Parallelization circular tube guided wave forward modeling method and system based on semi-analytic finite element

Abstract

The invention relates to a parallelization circular tube guided wave forward modeling method and system based on a semi-analytic finite element. The method comprises the following steps of: firstly, performing finite element discretization in a radial direction according to a circular tube parameter and an excitation signal to obtain a finite element discretization form of an equation; then boundary conditions are added, four-order finite difference discretization is carried out in the axial direction and the circumferential direction according to the axial grid parameters and the axial grid parameters under the boundary conditions, and a difference format is obtained through solving; and solving the to-be-processed wave field data according to the difference format, and processing an obtained solution set to obtain a wave field snapshot of a round tube guided wave forward modeling algorithm, thereby completing round tube guided wave forward modeling. Compared with the prior art, the method has the advantages of improving time efficiency and space efficiency, effectively inhibiting numerical dispersion and the like.

Description

Technical Field

[0001] The present invention relates to the field of exploration technologies, and in particular, to a parallelized circular tube guided wave forward modeling method and system based on semi-analytical finite elements. Background Art

[0002] Pipeline structures are widely used in thermal power units of power stations. There are a large number of support occlusion parts in such pipelines, and they work in harsh conditions such as high temperature, high pressure, and strong corrosion for a long time. Cracks, corrosion and other defects are extremely likely to occur during their service process. In recent years, reports of casualties and economic losses caused by pipeline failure and damage are common. Therefore, it is urgent to solve the problem of damage detection in the support occlusion parts of high-temperature pipelines. Since in the current actual application scenarios, the forward calculation of pipeline elastic waves is the basis for studying the propagation of elastic waves and inverse time migration imaging, which is generally divided into numerical simulation and physical analytical simulation. Considering that the analytical solution under the circular tube system is extremely complex and difficult to adapt to complex boundary conditions, the numerical simulation method is generally selected to study the propagation law of guided waves in circular tubes.

[0003] Currently, the mainstream methods for elastic wave simulation are: finite difference method, finite element method, boundary element method, spectral element method, and discontinuous Galerkin method. The finite difference method has the advantages of fast calculation speed, small memory occupation, and convenient parallel calculation. However, when dealing with circular tube problems, the algorithm has complex free boundary conditions for the inner and outer walls of the circular tube, difficult calculation of radial difference coefficients, and difficulties in parallelization, which limit its application in circular tube problems. For the full-wave simulation methods using finite elements and spectral elements, the boundary treatment is easy, but they will face problems such as high running memory occupation and inability to be parallelized. The discontinuous Galerkin method will have problems such as mesh mismatch when solving guided wave problems. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a parallelized circular tube guided wave forward modeling method and system based on semi-analytical finite elements.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] According to one aspect of the present invention, a parallelized circular tube guided wave forward modeling method based on semi-analytical finite elements is provided, including the following steps:

[0007] S1. Determine the circular tube parameters and excitation signals;

[0008] S2. According to the circular tube parameters and excitation signals, perform finite element discretization in the radial direction to obtain the finite element discretized form of the equation;

[0009] S3. Use the finite element discretized form of the equation to obtain the dispersion curve when the circumferential direction is 0, and thereby determine the axial and circumferential grid parameters;

[0010] S4, adding boundary conditions, and under the boundary conditions, performing fourth-order finite difference discretization in the axial and circumferential directions according to the axial and axial grid parameters, and solving to obtain the difference format;

[0011] S5. Solve the wave field data to be processed according to the differential format, and process the obtained solution set to obtain the wave field snapshot of the circular pipe guided wave forward algorithm, which is used to study the elastic wave propagation and reverse time migration imaging in the pipeline and complete the damage detection of the blocked part of the pipeline.

[0012] As a preferred technical solution, the circular tube parameters in S1 include material parameters and geometric parameters, wherein the material parameters include Young's modulus, Poisson's ratio and density of the circular tube; and the geometric parameters include the inner diameter and outer diameter of the circular tube.

