Method and system for detecting and positioning guided wave damage of underwater water filling pipeline based on SAFE-PML model

Abstract

The invention discloses a guided wave damage detection and positioning method and system for an underwater water filling pipeline based on an SAFE-PML model. The method comprises the following steps: establishing a guided wave SAFE wave equation of a water filling pipeline waveguide system in a limited fluid domain; the guided wave SAFE wave equation of the water filling pipeline in the limited fluid domain is expanded to the water filling pipeline waveguide system in the infinite fluid domain through a PML coordinate stretching function, and a complete guided wave SAFE wave equation of the underwater water filling pipeline waveguide system is obtained; the guided wave mode speed and the wave structure existing in the complete underwater water filling pipeline are extracted; the independent guided wave mode is excited for the wave structure of the guided wave mode, and damage detection and positioning are carried out on the pipeline through the time characteristics of the reflected wave of the guided wave time domain signal. The damage detection of the underwater water filling pipeline is realized by analyzing the propagation characteristics of the underwater water filling pipeline.

Description

Technical Field

[0001] The present invention relates to an ultrasonic guided wave damage detection method, and in particular to a guided wave damage detection and positioning method and system for underwater water-filled pipelines based on a SAFE-PML model. Background Art

[0002] Pipelines are used in many fields. Due to the influence of seawater and internal chemical media, various damage and aging defects may develop and expand, leading to pipeline failure and seriously affecting transportation efficiency. Therefore, damage detection technology based on ultrasonic guided waves is often used for non-destructive inspection and assessment of underwater water-filled pipelines. The speed of guided waves in underwater environments is affected by temperature and pressure, and they typically have multiple complex modes with different sound speeds. When encountering damage, multiple reflected waves are generated, and the receiver collects the corresponding signals for subsequent analysis and processing. However, traditional guided wave damage detection methods lack effective methods for analyzing guided wave propagation characteristics. They usually require signal processing methods to compare the detection signal with the baseline signal (the signal from the intact state) to extract the damage signal and obtain information such as damage energy attenuation. This damage indicator extraction method usually requires complex signal analysis and processing, and cannot accurately and directly construct a linear mapping relationship between the guided wave signal and the damage location in the time domain signal of the guided wave. Summary of the Invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a guided wave damage detection and positioning method for underwater water-filled pipes based on the SAFE-PML model, which realizes damage detection of underwater water-filled pipes by analyzing the propagation characteristics of underwater water-filled pipes.

[0004] Technical Solution: To achieve the above objectives, the present invention provides a guided wave damage detection and location method for underwater water-filled pipelines based on the SAFE-PML model, comprising the following steps:

[0005] S1. Establish the guided wave SAFE wave equation for the water-filled pipe waveguide system in a finite fluid domain;

[0006] S2: The guided wave SAFE wave equation of the water-filled pipe in the finite fluid domain is extended to the water-filled pipe waveguide system in the infinite fluid domain through the PML coordinate stretching function, and the guided wave SAFE wave equation of the complete underwater water-filled pipe waveguide system is obtained;

[0007] S3: Extract the guided wave mode velocity and wave structure existing in the complete underwater water-filled pipeline;

[0008] S4: The wave structure of the guided wave mode excites a separate guided wave mode, and the damage of the pipeline is detected and located through the time characteristics of the reflected wave of the guided wave time domain signal.

[0009] Optionally, step S1 specifically includes the following steps:

[0010] For the cross section of the water-filled pipe waveguide system in a finite fluid domain, the nodes are discretized from the internal fluid to the cutoff of the fluid domain outside the pipe:

[0011] r=[r1,r2,r3,…r s ,…r f ,…r m ](1)

[0012] Where r represents the node coordinate set, r 1～ r s-1 represents the node coordinates of the fluid inside the pipe, r s represents the node coordinates where the pipe is coupled with the internal fluid, r s+1～ r f-1 represents the node coordinates of the pipeline, r f represents the node coordinates where the pipeline is coupled with the external fluid domain, r f+1～ r m Represents the node coordinates of the fluid in the external fluid domain, which is discretized using m nodes;

[0013] The nodal wave equation of guided waves in the pipeline is established in the cylindrical coordinate system and expressed as:

[0014] (K1+inK2+ikK3+knK4+n 2 K5+k 2 K6-ω 2 M)U n =0 (2)

[0015] Where M represents the node mass matrix of the pipeline, K1, K2, K3, K4, K5, and K6 represent the node stiffness matrix of the pipeline. The node mass matrix and node stiffness matrix are derived according to the material properties, geometry, and node coordinates of the pipeline. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and U n represents the wave structure of the mode in the pipe,

[0016] Establish the nodal wave equation of guided waves in the fluid in the cylindrical coordinate system:

[0017]

[0018] The superscript f represents the node stiffness matrix and node mass matrix in the fluid, which are derived based on the material properties of the fluid and the node coordinates. n represents the velocity potential of water;

[0019] The waveguide system composed of water-filled pipes in a finite fluid domain is a fluid-solid coupling system. The fluid-solid coupling integral H is introduced in the process of equation assembly. s With r f Existence:

[0020] H=2πrN u (r) T nN φ (r) T (4)

[0021] N u (r) represents the shape function of the pipe, N φ (r) represents the shape function of water, and r in the fluid-structure coupling integral is r s or r f , establish the coupling node stiffness matrix K at the fluid-solid coupling node in the wave equation coup :

[0022]

[0023] ρ1 represents the density of the pipe material, and ρ2 represents the density of the fluid;

[0024] Assemble the wave equations of the guided wave at the pipeline node, fluid node and fluid-solid coupling node, that is, assemble formulas (2), (3) and (5), and establish the guided wave SAFE wave equation of the water-filled pipeline waveguide system in the finite fluid domain:

[0025]

[0026] Among them, K2 and K3 are skew-symmetric complex matrices, and It represents the symmetric form of K2 and K3 obtained by T transformation. The remaining matrices are all symmetric matrices and remain unchanged after T transformation.

[0027] Optionally, step S2 specifically includes the following steps:

[0028] By using the PML coordinate stretching function, the PML range is set from the outer surface of the pipe to the end of the fluid domain outside the pipe, and the new coordinates after stretching are obtained.

[0029]

[0030] where r 1＝ [r f ,…r m ], represents the node coordinate set of the fluid domain outside the pipe, Represents the new coordinate set after stretching, r i represents the node coordinates of the fluid domain outside the pipe, γ(ri ) is the stretching function that defines the PML, and its expression is:

[0031]

[0032] a and b are parameters that quantify the damping characteristics of the PML and are set according to the material parameters of the surrounding medium. The PML defined using the stretching function absorbs leaky waves through a finite thickness layer, converting the continuum of radiation modes into discrete PML modes, simulating an infinite surrounding medium.

[0033] Modify the nodal wave equations only for the fluid domain outside the pipe:

[0034]

[0035] where f(r i ) represents the node coordinate r i The node wave equation at Indicates the node coordinate r after stretching i The node wave equation at ;

[0036] Assemble node r1 to node The nodal wave equation of the pipeline is used to form the global guided wave SAFE wave equation. The nodal wave equation of the fluid domain outside the pipeline in formula (6) is modified through formulas (7), (8), (9) and (10) to establish the guided wave SAFE wave equation of the complete waveguide system based on the underwater water-filled pipeline:

[0037]

[0038] in Represents the wave structure U containing the guided wave in the pipe n and water velocity potential φ n T transformation vector, subscripts of mass matrix and stiffness matrix (·) Represents the matrix in the guided wave SAFE wave equation.

