Circular tube fatigue crack detection method based on asymmetric second harmonic energy focusing change rule

Abstract

The invention provides a circular tube fatigue crack detection method based on an asymmetric second harmonic energy focusing change rule. An excitation sensor and a receiving sensor are arranged on a circular tube at an interval of 1 / 4 of an axial distance change period of an asymmetric second harmonic energy focusing degree; performing time-frequency analysis on the M circumferential position receiving signals through wavelet time-frequency transformation based on Morse wavelet basis to extract asymmetric second harmonics; the asymmetric second harmonic energy focusing degree of the M circumferential positions is calculated through the energy focusing index I; comparing the calculated focusing degree of the asymmetric second harmonic with the quantitative relationship between the focusing degree of the asymmetric second harmonic energy and the fatigue crack position through the quantitative relationship between the focusing degree of the asymmetric second harmonic energy and the fatigue crack position established on the basis of a fatigue crack induced asymmetric second harmonic model; whether fatigue cracks exist in the circular tube and the axial and circumferential positions of the fatigue cracks are evaluated.

Description

Technical Field

[0001] The invention belongs to the technical field of nondestructive testing of round tubes, and in particular relates to a method for detecting fatigue cracks in round tubes based on asymmetric second harmonic energy focusing variation rules. Background Art

[0002] Circular tube structures are widely used in key mechanical components in the fields of aerospace, rail transit, and intelligent manufacturing. Common circular tube structures include aircraft hydraulic actuators, automobile engine high-pressure oil pipes, high-speed train hollow axles, etc. Their quality reliability is closely related to the safety of their service systems. These key mechanical components are under the action of alternating loads for a long time and have high replacement costs. Therefore, it is necessary to detect early fatigue cracks in circular tube structures and to maintain and replace them in a timely manner to prevent crack expansion and accidents.

[0003] At present, there are mainly infrared thermal imaging, laser, eddy current, magnetic flux leakage, acoustic emission, penetration, microwave, magnetic powder and other circular tube structure detection technologies. In general, although there are many detection methods for circular tube structures, each with its own advantages, these detection methods are limited by various factors (such as low resolution, low detection efficiency, unsuitable for detecting specimens with covering layers, and susceptible to external factors), and it is difficult to fully meet the needs in the detection and evaluation of early fatigue cracks in circular tube structures. Traditional linear ultrasonic guided waves have advantages that other detection methods do not have in the detection of circular tube structure defects due to their characteristics of fast speed, long distance and low attenuation. However, it is only sensitive to defects of open cracks close to its wavelength, and cannot detect small damage such as early fatigue cracks. Although nonlinear ultrasonic guided waves are suitable for the detection and evaluation of early fatigue cracks in structures, traditional nonlinear symmetrical guided waves are difficult to locate fatigue cracks in circular tubes. At the same time, traditional nonlinear symmetrical guided waves need to compare the nonlinear coefficients by monitoring the circular tube to determine whether there is fatigue cracks in the circular tube, which is time-consuming and labor-intensive.

[0004] In addition, compared with other plate-shaped structures, circular tubes produce more modes, which will affect the results of ultrasonic guided wave defect detection. Therefore, the detection schemes proposed in the prior art for structures of other shapes are usually difficult to transplant to the detection of circular tubes. Summary of the invention

[0005] In view of the defects and shortcomings of the prior art, the purpose of the present invention is to use the fatigue crack induced asymmetric second harmonic model to realize parameter-free detection and positioning of fatigue cracks in circular tubes, and to propose a circular tube fatigue crack detection method based on the change law of asymmetric second harmonic energy focusing.

[0006] The technical solution specifically adopted by the present invention to solve the technical problem is:

[0007] A circular tube fatigue crack detection method based on the law of asymmetric second harmonic energy focusing variation: excitation and receiving sensors are arranged on the circular tube at a spacing of one quarter of the period of variation of the asymmetric second harmonic energy focusing degree with axial distance; time-frequency analysis is performed on the received signals at M circumferential positions by wavelet time-frequency transform based on Morse wavelet basis to extract asymmetric second harmonics; the asymmetric second harmonic energy focusing degrees at M circumferential positions are calculated by using energy focusing index I; the quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack position is established based on a fatigue crack-induced asymmetric second harmonic model, and the calculated asymmetric second harmonic focusing degree is compared with the quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack position to evaluate whether the circular tube has fatigue cracks and its axial and circumferential positions.