[0013] As a preferred technical solution, the specific steps of performing finite element discretization in the radial direction in S2 are:

[0014] S21, perform one-dimensional meshing in the radial direction, and use shape functions for interpolation. Use motion equations and constitutive equations to establish strain and stress fields, which are used to construct weak form integral equations in S22;

[0015] S22. Derive the weak form integral equation of elastic dynamics in cylindrical coordinate system and discretize it to obtain the discretization representation of finite element;

[0016] S23, obtaining the global mass matrix and stiffness matrix from the discretization representation of the finite element;

[0017] S24. Arrange the global mass matrix and stiffness matrix to obtain the finite element discretization mode of the equation.

[0018] As a preferred technical solution, the determination of the axial and circumferential grid parameters in S3 is as follows: first, the finite element discretization form of the equation is converted to the frequency domain and wave number domain, and it is rewritten as a generalized eigenvalue problem, and then the dispersion curve of the circular tube at the frequency is calculated. Then, the minimum phase velocity, minimum wavelength, and minimum group velocity of the maximum frequency component in the excitation are determined, and the axial and circumferential grid parameters are determined by the above parameters.

[0019] As a preferred technical solution, the axial and circumferential grid parameters include the grid step size and the corresponding time step size.

[0020] As a preferred technical solution, the boundary conditions added in S4 include adding fixed constraints in the axial direction, adding periodic boundary conditions in the circumferential direction, and adding a perfect matching layer in the axial direction.

[0021] As a preferred technical solution, the perfect matching layer is added to the two axial boundaries, specifically adopting the Cerjan absorbing boundary, that is, setting increasing damping at the boundary, and the specific formula of the damping coefficient is:

[0022]

[0023] Where α is the damping coefficient; α max is the maximum damping coefficient, x is the distance from the point in the matching layer to the boundary, and L is the length of the matching layer.

[0024] As a preferred technical solution, the specific steps of solving the data to be processed according to the difference format in S5 are:

[0025] S51, initializing the wave field data to be processed on a graphics processing unit (GPU);

[0026] S52, calling the Compute Unified Device Architecture (CUDA), performing wave field extrapolation in a differential format, and outputting the wave field data of the current time step to a solution set at every preset time step;

[0027] S53, determine whether the preset total solution time is reached, if so, transmit the solution set back to the central processing unit (CPU), if not, return to step S52.

[0028] As a preferred technical solution, the wave field data includes the axial displacement, circumferential displacement and out-of-plane displacement of the wave field.

[0029] According to another aspect of the present invention, a parallelized circular tube waveguide forward modeling system based on semi-analytical finite elements is provided. The system is operated by a parallelized circular tube waveguide forward modeling method based on semi-analytical finite elements as described above. The system includes a parameter determination module, a finite element discretization module, a dispersion curve module and a forward solution module.

[0030] Among them, the parameter determination module is used to determine the circular tube parameters and the excitation signal; the finite element discretization module is used to perform finite element discretization in the radial direction according to the circular tube parameters and the excitation signal to obtain the finite element discretization form of the equation; the dispersion curve module is used to use the finite element discretization form of the equation to obtain the dispersion curve when the circumferential direction is 0, and thereby determine the axial and circumferential grid parameters; the boundary processing module is used to add boundary conditions, and perform fourth-order finite difference discretization under the boundary conditions to obtain the difference format; the forward simulation module is used to solve the wave field data to be processed according to the difference format, and process the obtained solution set to obtain the wave field snapshot of the circular tube guided wave forward modeling algorithm, and complete the circular tube guided wave forward modeling.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] 1. In the present invention, firstly, finite element discretization is performed in the radial direction according to the parameters of the circular tube and the excitation signal to obtain the finite element discretization form of the equation; then boundary conditions are added, and under the boundary conditions, fourth-order finite difference discretization is performed in the axial and circumferential directions according to the axial and axial grid parameters to obtain the difference format; the wave field data to be processed is solved according to the difference format, and the obtained solution set is processed to obtain the wave field snapshot of the circular tube guided wave forward algorithm, which is used to study the propagation of elastic waves in the pipeline and reverse time migration imaging, and complete the damage detection of the obstructed part of the pipeline. The present invention performs finite element discretization in the radial direction, and uses the finite difference method for discretization in the axial and circumferential directions, and constructs a highly parallelized calculation format, so that the guided wave forward method in the present invention has low running memory usage and can be processed in parallel. Under the simulation of the same problem, the memory usage of the time domain implicit model commonly used in the time domain forward method is reduced by about 40%, which improves the space efficiency and time efficiency of the computer in processing such problems.