[0039] Optionally, step S3 specifically includes the following steps:

[0040] The characteristic equation of underwater water-filled pipeline based on SAFE-PML is established, and the problem of solving the guided wave SAFE wave equation formula (11) is converted into a linear eigenvalue solution problem:

[0041] [A-kB]ψ=0 (12)

[0042] [B - 1A-kI]ψ=0 (13)

[0043]

[0044] Where I represents the unit vector, and the characteristic equation formula (13) is solved to obtain N eigenvalues ​​k j With 2N eigenvectors, N is the number of guided wave modes, and the eigenvalue k j is the wave number of the guided wave mode, and each eigenvalue corresponds to a left eigenvector ψ lj and a right eigenvector ψ rj ; Based on the symmetry of the global stiffness matrix and the mass matrix, the left eigenvector and the right eigenvector are the same and are both written as eigenvector ψ j , the elements in the eigenvector are node displacements or velocity potentials; in the fluid nodes 1 to s-1 and f+1 to m, each node corresponds to one degree of freedom, and in the pipe nodes s to f, each node corresponds to the radial, tangential, and axial degrees of freedom r, θ, z of the underwater water-filled pipe waveguide system. Finally, the eigenvector ψ is solved. j The length of is twice the number of degrees of freedom, 2m+4f-4s+4; where the eigenvector ψ j The vectors in the range of (m+2f-2s+3) to (2m+4f-4s+4) include the velocity potential of the guided wave mode j in the fluid domain and the wave structure in the pipeline. The eigenvector ψ j The vectors in the range of (m+2f-s+2) to (m+5f-4s+4) represent the wave structure of the guided wave mode j in the pipeline; the wave number k j Calculate the j-mode velocity of the guided wave mode:

[0045]

[0046] Where dω and dk j is the angular frequency ω and the wave number k of the guided wave mode j j The differential operator of .

[0047] Optionally, step S4 specifically includes the following steps:

[0048] Using a piezoelectric transducer to excite an array, a separate guided wave mode is excited based on the wave structure of the guided wave mode. There are N modes of guided waves in underwater water-filled pipes:

[0049] v g =[v1,v2,v3,…,v j ,…,v N ](18)

[0050] where v g is the mode velocity of the guided wave mode, U n is the wave structure of the guided wave:

[0051]

[0052] u is the nodal displacement of the guided wave mode, the subscripts r, θ, and z represent the degrees of freedom of each node in three different directions, representing the radial, tangential, and axial displacements of the guided wave mode, respectively, n represents the number of pipeline nodes, n = f - s + 1, and j represents the j-mode of the guided wave;

[0053] The piezoelectric transducer excitation array is designed according to the wave structure of the guided wave mode j. The array consists of three transducers:

[0054]

[0055] p1, p2, and p3 represent the vibration amplitudes of the three piezoelectric transducers at a center frequency of ω / 2π. The subscripts 1, 2, and 3 indicate that the transducers vibrate in radial, tangential, and axial directions, respectively. A piezoelectric transducer array is used to excite guided wave mode j in an underwater water-filled pipe. When the guided wave propagates through a pipe damage, a reflected wave is generated. The occurrence time of the damage reflected wave in the guided wave time domain signal is extracted by the piezoelectric transducer's self-transmission and self-reception method. The damage is then located based on the mode velocity of guided wave mode j:

[0056]

[0057] t represents the time when the guided wave damage reflection signal appears, v j represents the mode velocity of the guided wave mode j, X represents the distance between the pipeline damage and the piezoelectric transducer array, and the damage location is obtained.

[0058] Based on the same inventive concept, the present invention provides a guided wave damage detection and positioning system for underwater water-filled pipelines based on the SAFE-PML model, comprising:

[0059] The wave equation building module is used to establish the guided wave SAFE wave equation for the water-filled pipe waveguide system in a finite fluid domain;

[0060] The wave equation extension module is used to extend the guided wave SAFE wave equation of a water-filled pipe in a finite fluid domain to a water-filled pipe waveguide system in an infinite fluid domain through the PML coordinate stretching function, thereby obtaining the guided wave SAFE wave equation of a complete underwater water-filled pipe waveguide system;

[0061] The wave structure extraction module is used to extract the guided wave mode velocity and wave structure existing in the complete underwater water-filled pipeline;

[0062] The damage detection and positioning module is used to excite a separate guided wave mode based on the wave structure of the guided wave mode, and detect and locate pipeline damage through the time characteristics of the reflected wave of the guided wave time domain signal.

[0063] Optionally, in the wave equation construction module, a node discretization is performed on the cross section of the water-filled pipe waveguide system in the finite fluid domain, from the internal fluid to the cutoff of the fluid domain outside the pipe:

[0064] r=[r1,r2,r3,…r s ,…r f ,…r m ](1)

[0065] Where r represents the node coordinate set, r 1～ r s-1 represents the node coordinates of the fluid inside the pipe, r s represents the node coordinates where the pipe is coupled with the internal fluid, r s+1～ r f-1 represents the node coordinates of the pipeline, r f represents the node coordinates where the pipeline is coupled with the external fluid domain, r f+1～ r m Represents the node coordinates of the fluid in the external fluid domain, which is discretized using m nodes;

[0066] The nodal wave equation of guided waves in the pipeline is established in the cylindrical coordinate system and expressed as:

[0067] (K1+inK2+ikK3+knK4+n 2 K5+k 2 K6-ω 2 M)U n =0 (2)

[0068] Where M represents the node mass matrix of the pipeline, K1, K2, K3, K4, K5, and K6 represent the node stiffness matrix of the pipeline. The node mass matrix and node stiffness matrix are derived according to the material properties, geometry, and node coordinates of the pipeline. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and U n represents the wave structure of the mode in the pipe,

[0069] Establish the nodal wave equation of guided waves in the fluid in the cylindrical coordinate system:

[0070]

[0071] The superscript f represents the node stiffness matrix and node mass matrix in the fluid, which are derived based on the material properties of the fluid and the node coordinates. n represents the velocity potential of water;

[0072] The waveguide system composed of water-filled pipes in a finite fluid domain is a fluid-solid coupling system. The fluid-solid coupling integral H is introduced in the process of equation assembly. s With r f Existence:

[0073] H=2πrN u (r) T nN φ (r) T (4)

[0074] N u (r) represents the shape function of the pipe, N φ (r) represents the shape function of water, and r in the fluid-structure coupling integral is r s or r f , establish the coupling node stiffness matrix K at the fluid-solid coupling node in the wave equation coup :

[0075]

[0076] ρ1 represents the density of the pipe material, and ρ2 represents the density of the fluid;

[0077] Assemble the wave equations of the guided wave at the pipeline node, fluid node and fluid-solid coupling node, that is, assemble formulas (2), (3) and (5), and establish the guided wave SAFE wave equation of the water-filled pipeline waveguide system in the finite fluid domain:

[0078]

[0079] Among them, K2 and K3 are skew-symmetric complex matrices, and It represents the symmetric form of K2 and K3 obtained by T transformation. The remaining matrices are all symmetric matrices and remain unchanged after T transformation.

[0080] Optionally, the wave equation expansion module uses the PML coordinate stretching function, and the PML range is set from the outer surface of the pipe to the end of the fluid domain outside the pipe to obtain the stretched new coordinates.

