown in formula (4):
Figure BDA0002463149310000043
in the formula: phi (k, r-m) is a space-wave number filtering weight function of the m piezoelectric sensors in the r linear array, lr-mThe distance between the m piezoelectric sensors in the r linear array and an origin is represented, i is an imaginary number unit, k is the central wave number of a space-wave number filtering weight function, and e is a natural constant;
secondly, selecting a next wave number filtering value k + delta k, and calculating the space-wave number filtering of the r-number linear array damage scattering signal under the omega frequency when calculating the wave number filtering value according to the space-wave number filtering processResultant value phir(omega, k + delta k, t) until all the set wave number filtering values are calculated; thus, under the omega frequency and at each moment t, a space-wave number filtering synthesis value under each wave number filtering value k is obtained;
selecting the wave number corresponding to the maximum value of the image pixel value in the wave number-time image of the r number linear array under the omega frequency as the wave number k of the linear array damage scattering signal under the frequencya-ω-r(ii) a The corresponding moment at the maximum value of the pixel value is the moment t when the damage scattering signal of the linear array reaches the linear arrayR-ω-r。
The third step is realized by the following specific steps:
using wave number k of r number linear array damage scattering signal under omega frequencya-ω-rCalculating the angle theta of the damagea：
Figure BDA0002463149310000051
Figure BDA0002463149310000052
In the formula: thetaaFor calculated damage angle, θa-ωFor the calculated damage angle at the omega frequency,
Figure BDA0002463149310000053
is omega1The calculated damage angle at the frequency is used,
Figure BDA0002463149310000054
is omega2Calculated damage angle, k, at frequencya-ω-IWave number, k of I number linear array damage scattering signal under omega frequencya-ω-IIThe wave number of the damage scattering signals of the No. II linear array under the omega frequency is shown.
The concrete implementation process of the step four is as follows:
firstly, using wave number k of I-line array and II-line array damage scattering signals under omega frequencya-ω-IAnd ka-ω-IICalculating Lamb wave under omega frequencyWave number k ofa-ω：
Figure BDA0002463149310000055
Second, using ω1And ω2Calculating the wave velocity c of the Lamb wave by the wave number of the Lamb wave under two frequenciesg：
Figure BDA0002463149310000061
In the formula:
Figure BDA0002463149310000062
is omega1The wave number of Lamb waves at a frequency,
Figure BDA0002463149310000063
is omega2The wave number of Lamb waves at frequency;
finally, the wave velocity c of the Lamb wave is usedgAnd the time t when the damage scattering signal reaches the linear arrayR-ω-rCalculating the distance L of the damagea：
Figure BDA0002463149310000064
In the formula:
Figure BDA0002463149310000065
is omega1The arrival time of the I-number linear array damage scattering signal under the frequency,
Figure BDA0002463149310000066
is omega1The arrival time of the No. II linear array damage scattering signal under the frequency,
Figure BDA0002463149310000067
is omega1The starting time of the Lamb wave excitation signal at the frequency,
Figure BDA0002463149310000068
is omega2The arrival time of the I-number linear array damage scattering signal under the frequency,
Figure BDA0002463149310000069
is omega2The arrival time of the No. II linear array damage scattering signal under the frequency,
Figure BDA00024631493100000610
is omega2Starting time of Lamb wave excitation signal under frequency;
the final localization of the lesion is achieved as (θ)a,La)。
The invention has the following beneficial effects:
1. the Lamb wave velocity is calculated on line by utilizing the Lamb wave number obtained by the space-wave number filter, and the Lamb wave velocity is not required to be obtained in advance.
2. The Lamb wave velocity calculated on line is the Lamb wave velocity at the angle, and the influence of structural material parameter anisotropy on the damage positioning result is inhibited.
3. And the damage angle and distance are calculated by adopting double frequencies, so that the influence of various noises on damage positioning is reduced.
4. The method is beneficial to promoting the application of the space-wave number filter damage positioning method in the field of engineering structure health monitoring.
Drawings
Fig. 1 is a signal processing flow chart of an impairment wavenumber-free localization method based on a space-wavenumber filter.