[0033] 2. In the present invention, numerical dispersion is effectively suppressed by adding fixed constraints in the axial direction, periodic boundary conditions in the circumferential direction, and a perfect matching layer in the axial direction.

[0034] 3. In the present invention, a perfect matching layer is added to two axial boundaries, specifically a Cerjan absorption boundary is adopted, that is, an increasing damping is set at the boundary to simulate the propagation behavior of guided waves in an infinite medium, so that the scale of the solution model is reduced while obtaining reliable results.

[0035] 4. The present invention adopts the graphics card parallelization technology based on the CUDA library in the forward simulation, that is, when solving the data to be processed according to the differential format, CUDA is called to improve the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the steps of the parallelized circular tube guided wave forward modeling method in the present invention;

[0037] Figure 2 It is a flowchart of the steps of the parallelized circular tube guided wave forward modeling method in the present invention;

[0038] Figure 3a Schematic diagram of phase velocity curve when the circumferential order of the circular tube is 0 in the embodiment;

[0039] Figure 3b Schematic diagram of the group velocity curve when the circumferential order of the circular tube is 0 in the embodiment;

[0040] Figure 4a It is a schematic diagram of a wave field snapshot of the off-plane displacement of the circular tube guided wave forward algorithm in the embodiment;

[0041] Figure 4b It is a schematic diagram of a wave field snapshot of the circumferential displacement of the circular tube guided wave forward algorithm in the embodiment;

[0042] Figure 4c Schematic diagram of the wave field snapshot of the axial displacement of the circular tube guided wave forward algorithm in the embodiment. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0044] Pipeline structures are widely used in thermal power units in power plants. Such pipelines have a large number of supporting and shielding parts and work in harsh working conditions such as high temperature, high pressure, and strong corrosion for a long time. They are prone to cracks, corrosion and other defects during service. In recent years, reports of casualties and economic losses caused by pipeline failure and damage are common. Therefore, it is urgent to solve the problem of damage detection in high-temperature pipeline supporting and shielding parts. In current practical application scenarios, pipeline elastic wave forward calculation is the basis for studying elastic wave propagation and reverse time migration imaging. It is generally divided into numerical simulation and physical analytical simulation. Considering that the analytical solution under the circular pipe system is extremely complex and difficult to adapt to complex boundary conditions, numerical simulation methods are generally used to study the propagation law of guided waves in circular pipes.

[0045] The mainstream methods currently used for elastic wave simulation are: finite difference method, finite element method, boundary element method, spectral element method, and discontinuous Galerkin method. The advantages of the finite difference method are fast calculation speed, small memory usage, and easy parallel computing. However, when dealing with circular tube problems, the algorithm is more complicated to deal with the free boundary conditions of the inner and outer walls of the circular tube, and the radial differential coefficients are difficult to calculate. Problems such as difficulty in parallel limit its application in circular tube problems. The use of finite element and spectral element methods for full-wave simulation is easy to handle boundaries, but it will face problems such as high memory usage and inability to parallelize processing. The discontinuous Galerkin method will have problems such as grid mismatch when solving guided wave problems.

[0046] In order to solve the above problems, a parallelized circular tube guided wave forward modeling method based on semi-analytical finite element was proposed.

[0047] Example 1

[0048] In this embodiment, a parallelized circular tube guided wave forward modeling method based on semi-analytical finite element is applied, such as Figure 1 As shown, the following steps are included:

[0049] S1, determine the parameters of the round tube and the excitation signal;

[0050] S2. According to the tube parameters and the excitation signal, finite element discretization is performed in the radial direction to obtain the finite element discretization form of the equation;

[0051] S3, using the finite element discretization form of the equation to obtain the dispersion curve when the circumferential direction is 0, and thereby determine the axial and circumferential grid parameters;

[0052] S4, adding boundary conditions, and under the boundary conditions, performing fourth-order finite difference discretization in the axial and circumferential directions according to the axial and axial grid parameters, and solving to obtain the difference format;

[0053] S5. Solve the wave field data to be processed according to the differential format, and process the obtained solution set to obtain the wave field snapshot of the circular pipe guided wave forward algorithm, which is used to study the elastic wave propagation and reverse time migration imaging in the pipeline and complete the damage detection of the blocked part of the pipeline.