[0081]

[0082] where r 1＝ [r f ,…r m ], represents the node coordinate set of the fluid domain outside the pipe, Represents the new coordinate set after stretching, r i represents the node coordinates of the fluid domain outside the pipe, γ(r i ) is the stretching function that defines the PML, and its expression is:

[0083]

[0084] a and b are parameters that quantify the damping characteristics of the PML and are set according to the material parameters of the surrounding medium. The PML defined using the stretching function absorbs leaky waves through a finite thickness layer, converting the continuum of radiation modes into discrete PML modes, simulating an infinite surrounding medium.

[0085] Modify the nodal wave equations only for the fluid domain outside the pipe:

[0086]

[0087] where f(r i ) represents the node coordinate r i The node wave equation at Indicates the node coordinate r after stretching i The node wave equation at ;

[0088] Assemble node r1 to node The nodal wave equation of the pipeline is used to form the global guided wave SAFE wave equation. The nodal wave equation of the fluid domain outside the pipeline in formula (6) is modified through formulas (7), (8), (9) and (10) to establish the guided wave SAFE wave equation of the complete waveguide system based on the underwater water-filled pipeline:

[0089]

[0090] in Represents the wave structure U containing the guided wave in the pipe n and water velocity potential φ n T transformation vector, subscripts of mass matrix and stiffness matrix (·) Represents the matrix in the guided wave SAFE wave equation.

[0091] Optionally, the wave structure extraction module establishes a characteristic equation of the underwater water-filled pipeline based on SAFE-PML, and converts the problem of solving the guided wave SAFE wave equation formula (11) into a linear eigenvalue solution problem:

[0092] [A-kB]ψ=0 (12)

[0093] [B -1 A-kI]ψ=0 (13)

[0094]

[0095] Where I represents the unit vector, and the characteristic equation formula (13) is solved to obtain N eigenvalues ​​k j With 2N eigenvectors, N is the number of guided wave modes, and the eigenvalue k j is the wave number of the guided wave mode, and each eigenvalue corresponds to a left eigenvector ψ lj and a right eigenvector ψrj ; Based on the symmetry of the global stiffness matrix and the mass matrix, the left eigenvector and the right eigenvector are the same and are both written as eigenvector ψ j , the elements in the eigenvector are node displacements or velocity potentials; in the fluid nodes 1 to s-1 and f+1 to m, each node corresponds to one degree of freedom, and in the pipe nodes s to f, each node corresponds to the radial, tangential, and axial degrees of freedom r, θ, z of the underwater water-filled pipe waveguide system. Finally, the eigenvector ψ is solved. j The length of is twice the number of degrees of freedom, 2m+4f-4s+4; where the eigenvector ψ j The vectors in the range of (m+2f-2s+3) to (2m+4f-4s+4) include the velocity potential of the guided wave mode j in the fluid domain and the wave structure in the pipeline. The eigenvector ψ j The vectors in the range of (m+2f-s+2) to (m+5f-4s+4) represent the wave structure of the guided wave mode j in the pipeline; the wave number k j Calculate the j-mode velocity of the guided wave mode:

[0096]

[0097] Where dω and dk j is the angular frequency ω and the wave number k of the guided wave mode j j The differential operator of .

[0098] Optionally, the damage detection and positioning module uses a piezoelectric transducer excitation array to excite a separate guided wave mode for the wave structure of the guided wave mode. There are N modes of guided waves in underwater water-filled pipes:

[0099] v g =[v1,v2,v3,…,v j ,…,v N ](18)

[0100] where v g is the mode velocity of the guided wave mode, U n is the wave structure of the guided wave:

[0101]

[0102] u is the nodal displacement of the guided wave mode, the subscripts r, θ, and z represent the degrees of freedom of each node in three different directions, representing the radial, tangential, and axial displacements of the guided wave mode, respectively, n represents the number of pipeline nodes, n = f - s + 1, and j represents the j-mode of the guided wave;

[0103] The piezoelectric transducer excitation array is designed according to the wave structure of the guided wave mode j. The array consists of three transducers:

[0104]

[0105] p1, p2, and p3 represent the vibration amplitudes of the three piezoelectric transducers at a center frequency of ω / 2π. The subscripts 1, 2, and 3 indicate that the transducers vibrate in radial, tangential, and axial directions, respectively. A piezoelectric transducer array is used to excite guided wave mode j in an underwater water-filled pipe. When the guided wave propagates through a pipe damage, a reflected wave is generated. The occurrence time of the damage reflected wave in the guided wave time domain signal is extracted by the piezoelectric transducer's self-transmission and self-reception method. The damage is then located based on the mode velocity of guided wave mode j:

[0106]

[0107] t represents the time when the guided wave damage reflection signal appears, v j represents the mode velocity of the guided wave mode j, X represents the distance between the pipeline damage and the piezoelectric transducer array, and the damage location is obtained.

[0108] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention integrates the guided wave numerical analysis model SAFE and the perfectly matched layer PML to realize the guided wave mode calculation of the underwater water-filled pipeline; the present invention establishes the wave equation of the guided wave through the SAFE method, and the calculation complexity is lower; PML converts the infinite surrounding medium into a finite layer to establish the wave equation of the complete waveguide system, and optimizes the unboundedness problem of the open waveguide system; the SAFE of the present invention converts the wave equation into a characteristic equation, and converts the guided wave mode calculation into eigenvalue solution, and extracts the group velocity and mode wave structure of the guided wave mode from the solved eigenvalues ​​and eigenvectors, which are effectively combined with PML to comprehensively obtain the guided wave mode velocity and wave structure in the complete underwater water-filled pipeline, design a piezoelectric transducer array for guided wave mode excitation according to the guided wave mode wave structure, extract the time domain characteristics of the guided wave signal, accurately and directly extract the pipeline damage information, and realize high-precision detection and positioning of underwater water-filled pipeline damage. The present invention realizes underwater water-filled pipeline damage detection without the need for guided wave time domain signal processing and without baseline signals. It directly uses the collected guided wave time domain signals to locate the damage, 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

[0109] Figure 1 is a flow chart of the present invention;

[0110] Figure 2 Schematic diagram of the SAFE model of the underwater water-filled pipeline in the present invention;

[0111] Figure 3 Schematic diagram of the SAFE-PML model of the underwater water-filled pipeline in the present invention;

[0112] Figure 4 Schematic diagram of the guided wave mode velocity in the present invention;

[0113] Figure 5 Schematic diagram of the waveguide mode structure of the present invention;

[0114] Figure 6 Schematic diagram of the lossless waveguide time domain signal in the present invention;

[0115] Figure 7 Schematic diagram of a lossy waveguide time domain signal in the present invention;

[0116] Figure 8 This is a flow chart of the guided wave mode excitation detection of underwater water-filled pipelines in the present invention;

[0117] Figure 9 Schematic diagram of the modules of the system in the present invention. DETAILED DESCRIPTION

[0118] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0119] like Figure 1 As shown, the present invention discloses a guided wave damage detection and location method for underwater water-filled pipelines based on the SAFE-PML model, comprising the following steps:

[0120] S1: Establish the guided wave SAFE wave equation for a water-filled pipe in a finite fluid domain;

[0121] like Figure 2 As shown in the figure, the cross section of the water-filled pipe waveguide system in the finite fluid domain is discretized from the internal fluid to the cutoff of the fluid domain outside the pipe:

[0122] r=[r1,r2,r3,…r s ,…r f ,…r m ](1)

