CN113567564B - Time domain bending ultrasonic guided wave large-range temperature compensation method considering amplitude compensation - Google Patents
Time domain bending ultrasonic guided wave large-range temperature compensation method considering amplitude compensation Download PDFInfo
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Abstract
The invention discloses a time domain bending ultrasonic guided wave large-range temperature compensation method considering amplitude compensation, which comprises the following steps of: arranging a piezoelectric patch for collecting ultrasonic guided wave signals in a monitored structure so as to collect ultrasonic guided wave monitoring signals in the structure at different temperatures and ultrasonic guided wave calibration signals for amplitude precompensation; acquiring an ultrasonic guided wave reference signal and a calibration signal at a certain temperature before a structure is damaged; acquiring an ultrasonic guided wave current signal and a current calibration signal of a current structure at another temperature; carrying out amplitude precompensation on the current ultrasonic guided wave signal according to the ultrasonic guided wave calibration signal; and performing time domain bending temperature compensation on the ultrasonic guided wave current signal after amplitude precompensation. The method of the invention introduces amplitude pre-compensation treatment on the basis of the time domain bending temperature compensation method, and realizes the large-range temperature compensation of the ultrasonic guided wave signals.
Description
Technical Field
The invention belongs to the field of structural health monitoring of ultrasonic guided waves, and particularly relates to a large-range temperature compensation method of a time-domain bending ultrasonic guided wave considering amplitude compensation.
Background
The ultrasonic guided wave damage monitoring method becomes one of the most effective aviation structure health monitoring methods, and is gradually put into engineering application. However, in practical application, the temperature change of the service environment of the aviation structure can affect the properties of the sensor, the glue layer and the measured structure, so that the ultrasonic guided wave monitoring signal is subjected to damage-independent additional change. Such ambient temperature effects can disturb or even overwhelm the actual lesion information in the monitored signal and ultimately reduce the reliability of the lesion monitoring results.
In order to solve the above problems, various temperature compensation methods exist at present, time domain warping is used as a flexible warping method for a time domain signal sequence, and the temperature compensation processing of time domain warping can be directly performed on a signal according to the waveform change of the current signal caused by temperature, so that the method is considered to have a huge development prospect. However, in practical application, as the temperature variation range is increased, the influence of temperature on the amplitude is gradually serious, and the compensation capability of time domain bending on the signal amplitude is limited, so that the temperature compensation range of the method on the ultrasonic guided wave is limited. This problem affects the application of time domain bending in the large-scale temperature compensation of practical ultrasonic guided waves.
Disclosure of Invention
In view of the above disadvantages of the prior art, an object of the present invention is to provide a method for compensating temperature of a large range of time-domain bending ultrasonic guided wave by considering amplitude compensation, so as to solve the problem in the prior art that the amplitude of a monitoring signal of the ultrasonic guided wave is significantly affected by a large range of temperature change, thereby severely reducing the temperature compensation effect.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses an ultrasonic guided wave large-range temperature compensation method based on time domain bending, which comprises the following steps of:
(1) arranging a piezoelectric patch for collecting ultrasonic guided wave signals in a monitored structure so as to collect ultrasonic guided wave monitoring signals in the structure at different temperatures and ultrasonic guided wave calibration signals for amplitude precompensation;
(2) acquiring an ultrasonic guided wave reference signal and a calibration signal at a certain temperature before a structure is damaged;
(3) acquiring an ultrasonic guided wave current signal and a current calibration signal of a current structure at another temperature;
(4) carrying out amplitude precompensation on the current ultrasonic guided wave signal according to the ultrasonic guided wave calibration signal;
(5) and performing time domain bending temperature compensation on the ultrasonic guided wave current signal after amplitude precompensation.
Further, the step (2) is specifically: at a certain temperature T 0 Next, an ultrasonic guided wave monitoring signal v0 (T) in a healthy structure is acquired 0 T) as the ultrasonic guided wave reference signal of the subsequent temperature compensation, and simultaneously acquiring the ultra required by the subsequent amplitude pre-compensationAcoustic guided wave calibration signal v R (T 0 T), t is a time variable.
