Single-mode guided wave defect detection method and system for underwater water filling pipeline

Abstract

The invention discloses a single-mode guided wave defect detection method and system for an underwater water filling pipeline. The method comprises the following steps: establishing an SAFE-PML wave equation of guided waves in the underwater water filling pipeline; converting the SAFE-PML wave equation into a guided wave characteristic equation, and constructing an expression of guided wave mode energy; establishing a mapping relation between the guided wave modal amplitude and the axial length of the piezoelectric transducer by using modal extension; solving and extracting excitation characteristics of a guided wave mode through a guided wave characteristic equation; parameters of the piezoelectric transducer are optimized according to guided wave excitation characteristics, guided wave signals are collected, the occurrence time of defect signals in the guided wave signals is obtained, and defect detection is conducted on the whole underwater water filling pipeline through a guided wave reflection method. According to the invention, guided wave mode single excitation and defect detection of the underwater water filling pipeline are realized.

Description

Technical Field

[0001] The present invention relates to ultrasonic guided wave detection, and in particular to a single-mode guided wave defect detection method and system for underwater water-filled pipelines. Background Art

[0002] Pipelines are widely used in many fields, including modern industry and energy transportation. However, because seawater microorganisms and internal chemical media can accelerate the corrosion process of metal pipes, pipes may experience periodic stress changes, generating and expanding various damage and aging defects, leading to underwater pipeline failure and seriously affecting energy transportation efficiency. Structural health monitoring technology based on guided waves is widely used to detect structural defects in underwater pipelines. Guided waves are typically excited by a sensor array composed of piezoelectric transducers, and the receiver collects the corresponding guided wave signals for subsequent analysis and processing. The time domain signal characteristics of guided waves will change due to defects and may manifest as linear characteristics such as signal attenuation and dispersion, with different characteristic information corresponding to different defects.

[0003] However, traditional guided wave defect detection methods lack effective single-mode guided wave excitation and defect signal feature extraction technologies. Complex signal processing and defect feature extraction algorithms are typically required for underwater guided wave time-domain signals. Extracting underwater pipeline defect signal characteristics and obtaining information such as defect propagation time and guided wave signal attenuation are essential. Existing defect feature recognition methods typically rely on complex guided wave time-domain signal processing methods, but are unable to accurately establish a direct mapping relationship between guided wave time-domain signals and defects. Summary of the Invention

[0004] Purpose of the invention: The first purpose of the present invention is to provide a single-mode guided wave defect detection method for underwater water-filled pipes, so as to realize single excitation and defect detection of guided wave modes in underwater water-filled pipes.

[0005] A second object of the present invention is to provide a single-mode guided wave defect detection system for underwater water-filled pipelines.

[0006] Technical Solution: To achieve the above objectives, the present invention provides a single-mode guided wave defect detection method for underwater water-filled pipelines, comprising the following steps:

[0007] S1. Establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes;

[0008] S2. Convert the SAFE-PML wave equation into the guided wave characteristic equation and construct an expression for the guided wave mode energy;

[0009] S3. Using modal expansion to establish a mapping relationship between the guided wave modal amplitude and the axial length of the piezoelectric transducer;

[0010] S4, extracting the excitation characteristics of the guided wave mode by solving the guided wave characteristic equation;

[0011] S5. Optimize the piezoelectric transducer parameters according to the guided wave excitation characteristics, collect the guided wave signal, obtain the appearance time of the defect signal in the guided wave signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline.

[0012] Optionally, in step S1, a mass matrix, a unit stiffness matrix, and a shape function are first established according to the material properties of the pipe and water and the pipe shape. The SAFE-PML model is used to establish a SAFE-PML wave equation for guided waves in an underwater water-filled pipe. The expression of the SAFE-PML wave equation is:

[0013]

[0014] Where M represents the mass matrix of the coupling term between the pipe and water, K1, K2, K3, K4, K5, and K6 represent the unit stiffness matrix of the coupling term between the pipe and water. Both the mass matrix and the unit stiffness matrix can be derived according to the material properties of the pipe and water. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and K2 and K3 are skew-symmetric complex matrices. and Indicates the symmetric form of K2 and K3 obtained by T transformation. K1, K4, K5, and K6 are all symmetric matrices. Symmetric matrices remain unchanged after T transformation. Indicates the displacement U of the pipeline node n and water velocity potential φ n The T transformation vector, K coup represents the coupling term at the water-solid coupling in the wave equation, K coup The expression is:

[0015]

[0016] Where ρ represents the material density, H represents the integral of the coupling term between water and pipe, which only exists at the coupling node between water and pipe. The expression of H is:

[0017] H=2πr s N u (r s ) T nN φ (r s ) T (3)

[0018] where r s is the coordinate of the coupling point between water and pipe, N u (r s ) represents the shape function of the pipe, N φ (r s ) represents the shape function of water.

[0019] Optionally, in step S2, the SAFE-PML wave equation formula (1) is first converted into the guided wave characteristic equation:

[0020] [A-kB]ψ=0 (4)

[0021] [B -1 A-kI]ψ=0 (5)

[0022]

[0023]

[0024]

[0025] Where I represents the unit vector, and after solving the waveguide characteristic equation (5), M eigenvalues ​​k are obtained. i With 2M eigenvectors, where i is 1 to M, each eigenvalue corresponds to a left eigenvector and a right eigenvector, M is the number of modes of the guided wave, and the eigenvalue k i That is the wave number of the guided wave mode finally solved;

[0026] Establish the biorthogonal relationship of the guided wave modes:

[0027]

[0028] where ψ li and ψ ri Represents the eigenvalue k i The corresponding left eigenvector and right eigenvector, subscript i is any number from 1 to M, δ i represents the Kronecker function, b i is the normalization factor, and the superscript T indicates the matrix transpose;

[0029] Substituting formula (7) and formula (8) into the orthogonal relationship formula (9), we get formula (10):

[0030]

[0031] Establish the relationship between the guided wave mode energy and wave number:

[0032] P i =-ωb i / 4k i (11)

[0033] Among them, P i is the energy of guided wave mode i, k i is the wave number of the guided wave mode;

[0034] Substituting formula (11) into formula (10), we can obtain the expression of guided wave mode energy:

[0035]

[0036] Optionally, in step S3, a mapping relationship between the guided wave modal amplitude and the stress tensor is established, and the energy of the guided wave in the underwater water-filled pipe waveguide system is kept balanced, that is:

[0037]