[0054] In this embodiment, firstly, elastic parameters such as Young's modulus, Poisson's ratio, density, etc. of the material, geometric parameters such as inner diameter and outer diameter of the circular tube, and simulation frequency are determined. The material parameters and geometric parameters are shown in Table 1.

[0055] Table 1 Material parameters and geometric parameters

[0056]

[0057] Then one-dimensional meshing is performed in the radial direction. Here, the displacement field is interpolated using the shape function of the linear representation of the node displacement, and the strain field and stress field are written using the equation of motion and the constitutive equation:

[0058] u(r,θ,z,t)=N(r)q(θ,z,t)

[0059] ε(r,θ,z,t)=B 1 q ,z +B 2 q ,θ +B 3 q

[0060] σ(r,θ,z,t)=C(t)ε(r,θ,z,t)

[0061] Among them, the matrix B 1 , B 2 , B 3 They are:

[0062] B 1 =L 1 N

[0063] B 2 =r -1 L 2 N

[0064] B 3 =L 3 N ,r +r -1 L 4 N

[0065] Among them, the coefficient matrix L 1 , L 2 , L 3 , L 4 They are:

[0066]

[0067] Where u represents the displacement field, ε represents the strain field, σ represents the stress field, and N(r) is the shape function matrix.

[0068] In this embodiment, taking the quadratic unit as an example and mapping it to the isoparametric unit, the shape function matrix can be expressed as:

[0069]

[0070] Where ξ is the field variable of the isoparametric unit.

[0071] In this embodiment, the weak form of the elastic dynamics equation is expressed as:

[0072] ∫∫δuT ρudV+∫∫δε T σdV=∫∫δu T tDV

[0073] Substituting it into the finite element, we get the discretization expression of the finite element. The specific expression is:

[0074]

[0075] Among them, the matrix expressions are:

[0076]

[0077] In the formula, m e is the unit mass matrix, k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , are the stiffness matrices of the system respectively. C is the material elasticity matrix; ρ e is the material density; N is the shape function matrix; r is the radius.

[0078] In this embodiment, the global mass matrix and stiffness matrix are obtained by a standard finite element assembly matrix procedure, and the finite element discretization form of the equation is obtained by arranging:

[0079]

[0080] In this embodiment, the analytical form is still retained in the axial and circumferential directions, which reduces the three-dimensional problem to a two-dimensional problem. On this basis, the decomposition relationship of different modes of the wave field can be further discussed, and a new solution is provided for the elastic waveguide problem.

[0081] In this embodiment, when the circumferential order is 0, the equation is written into the frequency domain and the wave number domain, and is rewritten as a generalized eigenvalue problem. The dispersion curve of the circular tube at this frequency is calculated according to the frequency of the excitation signal and the total solution time and other parameters. The phase velocity curve and the group velocity curve calculated in this embodiment are respectively as follows: Figure 3a , as shown in 3b.

[0082] Afterwards, determine the minimum phase velocity, minimum wavelength, and minimum group velocity of the maximum frequency component in the excitation model:

[0083] [A(ω)-k n B(ω)]V n =0

[0084] Among them, the system matrices A and B are:

[0085]

[0086] Among them, k n is the characteristic wave number, and the phase velocity is calculated according to formula (10):

[0087]

[0088] The group velocity is calculated as:

[0089]

[0090] In this embodiment, in order to simulate an infinite area in the axial direction, a perfect matching layer is added in the axial direction to achieve perfect absorption of the incident wave, which is more in line with the actual working conditions in a small calculation scale. In some embodiments, a Cerjan absorption boundary is adopted, that is, an increasing damping is set at the boundary, and the damping coefficient can be expressed as:

[0091]

[0092] In the formula, α max is the maximum damping coefficient, x is the distance from the point in the matching layer to the boundary, and L is the length of the matching layer. In some cases, α can be taken max =10f, f is the center frequency of the excitation signal.