FIG. 2 is a schematic diagram of an embodiment of a piezoelectric sensor arrangement, a damage location, and a two-dimensional rectangular coordinate system.
Figure 3 is a graph of the health reference signal for line I at 40kHz frequency.
Figure 4 is a graph of the health reference signal for line II at 40kHz frequency.
Figure 5 is a graph of the health reference signal for the number I bar at a frequency of 41 kHz.
Figure 6 is a graph of the health reference signal for line II at a frequency of 41 kHz.
Figure 7 is an on-line monitoring signal diagram of the number I linear array at a frequency of 40 kHz.
Figure 8 is an online monitoring signal diagram of number II linear array at 40kHz frequency.
Figure 9 is an on-line monitoring signal diagram of the number I linear array at the frequency of 41 kHz.
Figure 10 is an online monitoring signal graph of number II linear array at 41kHz frequency.
Figure 11 is a graph of the damage scatter signal of the number I linear array at a frequency of 40 kHz.
Figure 12 is a graph of the damage scatter signal of No. II line at a frequency of 40 kHz.
FIG. 13 is a graph of the damage scatter signal of the No. I bar at a frequency of 41 kHz.
Figure 14 is a graph of the damage scatter signal of No. II line at 41kHz frequency.
Figure 15 is a wave number versus time image of number I bars at a frequency of 40 kHz.
Figure 16 is a wave number versus time image of No. II bars at a frequency of 40 kHz.
Fig. 17 is a wave number-time image of the I-number bars at a frequency of 41 kHz.
Figure 18 is a wave number versus time image of No. II bars at a frequency of 41 kHz.
FIG. 19 is a timing diagram of the start of a Lamb wave excitation signal at a frequency of 40 kHz.
FIG. 20 is a diagram showing the start timing of a Lamb wave excitation signal at a frequency of 41 kHz.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
Firstly, acquiring a double-frequency damage scattering signal in a structure by using a cross array; then, obtaining wave number-time images of two linear array damage scattering signals in the cross array under each frequency by using a space-wave number filter, and obtaining the wave number and arrival time of the two linear array damage scattering signals under each frequency; secondly, calculating the angle of the damage and the wave speed of Lamb waves by using the wave number of the damage scattering signals; and finally, calculating the damage distance by using the wave speed of the Lamb wave and the arrival time of the damage scattering signal, and finally realizing the positioning of the damage.
FIG. 1 is a cross matrix and space based on the present inventionThe signal processing flow chart of the damage positioning method of the inter-wave number filter comprises the following steps: the structure is provided with a cross array formed by two linear arrays which are vertically crossed, and the exciting elements respectively excite the center frequency omega in the structure when the structure is in a healthy state1And ω2The cross array collects Lamb wave response signals of the structure as health reference signals of the structure; when the structure is damaged, the exciting elements respectively excite the structure again to have a central frequency of omega1And ω2The cross array collects Lamb wave response signals of the structure as online monitoring signals of the structure; extracting a damage scattering signal by using a health reference signal and an online monitoring signal of the structure; setting wave number filtering range and interval of a space-wave number filter, and respectively carrying out space-wave number filtering on the damaged scattering signals of the linear arrays I and II in the cross array under each frequency to obtain the wave number and arrival time of the damaged scattering signals of the linear arrays I and II under each frequency; calculating the damage angle and the Lamb wave velocity by using the wave numbers of the damage scattering signals of the No. I linear array and the No. II linear array under each frequency; and calculating the damage distance by using the wave speed of Lamb waves and the arrival time of the damage scattering signals of the I linear array and the II linear array under each frequency, and finally realizing the positioning of the damage.
Example the test piece was a glass fiber epoxy board having dimensions of 600mm × 600mm × 2mm (length × width × thickness), and the excitation/sensing element was a PZT-5A type piezoelectric sensor having a diameter of 8mm and a thickness of 0.4 mm. The experimental equipment is an aviation structure health monitoring integrated piezoelectric multi-channel scanning system.