Further, the step (3) is specifically: at another temperature T 1 Then, respectively acquiring the current signals v1 (T) of the ultrasonic guided waves to be temperature compensated in the current structure 1 T) and the ultrasonic guided wave current calibration signal v R (T 1 ,t)。
Further, the step (4) specifically comprises: according to ultrasonic guided wave calibration signals v acquired at two temperatures R (T 0 T) and the ultrasonic guided wave current calibration signal v R (T 1 T) current signal v1 (T) of ultrasonic guided wave 1 T) carrying out amplitude pre-compensation treatment to obtain the ultrasonic guided wave current signal v1 after amplitude pre-compensation AC (T 1 ,t)。
Further, the pre-compensating the amplitude of the current ultrasonic guided wave signal according to the calibration signal of the ultrasonic guided wave in the step (4) specifically includes:
determining a certain temperature T 0 Lower ultrasonic guided wave calibration signal v R (T 0 T) and a further temperature T 1 Lower ultrasonic guided wave current calibration signal v R (T 1 T) amplitude of the direct wave Av R (T 0 ) And Av R (T 1 )；
Obtaining the amplitude precompensation factor beta ═ Av R (T 0 )/Av R (T 1 )；
Calculating the amplitude pre-compensated current signal of the ultrasonic guided wave as v1 AC (T 1 ,t)＝βv1(T 1 ,t)。
Further, the step (5) specifically comprises: with ultrasonic guided wave reference signal v0 (T) 0 T) as a reference, and pre-compensating the amplitude of the current signal v1 of the ultrasonic guided wave AC (T 1 T) performing time-domain bending temperature compensation to finally obtain the ultrasonic guided wave current signal v1 after time-domain bending temperature compensation ITDW (T 1 ,t)。
Further, the time-domain bending temperature compensation of the ultrasonic guided wave current signal after amplitude precompensation in the step (5) specifically includes:
based on ultrasonic guided wave reference signalsNumber v0 (T) 0 T) of the respective signal data points { x } 1 ,x 2 ,…,x i ,…,x N And amplitude pre-compensated current signal v1 of ultrasonic guided wave AC (T 1 T) of the respective signal data points y 1 ,y 2 ,…,y j ,…,y M Wherein N and M are each v0 (T) 0 T) and v1 AC (T 1 T) number of data points, x i And y j Are respectively v0 (T) 0 T) ith data point and v1 AC (T 1 T) j-th data point, i is more than or equal to 1 and less than or equal to N, j is more than or equal to 1 and less than or equal to M, and v0 (T) is obtained 0 T) and v1 AC (T 1 T) distance matrix D between N×M Whose matrix elements are calculated as
D(i,j)＝||x i -y j || 2
In the formula, | | | calving 2 Denotes x i And y j The Euclidean distance between;
v0 (T) is determined according to the following recursive formula 0 T) and v1 AC (T 1 T) accumulated distance matrix A N×M ：
A(i,j)＝D(i,j)+min[w·A(i-1,j),A(i-1,j-1),w·A(i,j-1)]
Wherein A (i, j) is A N×M A (1,1) ═ D (1,1), min [, [ 2 ] ]]The minimum value selection operation is expressed, w is a bending coefficient, and the value range is more than or equal to 1 and less than 2;
then v0 (T) 0 T) and v1 AC (T 1 T) is defined as characterizing v0 (T) 0 T) and v1 AC (T 1 T) the ordered pairs of data points between which the optimal pairwise mapping relationship is formed, i.e.: p ═ P 1 ,p 2 ,…,p k ,…,p K K is more than or equal to 1 and less than or equal to K, max (N, M) is more than or equal to K and less than or equal to N + M +1, and the ordered number pairs p k ＝(i k ,j k ) Indicates that v0 (T) 0 T) th of k Data points
And v1 AC (T 1 J in t) k Data points
Are matched, i is more than or equal to 1 k ≤N，1≤j k Less than or equal to M; at A N×M In which p is K (N, M) as starting point, p 1 (1,1) is an end point, and the iterative search mode is as follows:
wherein (a, b) is E [ (0,1), (1,0), (1,1)]，i k -a≥1，j k B ≧ 1, and P ═ P determined in reverse 1 ,p 2 ,…,p k ,…,p K }；
In sequence according to P ═ P 1 ,p 2 ,…,p k ,…,p K In each ordinal number p k ＝(i k ,j k ) V1 AC (T 1 J in t) k A data point y jk Assigned as ith in the new current signal k For each data point, we obtained:
in the formula, v1 ITDW (T 1 And t) is the ultrasonic guided wave current signal after time domain bending temperature compensation.