[0093] In this embodiment, taking the two-point difference format as an example, the grid size is determined according to the minimum phase velocity:

[0094]

[0095] According to the CFL condition of the system, the time step is determined by setting the CFL condition number to 0.6:

[0096]

[0097] According to different boundary conditions, the difference format is given:

[0098]

[0099] In this embodiment, the data is initialized on the GPU, and the wave field is extrapolated according to the difference format obtained above, and the data is transferred back to the CPU for storage every three time steps.

[0100] According to different actual situations, post-processing has different forms. For example, in estimating the material constitutive model, it is necessary to collect wave field data on a line and perform a two-dimensional Fourier transform. In actual detection, if reverse time migration or full waveform inversion is used, it is necessary to use zero-delay cross-correlation to process the forward and reverse wave fields. The wave field snapshot obtained in this embodiment is as follows Figure 4a , 4b4a is a schematic diagram of a wave field snapshot of the off-plane displacement of the circular tube guided wave forward algorithm, 4b is a schematic diagram of a wave field snapshot of the circumferential displacement of the circular tube guided wave forward algorithm, and 4c is a schematic diagram of a wave field snapshot of the axial displacement of the circular tube guided wave forward algorithm.

[0101] In summary, this method performs finite element discretization in the radial direction and uses the finite difference method for discretization in the axial circumferential direction, and constructs a highly parallelized calculation format, so that the running memory occupancy of its guided wave forward modeling method is low and can be processed in parallel. Under the simulation of the same problem, the memory occupancy is reduced by about 40% compared with the time domain implicit model commonly used in the time domain forward modeling method, which improves the space efficiency and time efficiency of computers in processing such problems.

[0102] Example 2

[0103] In this embodiment, a parallelized circular tube waveguide forward modeling system based on semi-analytical finite elements is applied, and the system includes a parameter determination module, a finite element discretization module, a dispersion curve module and a forward solution module;

[0104] Among them, the parameter determination module is used to determine the circular tube parameters and the excitation signal; the finite element discretization module is used to perform finite element discretization in the radial direction according to the circular tube parameters and the excitation signal to obtain the finite element discretization form of the equation; the dispersion curve module is used to use the finite element discretization form of the equation to obtain the dispersion curve when the circumferential direction is 0, and thereby determine the axial and circumferential grid parameters; the boundary processing module is used to add boundary conditions, and perform fourth-order finite difference discretization under the boundary conditions to obtain the difference format; the forward simulation module is used to solve the wave field data to be processed according to the difference format, and process the obtained solution set to obtain the wave field snapshot of the circular tube guided wave forward modeling algorithm, and complete the circular tube guided wave forward modeling.

[0105] In this embodiment, the elastic parameters of the material such as Young's modulus, Poisson's ratio, density, etc., the geometric parameters such as the inner diameter and outer diameter of the circular tube, and the simulation frequency are first determined. The material parameters and geometric parameters are shown in Table 2.

[0106] Table 2 Material parameters and geometric parameters

[0107]

[0108] Then one-dimensional meshing is performed in the radial direction. Here, the displacement field is interpolated using the shape function of the linear representation of the node displacement, and the strain field and stress field are written using the equation of motion and the constitutive equation:

[0109] u(r,θ,z,t)=N(r)q(θ,z,t)

[0110] ε(r,θ,z,t)=B 1 q ,z+B 2 q ,θ +B 3 q

[0111] σ(r,θ,z,t)=C(t)ε(r,θ,z,t)

[0112] Among them, the matrix B 1 , B 2 , B 3 They are:

[0113] B 1 =L 1 N

[0114] B 2 =r -1 L 2 N

[0115] B 3 =L 3 N ,r +r -1 L 4 N

[0116] Among them, the coefficient matrix L 1 , L 2 , L 3 , L 4 They are:

[0117]

[0118]

[0119] Where u represents the displacement field, ε represents the strain field, σ represents the stress field, and N(r) is the shape function matrix.

[0120] In this embodiment, taking the quadratic unit as an example and mapping it to the isoparametric unit, the shape function matrix can be expressed as:

[0121]

[0122] Where ξ is the field variable of the isoparametric unit.

[0123] In this embodiment, the weak form of the elastic dynamics equation is expressed as:

[0124] ∫∫δu T ρudV+∫∫δε T σdV=∫∫δu T tDV

[0125] Substituting it into the finite element, we get the discretization expression of the finite element. The specific expression is:

[0126]

[0127] Among them, the matrix expressions are:

[0128]

[0129]

[0130] In the formula, m e is the unit mass matrix, k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , are the stiffness matrices of the system respectively. C is the material elasticity matrix; ρ e is the material density; N is the shape function matrix; r is the radius.