[0123] Where r represents the node coordinate set, r 1～ r s-1 represents the node coordinates of the fluid inside the pipe, r s represents the node coordinates where the pipe is coupled with the internal fluid, r s+1～ r f-1 represents the node coordinates of the pipeline, r f represents the node coordinates where the pipeline is coupled with the external fluid domain, r f+1～ r m Represents the node coordinates of the fluid in the external fluid domain, which is discretized using m nodes;

[0124] The nodal wave equation of guided waves in the pipeline is established in the cylindrical coordinate system and expressed as:

[0125] (K1+inK2+ikK3+knK4+n 2 K5+k 2 K6-ω 2 M)U n =0 (2)

[0126] Where M represents the node mass matrix of the pipeline, the pipeline is a copper pipe, K1, K2, K3, K4, K5, K6 represent the node stiffness matrix of the pipeline, the node mass matrix and the node stiffness matrix are derived according to the material properties, geometry and node coordinates of the pipeline, ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, U n represents the wave structure of the mode in the pipe, Set the number of nodes in the pipeline to 6 and the number of degrees of freedom to 18;

[0127] Establish the nodal wave equation of guided waves in the fluid in the cylindrical coordinate system:

[0128]

[0129] The superscript f represents the node stiffness matrix and node mass matrix in the fluid, which are derived based on the material properties of the fluid and the node coordinates. n Represents the velocity potential of water; set the number of nodes in the water to 10. A single node in the water contains only one degree of freedom, and the number of degrees of freedom of water is 10;

[0130] The waveguide system composed of water-filled pipes in a finite fluid domain is a fluid-solid coupling system. The fluid-solid coupling integral H is introduced in the process of equation assembly. s With r f Existence:

[0131] H=2πrN u (r) T nN φ (r) T (4)

[0132] N u (r) represents the shape function of the pipe, N φ (r) represents the shape function of water, and r in the fluid-structure coupling integral is r s or r f , establish the coupling node stiffness matrix K at the fluid-solid coupling node in the wave equation coup :

[0133]

[0134] ρ1 represents the density of the pipe material, and ρ2 represents the density of the fluid;

[0135] Assemble the wave equations of the guided wave at the pipeline node, fluid node and fluid-solid coupling node, that is, assemble formulas (2), (3) and (5), and establish the guided wave SAFE wave equation of the water-filled pipeline waveguide system in the finite fluid domain:

[0136]

[0137] Among them, K2 and K3 are skew-symmetric complex matrices, and Indicates the symmetric form of K2 and K3 obtained by T transformation. The remaining matrices are symmetric matrices and remain unchanged after T transformation.

[0138] S2: The guided wave SAFE wave equation of the water-filled pipe in the finite fluid domain is extended to the water-filled pipe waveguide system in the infinite fluid domain through the PML coordinate stretching function, and the guided wave SAFE wave equation of the complete underwater water-filled pipe waveguide system is obtained;

[0139] like Figure 3 As shown, by using the PML coordinate stretching function, the PML range is set from the outer surface of the pipe to the end of the fluid domain outside the pipe, and the new coordinates after stretching are obtained.

[0140]

[0141] where r 1＝ [r f ,…r m ], represents the node coordinate set of the fluid domain outside the pipe, Represents the new coordinate set after stretching, r i represents the node coordinates of the fluid domain outside the pipe, γ(r i ) is the stretching function that defines the PML, and its expression is:

[0142]

[0143] a and b are parameters that quantify the PML damping characteristics. They are set according to the material parameters of the surrounding medium to keep the PML characteristics consistent with those of the surrounding medium and perfectly match the impedance of the surrounding material. A setting of a = 6 and b = 7 is acceptable. The PML defined by the stretching function absorbs leaky waves through a finite thickness layer, converting the continuum of the radiation pattern into discrete PML modes, simulating an infinite surrounding medium.

[0144] Modify the nodal wave equations only for the fluid domain outside the pipe:

[0145]

[0146] where f(r i ) represents the node coordinate r i The node wave equation at Indicates the node coordinate r after stretching i The node wave equation at ;

[0147] Assemble node r1 to node The nodal wave equation of the pipeline is used to form the global guided wave SAFE wave equation. The nodal wave equation of the fluid domain outside the pipeline in formula (6) is modified through formulas (7), (8), (9) and (10) to establish the guided wave SAFE wave equation of the complete waveguide system based on the underwater water-filled pipeline:

[0148]

[0149] in Represents the wave structure U containing the guided wave in the pipe n and water velocity potential φ n T transformation vector, subscripts of mass matrix and stiffness matrix (·) Represents the matrix in the guided wave SAFE wave equation; Set the number of nodes in the PML layer to 4, a single node in the water contains only one degree of freedom, and the number of degrees of freedom of water is 4;

[0150] S3: Extract the guided wave mode velocity and wave structure existing in the complete underwater water-filled pipeline;

[0151] like Figure 4 and Figure 5 As shown in the figure, the characteristic equation of underwater water-filled pipeline based on SAFE-PML is established, and the problem of solving the guided wave SAFE wave equation formula (11) is converted into a linear eigenvalue solution problem:

[0152] [A-kB]ψ=0 (12)

[0153] [B -1 A-kI]ψ=0 (13)

[0154]

[0155] Where I represents the unit vector, the frequency f is set in steps of 200 Hz, and 2000 frequency points are taken from 1 to 400 kHz to solve the characteristic equation formula (13) to obtain N eigenvalues ​​k j With 2N eigenvectors, specifically N = 18, that is, to obtain 18 solutions of waveguide modes, N is the number of waveguide modes, and the eigenvalue k j is the wave number of the guided wave mode, and each eigenvalue corresponds to a left eigenvector ψ lj and a right eigenvector ψ rj ; Based on the symmetry of the global stiffness matrix and the mass matrix, the left eigenvector and the right eigenvector are the same and are both written as eigenvector ψ j, the elements in the eigenvector are node displacements or velocity potentials; in the fluid nodes 1 to s-1 and f+1 to m, each node corresponds to one degree of freedom, and in the pipe nodes s to f, each node corresponds to the radial, tangential, and axial degrees of freedom r, θ, z of the underwater water-filled pipe waveguide system. Finally, the eigenvector ψ is solved. j The length of is twice the number of degrees of freedom, 2m+4f-4s+4; where the eigenvector ψ j The vectors in the range of (m+2f-2s+3) to (2m+4f-4s+4) include the velocity potential of the guided wave mode j in the fluid domain and the wave structure in the pipeline. The eigenvector ψ j The vectors in the range of (m+2f-s+2) to (m+5f-4s+4) represent the wave structure of the guided wave mode j in the pipeline; the wave number k j Calculate the j-mode velocity of the guided wave mode:

[0156]

[0157] Where dω and dk j is the angular frequency ω and the wave number k of the guided wave mode j j The differential operator of

[0158] S4: As Figure 6 、 Figure 7 and Figure 8 As shown, the wave structure of the guided wave mode excites a separate guided wave mode, and the time characteristics of the reflected wave of the guided wave time domain signal are used to analyze 18 modes of the pipeline:

[0159] v g =[v1,v2,v3,…,v j ,…,v N ]=[v1,v2,v3,…,v j ,…,v 18 ](18)

[0160] where v g is the mode velocity of the guided wave mode, U n is the wave structure of the guided wave:

[0161]

[0162]