The invention has the beneficial effects that:
according to the method, amplitude pre-compensation processing is introduced on the basis of time domain bending temperature compensation, so that the problem that the time domain bending method seriously reduces the temperature compensation effect because the amplitude of the ultrasonic guided wave monitoring signal is obviously influenced due to large-range temperature change is solved, and large-range temperature compensation in actual ultrasonic guided wave damage monitoring is facilitated.
Drawings
FIG. 1 is a schematic flow diagram of the method of the present invention;
FIG. 2 is a schematic view of the arrangement of piezoelectric plates and simulated damage in an aluminum plate structure;
FIG. 3 is a reference signal in the case of no temperature difference in the monitoring processv0 1-2 (25 ℃, t) and the ideal damage signal v1 1-2 Waveform contrast plot of (25 ℃, t);
FIG. 4 is a reference signal v0 for a 25 deg.C temperature difference in a monitoring process 1-2 (25 ℃, t) and injury Signal v1 1-2 Waveform contrast plot of (50 ℃, t);
FIG. 5 shows Lamb wave calibration signal v0 3-4 (25 ℃, t) and v1 3-4 A in (50 ℃, t) 0 A mode through oscillogram;
FIG. 6 is the original impairment Signal v1 1-2 (50 ℃, t) and amplitude pre-compensation processing result thereof
A waveform comparison graph of (a);
FIG. 7 is a pair v1 1-2 (50 ℃ C., t) Damage signal obtained by ITDW temperature compensation
And the ideal damage signal v1 1-2 Waveform contrast plots of (25 ℃, t);
FIG. 8 is a pair v1 1-2 (50 ℃, t) Damage signal obtained by TDW temperature compensation
And the ideal damage signal v1 1-2 Waveform contrast plots of (25 ℃, t);
FIG. 9 is a graph formed by v1 1-2 (50 ℃, t) and v0 1-2 (25 ℃, t) original damage scattering signal s obtained by difference signal processing 1-2 (50 ℃ C., t) and the ideal lesion scattering signal s 1-2 Waveform contrast plots of (25 ℃, t);
FIG. 10 is a schematic view of a display device
And v0 1-2 (25 ℃, t) damage scattering signal obtained by processing difference signal
And the ideal damage scattering signal s 1-2 Waveform contrast plot of (25 ℃, t);
FIG. 11 is a schematic view of a hand-held tool made of
And v0 1-2 (25 ℃, t) damage scattering signal obtained by difference signal processing
And ideal damage scattering signal s 1-2 Waveform of (25 ℃, t) is shown.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
This example uses as the object of study a typical guided ultrasonic wave of Lamb waves propagating in a structure of an aluminum plate of LY21, which has dimensions 400mm × 400mm × 1.5 mm. The excitation signal is 5-peak sine modulation signal with center frequency of 90kHz, so that the collected Lamb wave signal is A 0 The mode is dominant. In the embodiment, the environment temperature when collecting Lamb wave health signals and damage signals is respectively 25 ℃ and 50 ℃, then the Lamb wave health signals at the normal temperature of 25 ℃ are used as reference signals, and the damage signals at the temperature of 50 ℃ are subjected to temperature compensation processing, so that the influence of temperature change on the Lamb wave signals is eliminated.
