Detection method of arched concrete-filled steel tube bridges based on dispersion characteristics of ultrasonic guided waves

Abstract

The present invention relates to the technical field of ultrasonic guided wave nondestructive testing. Specifically, a method for inspecting arched steel tube concrete-filled bridges based on the dispersion characteristics of ultrasonic guided waves is disclosed. The method utilizes a "theoretical derivation-simulation verification-experimental analysis" approach, including the following steps: first, establishing a wave characteristic equation based on a rotating coordinate system and a semi-analytical finite element method, deriving a guided wave dispersion equation, and obtaining a dispersion curve through numerical calculation to determine the optimal monitoring mode and excitation frequency range; then, constructing a three-dimensional finite element model for wave field numerical simulation, and verifying the model's reliability by comparing the theoretical solution with the simulated solution; then, conducting ultrasonic guided wave inspection experiments, collecting time-domain signals, and extracting measured dispersion characteristics; finally, establishing theoretical predictions through time-frequency analysis, comparing numerical simulation data with experimental data, and verifying the accuracy of the theoretical model through error analysis. The present invention can accurately detect defects in arched steel tube concrete-filled bridges, improving the reliability and practicality of complex structural damage identification.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic guided wave nondestructive testing, and in particular to a method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves. Background Art

[0002] Arched concrete-filled steel tube structures, with their high load-bearing efficiency and combined mechanical properties, have become the core load-bearing system for projects such as long-span and heavy-load bridges. However, in complex service environments, they are prone to multi-scale damage: debonding at the steel tube-concrete interface weakens the composite effect, and the steel tube wall can be affected by the concrete and crack. Traditional detection methods (such as visual inspection, tapping, or local strain monitoring) have significant limitations: they cannot accurately locate the target, lack sensitivity, and have low detection efficiency, making them difficult to meet the full-scale monitoring needs of large structures.

[0003] Ultrasonic guided wave technology, with its unique long-distance propagation capability, multimodal excitation characteristics, and high sensitivity to minor damage, has demonstrated significant technical advantages in the field of nondestructive testing of composite materials. Research has confirmed that the dispersion characteristics (group velocity, phase velocity, etc.) and propagation attenuation behavior of guided waves are sensitive to changes in the elastic parameters within the material. In particular, multimodal characteristics such as Lamb waves and SH waves can provide multidimensional diagnostic information for interface damage identification. However, in engineering practice, heterogeneous material interfaces in typical layered composite structures, such as steel tube concrete, induce complex guided wave mode conversion and energy dissipation phenomena, resulting in blurred detection signal characteristics. To overcome this technical bottleneck, it is proposed to use low-frequency non-dispersive modes for detection. A numerical model of the waveguide structure is established based on the semi-analytical finite element method. Joint time-frequency analysis is achieved through wavelet transforms and Hilbert-Huang transforms. Combining dispersion characteristic control with signal feature decoupling strategies, this systematically addresses the complexity of guided wave propagation characteristics caused by heterogeneous interfaces. Summary of the Invention

[0004] The present invention aims to provide an inspection method for arched concrete-filled steel tube bridges based on the dispersion characteristics of ultrasonic guided waves, addressing the current challenge of insufficient accuracy in detecting damage to curved structures. By constructing a database of dispersion curves and combining it with a time-frequency domain joint analytical algorithm, the method enables precise localization of millimeter-level defects within arch ribs.

[0005] To achieve the above objectives, the present invention provides a method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves, comprising the following steps:

[0006] S1. Establish a rotating coordinate system based on the arched steel tube concrete arch structure;

[0007] S2. Use the semi-analytical finite element method to establish the wave characteristic equation of the arched steel tube concrete and obtain the guided wave dispersion characteristic equation of the arched steel tube concrete;

[0008] S3. Calculate the theoretical wave number, phase velocity, and group velocity dispersion curves of the arched steel tube concrete, analyze the vibration dispersion characteristics of the guided wave mode at different frequencies, and determine the optimal monitoring mode and excitation frequency range;

[0009] S4. Construct a three-dimensional finite element model of the arched steel tube concrete structure according to S1, S2 and S3, and draw a simulation dispersion curve diagram in combination with the finite element modeling;

[0010] S5. Conduct ultrasonic guided wave testing experiments on arched steel tube concrete structures according to S3 and S4, and derive experimental data;

[0011] S6. Process the experimental data derived from S5, and compare and analyze the experimental data with the simulation and theoretical data.