The embodiment comprises the following steps:
the method comprises the following steps: obtaining dual frequency impairment scatter signals
The structure is provided with a cross array, and two linear arrays in the cross array are respectively marked as a linear array I and a linear array II. The two linear arrays are composed of 7 PZT-5A piezoelectric sensors, and the distance between the central points of two adjacent piezoelectric sensors is delta x which is 10 mm. The serial numbers of the piezoelectric sensors of the linear array I are PZT I-1, PZT I-2, … and PZT I-7 from left to right, and the serial numbers of the piezoelectric sensors of the linear array II are PZT II-1, PZT II-2, … and PZT II-7 from bottom to top. And sticking a piezoelectric sensor on the back of the test piece and the central point of the cross array as an excitation element of the cross array. A schematic of the specimen shape, piezoelectric sensor position, and two-dimensional rectangular coordinate system is shown in fig. 2.
Setting an integrated piezoelectric multi-channel scanning system for monitoring the health of an aeronautical structure to work in an active mode, selecting five-wave-crest narrow-band sine excitation signals, wherein the center frequencies of the excitation signals are 40kHz and 41kHz respectively, and the amplitudes of the excitation signals are +/-70V; the sampling frequency of the system is set to 10MHz, the number of sampling points is 8000, the pre-collection length is 1000 sampling points, and the trigger voltage is 6V.
Firstly, when the test piece is in a healthy state, the excitation element respectively excites Lamb waves with center frequencies of 40kHz and 41kHz in the test piece, and the cross array collects Lamb wave response signals of the structure as health reference signals H (omega, r-m, t) of the structure, as shown in fig. 3, 4, 5 and 6.
When the damage occurs to the test piece, the coordinate position of the damage is (60 degrees, 300mm), the excitation element excites Lamb waves with center frequencies of 40kHz and 41kHz again in the test piece, and the cross array collects Lamb wave response signals of the structure as online monitoring signals D (omega, r-m, t) of the structure, as shown in FIG. 7, FIG. 8, FIG. 9 and FIG. 10.
The health reference signal is subtracted from the on-line monitoring signal to extract the damage scatter signal f (ω, r-m, t), as shown in fig. 11, 12, 13 and 14.
Step two: space-wave number filtering for dual frequency impairment scatter signals
According to the array element distance delta x of the linear array being 10mm, the wave number filtering range of the space-wave number filter is set to be [ -314rad/m,314rad/m ], and the wave number filtering interval is set to be delta k being 0.1 rad/m. The two linear array damage scattering signals in the cross array at the frequencies of 40kHz and 41kHz are respectively subjected to space-wave number filtering, and the filtered wave number-time images are shown in fig. 15, fig. 16, fig. 17 and fig. 18.
From FIG. 15, the wave number of the I number linear array damage scattering signal at the frequency of 40kHz is ka-40-I131.7rad/m, arrival time tR-40-I0.4168 ms. From FIG. 16, 4 can be obtainedThe wave number of the No. II linear array damage scattering signal under the frequency of 0kHz is ka-40-II227.5rad/m, arrival time tR-40-II0.4165 ms. From FIG. 17, it can be obtained that the wave number of the I number linear array damage scattering signal at the frequency of 41kHz is ka-41-I133.1rad/m, arrival time tR-41-I0.4137 ms. From FIG. 18, the wave number of the No. II linear array damage scattering signal at 41kHz frequency is ka-41-II230.6rad/m, arrival time tR-41-II＝0.4141ms。
Step three: calculating the damage angle
Wave number k of damage scattering signal using I number linear arraya-40-I＝131.7rad/m、ka-41-IWave number k of No. 133.1rad/m and No. II linear array damage scattering signala-40-II＝227.5rad/m、ka-41-II230.6rad/m, the angle of the lesion can be calculated as θa60.0 °, as shown in equation (10), equation (11), and equation (12).
Figure BDA0002463149310000111
Figure BDA0002463149310000112
Figure BDA0002463149310000113
Step four: calculating the distance of the damage
Firstly, the wave number k of the I number linear array damage scattering signal under the frequency of 40kHz is useda-40-IWave number k of No. 131.7rad/m and No. II linear array damage scattering signala-40-II227.5rad/m, the number of Lamb waves can be calculated as k at 40kHza-40262.9rad/m, as shown in equation (13).