Referring to fig. 1, a time domain bending ultrasonic guided wave large-range temperature compensation method considering amplitude compensation according to the present invention includes the following steps:
(1) arranging a piezoelectric sheet for collecting Lamb wave signals in the structure;
as shown in FIG. 2, 4 piezoelectric sheets P are arranged on the surface of the aluminum plate structure 1 、P 2 、P 3 And P 4 A Cartesian coordinate system is established by taking the center of the aluminum plate as an origin, and the coordinates of the piezoelectric patches are shown in a table 1;
TABLE 1
Selecting pairs of piezoelectric sheets P 3-4 Acquisition for amplitude precompensationLamb wave calibration signal, pair of piezoelectric plates P 1-2 And (5) performing temperature compensation processing on the Lamb wave signals in the step (A).
(2) Collecting Lamb wave reference signals and calibration signals of a healthy aluminum plate at the temperature of 25 ℃;
separately collecting P in a healthy aluminum plate at an ambient temperature of 25 deg.C 1-2 Lamb wave health signal v0 in (1) 1-2 (25 ℃, t) and P 3-4 Lamb wave health signal v0 in (1) 3-4 (25 ℃, t) wherein v0 1-2 (25 ℃, t) as a reference signal for temperature compensation, and v0 3-4 (25 ℃, t) as a calibration signal for amplitude pre-compensation.
(3) Collecting a Lamb wave damage signal and a current calibration signal of the aluminum plate in a damage state at the temperature of 50 ℃;
when the ambient temperature became 50 ℃ and damage D (shown in fig. 2) occurred at the (69, 45) coordinates in the aluminum plate, the pair of piezoelectric sheets P were collected respectively 1-2 Lamb wave damage signal v1 in (1) 1-2 (50 ℃ C., t) and piezoelectric sheet pair P 3-4 Current calibration signal v1 for amplitude pre-compensation 3-4 (50℃,t)；
It should be noted that the health signal v0 collected from the healthy aluminum plate at 25 ℃ in this experiment 1-2 (25 ℃, t) as a reference signal, and a damage signal v1 at 50 DEG C 1-2 Temperature compensation is carried out at 50 ℃ and t, so that the waveform of the signal is close to the ideal damage signal v1 collected in an aluminum plate at 25 DEG C 1-2 (25 ℃, t) to eliminate the effect of temperature changes on damage monitoring. Therefore, v1 is examined for practical purposes 1-2 Temperature compensation effect of (50 ℃, t), and P at 25 ℃ is collected before the aluminum plate is damaged 1-2 Ideal damage signal v1 in 1-2 (25 ℃, t) as a reference for investigating the effect of temperature compensation;
FIG. 3 shows a reference signal v0 in the case of no temperature difference in the monitoring process 1-2 (25 ℃, t) and the ideal damage signal v1 1-2 A waveform comparison graph of (25 ℃, t) shows that the waveforms of the two are consistent under the same environmental temperature, and only the waveform difference caused by the damage occurs in a 120-170 mu s time domain interval where the theoretical position of the damage scattering wave packet is located;
FIG. 4 shows the presence of a temperature of 25 ℃ during the monitoring processReference signal v0 in the poor case 1-2 (25 ℃, t) and injury Signal v1 1-2 Waveform contrast plot of (50 ℃, t), results show that a wide range of temperature changes at 25 ℃ severely affects v1 1-2 The phase of each data point (50 ℃, t) causes the waveform to generate a lagging phenomenon, and the amplitude of the signal generates obvious attenuation, so that the waveform is obviously deviated from v0 1-2 (25 ℃, t), this temperature variation vs. v1 1-2 The influence of (50 ℃, t) easily submerges the signal change caused by the damage, so that the subsequent damage scattering signal is difficult to accurately extract.