[0163] u is the nodal displacement of the guided wave mode, the subscripts r, θ, and z represent the degrees of freedom of each node in three different directions, representing the radial, tangential, and axial displacements of the guided wave mode, respectively, n represents the number of pipeline nodes, n = 6, n = f-s + 1, and j represents the j-mode of the guided wave;

[0164] The piezoelectric transducer excitation array is designed according to the wave structure of the guided wave mode j. The array consists of three transducers:

[0165]

[0166] p1, p2, and p3 represent the vibration amplitudes of the three piezoelectric transducers at a center frequency of ω / 2π = 360 kHz. The subscripts 1, 2, and 3 indicate that the transducers vibrate in radial, tangential, and axial directions, respectively. A piezoelectric transducer array is used to excite guided wave mode j in an underwater water-filled pipe. When the guided wave propagates through a pipe damage, a reflected wave is generated. The occurrence time of the damage reflected wave in the guided wave time domain signal is extracted by the piezoelectric transducer's self-transmission and self-reception method. The damage is then located based on the mode velocity of guided wave mode j:

[0167]

[0168] t represents the time when the guided wave damage reflection signal appears, v j represents the mode velocity of the guided wave mode j, v 18 represents the mode velocity of the 18th guided wave mode, and x represents the distance between the pipeline damage and the piezoelectric transducer array, which is used to obtain the damage location.

[0169] The present invention uses the SAFE-PML model to establish the guided wave equation of an underwater water-filled pipeline. Six, ten, and four nodes are established in the water inside the pipeline, in the pipeline structure, and in the PML layer outside the pipeline, respectively. Each node in the water inside the pipeline and in the PML layer has one degree of freedom, and each node in the pipeline structure has three degrees of freedom. The coupling point between the pipeline and the water shares the same node, for a total of 18 nodes and 30 degrees of freedom.

[0170] Compared with the existing technology, the present invention uses an underwater water-filled pipeline guided wave method based on the SAFE-PML model for damage detection and positioning, converts the wave equation into a characteristic equation for solution, uses the solved eigenvalue to obtain the guided wave mode sound velocity, uses the solved eigenvector to obtain the wave structure of the guided wave mode, and performs mode excitation according to the wave structure. Compared with the calculation speed, the detection accuracy of the guided wave is 84%.

[0171] The waveguide signal extracted by the present invention is a waveguide signal collected under the condition that there is damage on the underwater water-filled pipeline. Therefore, the waveguide damage detection and positioning of the underwater water-filled pipeline based on the SAFE-PML model is carried out without the need for a baseline signal. Therefore, the present invention establishes the wave equation of the waveguide through the SAFE method, and by introducing PML, the infinite surrounding medium is converted into a finite layer to establish the wave equation of the complete waveguide system; the coordinates of the coupling point between the outside of the pipeline and the water are expanded to a finite range using a stretching function to optimize the unboundedness problem of the open waveguide system; SAFE converts the wave equation into a characteristic equation, and the waveguide mode calculation is converted into an eigenvalue solution. The waveguide mode velocity and wave structure in the complete underwater water-filled pipeline are extracted from the solved eigenvalues ​​and eigenvectors. A piezoelectric transducer array is designed for the waveguide mode wave structure to excite the waveguide mode, extract the time domain characteristics of the waveguide signal, accurately and directly extract the pipeline damage information, and perform high-precision detection and positioning of underwater water-filled pipeline damage.

[0172] The present invention solves the problem that the prior art cannot use a limited thickness layer to accurately simulate the infinite surrounding medium outside the underwater water-filled pipeline and obtain the propagation characteristic information of the guided wave mode of all modes of the underwater water-filled pipeline.

[0173] The SAFE-PML model proposed in this invention offers greater efficiency and lower computational complexity in calculating guided wave propagation problems in underwater water-filled pipes, significantly benefiting practical damage detection projects. The present invention utilizes the SAFE method to establish a wave equation for underwater water-filled pipes, improving the accuracy of calculating the effects of water-copper pipe interaction on guided wave propagation characteristics. The PML model addresses complex boundary conditions outside the pipe, effectively absorbing boundary reflections, reducing interference within the computational domain, and improving computational efficiency. The stretching function in the PML effectively combines the wave equation established by SAFE within the pipe and the water within it with the PML, converting the complete wave equation for the underwater water-filled pipe into a characteristic equation. This model comprehensively captures the propagation characteristics of multiple guided wave modes and extracts the physical information, group velocity, and wave structure of the guided wave modes within the underwater water-filled pipe. The present invention utilizes a piezoelectric transducer array to excite guided wave modes based on the wave structure, directly detecting and locating damage in underwater water-filled pipes using the modes' group velocity. This method enables underwater water-filled pipe damage detection without the need for time-domain signal processing of guided waves, expanding the engineering application of guided waves in complex environments and broadening the scope of ultrasonic guided wave nondestructive testing.

[0174] Example 2

[0175] like Figure 9 As shown, the present invention discloses a guided wave damage detection and positioning system for underwater water-filled pipelines based on the SAFE-PML model, comprising:

[0176] The wave equation building module is used to establish the guided wave SAFE wave equation for the water-filled pipe waveguide system in a finite fluid domain;

[0177] In the wave equation building block, the cross section of the water-filled pipe waveguide system in the finite fluid domain is discretized from the internal fluid to the cutoff of the fluid domain outside the pipe:

[0178] r=[r1,r2,r3,…r s ,…r f ,…r m ](1)

[0179] Where r represents the node coordinate set, r 1～ r s-1 represents the node coordinates of the fluid inside the pipe, r s represents the node coordinates where the pipe is coupled with the internal fluid, r s+1～ r f-1 represents the node coordinates of the pipeline, r f represents the node coordinates where the pipeline is coupled with the external fluid domain, r f+1～ r m Represents the node coordinates of the fluid in the external fluid domain, which is discretized using m nodes;

[0180] The nodal wave equation of guided waves in the pipeline is established in the cylindrical coordinate system and expressed as:

[0181] (K1+inK2+ikK3+knK4+n 2 K5+k 2 K6-ω 2 M)U n =0 (2)

[0182] Where M represents the node mass matrix of the pipeline, K1, K2, K3, K4, K5, and K6 represent the node stiffness matrix of the pipeline. The node mass matrix and node stiffness matrix are derived according to the material properties, geometry, and node coordinates of the pipeline. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and U n represents the wave structure of the mode in the pipe,

[0183] Establish the nodal wave equation of guided waves in the fluid in the cylindrical coordinate system:

[0184]

[0185] The superscript f represents the node stiffness matrix and node mass matrix in the fluid, which are derived based on the material properties of the fluid and the node coordinates. n represents the velocity potential of water;

[0186] The waveguide system composed of water-filled pipes in a finite fluid domain is a fluid-solid coupling system. The fluid-solid coupling integral H is introduced in the process of equation assembly. s With r f Existence:

[0187] H=2πrN u (r) T nN φ (r) T (4)

[0188] N u (r) represents the shape function of the pipe, N φ (r) represents the shape function of water, and r in the fluid-structure coupling integral is r s or r f , establish the coupling node stiffness matrix K at the fluid-solid coupling node in the wave equation coup :

[0189]

[0190] ρ1 represents the density of the pipe material, and ρ2 represents the density of the fluid;

[0191] Assemble the wave equations of the guided wave at the pipeline node, fluid node and fluid-solid coupling node, that is, assemble formulas (2), (3) and (5), and establish the guided wave SAFE wave equation of the water-filled pipeline waveguide system in the finite fluid domain:

[0192]

[0193] Among them, K2 and K3 are skew-symmetric complex matrices, and It represents the symmetric form of K2 and K3 obtained by T transformation. The remaining matrices are all symmetric matrices and remain unchanged after T transformation.