[0038] Where P is the total waveguide energy in the underwater water-filled pipe waveguide system, v1 represents the waveguide velocity in the axial direction of the underwater water-filled pipe waveguide system, v2 represents the waveguide velocity in the cross section of the underwater water-filled pipe waveguide system, T1 represents the stress tensor in the axial direction of the underwater water-filled pipe waveguide system, T2 represents the stress tensor in the cross section of the underwater water-filled pipe waveguide system, Indicates the three directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z The overall vector of the guided wave mode i in the underwater water-filled pipe waveguide system in the axial and cross-sectional solutions are expressed as:

[0039] v1=v i exp(ik i Z)T1=T i exp(ik i Z) (14)

[0040] v2=∑A i (Z)v i (r,θ)T2=∑A i (Z)T i (r,θ) (15)

[0041] Among them A i (Z) is the amplitude of the guided wave mode i, r, θ, and Z represent the distribution parameters of the piezoelectric transducer in the radial, tangential, and axial directions, respectively. The overall vector is split Three different directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z ;

[0042] Rewriting formula (13) yields:

[0043]

[0044] where n r 、n θ and n zrepresents the radial, tangential, and axial propagation directions of the guided wave along the underwater water-filled pipe waveguide system. Formula (16) is integrated over the cross section, and the Gaussian divergence theorem is used to establish the integral formula:

[0045]

[0046] Where T and v are the overall stress tensor and guided wave velocity in the underwater water-filled pipe waveguide system. Using the generalized orthogonal relationship, the ordinary differential equation (17) is established to obtain the amplitude of the guided wave mode i:

[0047]

[0048] The mapping relationship between the cross section, axial vector load and stress tensor T in the underwater water-filled pipe is established:

[0049]

[0050] Where p1(r, θ) and p2(Z) represent the cross-section and axial vector load functions of the piezoelectric transducer, respectively. Formula (19) is combined with formula (18) to establish the mapping relationship between the guided wave modal amplitude and the piezoelectric transducer parameters:

[0051]

[0052] To excite the axisymmetric guided wave mode suitable for guided wave defect detection in underwater water-filled pipelines, the piezoelectric transducer is arranged at an angle of 360° along the circumference of the pipeline, and the radial position of the piezoelectric transducer is on the outer surface of the pipeline. Formula (20) is rewritten to establish the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer:

[0053]

[0054] Among them, P i is the energy of guided wave mode i, which can be obtained by formula (12).

[0055] Optionally, in step S4, the SAFE-PML model is used to extract the excitation characteristics of the guided wave mode by solving the guided wave characteristic equation;

[0056] Set the values ​​of the circumferential order n and frequency f of the guided wave, the axial length Z of the piezoelectric transducer is 2L, and its range is 2-18mm, with a step of 2mm. Take 9 piezoelectric transducers with different axial lengths, L=1~9, and use formula (21) to calculate the guided wave modal amplitude combination A m :

[0057]

[0058] The subscript r indicates that the vibration direction of the piezoelectric transducer is radial, θ indicates that the vibration direction of the piezoelectric transducer is tangential, z indicates that the vibration direction of the piezoelectric transducer is axial, and i indicates the guided wave mode i;

[0059] Calculate the excitation amplitude ratio combination A of each mode in the same guided wave mode combination p :

[0060]

[0061]

[0062] e represents the vibration direction of the piezoelectric transducer, e = r, θ, z; A eiL represents the amplitude of the guided wave mode i excited by the vibration direction e and the axial length L of the piezoelectric transducer;

[0063] Select the excitation combination with the largest excitation amplitude of the mode to extract the excitation characteristics of the guided wave mode:

[0064] [(r,θ,z),Z]~max(A p )(25).

[0065] Optionally, in step S5, the piezoelectric transducer parameters are optimized according to the guided wave excitation characteristics, a multi-transmitter and single-receiver piezoelectric transducer arrangement is used to collect a single modal guided wave signal, extract the guided wave time domain signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline according to the appearance time of the defect reflection wave of the guided wave time domain signal:

[0066] A i =max(A p )(26)

[0067]

[0068] where v i represents the velocity of the i-th guided wave mode with the largest excitation amplitude, t0 represents the time when the receiving piezoelectric transducer receives the first wave packet signal, t represents the time when the receiving piezoelectric transducer receives the defect reflection wave signal, and x represents the distance between the pipeline defect and the receiving point.

[0069] Based on the same inventive concept, the present invention provides a single-mode guided wave defect detection system for underwater water-filled pipelines, comprising:

[0070] Wave equation building module, used to establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes;

[0071] Mode energy construction module, used to convert the SAFE-PML wave equation into the guided wave characteristic equation and construct an expression for the guided wave mode energy;

[0072] A mapping relationship building module is used to establish a mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer using mode expansion;

[0073] An excitation feature extraction module is used to extract the excitation features of the guided wave mode by solving the guided wave characteristic equation;

[0074] The defect detection module is used to optimize the piezoelectric transducer parameters according to the guided wave excitation characteristics, collect the guided wave signal, obtain the occurrence time of the defect signal in the guided wave signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline.

[0075] Optionally, in the wave equation construction module, a mass matrix, a unit stiffness matrix, and a shape function are first established according to the material properties of the pipe and water and the pipe shape. The SAFE-PML model is used to establish a SAFE-PML wave equation for guided waves in an underwater water-filled pipe. The expression of the SAFE-PML wave equation is:

[0076]

[0077] Where M represents the mass matrix of the coupling term between the pipe and water, K1, K2, K3, K4, K5, and K6 represent the unit stiffness matrix of the coupling term between the pipe and water. Both the mass matrix and the unit stiffness matrix can be derived according to the material properties of the pipe and water. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and K2 and K3 are skew-symmetric complex matrices. and Indicates the symmetric form of K2 and K3 obtained by T transformation. K1, K4, K5, and K6 are all symmetric matrices. Symmetric matrices remain unchanged after T transformation. Indicates the displacement U of the pipeline node n and water velocity potential φ n The T transformation vector, K coup represents the coupling term at the water-solid coupling in the wave equation, K coup The expression is:

[0078]

[0079] Where ρ represents the material density, H represents the integral of the coupling term between water and pipe, which only exists at the coupling node between water and pipe. The expression of H is:

[0080] H=2πr s N u (r s ) T nN φ (r s ) T (3)

[0081] where r s is the coordinate of the coupling point between water and pipe, N u (r s ) represents the shape function of the pipe, N φ (r s ) represents the shape function of water.