Figure BDA0002463149310000114
Using wave number k of I number linear array damage scattering signal under 41kHz frequencya-41-IWave number k of No. 133.1rad/m and No. II linear array damage scattering signala-41-IIThe number of Lamb waves k can be calculated at 41kHz as 230.6rad/ma-41266.3rad/m, as shown in equation (14).
Figure BDA0002463149310000121
Next, the wave number k of Lamb waves at frequencies of 40kHz and 41kHz was useda-40＝262.9rad/m、ka-41266.3rad/m, calculating the wave speed of Lamb wave as cg1856.5m/s, as shown in equation (15).
Figure BDA0002463149310000122
Calculating the starting time of the Lamb wave excitation signal at the frequencies of 40kHz and 41kHz by using the signal envelope method, as shown in FIGS. 19 and 20, the starting time of the Lamb wave excitation signal at the frequencies of 40kHz and 41kHz can be obtained as te-40＝0.1041ms、te-41＝0.1029ms。
Finally, the wave velocity c of the Lamb wave is usedg1856.5m/s, time t when the damage scattering signal reaches the linear arrayR-40-I＝0.4675ms、tR-40-II＝0.4662ms、tR-41-I0.4137ms and tR-41-II0.4141ms, the starting time t of Lamb wave excitation signale-40＝0.1041ms、te-41The distance of the injury is calculated to be L (0.1029 ms)a289.5mm, as shown in equation (16).
Figure BDA0002463149310000123
Finally, the position coordinate of the injury can be located to be (60 degrees, 289.5mm), and the distance error from the actual injury position (60 degrees, 300mm) is 10.5 mm.

Claims (1)

1. A damage non-wave-velocity positioning method based on a space-wave-number filter is characterized by comprising the following steps:
the method comprises the following steps: acquiring a dual-frequency damage scattering signal; the specific implementation process is as follows:
a cross array is arranged on the structure, and two linear arrays in the cross array are respectively marked as a linear array I and a linear array II; the two linear arrays are composed of M piezoelectric sensors, and the distance between the central points of two adjacent piezoelectric sensors is delta x; the piezoelectric sensors in the linear array I are sequentially numbered as I-1, I-2, …, I-M, … and I-M, and the piezoelectric sensors in the linear array II are sequentially numbered as II-1, II-2, …, II-M, … and II-M; arranging an active Lamb wave excitation element near the central point of the cross array;
firstly, when the structure is in a healthy state, the excitation elements respectively excite the structure to have a central frequency of omega1And ω2The Lamb wave of the structure is acquired by a cross array and used as a health reference signal H (omega, r-m, t) of the structure, omega is the central frequency of the Lamb wave, r is the serial number of a linear array, m is the serial number of a piezoelectric sensor in the linear array, r-m is a piezoelectric sensor m in the linear array, and t is sampling time;
secondly, after the structure is damaged, the exciting elements respectively excite the center frequency omega in the structure again1And ω2Collecting Lamb wave response signals of the structure by a cross array, and using the Lamb wave response signals as online monitoring signals D (omega, r-m, t) of the structure;
using the health reference signal H (omega, r-m, t) of the structure and the online monitoring signal D (omega, r-m, t) of the structure to extract a damage scattering signal f (omega, r-m, t), as shown in formula (1):
f(ω,r-m,t)＝D(ω,r-m,t)-H(ω,r-m,t) (1)
in the formula: f (omega, r-m, t) is a damage scattering signal of an m piezoelectric sensor of an r linear array in the cross array under the extracted omega frequency, D (omega, r-m, t) is an online monitoring signal of an m piezoelectric sensor of an r linear array in the cross array under the omega frequency, H (omega, r-m, t) is a health reference signal of an m piezoelectric sensor of an r linear array in the cross array under the omega frequency, omega is the central frequency of a Lamb wave, r is the serial number of the linear array, r-m is an m piezoelectric sensor in the r linear array, and t is sampling time;
step two: carrying out space-wave number filtering on the dual-frequency damage scattering signal; the specific implementation process is as follows:
first, the wave number filtering interval of the space-wave number filter is set to be delta k, and the wave number filtering range of the space-wave number filter is set to be (-k)s,+ks)，ksSpatial sampling wave number for linear array:
Figure FDA0003052554730000021
in the formula: delta x is the array element spacing of the linear array, and pi is the circumferential rate;