[0194] The wave equation extension module is used to extend the guided wave SAFE wave equation of a water-filled pipe in a finite fluid domain to a water-filled pipe waveguide system in an infinite fluid domain through the PML coordinate stretching function, thereby obtaining the guided wave SAFE wave equation of a complete underwater water-filled pipe waveguide system;

[0195] In the wave equation extension module, the PML coordinate stretching function is used. The PML range is set from the outer surface of the pipe to the end of the fluid domain outside the pipe to obtain the new coordinates after stretching.

[0196]

[0197] where r 1＝ [r f ,…r m], represents the node coordinate set of the fluid domain outside the pipe, Represents the new coordinate set after stretching, r i represents the node coordinates of the fluid domain outside the pipe, γ(r i ) is the stretching function that defines the PML, and its expression is:

[0198]

[0199] a and b are parameters that quantify the PML damping characteristics. They are set according to the material parameters of the surrounding medium to keep the PML characteristics consistent with those of the surrounding medium and perfectly match the impedance of the surrounding material. The PML defined by the stretching function absorbs leaky waves through a finite thickness layer, converting the continuum of the radiation pattern into discrete PML modes, simulating an infinite surrounding medium.

[0200] Modify the nodal wave equations only for the fluid domain outside the pipe:

[0201]

[0202] where f(r i ) represents the node coordinate r i The node wave equation at Indicates the node coordinate r after stretching i The node wave equation at ;

[0203] Assemble node r1 to node The nodal wave equation of the pipeline is used to form the global guided wave SAFE wave equation. The nodal wave equation of the fluid domain outside the pipeline in formula (6) is modified through formulas (7), (8), (9) and (10) to establish the guided wave SAFE wave equation of the complete waveguide system based on the underwater water-filled pipeline:

[0204]

[0205] in Represents the wave structure U containing the guided wave in the pipe n and water velocity potential φ n T transformation vector, subscripts of mass matrix and stiffness matrix (·) Represents the matrix in the guided wave SAFE wave equation.

[0206] The wave structure extraction module is used to extract the guided wave mode velocity and wave structure existing in the complete underwater water-filled pipeline;

[0207] In the wave structure extraction module, the characteristic equation of the underwater water-filled pipe based on SAFE-PML is established, and the problem of solving the guided wave SAFE wave equation formula (11) is converted into a linear eigenvalue solution problem:

[0208] [A-kB]ψ=0 (12)

[0209] [B -1 A-kI]ψ=0 (13)

[0210]

[0211] Where I represents the unit vector, and the characteristic equation formula (13) is solved to obtain N eigenvalues ​​k j With 2N eigenvectors, N is the number of guided wave modes, and the eigenvalue k j is the wave number of the guided wave mode, and each eigenvalue corresponds to a left eigenvector ψ lj and a right eigenvector ψ rj ; Based on the symmetry of the global stiffness matrix and the mass matrix, the left eigenvector and the right eigenvector are the same and are both written as eigenvector ψ j , the elements in the eigenvector are node displacements or velocity potentials; in the fluid nodes 1 to s-1 and f+1 to m, each node corresponds to one degree of freedom, and in the pipe nodes s to f, each node corresponds to the radial, tangential, and axial degrees of freedom r, θ, z of the underwater water-filled pipe waveguide system. Finally, the eigenvector ψ is solved. j The length of is twice the number of degrees of freedom, 2m+4f-4s+4; where the eigenvector ψ j The vectors in the range of (m+2f-2s+3) to (2m+4f-4s+4) include the velocity potential of the guided wave mode j in the fluid domain and the wave structure in the pipeline. The eigenvector ψ j The vectors in the range of (m+2f-s+2) to (m+5f-4s+4) represent the wave structure of the guided wave mode j in the pipeline; the wave number k j Calculate the j-mode velocity of the guided wave mode:

[0212]

[0213] Where dω and dk j is the angular frequency ω and the wave number k of the guided wave mode j j The differential operator of .

[0214] The damage detection and location module is used to excite a separate guided wave mode based on the wave structure of the guided wave mode. It detects and locates pipeline damage based on the time characteristics of the reflected wave of the guided wave time domain signal. The damage detection and location module uses a piezoelectric transducer excitation array to excite a separate guided wave mode based on the wave structure of the guided wave mode. There are N modes of guided waves in underwater water-filled pipelines:

[0215] v g =[v1,v2,v3,…,v j ,…,v N ](18)

[0216] where v g is the mode velocity of the guided wave mode, U n is the wave structure of the guided wave:

[0217]

[0218] u is the nodal displacement of the guided wave mode, the subscripts r, θ, and z represent the degrees of freedom of each node in three different directions, representing the radial, tangential, and axial displacements of the guided wave mode, respectively, n represents the number of pipeline nodes, n = f - s + 1, and j represents the j-mode of the guided wave;

[0219] The piezoelectric transducer excitation array is designed according to the wave structure of the guided wave mode j. The array consists of three transducers:

[0220]

[0221] p1, p2, and p3 represent the vibration amplitudes of the three piezoelectric transducers at a center frequency of ω / 2π. The subscripts 1, 2, and 3 indicate that the transducers vibrate in radial, tangential, and axial directions, respectively. A piezoelectric transducer array is used to excite guided wave mode j in an underwater water-filled pipe. When the guided wave propagates through a pipe damage, a reflected wave is generated. The occurrence time of the damage reflected wave in the guided wave time domain signal is extracted by the piezoelectric transducer's self-transmission and self-reception method. The damage is then located based on the mode velocity of guided wave mode j:

[0222]

[0223] t represents the time when the guided wave damage reflection signal appears, v j represents the mode velocity of the guided wave mode j, X represents the distance between the pipeline damage and the piezoelectric transducer array, and the damage location is obtained.

Claims

1. A guided wave damage detection and location method for underwater water-filled pipelines based on the SAFE-PML model, characterized in that: The steps include: S1. Establish the guided wave SAFE wave equation for the water-filled pipe waveguide system in a finite fluid domain; S2. The guided wave SAFE wave equation of the water-filled pipe in the finite fluid domain is extended to the water-filled pipe waveguide system in the infinite fluid domain by using the PML coordinate stretching function, and the guided wave SAFE wave equation of the complete underwater water-filled pipe waveguide system is obtained; S3, extracting the guided wave mode velocity and wave structure existing in the complete underwater water-filled pipeline; S4. Excite a separate guided wave mode based on the wave structure of the guided wave mode, and detect and locate pipeline damage through the time characteristics of the reflected wave of the guided wave time domain signal.