[0082] Optionally, the mode energy building module first converts the SAFE-PML wave equation formula (1) into the guided wave characteristic equation:

[0083] [A-kB]ψ=0 (4)

[0084] [B -1 A-kI]ψ=0 (5)

[0085]

[0086]

[0087]

[0088] Where I represents the unit vector, and after solving the waveguide characteristic equation (5), M eigenvalues ​​k are obtained. i With 2M eigenvectors, where i is 1 to M, each eigenvalue corresponds to a left eigenvector and a right eigenvector, M is the number of modes of the guided wave, and the eigenvalue k i That is the wave number of the guided wave mode finally solved;

[0089] Establish the biorthogonal relationship of the guided wave modes:

[0090]

[0091] where ψ li and ψ ri Represents the eigenvalue k i The corresponding left eigenvector and right eigenvector, subscript i is any number from 1 to M, δ i represents the Kronecker function, b i is the normalization factor, and the superscript T indicates the matrix transpose;

[0092] Substituting formula (7) and formula (8) into the orthogonal relationship formula (9), we get formula (10):

[0093]

[0094] Establish the relationship between the guided wave mode energy and wave number:

[0095] P i =-ωb i / 4ki (11)

[0096] Among them, P i is the energy of guided wave mode i, k i is the wave number of the guided wave mode;

[0097] Substituting formula (11) into formula (10), we can obtain the expression of guided wave mode energy:

[0098]

[0099] Optionally, a mapping relationship between the guided wave modal amplitude and the stress tensor is established in the mapping relationship building module, and the energy of the guided wave in the underwater water-filled pipe waveguide system is kept balanced, that is:

[0100]

[0101] Where P is the total waveguide energy in the underwater water-filled pipe waveguide system, v1 represents the waveguide velocity in the axial direction of the underwater water-filled pipe waveguide system, v2 represents the waveguide velocity in the cross section of the underwater water-filled pipe waveguide system, T1 represents the stress tensor in the axial direction of the underwater water-filled pipe waveguide system, T2 represents the stress tensor in the cross section of the underwater water-filled pipe waveguide system, Indicates the three directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z The overall vector of the guided wave mode i in the underwater water-filled pipe waveguide system in the axial and cross-sectional solutions are expressed as:

[0102] v1=v i exp(ik i Z)T1=T i exp(ik i Z) (14)

[0103] v2=∑A i (Z)v i (r,θ)T2=∑A i (Z)T i (r,θ)(15)

[0104] Among them A i (Z) is the amplitude of the guided wave mode i, r, θ, and Z represent the distribution parameters of the piezoelectric transducer in the radial, tangential, and axial directions, respectively. The overall vector is split Three different directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z ;

[0105] Rewriting formula (13) yields:

[0106]

[0107] where n r 、n θ and n z represents the radial, tangential, and axial propagation directions of the guided wave along the underwater water-filled pipe waveguide system. Formula (16) is integrated over the cross section, and the Gaussian divergence theorem is used to establish the integral formula:

[0108]

[0109] Where T and v are the overall stress tensor and guided wave velocity in the underwater water-filled pipe waveguide system. Using the generalized orthogonal relationship, the ordinary differential equation (17) is established to obtain the amplitude of the guided wave mode i:

[0110]

[0111] The mapping relationship between the cross section, axial vector load and stress tensor T in the underwater water-filled pipe is established:

[0112]

[0113] Where p1(r, θ) and p2(Z) represent the cross-section and axial vector load functions of the piezoelectric transducer, respectively. Formula (19) is combined with formula (18) to establish the mapping relationship between the guided wave modal amplitude and the piezoelectric transducer parameters:

[0114]

[0115] To excite the axisymmetric guided wave mode suitable for guided wave defect detection in underwater water-filled pipelines, the piezoelectric transducer is arranged at an angle of 360° along the circumference of the pipeline, and the radial position of the piezoelectric transducer is on the outer surface of the pipeline. Formula (20) is rewritten to establish the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer:

[0116]

[0117] Among them, P i is the energy of guided wave mode i, which can be obtained by formula (12).

[0118] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0119] (1) The present invention integrates the guided wave numerical model SAFE, modal expansion, and guided wave reflection method to achieve single guided wave mode excitation and defect detection in underwater water-filled pipelines;

[0120] (2) The present invention establishes the wave equation of the underwater water-filled pipe waveguide system through the SAFE mode, and uses numerical methods to solve it, thereby reducing the computational complexity; the guided wave mode expansion method establishes the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer, and optimizes the axial length design of the piezoelectric transducer when a single mode of the underwater water-filled pipe is excited; SAFE converts the wave equation of the underwater water-filled pipe waveguide system into a characteristic equation, effectively combines it with the mode expansion, and better adapts to the multi-phase medium environment of the underwater water-filled pipe guided wave detection, comprehensively obtains the relationship between the axial length design of the piezoelectric transducer in the underwater water-filled pipe and the excitation amplitude of all guided wave modes, selects the optimal detection mode, designs the piezoelectric transducer for a specific guided wave mode for single excitation, extracts the time domain characteristics of the guided wave signal, and uses the guided wave reflection method to realize the underwater water-filled pipe defect detection;

[0121] (3) The present invention realizes underwater water-filled pipe defect detection without the need for guided wave time domain signal processing. Through the guided wave reflection method, the collected guided wave time domain signal is directly used for defect detection, which expands the engineering application of guided waves in complex environments and improves the application scope of ultrasonic guided wave non-destructive testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 is a flow chart of the present invention;

[0123] Figure 2 Schematic diagram of the SAFE-PML model of the underwater water-filled pipeline in the present invention;

[0124] Figure 3 Schematic diagram of the design of guided wave mode excitation amplitude and piezoelectric transducer parameters in the present invention;

[0125] Figure 4 Schematic diagram of the relationship between the waveguide mode and the excitation amplitude in the present invention;

[0126] Figure 5 Schematic diagram of the relationship between the axial length of the piezoelectric transducer and the excitation amplitude ratio in the present invention;

[0127] Figure 6 is a schematic diagram of a defect signal in the present invention;

[0128] Figure 7 This is a flow chart of the selection and excitation detection of guided wave modes for underwater water-filled pipelines in the present invention;

[0129] Figure 8 Schematic diagram of the modules of the system in the present invention. DETAILED DESCRIPTION

[0130] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0131] Example 1: Figure 1As shown, the present invention discloses a single-mode guided wave defect detection method for underwater water-filled pipelines, comprising the following steps:

[0132] S1. Establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes;

[0133] like Figure 2 As shown, in step S1, the mass matrix, unit stiffness matrix and shape function are first established according to the material properties of the pipe and water and the pipe shape. The pipe is a copper pipe. The SAFE-PML model is used to establish the SAFE-PML wave equation of the guided wave in the underwater water-filled pipe. The expression of the SAFE-PML wave equation is:

[0134]