[0131] In this embodiment, the global mass matrix and stiffness matrix are obtained by a standard finite element assembly matrix procedure, and the finite element discretization form of the equation is obtained by arranging:

[0132]

[0133] In this embodiment, the analytical form is still retained in the axial and circumferential directions, which reduces the three-dimensional problem to a two-dimensional problem. On this basis, the decomposition relationship of different modes of the wave field can be further discussed, and a new solution is provided for the elastic waveguide problem.

[0134] In this embodiment, when the circumferential order is 0, the equation is written into the frequency domain and the wave number domain, and is rewritten as a generalized eigenvalue problem. The dispersion curve of the circular tube at this frequency is calculated according to the frequency of the excitation signal and the total solution time and other parameters. The phase velocity curve and the group velocity curve calculated in this embodiment are respectively as follows: Figure 3a , as shown in 3b.

[0135] Afterwards, determine the minimum phase velocity, minimum wavelength, and minimum group velocity of the maximum frequency component in the excitation model:

[0136] [A(ω)-k n B(ω)]V n =0

[0137] Among them, the system matrices A and B are:

[0138]

[0139] Among them, k n is the characteristic wave number, and the phase velocity is calculated according to formula (10):

[0140]

[0141] The group velocity is calculated as:

[0142]

[0143] In this embodiment, in order to simulate an infinite area in the axial direction, a perfect matching layer is added in the axial direction to achieve perfect absorption of the incident wave, which is more in line with the actual working conditions in a small calculation scale. In some embodiments, a Cerjan absorption boundary is adopted, that is, an increasing damping is set at the boundary, and the damping coefficient can be expressed as:

[0144]

[0145] In the formula, α max is the maximum damping coefficient, x is the distance from the point in the matching layer to the boundary, and L is the length of the matching layer. In some cases, α can be taken max =10f, f is the center frequency of the excitation signal.

[0146] In this embodiment, taking the two-point difference format as an example, the grid size is determined according to the minimum phase velocity:

[0147]

[0148] According to the CFL condition of the system, the time step is determined by setting the CFL condition number to 0.6:

[0149]

[0150] According to different boundary conditions, the difference format is given:

[0151]

[0152] In this embodiment, the data is initialized on the GPU, and the wave field is extrapolated according to the difference format obtained above, and the data is transferred back to the CPU for storage every three time steps.

[0153] According to different actual situations, post-processing has different forms. For example, in estimating the material constitutive model, it is necessary to collect wave field data on a line and perform a two-dimensional Fourier transform. In actual detection, if reverse time migration or full waveform inversion is used, it is necessary to use zero-delay cross-correlation to process the forward and reverse wave fields. The wave field snapshot obtained in this embodiment is as follows Figure 4a , 4b 4a is a schematic diagram of a wave field snapshot of the off-plane displacement of the circular tube guided wave forward algorithm, 4b is a schematic diagram of a wave field snapshot of the circumferential displacement of the circular tube guided wave forward algorithm, and 4c is a schematic diagram of a wave field snapshot of the axial displacement of the circular tube guided wave forward algorithm.

[0154] In summary, the system performs finite element discretization in the radial direction and finite difference method discretization in the axial circumferential direction, and constructs a highly parallelized calculation format, so that the running memory occupancy of its guided wave forward modeling method is low and can be processed in parallel. Under the simulation of the same problem, the memory occupancy is reduced by about 40% compared with the time domain implicit model commonly used in the time domain forward modeling method, which improves the space efficiency and time efficiency of computers in processing such problems.