2. The guided wave damage detection and location method according to claim 1, characterized in that: The step S1 specifically includes the following steps: For the cross section of the water-filled pipe waveguide system in a finite fluid domain, the nodes are discretized from the internal fluid to the cutoff of the fluid domain outside the pipe: r＝[r1,r2,r3,…r s ,…r f ,…r m ](1) Where r represents the node coordinate set, r 1～ r s-1 represents the node coordinates of the fluid inside the pipe, r s represents the node coordinates where the pipe is coupled with the internal fluid, r s+1～ r f-1 represents the node coordinates of the pipeline, r f represents the node coordinates where the pipeline is coupled with the external fluid domain, r f+1～ r m Represents the node coordinates of the fluid in the external fluid domain, which is discretized using m nodes; The nodal wave equation of guided waves in the pipeline is established in the cylindrical coordinate system and expressed as: (K1+inK2+ikK3+knK4+n 2 K5+k 2 K6-ω 2 M)U n =0 (2) Where M represents the node mass matrix of the pipeline, K1, K2, K3, K4, K5, and K6 represent the node stiffness matrix of the pipeline. The node mass matrix and node stiffness matrix are derived according to the material properties, geometry, and node coordinates of the pipeline. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and U n represents the wave structure of the mode in the pipe, Establish the nodal wave equation of guided waves in the fluid in the cylindrical coordinate system: The superscript f represents the node stiffness matrix and node mass matrix in the fluid, which are derived based on the material properties of the fluid and the node coordinates. n represents the velocity potential of water; The waveguide system composed of water-filled pipes in a finite fluid domain is a fluid-solid coupling system. The fluid-solid coupling integral H is introduced in the process of equation assembly. s With r f Existence: H=2πrN u (r) T nN φ (r) T (4) N u (r) represents the shape function of the pipe, N φ (r) represents the shape function of water, and r in the fluid-structure coupling integral is r s or r f , establish the coupling node stiffness matrix K at the fluid-solid coupling node in the wave equation coup : ρ1 represents the density of the pipe material, and ρ2 represents the density of the fluid; Assemble the wave equations of the guided wave at the pipeline node, fluid node and fluid-solid coupling node, that is, assemble formulas (2), (3) and (5), and establish the guided wave SAFE wave equation of the water-filled pipeline waveguide system in the finite fluid domain: Among them, K2 and K3 are skew-symmetric complex matrices, and It represents the symmetric form of K2 and K3 obtained by T transformation. The remaining matrices are all symmetric matrices and remain unchanged after T transformation.

3. The guided wave damage detection and location method according to claim 2, characterized in that: The step S2 specifically includes the following steps: By using the PML coordinate stretching function, the PML range is set from the outer surface of the pipe to the end of the fluid domain outside the pipe, and the new coordinates after stretching are obtained. where r 1＝ [r f ,…r m ], represents the node coordinate set of the fluid domain outside the pipe, Represents the new coordinate set after stretching, r i represents the node coordinates of the fluid domain outside the pipe, γ(r i ) is the stretching function that defines the PML, and its expression is: a and b are parameters that quantify the damping characteristics of the PML and are set according to the material parameters of the surrounding medium. The PML defined using the stretching function absorbs leaky waves through a finite thickness layer, converting the continuum of radiation modes into discrete PML modes, simulating an infinite surrounding medium. Modify the nodal wave equations only for the fluid domain outside the pipe: where f(r i ) represents the node coordinate r i The node wave equation at Indicates the node coordinate r after stretching i The node wave equation at ; Assemble node r1 to node The nodal wave equation of the pipeline is used to form the global guided wave SAFE wave equation. The nodal wave equation of the fluid domain outside the pipeline in formula (6) is modified through formulas (7), (8), (9) and (10) to establish the guided wave SAFE wave equation of the complete waveguide system based on the underwater water-filled pipeline: in Represents the wave structure U containing the guided wave in the pipe n and water velocity potential φ n T transformation vector, mass matrix and stiffness matrix subscript (·) Represents the matrix in the guided wave SAFE wave equation.

4. The guided wave damage detection and location method according to claim 3, characterized in that: The step S3 specifically includes the following steps: The characteristic equation of underwater water-filled pipeline based on SAFE-PML is established, and the problem of solving the guided wave SAFE wave equation formula (11) is converted into a linear eigenvalue solution problem: [A-kB]ψ=0 (12) [B -1 A-kI]ψ=0 (13) Where I represents the unit vector, and the characteristic equation formula (13) is solved to obtain N eigenvalues ​​k j With 2N eigenvectors, N is the number of guided wave modes, and the eigenvalue k j is the wave number of the guided wave mode, and each eigenvalue corresponds to a left eigenvector ψ lj and a right eigenvector ψ rj ; Based on the symmetry of the global stiffness matrix and the mass matrix, the left eigenvector and the right eigenvector are the same and are both written as eigenvector ψ j , the elements in the eigenvector are node displacements or velocity potentials; in the fluid nodes 1 to s-1 and f+1 to m, each node corresponds to one degree of freedom, and in the pipe nodes s to f, each node corresponds to the radial, tangential, and axial degrees of freedom r, θ, z of the underwater water-filled pipe waveguide system. Finally, the eigenvector ψ is solved. j The length of is twice the number of degrees of freedom, 2m+4f-4s+4; where the eigenvector ψ j The vectors in the range of (m+2f-2s+3) to (2m+4f-4s+4) include the velocity potential of the guided wave mode j in the fluid domain and the wave structure in the pipeline. The eigenvector ψ j The vectors in the range of (m+2f-s+2) to (m+5f-4s+4) represent the wave structure of guided wave mode j in the pipeline; By wave number k j Calculate the j-mode velocity of the guided wave mode: Where dω and dk j is the angular frequency ω and the wave number k of the guided wave mode j j The differential operator of .

5. The guided wave damage detection and location method according to claim 4, characterized in that: The step S4 specifically includes the following steps: Using a piezoelectric transducer to excite an array, a separate guided wave mode is excited based on the wave structure of the guided wave mode. There are N modes of guided waves in underwater water-filled pipes: v g =[v1,v2,v3,…,v j ,…,v N ] (18) where v g is the mode velocity of the guided wave mode, U n is the wave structure of the guided wave: u is the nodal displacement of the guided wave mode, the subscripts r, θ, and z represent the degrees of freedom of each node in three different directions, representing the radial, tangential, and axial displacements of the guided wave mode, respectively, n represents the number of pipeline nodes, n = f - s + 1, and j represents the j-mode of the guided wave; The piezoelectric transducer excitation array is designed according to the wave structure of the guided wave mode j. The array consists of three transducers: p1, p2, and p3 represent the vibration amplitudes of the three piezoelectric transducers at a center frequency of ω / 2π. The subscripts 1, 2, and 3 indicate that the transducers vibrate in radial, tangential, and axial directions, respectively. A piezoelectric transducer array is used to excite guided wave mode j in an underwater water-filled pipe. When the guided wave propagates through a pipe damage, a reflected wave is generated. The occurrence time of the damage reflected wave in the guided wave time domain signal is extracted by the piezoelectric transducer's self-transmission and self-reception method. The damage is then located based on the mode velocity of guided wave mode j: t represents the time when the guided wave damage reflection signal appears, v j represents the mode velocity of the guided wave mode j, X represents the distance between the pipeline damage and the piezoelectric transducer array, and the damage location is obtained.

6. A guided wave damage detection and location system for underwater water-filled pipelines based on the SAFE-PML model, characterized in that: include: The wave equation building module is used to establish the guided wave SAFE wave equation for the water-filled pipe waveguide system in a finite fluid domain; The wave equation extension module is used to extend the guided wave SAFE wave equation of a water-filled pipe in a finite fluid domain to a water-filled pipe waveguide system in an infinite fluid domain through the PML coordinate stretching function, thereby obtaining the guided wave SAFE wave equation of a complete underwater water-filled pipe waveguide system; The wave structure extraction module is used to extract the guided wave mode velocity and wave structure existing in the complete underwater water-filled pipeline; The damage detection and positioning module is used to excite a separate guided wave mode based on the wave structure of the guided wave mode, and detect and locate pipeline damage through the time characteristics of the reflected wave of the guided wave time domain signal.