[0135] Where M represents the mass matrix of the coupling term between the pipe and water, K1, K2, K3, K4, K5, and K6 represent the unit stiffness matrix of the coupling term between the pipe and water. Both the mass matrix and the unit stiffness matrix can be derived according to the material properties of the pipe and water. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and K2 and K3 are skew-symmetric complex matrices. and Indicates the symmetric form of K2 and K3 obtained by T transformation. K1, K4, K5, and K6 are all symmetric matrices. Symmetric matrices remain unchanged after T transformation. Indicates the displacement U of the pipeline node n and water velocity potential φ n The T transformation vector, K coup represents the coupling term at the water-solid coupling in the wave equation, K coup The expression is:

[0136]

[0137] Where ρ represents the material density, H represents the integral of the coupling term between water and pipe, which only exists at the coupling node between water and pipe. The expression of H is:

[0138] H=2πr s N u (r s ) T nN φ (r s ) T (3)

[0139] where r s is the coordinate of the coupling point between water and pipe, N u (r s ) represents the shape function of the pipe, N φ (r s) represents the shape function of water;

[0140] S2. Convert the SAFE-PML wave equation into the guided wave characteristic equation and construct an expression for the guided wave mode energy;

[0141] In step S2, the SAFE-PML wave equation (1) is first converted into the guided wave characteristic equation:

[0142] [A-kB]ψ=0 (4)

[0143] [B -1 A-kI]ψ=0 (5)

[0144]

[0145]

[0146]

[0147] Where I represents the unit vector, and after solving the waveguide characteristic equation (5), M eigenvalues ​​k are obtained. i With 2M eigenvectors, where i is 1 to M, each eigenvalue corresponds to a left eigenvector and a right eigenvector, M is the number of modes of the guided wave, and the eigenvalue k i That is the wave number of the guided wave mode finally solved;

[0148] Establish the biorthogonal relationship of the guided wave modes:

[0149]

[0150] where ψ li and ψ ri Represents the eigenvalue k i The corresponding left eigenvector and right eigenvector, subscript i is any number from 1 to M, δ i represents the Kronecker function, b i is the normalization factor, and the superscript T indicates the matrix transpose;

[0151] Substituting formula (7) and formula (8) into the orthogonal relationship formula (9), we get formula (10):

[0152]

[0153] Establish the relationship between the guided wave mode energy and wave number:

[0154] P i =-ωb i / 4k i (11)

[0155] Among them, P iis the energy of guided wave mode i, k i is the wave number of the guided wave mode;

[0156] Substituting formula (11) into formula (10), we can obtain the expression of guided wave mode energy:

[0157]

[0158] S3. Using modal expansion to establish a mapping relationship between the guided wave modal amplitude and the axial length of the piezoelectric transducer;

[0159] In step S3, a mapping relationship between the guided wave modal amplitude and the stress tensor is established, and the energy of the guided wave in the underwater water-filled pipe waveguide system is kept balanced, that is:

[0160]

[0161] Where P is the total waveguide energy in the underwater water-filled pipe waveguide system, v1 represents the waveguide velocity in the axial direction of the underwater water-filled pipe waveguide system, v2 represents the waveguide velocity in the cross section of the underwater water-filled pipe waveguide system, T1 represents the stress tensor in the axial direction of the underwater water-filled pipe waveguide system, T2 represents the stress tensor in the cross section of the underwater water-filled pipe waveguide system, Indicates the three directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z The overall vector of the guided wave mode i in the underwater water-filled pipe waveguide system in the axial and cross-sectional solutions are expressed as:

[0162] v1=v i exp(ik i Z)T1=T i exp(ik i Z) (14)

[0163] v2=∑A i (Z)v i (r,θ)T2=∑A i (Z)T i (r,θ)(15)

[0164] Among them A i (Z) is the amplitude of the guided wave mode i, r, θ, and Z represent the distribution parameters of the piezoelectric transducer in the radial, tangential, and axial directions, respectively. The overall vector is split Three different directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z ;

[0165] Rewriting formula (13) yields:

[0166]

[0167] where n r 、n θ and n z represents the radial, tangential, and axial propagation directions of the guided wave along the underwater water-filled pipe waveguide system. Formula (16) is integrated over the cross section, and the Gaussian divergence theorem is used to establish the integral formula:

[0168]

[0169] Where T and v are the overall stress tensor and guided wave velocity in the underwater water-filled pipe waveguide system. Using the generalized orthogonal relationship, the ordinary differential equation (17) is established to obtain the amplitude of the guided wave mode i:

[0170]

[0171] The mapping relationship between the cross section, axial vector load and stress tensor T in the underwater water-filled pipe is established:

[0172]

[0173] Where p1(r, θ) and p2(Z) represent the cross-section and axial vector load functions of the piezoelectric transducer, respectively. Formula (19) is combined with formula (18) to establish the mapping relationship between the guided wave modal amplitude and the piezoelectric transducer parameters:

[0174]

[0175] like Figure 3 、 Figure 4 and Figure 5 As shown in the figure, the axisymmetric guided wave mode suitable for guided wave defect detection in underwater water-filled pipelines is excited. The arrangement angle of the piezoelectric transducer along the circumference of the pipeline is set to 360°, and the radial position of the piezoelectric transducer is on the outer surface of the pipeline. Rewriting formula (20), the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer is established:

[0176]

[0177] Among them, P i is the energy of guided wave mode i, which can be obtained by formula (12);

[0178] S4, extracting the excitation characteristics of the guided wave mode by solving the guided wave characteristic equation;

[0179] In step S4, the SAFE-PML model is used to extract the excitation characteristics of the guided wave mode by solving the guided wave characteristic equation;

[0180] Set the values ​​of the circumferential order n and frequency f of the waveguide, which can be set to: n = 0, f = 350kHz;

[0181] The axial length of the piezoelectric transducer Z = 2L, which varies from 2 to 18 mm, with a step of 2 mm. Nine piezoelectric transducers with different axial lengths, L = 1 to 9, are taken. The guided wave modal amplitude combination A is calculated using formula (21): m :

[0182]

[0183] The subscript r indicates that the vibration direction of the piezoelectric transducer is radial, θ indicates that the vibration direction of the piezoelectric transducer is tangential, z indicates that the vibration direction of the piezoelectric transducer is axial, and i indicates the guided wave mode i;

[0184] Calculate the excitation amplitude ratio combination A of each mode in the same guided wave mode combination p :

[0185]

[0186]

[0187] e represents the vibration direction of the piezoelectric transducer, e = r, θ, z; a eiL represents the amplitude of the guided wave mode i excited by the vibration direction e and the axial length L of the piezoelectric transducer;

[0188] Select the excitation combination with the largest excitation amplitude of the mode to extract the excitation characteristics of the guided wave mode:

[0189] [(r,θ,z),Z]~max(A p )(25)

[0190] The excitation parameters selected for the optimal excitation guided wave mode are: the vibration direction of the piezoelectric transducer is θ, the axial length of the piezoelectric transducer is 4 mm, the center frequency is set to 350 kHz, and the excited guided wave mode is the 18th mode.