[0012] Preferably, the rotation coordinate system in S1 is as follows:

[0013] Any point in the Cartesian coordinate system ( x , y , z ) using quasi-cylindrical coordinate system It is expressed as shown in formula (1):

[0014] (1);

[0015] in, x , y , z represents the coordinates of a Cartesian coordinate system point, r Indicates arrival z The perpendicular distance of the axis is the radial coordinate, express r and x The angle with respect to the positive direction of the axis is the azimuth. z ' is the axial coordinate of the point in the quasi-cylindrical coordinate system, q is the polar coordinate radius, is the central angle of the circle.

[0016] Preferably, in S2, the semi-analytical finite element method is used to establish the wave characteristic equation of the arched steel tube concrete, and the guided wave dispersion characteristic equation of the arched steel tube concrete is obtained, as shown in formula (2):

[0017] (2);

[0018] Where, is the circular frequency; K 1. K 2 and K 3 is the system stiffness matrix; M is the system mass matrix; is the global node displacement vector; is the wave number; i Is an imaginary number.

[0019] Preferably, in S3, the theoretical wave number, phase velocity and group velocity dispersion curve of the structure are calculated according to the wave characteristic equation of the arched steel tube concrete arch structure, and the group velocity and phase velocity solution formula are specifically as follows:

[0020] (3);

[0021] (4)

[0022] Where, is the phase velocity; is the group velocity; is the right eigenvector; is the left eigenvector.

[0023] Preferably, in S3, a low-dispersion bending mode is selected as the optimal monitoring mode according to the vibration dispersion characteristics, and the optimal excitation frequency range is determined to be 0.5 kHz to 2.5 kHz.

[0024] Preferably, in S4, a three-dimensional finite element model of the arched steel tube concrete is constructed according to S1, S2 and S3, and material properties, boundary conditions and structural interface debonding defects are defined;

[0025] Among them, the material properties include steel density, steel Young's modulus, steel Poisson's ratio, concrete density, concrete Young's modulus and concrete Poisson's ratio;

[0026] The simulated wave number, phase velocity and group velocity dispersion curves are extracted and compared with the theoretical solution in S3 to verify the accuracy of the model.

[0027] Preferably, in S5, an electromagnetic ultrasonic array sensor is used in the ultrasonic guided wave detection experiment to collect time domain signals and extract measured dispersion characteristics, and ultrasonic guided waves are emitted to the arched steel tube concrete specimen, while recording experimental data including propagation distance, amplitude and time difference.

[0028] Preferably, in S6, damage location is performed through reflection and transmission coefficients in time-frequency analysis, the degree of material damage is reflected by the energy attenuation coefficient, the experimental data is compared with simulation and theoretical data, and the accuracy of the theoretical model is verified in combination with error analysis.

[0029] Therefore, the present invention adopts the above-mentioned inspection method of arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves, and the beneficial effects are as follows:

[0030] (1) This paper proposes a nondestructive monitoring method for arched steel tube concrete structures. By optimizing the sensor configuration and signal analysis algorithm, it achieves millimeter-level deformation detection accuracy while ensuring operational convenience. It is particularly suitable for long-term health monitoring of large-curvature bridge structures.

[0031] (2) The curvature change of the arch structure complicates the waveguide propagation path, and the wave may propagate along the curve or scatter, increasing the difficulty of signal analysis; reflection, refraction and mode conversion (such as longitudinal wave to transverse wave) are prone to occur at the interface between the steel pipe and the concrete, resulting in signal mixing; the present invention constructs a multi-physical field coupling detection model; through the combination of finite element simulation and experimental verification, the 0.5-2.5kHz characteristic frequency band is optimized and selected as the excitation frequency, and the bending mode is determined as the sensitive detection mode, which solves the above problems while improving the detection accuracy and efficiency.