7. The guided wave damage detection and location system according to claim 6, characterized in that: In the wave equation building module, the cross section of the water-filled pipe waveguide system in the finite fluid domain is discretized from the internal fluid to the cutoff of the fluid domain outside the pipe: r＝[r1,r2,r3,…r s ,…r f ,…r m ] (1) Where r represents the node coordinate set, r 1～ r s-1 represents the node coordinates of the fluid inside the pipe, r s represents the node coordinates where the pipe is coupled with the internal fluid, r s+1～ r f-1 represents the node coordinates of the pipeline, r f represents the node coordinates where the pipeline is coupled with the external fluid domain, r f+1～ r m Represents the node coordinates of the fluid in the external fluid domain, which is discretized using m nodes; The nodal wave equation of guided waves in the pipeline is established in the cylindrical coordinate system and expressed as: (K1+inK2+ikK3+knK4+n 2 K5+k 2 K6-ω 2 M)U n =0 (2) Where M represents the node mass matrix of the pipeline, K1, K2, K3, K4, K5, and K6 represent the node stiffness matrix of the pipeline. The node mass matrix and node stiffness matrix are derived according to the material properties, geometry, and node coordinates of the pipeline. ω represents the angular frequency, n represents the circumferential order of the guided wave, k represents the wave number of the mode, and U n represents the wave structure of the mode in the pipe, Establish the nodal wave equation of guided waves in the fluid in the cylindrical coordinate system: The superscript f represents the node stiffness matrix and node mass matrix in the fluid, which are derived based on the material properties of the fluid and the node coordinates. n represents the velocity potential of water; The waveguide system composed of water-filled pipes in a finite fluid domain is a fluid-solid coupling system. The fluid-solid coupling integral H is introduced in the process of equation assembly. s With r f Existence: H=2πrN u (r) T nN φ (r) T (4) N u (r) represents the shape function of the pipe, N φ (r) represents the shape function of water, and r in the fluid-structure coupling integral is r s or r f , establish the coupling node stiffness matrix K at the fluid-solid coupling node in the wave equation coup : ρ1 represents the density of the pipe material, and ρ2 represents the density of the fluid; Assemble the wave equations of the guided wave at the pipeline node, fluid node and fluid-solid coupling node, that is, assemble formulas (2), (3) and (5), and establish the guided wave SAFE wave equation of the water-filled pipeline waveguide system in the finite fluid domain: Among them, K2 and K3 are skew-symmetric complex matrices, and It represents the symmetric form of K2 and K3 obtained by T transformation. The remaining matrices are all symmetric matrices and remain unchanged after T transformation.

8. The guided wave damage detection and location system according to claim 7, characterized in that: In the wave equation extension module, the PML coordinate stretching function is used, and the PML range is set from the outer surface of the pipe to the end of the fluid domain outside the pipe to obtain the new coordinate after stretching. where r 1＝ [r f ,…r m ], represents the node coordinate set of the fluid domain outside the pipe, Represents the new coordinate set after stretching, r i represents the node coordinates of the fluid domain outside the pipe, γ(r i ) is the stretching function that defines the PML, and its expression is: a and b are parameters that quantify the damping characteristics of the PML and are set according to the material parameters of the surrounding medium. The PML defined using the stretching function absorbs leaky waves through a finite thickness layer, converting the continuum of radiation modes into discrete PML modes, simulating an infinite surrounding medium. Modify the nodal wave equations only for the fluid domain outside the pipe: where f(r i ) represents the node coordinate r i The node wave equation at Indicates the node coordinate r after stretching i The node wave equation at ; Assemble node r1 to node The nodal wave equation of the pipeline is used to form the global guided wave SAFE wave equation. The nodal wave equation of the fluid domain outside the pipeline in formula (6) is modified through formulas (7), (8), (9) and (10) to establish the guided wave SAFE wave equation of the complete waveguide system based on the underwater water-filled pipeline: in Represents the wave structure U containing the guided wave in the pipe n and water velocity potential φ n T transformation vector, subscripts of mass matrix and stiffness matrix (·) Represents the matrix in the guided wave SAFE wave equation.

9. The guided wave damage detection and location system according to claim 8, characterized in that: The wave structure extraction module establishes the underwater water-filled pipe characteristic equation based on SAFE-PML, and converts the guided wave SAFE wave equation formula (11) solution problem into a linear eigenvalue solution problem: [A-kB]ψ=0 (12) [B -1 A-kI]ψ=0 (13) Where I represents the unit vector, and the characteristic equation formula (13) is solved to obtain N eigenvalues ​​k j With 2N eigenvectors, N is the number of guided wave modes, and the eigenvalue k j is the wave number of the guided wave mode, and each eigenvalue corresponds to a left eigenvector ψ lj and a right eigenvector ψ rj ; Based on the symmetry of the global stiffness matrix and the mass matrix, the left eigenvector and the right eigenvector are the same and are both written as eigenvector ψ j , the elements in the eigenvector are node displacements or velocity potentials; in the fluid nodes 1 to s-1 and f+1 to m, each node corresponds to one degree of freedom, and in the pipe nodes s to f, each node corresponds to the radial, tangential, and axial degrees of freedom r, θ, z of the underwater water-filled pipe waveguide system. Finally, the eigenvector ψ is solved. j The length of is twice the number of degrees of freedom, 2m+4f-4s+4; where the eigenvector ψ j The vectors in the range of (m+2f-2s+3) to (2m+4f-4s+4) include the velocity potential of the guided wave mode j in the fluid domain and the wave structure in the pipeline. The eigenvector ψ j The vectors in the range of (m+2f-s+2) to (m+5f-4s+4) represent the wave structure of the guided wave mode j in the pipeline; the wave number k j Calculate the j-mode velocity of the guided wave mode: Where dω and dk j is the angular frequency ω and the wave number k of the guided wave mode j j The differential operator of .

10. The guided wave damage detection and location system according to claim 9, characterized in that: The damage detection and positioning module uses a piezoelectric transducer excitation array to excite a separate guided wave mode based on the wave structure of the guided wave mode. There are N modes of guided waves in underwater water-filled pipes: v g =[v1,v2,v3,…,v j ,…,v N ] (18) where v g is the mode velocity of the guided wave mode, U n is the wave structure of the guided wave: u is the nodal displacement of the guided wave mode, the subscripts r, θ, and z represent the degrees of freedom of each node in three different directions, representing the radial, tangential, and axial displacements of the guided wave mode, respectively, n represents the number of pipeline nodes, n = f - s + 1, and j represents the j-mode of the guided wave; The piezoelectric transducer excitation array is designed according to the wave structure of the guided wave mode j. The array consists of three transducers: p1, p2, and p3 represent the vibration amplitudes of the three piezoelectric transducers at a center frequency of ω / 2π. The subscripts 1, 2, and 3 indicate that the transducers vibrate in radial, tangential, and axial directions, respectively. A piezoelectric transducer array is used to excite guided wave mode j in an underwater water-filled pipe. When the guided wave propagates through a pipe damage, a reflected wave is generated. The occurrence time of the damage reflected wave in the guided wave time domain signal is extracted by the piezoelectric transducer's self-transmission and self-reception method. The damage is then located based on the mode velocity of guided wave mode j: t represents the time when the guided wave damage reflection signal appears, v j represents the mode velocity of the guided wave mode j, X represents the distance between the pipeline damage and the piezoelectric transducer array, and the damage location is obtained.

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