[0191] S5: Optimize the piezoelectric transducer parameters based on the guided wave excitation characteristics, collect the guided wave signal, obtain the occurrence time of the defect signal in the guided wave signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline;

[0192] like Figure 6 and Figure 7 As shown, in step S5, the piezoelectric transducer parameters are optimized according to the guided wave excitation characteristics, a multi-transmitter and single-receiver piezoelectric transducer arrangement is used to collect a single-mode guided wave signal, extract the guided wave time domain signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline based on the appearance time of the defect reflection wave of the guided wave time domain signal:

[0193] A i =max(A p )(26)

[0194]

[0195] where v i represents the velocity of the i-th guided wave mode with the largest excitation amplitude, t0 represents the time when the receiving piezoelectric transducer receives the first wave packet signal, t represents the time when the receiving piezoelectric transducer receives the defect reflection wave signal, and x represents the distance between the pipeline defect and the receiving point.

[0196] Specifically, based on the characteristics of guided wave excitation, the piezoelectric transducer vibration direction is designed to be θ. A multi-transmitter, single-receiver piezoelectric transducer arrangement is used, with the excitation piezoelectric transducers arranged 360° along the circumference of the pipeline. The axial length of all piezoelectric transducers is set to 4mm, and the center frequency is set to 350kHz. The receiving piezoelectric transducer is arranged 30mm away from the receiving transducer. The guided wave signal time domain is collected, and the guided wave time domain signal characteristics are extracted. The entire underwater water-filled pipeline is inspected for defects based on the number of wave packets in the guided wave time domain signal. Defects are located by the appearance time of the first reflected wave of the guided wave time domain signal:

[0197]

[0198] v 18 represents the group velocity of the 18th guided wave mode with the largest excitation amplitude, t0 represents the time when the receiving piezoelectric transducer receives the first wave packet signal, t represents the time when the receiving piezoelectric transducer receives the second wave packet signal, and x represents the distance between the pipeline defect and the excitation point, which is used to obtain the defect position in the pipeline.

[0199] The present invention solves the wave number solution of the axisymmetric guided wave mode propagating in an underwater water-filled pipe of order n=0 at a frequency of 350kHz, calculates the guided wave mode amplitude of the piezoelectric transducer when vibrating along r, θ, and z when the piezoelectric transducer is at 2mm, 4mm, 6mm, 8mm, 10mm, 12mm, 14mm, 16mm, and 18mm, and the ratio of the excitation amplitude of each mode, selects the optimal detection mode, and extracts the specific modal excitation parameters; uses the solved frequency and the extracted excitation parameters to design the piezoelectric transducer modal excitation, and successfully excites a single excitation specific guided wave mode in the underwater water-filled pipe.

[0200] The defect locations of underwater water-filled pipes obtained by the present invention are directly calculated from the guided wave time-domain signal. That is, the present invention performs single-mode guided wave defect detection for underwater water-filled pipes based on guided wave modal expansion without processing or analyzing the guided wave time-domain signal. Therefore, the present invention employs a specific formula, establishes the wave equation for guided waves via the SAFE method, and, by combining guided wave modal expansion, establishes the relationship between the guided wave modal force and the modal wavenumber. An orthogonal analytical expression for the guided wave modal force and the modal wavenumber is introduced to obtain an amplitude expression for the specific guided wave mode containing the stress tensor. The mapping relationship between the vector load function of the piezoelectric transducer and the stress tensor T is established. The relationship equation between the stress tensor and the guided wave mode amplitude is converted into the relationship equation between the guided wave mode amplitude and the piezoelectric transducer parameters. The axisymmetric guided wave mode is designed to be excited. The circumferential range of the piezoelectric transducer is 360°. The mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer is established. The guided wave mode amplitude is calculated by solving the eigenvalue and then extracting the piezoelectric transducer parameters for the guided wave mode excitation. According to the excitation parameters of the guided wave mode, a piezoelectric transducer array is designed to excite the guided wave mode, collect the guided wave time domain signal, and accurately and directly extract the pipeline defect information.

[0201] The guided wave mode expansion of the present invention is more efficient and has lower computational complexity in calculating guided wave mode excitation in underwater water-filled pipes. The present invention establishes a wave equation from the underwater water-filled pipe through the SAFE model, while capturing the guided wave mode information in the water, reducing the influence of complex modes in the water on the single-mode guided wave excitation; the guided wave mode expansion introduces the relationship equation between the guided wave mode amplitude and the stress tensor, directly establishes a mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer, reduces excessively complex interference in the computational domain, and improves computational efficiency; uses a piezoelectric transducer array, designs a piezoelectric transducer according to the extracted excitation parameters for excitation, and directly detects defects in underwater water-filled pipes through the modal group velocity. The present invention realizes underwater water-filled pipe defect detection without the need for guided wave time-domain signal analysis and processing, expands the engineering application of guided waves in complex environments, and improves the scope of application of ultrasonic guided wave non-destructive testing.

[0202] Example 2

[0203] like Figure 8 As shown, the present invention discloses a single-mode guided wave defect detection system for underwater water-filled pipelines, comprising:

[0204] Wave equation building module, used to establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes;

[0205] In the wave equation construction module, the mass matrix, element stiffness matrix, and shape function are first established based on the material properties of the pipe and water and the pipe shape. The SAFE-PML model is used to establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes. The expression of the SAFE-PML wave equation is:

[0206]

[0207] Where M represents the mass matrix of the coupling term between the pipe and water, K1, K2, K3, K4, K5, and K6 represent the unit stiffness matrix of the coupling term between the pipe and water. Both the mass matrix and the unit stiffness matrix can be derived according to the material properties of the pipe and water. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and K2 and K3 are skew-symmetric complex matrices. and Indicates the symmetric form of K2 and K3 obtained by T transformation. K1, K4, K5, and K6 are all symmetric matrices. Symmetric matrices remain unchanged after T transformation. Indicates the displacement U of the pipeline node n and water velocity potential φ n The T transformation vector, K coup represents the coupling term at the water-solid coupling in the wave equation, K coup The expression is:

[0208]

[0209] Where ρ represents the material density, H represents the integral of the coupling term between water and pipe, which only exists at the coupling node between water and pipe. The expression of H is:

[0210] H=2πr s N u (r s ) T nN φ (r s ) T (3)

[0211] where r s is the coordinate of the coupling point between water and pipe, N u (r s ) represents the shape function of the pipe, N φ (r s ) represents the shape function of water.