[0008] Furthermore, the time-frequency analysis of the received signals at the M circumferential positions by wavelet time-frequency transformation based on the Morse wavelet basis to extract the asymmetric second harmonic is specifically as follows: the asymmetric waveguide original signal x(t) collected at the M circumferential positions of the circular tube is subjected to wavelet time-frequency transformation based on the Morse wavelet basis. Among them, W(a,b) represents the wavelet coefficients, represents the wavelet function based on the Morse wavelet basis; a is the scale parameter, b is the translation parameter; and the asymmetric second harmonic signal is obtained by slicing at the time-frequency spectrum twice the excitation signal frequency; then according to the distance d between the excitation and receiving sensors and the asymmetric second harmonic group velocity c with a modulus N Ng The asymmetric second harmonic propagation time t = d / c Ng , and use t to index the second harmonic peak A in the asymmetric second harmonic signal 2f .

[0009] Furthermore, the energy focusing index is obtained by extracting the peak value of the asymmetric second harmonic signal to obtain the circumferential distribution of the energy of the asymmetric second harmonic, and then calculating the energy focusing degree of the asymmetric second harmonic.

[0010] Furthermore, the energy focusing index I is used to calculate the asymmetric second harmonic energy focusing degree of M circumferential positions. The energy focusing degree index I formula is: The energy ratio of the two circumferential ranges of the circular tube (270°, 0°) ∪ (0°, 90°) and (90°, 180°) ∪ (180°, 270°) is calculated as the energy focusing index of the asymmetric second harmonic; A 2f i,θ A represents the i-th signal among the M / 2 asymmetric waveguide signals collected within the circumferential range of the circular tube (270°, 0°)∪(0°, 90°), 2f i,θ+πrepresents the jth signal among the M / 2 asymmetric waveguide signals collected within the circumferential range of the circular tube (90°, 180°)∪(180°, 270°); x represents the M asymmetric waveguide signals collected within all circumferential positions of the circular tube, min(A i ) represents the minimum value among all signals.

[0011] Furthermore, the fatigue crack induced asymmetric second harmonic model specifically utilizes the periodic variation law of the asymmetric second harmonic energy focusing degree induced by fatigue crack to establish a quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of the fatigue crack.

[0012] Furthermore, the periodic variation law of the asymmetric second harmonic energy focusing degree is specifically expressed by the periodic formula of the variation of the asymmetric second harmonic energy focusing degree with the axial distance: Among them, R o ,R i are the inner and outer radii of the tube, ω is the frequency of the asymmetric waveguide, c Np It represents the phase velocity of the ultrasonic guided wave mode in the plate corresponding to the asymmetric guided wave mode with mode number N, and k is a non-negative integer.

[0013] Furthermore, the normal mode decomposition theory analysis method is used to obtain the quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack location.

[0014] Furthermore, the method specifically comprises the following steps:

[0015] First, the excitation and receiving ultrasonic guided wave sensors are pasted on the circular tube with a spacing d, which is equal to one-fourth of the length period of the asymmetric second harmonic energy focusing degree in the circular tube changing with the axial distance: T z / 4; the excitation sensor completely covers the circumference of the circular tube, and the receiving sensor partially covers the circumference of the circular tube;

[0016] The ultrasonic guided wave signal with an angular frequency of ω is excited by the excitation sensor, and M ultrasonic guided wave signals are collected at equal angles around the circumference of the circular tube by the receiving sensor, where M>3;

[0017] Then, the M ultrasonic guided wave signals obtained by the acquisition are subjected to wavelet time-frequency transformation based on the Morse wavelet basis to obtain M ultrasonic guided wave signal time-frequency spectra; the time-frequency spectra are sliced ​​at the double angular frequency 2ω to obtain an asymmetric second harmonic signal; according to the distance d between the excitation and receiving sensors and the asymmetric second harmonic group velocity c with a modulus N, Ng The asymmetric second harmonic propagation time t = d / c is calculated from the relationship Ng , and use t to index the second harmonic peak A in the asymmetric second harmonic signal 2f ;

[0018] Calculate the energy focusing index based on M second harmonic peaks;

[0019] Finally, according to the fatigue crack-induced asymmetric second harmonic model, the quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of the fatigue crack was established by utilizing the periodic variation law of the asymmetric second harmonic energy focusing degree induced by fatigue crack. The calculated energy focusing degree index was used to evaluate whether there was fatigue crack in the circular tube and its position.