then, a wave number filtered value k, -k is selecteds＜k＜ksAnd respectively carrying out space-wave number filtering on the two linear arrays:
Figure FDA0003052554730000022
in the formula: phir(omega, k, t) is the space-wave number filtering synthesis value of the r number linear array damage scattering signal under the omega frequency when the wave number filtering value is k,
Figure FDA0003052554730000023
for convolution operation, phi (k, r-m) is a space-wave number filtering weight function of the piezoelectric sensor with number m in the linear array with number r, as shown in formula (4):
Figure FDA0003052554730000024
in the formula: phi (k, r-m) is a space-wave number filtering weight function of the m piezoelectric sensors in the r linear array, lr-mThe distance between the m piezoelectric sensors in the r linear array and an origin is represented, i is an imaginary number unit, k is the central wave number of a space-wave number filtering weight function, and e is a natural constant;
secondly, the first step is to carry out the first,selecting the next wave number filtering value k + delta k, and calculating the space-wave number filtering synthesis value phi of the r number linear array damage scattering signal under omega frequency when calculating the wave number filtering value according to the space-wave number filtering processr(omega, k + delta k, t) until all the set wave number filtering values are calculated; thus, under the omega frequency and at each moment t, a space-wave number filtering synthesis value under each wave number filtering value k is obtained;
selecting the wave number corresponding to the maximum value of the image pixel value in the wave number-time image of the r number linear array under the omega frequency as the wave number k of the linear array damage scattering signal under the frequencya-ω-r(ii) a The corresponding moment at the maximum value of the pixel value is the moment t when the damage scattering signal of the linear array reaches the linear arrayR-ω-r；
Step three: calculating a damage angle; the specific implementation process is as follows:
using wave number k of r number linear array damage scattering signal under omega frequencya-ω-rCalculating the angle theta of the damagea：
Figure FDA0003052554730000031
Figure FDA0003052554730000032
In the formula: thetaaFor calculated damage angle, θa-ωFor the calculated damage angle at the omega frequency,
Figure FDA0003052554730000033
is omega1The calculated damage angle at the frequency is used,
Figure FDA0003052554730000034
is omega2Calculated damage angle, k, at frequencya-ω-IWave number, k of I number linear array damage scattering signal under omega frequencya-ω-IIThe wave number of the No. II linear array damage scattering signal under omega frequency is obtained;
step four: calculating a damage distance; the specific implementation process is as follows:
firstly, using wave number k of I-line array and II-line array damage scattering signals under omega frequencya-ω-IAnd ka-ω-IICalculating the wave number k of Lamb wave under omega frequencya-ω：
Figure FDA0003052554730000041
Second, using ω1And ω2Calculating the wave velocity c of the Lamb wave by the wave number of the Lamb wave under two frequenciesg：
Figure FDA0003052554730000042
In the formula:
Figure FDA0003052554730000043
is omega1The wave number of Lamb waves at a frequency,
Figure FDA0003052554730000044
is omega2The wave number of Lamb waves at frequency;
finally, the wave velocity c of the Lamb wave is usedgAnd the time t when the damage scattering signal reaches the linear arrayR-ω-rCalculating the distance L of the damagea：
Figure FDA0003052554730000045
In the formula:
Figure FDA0003052554730000046
is omega1The arrival time of the I-number linear array damage scattering signal under the frequency,
Figure FDA0003052554730000047
is omega1The arrival time of the No. II linear array damage scattering signal under the frequency,
Figure FDA0003052554730000048
is omega1The starting time of the Lamb wave excitation signal at the frequency,
Figure FDA0003052554730000049
is omega2The arrival time of the I-number linear array damage scattering signal under the frequency,
Figure FDA00030525547300000410
is omega2The arrival time of the No. II linear array damage scattering signal under the frequency,
Figure FDA00030525547300000411
is omega2Starting time of Lamb wave excitation signal under frequency; the final localization of the lesion is achieved as (θ)a,La)。
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