[0212] Mode energy construction module, used to convert the SAFE-PML wave equation into the guided wave characteristic equation and construct an expression for the guided wave mode energy;

[0213] In the mode energy building module, the SAFE-PML wave equation (1) is first converted into the guided wave characteristic equation:

[0214] [A-kB]ψ=0 (4)

[0215] [B -1 A-kI]ψ=0 (5)

[0216]

[0217]

[0218]

[0219] Where I represents the unit vector, and after solving the waveguide characteristic equation (5), M eigenvalues ​​k are obtained. i With 2M eigenvectors, where i is 1 to M, each eigenvalue corresponds to a left eigenvector and a right eigenvector, M is the number of modes of the guided wave, and the eigenvalue k i That is the wave number of the guided wave mode finally solved;

[0220] Establish the biorthogonal relationship of the guided wave modes:

[0221]

[0222] where ψ li and ψ ri Represents the eigenvalue k i The corresponding left eigenvector and right eigenvector, subscript i is any number from 1 to M, δ i represents the Kronecker function, b i is the normalization factor, and the superscript T indicates the matrix transpose;

[0223] Substituting formula (7) and formula (8) into the orthogonal relationship formula (9), we get formula (10):

[0224]

[0225] Establish the relationship between the guided wave mode energy and wave number:

[0226] P i =-ωb i / 4k i (11)

[0227] Among them, P i is the energy of guided wave mode i, k i is the wave number of the guided wave mode;

[0228] Substituting formula (11) into formula (10), we can obtain the expression of guided wave mode energy:

[0229]

[0230] A mapping relationship building module is used to establish a mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer using mode expansion;

[0231] The mapping relationship between the guided wave modal amplitude and the stress tensor is established in the mapping relationship construction module. The energy of the guided wave in the underwater water-filled pipe waveguide system is kept balanced, that is:

[0232]

[0233] Where P is the total waveguide energy in the underwater water-filled pipe waveguide system, v1 represents the waveguide velocity in the axial direction of the underwater water-filled pipe waveguide system, v2 represents the waveguide velocity in the cross section of the underwater water-filled pipe waveguide system, T1 represents the stress tensor in the axial direction of the underwater water-filled pipe waveguide system, T2 represents the stress tensor in the cross section of the underwater water-filled pipe waveguide system, Indicates the three directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z The overall vector of the guided wave mode i in the underwater water-filled pipe waveguide system in the axial and cross-sectional solutions are expressed as:

[0234] v1=v i exp(ik i Z)T1=T i exp(ik i Z) (14)

[0235] v2=∑A i (Z)v i (r,θ)T2=∑A i (Z)T i (r,θ)(15)

[0236] Among them A i (Z) is the amplitude of the guided wave mode i, r, θ, and Z represent the distribution parameters of the piezoelectric transducer in the radial, tangential, and axial directions, respectively. The overall vector is split Three different directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z ;

[0237] Rewriting formula (13) yields:

[0238]

[0239] where n r 、n θ and nz represents the radial, tangential, and axial propagation directions of the guided wave along the underwater water-filled pipe waveguide system. Formula (16) is integrated over the cross section, and the Gaussian divergence theorem is used to establish the integral formula:

[0240]

[0241] Where T and v are the overall stress tensor and guided wave velocity in the underwater water-filled pipe waveguide system. Using the generalized orthogonal relationship, the ordinary differential equation (17) is established to obtain the amplitude of the guided wave mode i:

[0242]

[0243] The mapping relationship between the cross section, axial vector load and stress tensor T in the underwater water-filled pipe is established:

[0244]

[0245] Where p1(r, θ) and p2(Z) represent the cross-section and axial vector load functions of the piezoelectric transducer, respectively. Formula (19) is combined with formula (18) to establish the mapping relationship between the guided wave modal amplitude and the piezoelectric transducer parameters:

[0246]

[0247] To excite the axisymmetric guided wave mode suitable for guided wave defect detection in underwater water-filled pipelines, the piezoelectric transducer is arranged at an angle of 360° along the circumference of the pipeline, and the radial position of the piezoelectric transducer is on the outer surface of the pipeline. Formula (20) is rewritten to establish the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer:

[0248]

[0249] Among them, P i is the energy of guided wave mode i, which can be obtained by formula (12).

[0250] An excitation feature extraction module is used to extract the excitation features of the guided wave mode by solving the guided wave characteristic equation;

[0251] The SAFE-PML model is used in the excitation feature extraction module to extract the excitation features of the guided wave mode by solving the guided wave characteristic equation;

[0252] Set the values ​​of the circumferential order n and frequency f of the guided wave, the axial length Z of the piezoelectric transducer is 2L, and its range is 2-18mm, with a step of 2mm. Take 9 piezoelectric transducers with different axial lengths, L=1~9, and use formula (21) to calculate the guided wave modal amplitude combination A m :

[0253]

[0254] The subscript r indicates that the vibration direction of the piezoelectric transducer is radial, θ indicates that the vibration direction of the piezoelectric transducer is tangential, z indicates that the vibration direction of the piezoelectric transducer is axial, and i indicates the guided wave mode i;

[0255] Calculate the excitation amplitude ratio combination A of each mode in the same guided wave mode combination p :

[0256]

[0257]

[0258] e represents the vibration direction of the piezoelectric transducer, e = r, θ, z; A eiL represents the amplitude of the guided wave mode i excited by the vibration direction e and the axial length L of the piezoelectric transducer;

[0259] Select the excitation combination with the largest excitation amplitude of the mode to extract the excitation characteristics of the guided wave mode:

[0260] [(r,θ,z),Z]~max(A p )(25).

[0261] The defect detection module is used to optimize the piezoelectric transducer parameters according to the guided wave excitation characteristics, collect the guided wave signal, obtain the appearance time of the defect signal in the guided wave signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline.

[0262] In the defect detection module, the piezoelectric transducer parameters are optimized based on the guided wave excitation characteristics. A multi-transmitter, single-receiver piezoelectric transducer arrangement is used to collect a single-mode guided wave signal, extract the guided wave time domain signal, and use the guided wave reflection method to detect defects in the entire underwater water-filled pipeline based on the appearance time of the defect reflection wave in the guided wave time domain signal:

[0263] A i =max(A p )(26)

[0264]

[0265] where v i represents the velocity of the i-th guided wave mode with the largest excitation amplitude, t0 represents the time when the receiving piezoelectric transducer receives the first wave packet signal, t represents the time when the receiving piezoelectric transducer receives the defect reflection wave signal, and x represents the distance between the pipeline defect and the receiving point.