[0155] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A parallelized circular tube guided wave forward modeling method based on semi-analytical finite element, characterized in that: The following steps are involved: S1, determine the parameters of the round tube and the excitation signal; S2. According to the tube parameters and the excitation signal, finite element discretization is performed in the radial direction to obtain the finite element discretization form of the equation; S3, using the finite element discretization form of the equation to obtain the dispersion curve when the circumferential direction is 0, and thereby determine the axial and circumferential grid parameters; S4, adding boundary conditions, and under the boundary conditions, performing fourth-order finite difference discretization in the axial and circumferential directions according to the axial and axial grid parameters, and solving to obtain the difference format; S5. Solve the wave field data to be processed according to the differential format, and process the obtained solution set to obtain the wave field snapshot of the circular pipe guided wave forward algorithm, which is used to study the elastic wave propagation and reverse time migration imaging in the pipeline and complete the damage detection of the blocked part of the pipeline.

2. According to the parallelized circular tube guided wave forward modeling method based on semi-analytical finite element method in claim 1, it is characterized in that: The circular tube parameters in S1 include material parameters and geometric parameters, wherein the material parameters include Young's modulus, Poisson's ratio and density of the circular tube; and the geometric parameters include the inner diameter and outer diameter of the circular tube.

3. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 1 is characterized in that: The specific steps of performing finite element discretization in the radial direction in S2 are: S21, perform one-dimensional meshing in the radial direction, and use shape functions for interpolation. Use motion equations and constitutive equations to establish strain and stress fields, which are used to construct weak form integral equations in S22; S22. Derive the weak form integral equation of elastic dynamics in cylindrical coordinate system and discretize it to obtain the discretization representation of finite element; S23, obtaining the global mass matrix and stiffness matrix from the discretization representation of the finite element; S24. Arrange the global mass matrix and stiffness matrix to obtain the finite element discretization mode of the equation.

4. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 1 is characterized in that: The determination of the axial and circumferential grid parameters in S3 is specifically as follows: first, the finite element discrete form of the equation is converted into the frequency domain and wave number domain, and it is rewritten as a generalized eigenvalue problem, and then the dispersion curve of the circular tube at the frequency is calculated; then the minimum phase velocity, minimum wavelength and minimum group velocity of the maximum frequency component in the excitation are determined, and then the axial and circumferential grid parameters are determined by the above parameters.

5. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 4 is characterized in that: The axial and circumferential grid parameters include a grid step and a corresponding time step.

6. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 1, characterized in that: The added boundary conditions in S4 include adding fixed constraints in the axial direction, adding periodic boundary conditions in the circumferential direction, and adding a perfect matching layer in the axial direction.

7. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 6, characterized in that: The perfect matching layer is added to the two axial boundaries, specifically adopting a Cerjan absorption boundary, that is, setting an increasing damping at the boundary, and the specific formula of the damping coefficient is: Where α is the damping coefficient; α max is the maximum damping coefficient, x is the distance from the point in the matching layer to the boundary, and L is the length of the matching layer.

8. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 1, characterized in that: The specific steps of solving the data to be processed according to the difference format in S5 are: S51, initializing the wave field data to be processed on the GPU; S52, calling CUDA, performing wave field extrapolation in a differential format, and outputting the wave field data of the current time step to a solution set at every preset time step; S53, determine whether the preset total solution time is reached, if so, transmit the solution set back to the CPU, if not, return to step S52.

9. The parallelized circular tube guided wave forward modeling method based on semi-analytical finite element according to claim 8, characterized in that: The wavefield data includes axial displacement, circumferential displacement and out-of-plane displacement of the wavefield.

10. A parallelized circular tube waveguide forward modeling system based on semi-analytical finite element, characterized in that: The system is operated by a parallelized circular tube guided wave forward modeling method based on semi-analytical finite elements as described in any one of claims 1 to 9, and the system includes a parameter determination module, a finite element discretization module, a dispersion curve module and a forward solution module; The parameter determination module is used to determine the tube parameters and the excitation signal; The finite element discretization module is used to perform finite element discretization in the radial direction according to the tube parameters and the excitation signal to obtain the finite element discretization form of the equation; The dispersion curve module is used to obtain the dispersion curve when the circumferential direction is 0 by using the finite element discretization form of the equation, and thereby determine the axial and circumferential grid parameters; The boundary processing module is used to add boundary conditions and perform fourth-order finite difference discretization under the boundary conditions to obtain a difference format; The forward modeling module is used to solve the wave field data to be processed according to the differential format, and process the obtained solution set to obtain the wave field snapshot of the circular tube guided wave forward modeling algorithm, and complete the circular tube guided wave forward modeling.

Images