(4) Amplitude precompensation is carried out on the Lamb wave damage signal according to the calibration signal;
will P 3-4 Lamb wave calibration signal v0 collected at 25 deg.C 3-4 The current calibration signal v1 was acquired at (25 ℃, t) and 50 ℃ temperatures 3-4 A in (50 ℃, t) 0 The amplitudes of the modal direct waves (as shown in FIG. 5) are extracted as A _ v0 3-4 (25 ℃, t) 4.7100V and A _ V1 3-4 (50℃)＝4.0323V；
According to the formula β ═ a _ v0 3-4 (25℃)/A_v1 3-4 Finding the amplitude precompensation factor beta (1.1681) (50 ℃);
calculating an amplitude precompensated Lamb wave damage signal as
Original damage signal v1 1-2 (50 ℃, t) and amplitude pre-compensation processing result thereof
The waveform of (2) is shown in fig. 6.
(5) Performing time domain bending temperature compensation on the Lamb wave damage signal after amplitude precompensation;
according to the damage signal after the amplitude precompensation treatment
And a reference signal v0 1-2 Calculating Euclidean distance of each point at each data point of (25 ℃, t) to obtain a distance matrix D;
according to A (i, j) ═ D (i, j)+min[w·A(i-1,j),A(i-1,j-1),w·A(i,j-1)]Recursion to obtain
And v0 1-2 Cumulative distance matrix A between (25 ℃, t) 5061×5061 Wherein A (i, j) is A 5061×5061 Let a (1,1) ═ D (1,1) be the starting point for forward construction of the cumulative distance matrix, w is the warping factor, and in this embodiment, w is taken to be 1.02;
then will be
And v0 1-2 Defining an optimal time-domain warping path between (25 ℃, t) as characterizing
And v0 1-2 (25 ℃, t) the ordered pairs of data points that are the best pair mapping between data points, i.e.: p best ＝{p 1 ,p 2 ,…,p k ,…,p 5186 K is more than or equal to 1 and less than or equal to 5186; ordinal number pair p k ＝(i k ,j k ) Show that
Middle (i) k A data point
And v0 1-2 J in (25 ℃, t) k Data points
Are paired, then at A 5186×5186 In which p is 5186 Starting point, ═ p (5186), p 1 As an end point, (1,1) is searched iteratively as follows:
wherein (a, b) is an element (0,1), (1,0), (1,1)]，i k -a≥1，j k -b≥1, reversely determine
And v0 1-2 Optimum bending path P between (25 ℃, t) best ；
In sequence according to P best ＝{p 1 ,p 2 ,…,p k ,…,p 5186 In each ordinal number p k ＝(i k ,j k ) Will be
Middle (j) th k A data point
Assigned as i-th in the new impairment Signal k For each data point, we obtained:
FIG. 7 is a drawing showing
And the ideal damage signal v1 1-2 The waveform of the two waveforms are basically consistent in comparison with the waveform of (25 ℃, t), which shows that the ITDW method not only compensates
The phase change caused by the temperature change in the whole time domain range and the amplitude change under the condition of 25 ℃ temperature difference also obtain better compensation effect due to amplitude precompensation.
To show the technical effect of amplitude pre-compensation, the embodiment pairs v1 1-2 (50 ℃, t) performing time domain bending temperature compensation treatment to obtain
FIG. 8 is a drawing showing
And the ideal damage signal v1 1-2 Waveform comparison plot of (25 deg.C, t),
and v1 1-2 The phases of (25 deg.c, t) substantially coincide, but since the amplitude compensation of the signal is not taken into account,
the amplitudes of the direct wave (within the time domain range of 90-140 mus in fig. 8) and the boundary reflection signal (within the time domain range of 150-250 mus in fig. 8) are not well corrected, resulting in failure of temperature compensation;
with reference to fig. 7 to 8, it can be known that the method of the present invention introduces amplitude pre-compensation processing based on the time domain bending temperature compensation method, and the amplitude pre-compensation can initially complete compensation of the temperature-amplitude effect, so that the amplitude change is reduced to a size range that can be compensated adaptively by the conventional TDW temperature compensation method, thereby improving accuracy of damage monitoring in a large-range temperature difference environment.