Claims

1. A single-mode guided wave defect detection method for underwater water-filled pipelines, characterized in that: The steps include: S1. Establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes; S2. Convert the SAFE-PML wave equation into the guided wave characteristic equation and construct an expression for the guided wave mode energy; S3. Using modal expansion to establish a mapping relationship between the guided wave modal amplitude and the axial length of the piezoelectric transducer; S4, extracting the excitation characteristics of the guided wave mode by solving the guided wave characteristic equation; S5. Optimize the piezoelectric transducer parameters according to the guided wave excitation characteristics, collect the guided wave signal, obtain the appearance time of the defect signal in the guided wave signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline.

2. The single-mode guided wave defect detection method according to claim 1, characterized in that: In step S1, a mass matrix, a unit stiffness matrix, and a shape function are first established according to the material properties of the pipe and water and the pipe shape. The SAFE-PML model is used to establish the SAFE-PML wave equation of the guided wave in the underwater water-filled pipe. The expression of the SAFE-PML wave equation is: Where M represents the mass matrix of the coupling term between the pipe and water, K1, K2, K3, K4, K5, and K6 represent the unit stiffness matrix of the coupling term between the pipe and water. Both the mass matrix and the unit stiffness matrix can be derived according to the material properties of the pipe and water. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and K2 and K3 are skew-symmetric complex matrices. and Indicates the symmetric form of K2 and K3 obtained by T transformation. K1, K4, K5, and K6 are all symmetric matrices. Symmetric matrices remain unchanged after T transformation. Indicates the displacement U of the pipeline node n and water velocity potential φ n The T transformation vector, K coup represents the coupling term at the water-solid coupling in the wave equation, K coup The expression is: Where ρ represents the material density, H represents the integral of the coupling term between water and pipe, which only exists at the coupling node between water and pipe. The expression of H is: H=2πr s N u (r s ) T nN φ (r s ) T (3) where r s is the coordinate of the coupling point between water and pipe, N u (r s ) represents the shape function of the pipe, N φ (r s ) represents the shape function of water.

3. The single-mode guided wave defect detection method according to claim 2, characterized in that: In step S2, the SAFE-PML wave equation (1) is first converted into the guided wave characteristic equation: [A-kB]ψ=0 (4) [B - A-kI]ψ=0 (5) Where I represents the unit vector, and after solving the waveguide characteristic equation (5), M eigenvalues ​​k are obtained. i With 2M eigenvectors, where i is 1 to M, each eigenvalue corresponds to a left eigenvector and a right eigenvector, M is the number of modes of the guided wave, and the eigenvalue k i That is the wave number of the guided wave mode finally solved; Establish the biorthogonal relationship of the guided wave modes: where ψ li and ψ ri Represents the eigenvalue k i The corresponding left eigenvector and right eigenvector, subscript i is any number from 1 to M, δ i represents the Kronecker function, b i is the normalization factor, and the superscript T indicates the matrix transpose; Substituting formula (7) and formula (8) into the orthogonal relationship formula (9), we get formula (10): Establish the relationship between the guided wave mode energy and wave number: P i =-ωb i / 4k i (11) Among them, P i is the energy of guided wave mode i, k i is the wave number of the guided wave mode; Substituting formula (11) into formula (10), we can obtain the expression of guided wave mode energy:

4. The single-mode guided wave defect detection method according to claim 3, characterized in that: In step S3, a mapping relationship between the guided wave modal amplitude and the stress tensor is established, and the energy of the guided wave in the underwater water-filled pipe waveguide system is kept balanced, that is: Where P is the total waveguide energy in the underwater water-filled pipe waveguide system, v1 represents the waveguide velocity in the axial direction of the underwater water-filled pipe waveguide system, v2 represents the waveguide velocity in the cross section of the underwater water-filled pipe waveguide system, T1 represents the stress tensor in the axial direction of the underwater water-filled pipe waveguide system, T2 represents the stress tensor in the cross section of the underwater water-filled pipe waveguide system, Indicates the three directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z The overall vector of the guided wave mode i in the underwater water-filled pipe waveguide system in the axial and cross-sectional solutions are expressed as: v1=v i exp(i) i Z)T1=T i exp(i) i Z) (14) v2=∑A i (Z)v i (r,θ)T2=∑A i (Z)T i (r,θ) (15) Among them A i (Z) is the amplitude of the guided wave mode i, r, θ, and Z represent the distribution parameters of the piezoelectric transducer in the radial, tangential, and axial directions, respectively. The overall vector is split Three different directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z ; Rewriting formula (13) yields: where n r 、n θ and n z represents the radial, tangential, and axial propagation directions of the guided wave along the underwater water-filled pipe waveguide system. Formula (16) is integrated over the cross section, and the Gaussian divergence theorem is used to establish the integral formula: Where T and v are the overall stress tensor and guided wave velocity in the underwater water-filled pipe waveguide system. Using the generalized orthogonal relationship, the ordinary differential equation (17) is established to obtain the amplitude of the guided wave mode i: The mapping relationship between the cross section, axial vector load and stress tensor T in the underwater water-filled pipe is established: Where p1(r, θ) and p2(Z) represent the cross-section and axial vector load functions of the piezoelectric transducer, respectively. Formula (19) is combined with formula (18) to establish the mapping relationship between the guided wave modal amplitude and the piezoelectric transducer parameters: To excite the axisymmetric guided wave mode suitable for guided wave defect detection in underwater water-filled pipelines, the piezoelectric transducer is arranged at an angle of 360° along the circumference of the pipeline, and the radial position of the piezoelectric transducer is on the outer surface of the pipeline. Formula (20) is rewritten to establish the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer: Among them, P i is the energy of guided wave mode i, which can be obtained by formula (12).

5. The single-mode guided wave defect detection method according to claim 4, characterized in that: In step S4, the SAFE-PML model is used to extract the excitation characteristics of the guided wave mode by solving the guided wave characteristic equation; Set the values ​​of the circumferential order n and frequency f of the guided wave, the axial length Z of the piezoelectric transducer is 2L, and its range is 2-18mm, with a step of 2mm. Take 9 piezoelectric transducers with different axial lengths, L=1~9, and use formula (21) to calculate the guided wave modal amplitude combination A m : The subscript r indicates that the vibration direction of the piezoelectric transducer is radial, θ indicates that the vibration direction of the piezoelectric transducer is tangential, z indicates that the vibration direction of the piezoelectric transducer is axial, and i indicates the guided wave mode i; Calculate the excitation amplitude ratio combination A of each mode in the same guided wave mode combination p : e represents the vibration direction of the piezoelectric transducer, e = r, θ, z; A eiL represents the amplitude of the guided wave mode i excited by the vibration direction e and the axial length L of the piezoelectric transducer; Select the excitation combination with the largest excitation amplitude of the mode to extract the excitation characteristics of the guided wave mode: [(r,θ,z),Z]~max(A p )(25)。 6. The single-mode guided wave defect detection method according to claim 5, characterized in that: In step S5, the piezoelectric transducer parameters are optimized according to the guided wave excitation characteristics, a multi-transmitter and single-receiver piezoelectric transducer arrangement is used to collect a single-mode guided wave signal, extract the guided wave time domain signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline based on the appearance time of the defect reflection wave of the guided wave time domain signal: A i =max(A p )(26) where v i represents the velocity of the i-th guided wave mode with the largest excitation amplitude, t0 represents the time when the receiving piezoelectric transducer receives the first wave packet signal, t represents the time when the receiving piezoelectric transducer receives the defect reflection wave signal, and x represents the distance between the pipeline defect and the receiving point.