[0032] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is an overall flow chart of an embodiment of a method for detecting an arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves according to the present invention;

[0034] Figure 2 A three-dimensional model diagram of an arched steel tube concrete arch structure according to an embodiment of the method for detecting an arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves of the present invention;

[0035] Figure 3 4. A quasi-cylindrical coordinate system diagram of an arched steel tube concrete-filled arch structure according to an embodiment of the method for detecting an arched steel tube concrete-filled bridge based on the dispersion characteristics of ultrasonic guided waves of the present invention;

[0036] Figure 4 1. This is a phase velocity dispersion curve diagram of an arched steel tube concrete-filled arch structure according to an embodiment of the method for detecting an arched steel tube concrete-filled bridge based on the dispersion characteristics of ultrasonic guided waves of the present invention;

[0037] Figure 5 3. This is a wave number dispersion curve of an arched steel tube concrete arch structure according to an embodiment of the method for detecting an arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves of the present invention;

[0038] Figure 6 1. It is a group velocity dispersion curve diagram of an arched steel tube concrete arch structure according to an embodiment of the method for detecting an arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves of the present invention;

[0039] Figure 7 Schematic diagram of an ultrasonic guided wave detection system according to an embodiment of the method for detecting an arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves of the present invention. DETAILED DESCRIPTION

[0040] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0041] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0042] This invention is a method for inspecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves. Addressing the analytical challenges of guided wave propagation due to the complex geometry and material interface coupling of these composite structures, the method optimizes the algorithm based on the traditional semi-analytical finite element method. By constructing a rotating coordinate system, the method achieves a precise parametric representation of the spatial curved surface of the arch ribs. By combining nonlinear perturbation theory with the multimodal dispersion characteristics of guided waves, the method ultimately derives a multi-parameter joint evaluation model based on wave number variation, phase velocity variation, and group velocity variation. This model establishes a quantitative mapping relationship between guided wave characteristic parameters and key quality indicators such as structural interface debonding defects. By introducing tensor analysis tools to process the wave equation in a rotating coordinate system, the method significantly improves the accuracy of numerical simulations of guided wave propagation paths in complex curved plate-shell structures, providing a new theoretical framework for nondestructive testing of key arch bridge components.

[0043] like Figure 1 As shown, the detection method of arched steel tube concrete bridge based on the dispersion characteristics of ultrasonic guided waves includes the following steps:

[0044] S1, based on the arched steel tube concrete arch structure Figure 2 As shown, establish a rotating coordinate system as follows:

[0045] like Figure 3 As shown, any point in the Cartesian coordinate system ( x , y , z ) using quasi-cylindrical coordinate system It is expressed as shown in formula (1):

[0046] (1).

[0047] in, x , y , z represents the coordinates of a Cartesian coordinate system point, r Indicates arrival z The perpendicular distance of the axis is the radial coordinate, express r and x The angle with respect to the positive direction of the axis is the azimuth. z ' is the axial coordinate of the point in the quasi-cylindrical coordinate system, q is the polar coordinate radius, is the central angle of the circle.

[0048] It should be noted that the quasi-cylindrical coordinate system used in the present invention has a curved axis, rather than the straight z-axis of cylindrical coordinates.

[0049] S2. Use the semi-analytical finite element method to establish the wave characteristic equation of the arched steel tube concrete, and obtain the guided wave dispersion characteristic equation of the arched steel tube concrete, as shown in formula (2):

[0050] (2);

[0051] Where, is the circular frequency; K 1. K 2 and K 3 is the system stiffness matrix; M is the system mass matrix; is the global node displacement vector; is the wave number; i Is an imaginary number.

[0052] S3. According to the wave characteristic equation of the arched steel tube concrete arch structure, the theoretical wave number, phase velocity and group velocity dispersion curve of the arched steel tube concrete are calculated as follows: Figure 4-6 As shown in Figure 2, the formulas for solving the group velocity and phase velocity are as follows:

[0053] (3);

[0054] (4);

[0055] Where, is the phase velocity; is the group velocity; is the right eigenvector; is the left eigenvector.