[0020] Compared with the prior art, the present invention and its preferred embodiments have at least the following beneficial effects:

[0021] 1. Compared with the traditional symmetric ultrasonic guided wave detection method, the defect-induced asymmetric second harmonic model established in the present invention can realize parameter-free detection of fatigue cracks in the tube and evaluate its axial and circumferential positions; the asymmetric ultrasonic guided wave used can establish a quantitative relationship with the axial and circumferential positions of the defects in the circular tube due to the characteristic that the degree of energy focusing changes with the change of axial propagation, and has advantages in defect location that the traditional symmetric ultrasonic guided wave, such as L(0,2), does not have.

[0022] 2. The length period formula of the asymmetric second harmonic energy focusing degree in a circular tube as a function of axial distance derived by the present invention is the theoretical basis for the spacing between the excitation and receiving sensors;

[0023] 3. The time-frequency analysis method based on Morse wavelet basis proposed in the present invention can extract purer asymmetric second harmonics compared with other second harmonic extraction methods; and can obtain the correct energy focusing law that matches the NME theoretical prediction.

[0024] 4. There is a quantitative relationship between the asymmetric second harmonic energy focusing index I designed by the present invention and the fatigue crack position. The presence of fatigue cracks and their positions in the round tube can be directly evaluated by the size of the second harmonic energy focusing index. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0026] Figure 1 This is a diagram showing the theoretical and simulation results of the quantitative relationship between the fatigue crack position predicted by the fatigue crack induced asymmetric second harmonic model and the degree of asymmetric second harmonic energy focusing in an embodiment of the present invention.

[0027] Figure 2 Schematic diagram of an experiment of a fatigue crack detection method in an embodiment of the present invention.

[0028] Figure 3This is a signal diagram of each step of extracting relatively pure asymmetric second harmonic using the wavelet time-frequency transform method based on the Morse wavelet basis in an embodiment of the present invention.

[0029] Figure 4 This is a diagram showing the prediction results of the axial and circumferential positions of a fatigue crack by using the quantitative relationship between the asymmetric second harmonic energy focusing index and the fatigue crack position in an embodiment of the present invention. DETAILED DESCRIPTION

[0030] In order to make the features and advantages of the present invention more clearly understood, the following embodiments are specifically described in detail as follows:

[0031] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0032] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0033] In the basic design of the embodiment of the present invention, the excitation and receiving sensors are arranged on the circular tube at a spacing of one-fourth of the period of the asymmetric second harmonic energy focusing degree changing with the axial distance. The received signals at M circumferential positions are subjected to time-frequency analysis by wavelet time-frequency transformation based on the Morse wavelet basis to extract relatively pure asymmetric second harmonics. The asymmetric second harmonic energy focusing degree at M circumferential positions is calculated using the energy focusing index I. A quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack position is established based on the fatigue crack-induced asymmetric second harmonic model. The calculated asymmetric second harmonic focusing degree is compared with the quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack position to evaluate whether the circular tube has a fatigue crack and its axial and circumferential position.

[0034] In a typical implementation process of the scheme of the present invention, first, the excitation and receiving sensors are arranged in the circular tube at a spacing equal to one-fourth of the length period of the asymmetric second harmonic energy focusing degree changing with the axial distance. The asymmetric waveguide signal collected at M (M>3) circumferential positions of the circular tube is subjected to wavelet time-frequency transformation, and the asymmetric second harmonic signal is sliced ​​to obtain the asymmetric second harmonic signal. Secondly, the peak values ​​of these asymmetric second harmonic signals are extracted to obtain the circumferential energy distribution of the asymmetric second harmonic, and the energy focusing degree of the asymmetric second harmonic is calculated. Finally, the periodic variation law of the asymmetric second harmonic energy focusing degree induced by fatigue cracks is used to establish a quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential position of the fatigue crack, and the presence or absence of fatigue cracks and their positions in the circular tube are evaluated by the asymmetric second harmonic energy focusing degree. In this way, the detection and positioning of fatigue cracks in circular tubes based on asymmetric waveguide second harmonics are realized.

[0035] The design points of the present invention include:

[0036] (1) Using the period T of the asymmetric second harmonic energy focusing degree in the circular tube changing with the axial distance z Determine the spacing between the excitation and receiving sensors; (2) Use the wavelet time-frequency transform based on the Morse wavelet basis to extract relatively pure asymmetric second harmonics; (3) Use the energy focusing index formula to calculate the energy focusing degree of the collected asymmetric second harmonic signal; (4) Use the fatigue crack-induced asymmetric second harmonic model to establish a quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of the fatigue crack; and use the energy focusing degree calculated in (3) to compare the quantitative relationship between the energy focusing degree of the asymmetric second harmonic generated by the fatigue crack and the fatigue crack position to evaluate whether there is fatigue and its axial and circumferential positions.