To illustrate the method of the invention more intuitively, it is further analyzed next by the scattered signal waveform:
from a reference signal v0 1-2 (25 ℃, t) and the respective injury signals v1 as above 1-2 (25℃,t)、v1 1-2 (50℃,t)、
And
performing signal difference operation to sequentially obtain ideal scattering signals s without temperature difference in the monitoring process 1-2 (25 ℃, t), original scattered signal s 1-2 (50 ℃, t) TDW temperature compensation methodProcessed scatter signal
And the scattering signal after time domain bending temperature compensation processing considering amplitude compensation
FIG. 9 is s 1-2 (50 ℃, t) and s 1-2 The waveforms of (25 ℃, t) are compared with each other, and the black square is the theoretical damage position. Since the temperature compensation process is not performed, in A 0 Obvious residual signals exist in boundary reflection (150-250 mu s in figure 9) of mode direct waves (90-140 mu s in figure 9), and residual signal wave packets with large amplitude interfere or even submerge damage scattered wave packets with small amplitude, so that the extraction of damage information is seriously influenced;
FIG. 10 is a drawing showing
And s 1-2 The waveforms of (25 ℃, t) are compared with each other, and the black square is the theoretical damage position. The TDW temperature compensation method effectively compensates the phase difference caused by temperature change, but because amplitude compensation is not carried out, residual direct waves and residual boundary reflection (within the time domain ranges of 90-140 mu s and 200-250 mu s in figure 10) are only partially reduced;
FIG. 11 is a schematic view of
And s 1-2 The waveforms of (25 ℃, t) are compared with each other, and the black square is the theoretical damage position. Because the amplitude pre-compensation processing is added to the ITDW on the basis of the TDW method, the influence of large-range temperature change on the signal amplitude is eliminated, the residual direct wave and the residual boundary reflected wave packet (in the time domain ranges of 90 mu s-140 mu s and 150 mu s-250 mu s in the graph 11) are effectively inhibited, and the damage scattered wave packet is highly consistent with the ideal case, which shows that the ITDW temperature compensation method has a better compensation result.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (1)
1. A time domain bending ultrasonic guided wave large-range temperature compensation method considering amplitude compensation is characterized by comprising the following steps:
(1) arranging a piezoelectric patch for collecting ultrasonic guided wave signals in a monitored structure so as to collect ultrasonic guided wave monitoring signals in the structure at different temperatures and ultrasonic guided wave calibration signals for amplitude precompensation;
(2) acquiring an ultrasonic guided wave reference signal and a calibration signal at a certain temperature before a structure is damaged;
(3) acquiring an ultrasonic guided wave current signal and a current calibration signal of a current structure at another temperature;
(4) carrying out amplitude precompensation on the current ultrasonic guided wave signal according to the ultrasonic guided wave calibration signal;
(5) performing time domain bending temperature compensation on the ultrasonic guided wave current signal after amplitude precompensation;
the step (2) is specifically as follows: at a certain temperature T 0 Next, an ultrasonic guided wave monitoring signal v0 (T) in a healthy structure is acquired 0 T) as the ultrasonic guided wave reference signal of subsequent temperature compensation, and simultaneously acquiring the ultrasonic guided wave calibration signal v required by subsequent amplitude pre-compensation R (T 0 T), t is a time variable;
the step (3) is specifically as follows: at another temperature T 1 Next, respectively collecting the current signals v1 (T) of the ultrasonic guided waves to be temperature compensated in the current structure 1 T) and current calibration signal v of ultrasonic guided wave R (T 1 ,t)；