7. A single-mode guided wave defect detection system for underwater water-filled pipelines, characterized in that: include: Wave equation building module, used to establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes; Mode energy construction module, used to convert the SAFE-PML wave equation into the guided wave characteristic equation and construct an expression for the guided wave mode energy; A mapping relationship building module is used to establish a mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer using mode expansion; An excitation feature extraction module is used to extract the excitation features of the guided wave mode by solving the guided wave characteristic equation; The defect detection module is used to optimize the piezoelectric transducer parameters according to the guided wave excitation characteristics, collect the guided wave signal, obtain the occurrence time of the defect signal in the guided wave signal, and use the guided wave reflection method to perform defect detection on the entire underwater water-filled pipeline.

8. The single-mode guided wave defect detection system according to claim 7, characterized in that: In the wave equation construction module, the mass matrix, element stiffness matrix, and shape function are first established according to the material properties of the pipe and water and the pipe shape. The SAFE-PML model is used to establish the SAFE-PML wave equation for guided waves in underwater water-filled pipes. The expression of the SAFE-PML wave equation is: Where M represents the mass matrix of the coupling term between the pipe and water, K1, K2, K3, K4, K5, and K6 represent the unit stiffness matrix of the coupling term between the pipe and water. Both the mass matrix and the unit stiffness matrix can be derived according to the material properties of the pipe and water. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and K2 and K3 are skew-symmetric complex matrices. and Indicates the symmetric form of K2 and K3 obtained by T transformation. K1, K4, K5, and K6 are all symmetric matrices. Symmetric matrices remain unchanged after T transformation. Indicates the displacement U of the pipeline node n and water velocity potential φ n The T transformation vector, K coup represents the coupling term at the water-solid coupling in the wave equation, K coup The expression is: Where ρ represents the material density, H represents the integral of the coupling term between water and pipe, which only exists at the coupling node between water and pipe. The expression of H is: H=2πr s N u (r s ) T nN φ (r s ) T (3) where r s is the coordinate of the coupling point between water and pipe, N u (r s ) represents the shape function of the pipe, N φ (r s ) represents the shape function of water.

9. The single-mode guided wave defect detection system according to claim 8, characterized in that: In the mode energy building block, the SAFE-PML wave equation (1) is first converted into the guided wave characteristic equation: [A-kB]ψ=0 (4)[B -1 A-kI]ψ=0 (5) Where I represents the unit vector, and after solving the waveguide characteristic equation (5), M eigenvalues ​​k are obtained. i With 2M eigenvectors, where i is 1 to M, each eigenvalue corresponds to a left eigenvector and a right eigenvector, M is the number of modes of the guided wave, and the eigenvalue k i That is the wave number of the guided wave mode finally solved; Establish the biorthogonal relationship of the guided wave modes: where ψ li and ψ ri Represents the eigenvalue k i The corresponding left eigenvector and right eigenvector, subscript i is any number from 1 to M, δ i represents the Kronecker function, b i is the normalization factor, and the superscript T indicates the matrix transpose; Substituting formula (7) and formula (8) into the orthogonal relationship formula (9), we get formula (10): Establish the relationship between the guided wave mode energy and wave number: P i =-ωb i / 4k i (11) Among them, P i is the energy of guided wave mode i, k i is the wave number of the guided wave mode; Substituting formula (11) into formula (10), we can obtain the expression of guided wave mode energy:

10. The single-mode guided wave defect detection system according to claim 9, characterized in that: The mapping relationship building module establishes a mapping relationship between the guided wave modal amplitude and the stress tensor, and the energy of the guided wave in the underwater water-filled pipe waveguide system is kept balanced, that is: Where P is the total waveguide energy in the underwater water-filled pipe waveguide system, v1 represents the waveguide velocity in the axial direction of the underwater water-filled pipe waveguide system, v2 represents the waveguide velocity in the cross section of the underwater water-filled pipe waveguide system, T1 represents the stress tensor in the axial direction of the underwater water-filled pipe waveguide system, T2 represents the stress tensor in the cross section of the underwater water-filled pipe waveguide system, Indicates the three directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z The overall vector of the guided wave mode i in the underwater water-filled pipe waveguide system in the axial and cross-sectional solutions are expressed as: v1=v i exp(i) i Z)T1=T i exp(i) i Z) (14) v2=∑A i (Z)v i (r,θ)T2=∑A i (Z)T i (r,θ) (15) Among them A i (Z) is the amplitude of the guided wave mode i, r, θ, and Z represent the distribution parameters of the piezoelectric transducer in the radial, tangential, and axial directions, respectively. The overall vector is split Three different directions n in the underwater water-filled pipe waveguide system r ,n θ ,n z ; Rewriting formula (13) yields: where n r 、n θ and n z represents the radial, tangential, and axial propagation directions of the guided wave along the underwater water-filled pipe waveguide system. Formula (16) is integrated over the cross section, and the Gaussian divergence theorem is used to establish the integral formula: Where T and v are the overall stress tensor and guided wave velocity in the underwater water-filled pipe waveguide system. Using the generalized orthogonal relationship, the ordinary differential equation (17) is established to obtain the amplitude of the guided wave mode i: The mapping relationship between the cross section, axial vector load and stress tensor T in the underwater water-filled pipe is established: Where p1(r, θ) and p2(Z) represent the cross-section and axial vector load functions of the piezoelectric transducer, respectively. Formula (19) is combined with formula (18) to establish the mapping relationship between the guided wave modal amplitude and the piezoelectric transducer parameters: To excite the axisymmetric guided wave mode suitable for guided wave defect detection in underwater water-filled pipelines, the piezoelectric transducer is arranged at an angle of 360° along the circumference of the pipeline, and the radial position of the piezoelectric transducer is on the outer surface of the pipeline. Formula (20) is rewritten to establish the mapping relationship between the guided wave mode amplitude and the axial length of the piezoelectric transducer: Among them, P i is the energy of guided wave mode i, which can be obtained by formula (12).

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