[0037] Specifically, the length period of the asymmetric second harmonic energy focusing degree in the circular tube changes with the axial distance is:

[0038] The above formula gives the length period of the second harmonic energy focusing degree of a certain asymmetric waveguide mode in a circular tube of a specific material and size as the axial propagation distance changes. o ,R i are the inner and outer radii of the tube, ω is the frequency of the asymmetric waveguide, c Np It represents the phase velocity of the waveguide mode in the plate corresponding to the asymmetric waveguide mode with modulus N. When detecting fatigue cracks, the signal acquisition mode of one excitation and one reception is adopted, thereby determining that the axial distance between the excitation and receiving sensors is equal to T z / 4.

[0039] Asymmetric second harmonic extraction method based on Morse wavelet time-frequency transform: The asymmetric waveguide original signal x(t) collected at M circumferential positions of the circular tube is subjected to wavelet time-frequency transform based on Morse wavelet basis. Among them, W(a,b) represents the wavelet coefficients, represents the wavelet function based on the Morse wavelet basis. a is the scale parameter and b is the translation parameter. The asymmetric second harmonic signal is obtained by slicing at the time-frequency spectrum twice the excitation signal frequency. Then, according to the distance d between the excitation and receiving sensors and the asymmetric second harmonic group velocity c with a modulus N, Ng The asymmetric second harmonic propagation time t = d / c Ng , and use t to index the second harmonic peak A in the asymmetric second harmonic signal 2f .

[0040] It should be noted that, in the present invention, the "energy focusing" used specifically refers to the change in the circumferential energy distribution of the asymmetric second harmonic caused by microcracks with the increase of the axial propagation distance, rather than the simple superposition of ultrasonic guided waves excited by different sensors at the same position.

[0041] The asymmetric ultrasonic guided wave L(M,2) used in the present invention can establish a quantitative relationship with the axial and circumferential positions of defects in the circular tube due to the characteristic that the degree of energy focusing changes with the change of axial propagation. It has advantages in defect positioning that traditional symmetric ultrasonic guided waves, such as T(0,1), do not have.

[0042] In the present invention, the energy focusing index I is: The energy ratio of the two circumferential ranges of the circular tube (270°, 0°) ∪ (0°, 90°) and (90°, 180°) ∪ (180°, 270°) is calculated as the energy focusing index of the asymmetric second harmonic. 2f i,θ A represents the i-th signal among the M / 2 asymmetric waveguide signals collected within the circumferential range of the circular tube (270°, 0°)∪(0°, 90°), 2f i,θ+π represents the jth signal among the M / 2 asymmetric waveguide signals collected within the circumferential range of the circular tube (90°, 180°)∪(180°, 270°). x represents the M asymmetric waveguide signals collected within all circumferential positions of the circular tube.

[0043] Fatigue crack induced asymmetric second harmonic model: Using the periodic variation of the asymmetric second harmonic energy focusing degree induced by fatigue cracks, a quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of fatigue cracks is established. This facilitates the use of the calculated asymmetric second harmonic energy focusing degree to assess the presence of fatigue cracks and their axial and circumferential positions.

[0044] The periodic formula of the asymmetric second harmonic energy focusing degree changing with the axial distance is: Among them, R o ,R i are the inner and outer radii of the tube, ω is the frequency of the asymmetric waveguide, c Np It represents the phase velocity of the ultrasonic guided wave mode in the plate corresponding to the asymmetric guided wave mode with modulus N. The derivation process of this formula is as follows:

[0045] As a preferred solution of this embodiment, the wavelength of the asymmetric waveguide mode L(N,M) is The corresponding Lamb wave wavelength λ in the plate corresponding to the circular tube N The formula for calculation is:

[0046]

[0047] According to the relationship between wave number, frequency and phase velocity, we can get:

[0048]

[0049] At the same time, due to The value is much smaller than 1, so the above formula can be further simplified:

[0050]

[0051] The wave number at this time The expression is:

[0052]

[0053] Therefore, the distance factor The formula for the change distance period of asymmetric waveguide energy distribution is:

[0054] As a preferred solution of this embodiment, the wavelet time-frequency transform formula based on the Morse wavelet basis is: Where W(a,b) represents the wavelet coefficients, x(t) is the original signal, is the wavelet mother function, a is the scale factor, and b is the time shift factor. The result after wavelet transform, namely the wavelet coefficient, contains information in three dimensions: time, frequency, and amplitude at different time frequencies. By extracting the information of amplitude variation over time at a specified frequency, the peak value of the specified frequency can be accurately obtained, thereby calculating the nonlinear index. The Matlab program for wavelet time-frequency transform based on Morse wavelet basis is as follows:

[0055]

[0056]

[0057] As a preferred solution of this embodiment, fatigue cracks are regarded as the excitation source of asymmetric second harmonics based on the fatigue crack induced asymmetric second harmonic model. The quantitative relationship between the degree of asymmetric second harmonic energy focusing induced by fatigue cracks and the fatigue crack position is established by using the change law of asymmetric second harmonic energy focusing generated by fatigue cracks. In this embodiment, the quantitative relationship between the degree of asymmetric second harmonic energy focusing and the fatigue crack position is obtained by using the normal mode decomposition theory analysis method. The Matlab program of this method is as follows:

[0058]

[0059]

[0060] Finally, this embodiment provides a preferred specific implementation process as follows:

[0061] Step S1: Paste the excitation and receiving ultrasonic guided wave sensors on the circular tube with a spacing d, and the spacing d is equal to one-fourth of the length period of the asymmetric second harmonic energy focusing degree in the circular tube changing with the axial distance: T z / 4. The excitation sensor completely covers the circumference of the round tube, and the receiving sensor partially covers the circumference of the round tube;

[0062] Step S2: exciting an ultrasonic guided wave signal with an angular frequency of ω by an excitation sensor, and collecting M ultrasonic guided wave signals at equal angles around the circumference of the circular tube by a receiving sensor;

[0063] Step S3: Perform wavelet time-frequency transformation based on Morse wavelet basis on the M collected ultrasonic guided wave signals to obtain M ultrasonic guided wave signal time-frequency spectra. Slice these time-frequency spectra at the double angular frequency 2ω to obtain an asymmetric second harmonic signal. According to the distance d between the excitation and receiving sensors and the asymmetric second harmonic group velocity c with a modulus N, Ng The asymmetric second harmonic propagation time t = d / c Ng , and use t to index the second harmonic peak A in the asymmetric second harmonic signal 2f ;

[0064] Step S4: Substituting the M second harmonic peaks into the formula of energy focusing index I to calculate the energy focusing index;

[0065] Step S5: According to the fatigue crack induced asymmetric second harmonic model, the quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of the fatigue crack is established by utilizing the periodic variation law of the asymmetric second harmonic energy focusing degree induced by fatigue crack, and the presence of fatigue cracks in the circular tube and its position are evaluated by the calculated energy focusing degree index.

[0066] The results of its implementation and testing are as follows Figure 1-Figure 4 shown.

[0067] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0068] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0069] The present invention is not limited to the above-mentioned optimal implementation mode. Anyone can derive various other forms of a circular tube fatigue crack detection method based on the change law of asymmetric second harmonic energy focusing under the inspiration of the present invention. All equal changes and modifications made within the scope of the invention application of the present invention should fall within the scope of the present invention.

Claims

1. A method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing, characterized in that: The excitation and receiving sensors are arranged on the circular tube at a spacing of one quarter of the period of variation of the asymmetric second harmonic energy focusing degree with the axial distance; the receiving signals at M circumferential positions are subjected to time-frequency analysis by wavelet time-frequency transform based on Morse wavelet basis to extract the asymmetric second harmonic; the asymmetric second harmonic energy focusing degree at M circumferential positions is calculated by using the energy focusing index I; The quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack position is established based on the fatigue crack induced asymmetric second harmonic model. The calculated asymmetric second harmonic focusing degree is compared with the quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack position to evaluate whether there is fatigue crack in the circular tube and its axial and circumferential positions.