The step (4) is specifically as follows: according to ultrasonic guided wave calibration signals v acquired at two temperatures R (T 0 T) and the ultrasonic guided wave current calibration signal v R (T 1 T) current signal v1 (T) for ultrasonic guided waves 1 T) carrying out amplitude pre-compensation treatment to obtain the ultrasonic guided wave current signal v1 after amplitude pre-compensation AC (T 1 ,t)；
The amplitude precompensation of the ultrasonic guided wave current signal according to the ultrasonic calibration signal in the step (4) specifically comprises the following steps:
determining a certain temperature T 0 Lower ultrasonic guided wave calibration signal v R (T 0 T) and a further temperature T 1 Lower ultrasonic guided wave current calibration signal v R (T 1 T) amplitude of the direct wave Av R (T 0 ) And Av R (T 1 )；
Calculating amplitude precompensation factor beta (Av) R (T 0 )/Av R (T 1 )；
Calculating the amplitude pre-compensated current signal of the ultrasonic guided wave as v1 AC (T 1 ,t)＝βv1(T 1 ,t)；
The step (5) is specifically as follows: with ultrasonic guided wave reference signal v0 (T) 0 T) as a reference, and pre-compensating the amplitude of the current signal v1 of the ultrasonic guided wave AC (T 1 T) performing time-domain bending temperature compensation to obtain a time-domain bending temperature compensated ultrasonic guided wave current signal v1 ITDW (T 1 ,t)；
The time domain bending temperature compensation of the ultrasonic guided wave current signal after amplitude precompensation in the step (5) specifically comprises the following steps:
according to the ultrasonic guided wave reference signal v0 (T) 0 T) of the respective signal data points { x } 1 ,x 2 ,…,x i ，…,x N And amplitude pre-compensated current signal v1 of ultrasonic guided wave AC (T 1 T) of the respective signal data points { y } 1 ,y 2 ,…,y j ,…,y M Wherein N and M are each v0 (T) 0 T) and v1 AC (T 1 T) number of data points, x i And y j Are respectively v0 (T) 0 T) ith data point and v1 AC (T 1 T) j of j data points, i is more than or equal to 1 and less than or equal to N, j is more than or equal to 1 and less than or equal to M, and v0 (T) is obtained 0 T) and v1 AC (T 1 Distance matrix D between t) N×M The matrix elements are calculated as:
D(i,j)＝||x i -y j || 2
in the formula, | | | non-conducting phosphor 2 Denotes x i And y j The euclidean distance between them;
v0 (T) is determined according to the following recursive formula 0 T) and v1 AC (T 1 T) of the cumulative distance matrix A N×M ：
A(i,j)＝D(i,j)+min[w·A(i-1,j),A(i-1,j-1),w·A(i,j-1)]
Wherein A (i, j) is A N×M A (1,1) ═ D (1,1), min [, [ 2 ] ]]The minimum value selection operation is expressed, w is a bending coefficient, and the value range is more than or equal to 1 and less than 2;
then v0 (T) 0 T) and v1 AC (T 1 T) is defined as characterizing v0 (T) 0 T) and v1 AC (T 1 T) the ordered pairs of data points between which the optimal pairwise mapping relationship is formed, i.e.: p ═ P 1 ,p 2 ,…,p k ,…,p K K is more than or equal to 1 and less than or equal to K, max (N, M) is more than or equal to K and less than or equal to N + M +1, and the ordered number pairs p k ＝(i k ,j k ) Indicates that v0 (T) 0 T) th of k A data point
And v1 AC (T 1 J in t) k A data point
Are matched, i is more than or equal to 1 k ≤N，1≤j k Less than or equal to M; in A N×M In which p is K (N, M) as starting point, p 1 (1,1) is an end point, and the iterative search mode is as follows:
wherein (a, b) is E [ (0,1), (1,0), (1,1)]，i k -a≥1，j k B ≧ 1, and P ═ P is determined in reverse 1 ,p 2 ,…,p k ,…，p K }；
In sequence according to P ═ P 1 ,p 2 ,…,p k ,…,p K In each ordinal number p k ＝(i k ,j k ) V1 AC (T 1 J in t) k Data points
Assigned as ith in the new current signal k For each data point, we obtained:
in the formula, v1 ITDW (T 1 And t) is the ultrasonic guided wave current signal after time domain bending temperature compensation.
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