2. The method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing according to claim 1 is characterized in that: The method of performing time-frequency analysis on the received signals at M circumferential positions by wavelet time-frequency transform based on Morse wavelet basis to extract the asymmetric second harmonic is as follows: performing wavelet time-frequency transform based on Morse wavelet basis on the asymmetric waveguide original signal x(t) collected at M circumferential positions of the circular tube Among them, W(a,b) represents the wavelet coefficients, represents the wavelet function based on the Morse wavelet basis; a is the scale parameter, b is the translation parameter; and the asymmetric second harmonic signal is obtained by slicing at the time-frequency spectrum twice the excitation signal frequency; then according to the distance d between the excitation and receiving sensors and the asymmetric second harmonic group velocity c with a modulus N Ng The asymmetric second harmonic propagation time t = d / c Ng , and use t to index the second harmonic peak A in the asymmetric second harmonic signal 2f .

3. The method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing according to claim 1 is characterized in that: The energy focusing index is obtained by extracting the peak value of the asymmetric second harmonic signal to obtain the circumferential distribution of the energy of the asymmetric second harmonic, and then calculating the energy focusing degree of the asymmetric second harmonic.

4. The method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing according to claim 1, characterized in that: The energy focusing index I is used to calculate the asymmetric second harmonic energy focusing degree of M circumferential positions. The energy focusing degree index I formula is: The energy ratio of the two circumferential ranges of the circular tube (270°, 0°) ∪ (0°, 90°) and (90°, 180°) ∪ (180°, 270°) is calculated as the energy focusing index of the asymmetric second harmonic; A 2f i,θ A represents the i-th signal among the M / 2 asymmetric waveguide signals collected within the circumferential range of the circular tube (270°, 0°)∪(0°, 90°), 2f i,θ+π represents the jth signal among the M / 2 asymmetric waveguide signals collected within the circumferential range of the circular tube (90°, 180°)∪(180°, 270°); x represents the M asymmetric waveguide signals collected within all circumferential positions of the circular tube, min(A i ) represents the minimum value among all signals.

5. The method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing according to claim 1, characterized in that: The fatigue crack induced asymmetric second harmonic model specifically utilizes the periodic variation law of the asymmetric second harmonic energy focusing degree induced by fatigue crack to establish a quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of the fatigue crack.

6. A method for detecting fatigue cracks in a circular tube based on asymmetric second harmonic energy focusing variation law according to claim 5, characterized in that: The periodic variation law of the asymmetric second harmonic energy focusing degree is specifically expressed by the periodic formula of the asymmetric second harmonic energy focusing degree varying with the axial distance: Among them, R o ,R i are the inner and outer radii of the tube, ω is the frequency of the asymmetric waveguide, c Np It represents the phase velocity of the ultrasonic guided wave mode in the plate corresponding to the asymmetric guided wave mode with mode number N, and k is a non-negative integer.

7. The method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing according to claim 1, characterized in that: The normal mode decomposition theory is used to obtain the quantitative relationship between the asymmetric second harmonic energy focusing degree and the fatigue crack location.

8. The method for detecting fatigue cracks in a circular tube based on the variation law of asymmetric second harmonic energy focusing according to claim 1 is characterized in that: The specific steps include: First, the excitation and receiving ultrasonic guided wave sensors are pasted on the circular tube with a spacing d, which is equal to one-fourth of the length period of the asymmetric second harmonic energy focusing degree in the circular tube changing with the axial distance: T z / 4; the excitation sensor completely covers the circumference of the circular tube, and the receiving sensor partially covers the circumference of the circular tube; The ultrasonic guided wave signal with an angular frequency of ω is excited by the excitation sensor, and M ultrasonic guided wave signals are collected at equal angles around the circumference of the circular tube by the receiving sensor, where M>3; Then, the M ultrasonic guided wave signals obtained by the acquisition are subjected to wavelet time-frequency transformation based on the Morse wavelet basis to obtain M ultrasonic guided wave signal time-frequency spectra; the time-frequency spectra are sliced ​​at the double angular frequency 2ω to obtain an asymmetric second harmonic signal; according to the distance d between the excitation and receiving sensors and the asymmetric second harmonic group velocity c with a modulus N, Ng The asymmetric second harmonic propagation time t = d / c is calculated from the relationship Ng , and use t to index the second harmonic peak A in the asymmetric second harmonic signal 2f ; Calculate the energy focusing index based on M second harmonic peaks; Finally, according to the fatigue crack-induced asymmetric second harmonic model, the quantitative relationship between the asymmetric second harmonic energy focusing degree and the axial and circumferential positions of the fatigue crack was established by utilizing the periodic variation law of the asymmetric second harmonic energy focusing degree induced by fatigue crack. The calculated energy focusing degree index was used to evaluate whether there was fatigue crack in the circular tube and its position.

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