[0056] The vibration dispersion characteristics (wavenumber dispersion curves, phase velocity dispersion curves, and group velocity dispersion curves) of the guided wave modes of the arched steel tube concrete-filled arch structure at different frequencies were analyzed, and the corresponding modes of the arched steel tube concrete-filled arch structure at different frequencies were obtained. The low-dispersion bending mode was selected as the optimal monitoring mode, and the optimal excitation frequency, i.e., the optimal detection frequency range, was determined to be 0.5kHz to 2.5kHz.

[0057] S4. Construct a three-dimensional finite element model of the arched steel tube concrete structure based on S1, S2, and S3, and define material properties, boundary conditions, and structural interface debonding defects; wherein the material properties include steel density, steel Young's modulus, steel Poisson's ratio, concrete density, concrete Young's modulus, and concrete Poisson's ratio.

[0058] Combined with finite element modeling, the simulation dispersion curve is drawn, and the simulation wave number, phase velocity and group velocity dispersion curves are extracted and compared with the theoretical solution in S3 to verify the model accuracy.

[0059] S5. According to S3 and S4, an ultrasonic guided wave detection experiment of the arched steel tube concrete structure is carried out. An electromagnetic ultrasonic array sensor is used to collect time domain signals and extract the measured dispersion characteristics. Ultrasonic guided waves are emitted to the arched steel tube concrete specimens. At the same time, the experimental data including propagation distance, amplitude and time difference are recorded and exported.

[0060] S6. Process the experimental data derived from S5, locate the damage through the reflection and transmission coefficients in time-frequency analysis, reflect the degree of material damage through the energy attenuation coefficient, compare the experimental data with the simulation and theoretical data, and verify the accuracy of the theoretical model through error analysis.

[0061] Example 1

[0062] The mathematical model of the semi-analytical finite element method is applicable to the stress wave propagating in the waveguide medium in vacuum. The method is applicable to any complex cross section. Considering the finite element unit is composed of Small quadrilaterals on the plane and The curved edges in the direction.

[0063] Strain and simple harmonic displacement u The relationship can be expressed as:

[0064] (5);

[0065] Where L is the differential operator, express r and x The angle with respect to the positive direction of the axis is the azimuth. z ' is the axial coordinate of the point in the quasi-cylindrical coordinate system, 、 、 z 'Differential operator in direction, Express r Seek derivation, Express z 'Derivative.

[0066] The strain matrix is ​​sorted as follows:

[0067] (6);

[0068] Where, 、 is the strain matrix, N Expressed as a shape function, 、 Indicates r and Directional form function.

[0069] For viscoelastic waveguide media, the matrix C is a complex matrix that describes the damping characteristics of the material. When damping is ignored, the material stiffness matrix C is:

[0070] (7);

[0071] Where C is the material stiffness matrix, E is the elastic modulus, v is Poisson's ratio.

[0072] The material constitutive relationship is:

[0073] (8);

[0074] Where, is stress; For strain.

[0075] Combining the above formulas, the governing equation of the waveguide structure is obtained:

[0076] (9);

[0077] in, is the circular frequency; K 1. K 2 and K 3 is the system stiffness matrix; M is the system mass matrix; is the global node displacement vector; is the wave number; i Is an imaginary number.

[0078] Formula (9) is converted into the first-order wave number characteristic equation as follows:

[0079] (10);

[0080] (11).

[0081] For any given frequency , solving equation (10) to obtain 2M eigenvalues And the corresponding 2M eigenvectors. These eigenvalues ​​include the wave numbers of the forward wave and the reverse wave. From equation (10), we can get 2M left eigenvectors and the right eigenvector . No. m Mode at frequency The phase velocity at is expressed as:

[0082] (12);

[0083] Where, represents the phase velocity, is the wave number of the mode.

[0084] Using eigenvalues ​​and eigenvectors, the displacement field of the forward wave in the curved region can be obtained as:

[0085] (13);

[0086] in, is the right eigenvector Upper part; is the line source loading point; The first step is determined by the geometric and boundary conditions m The amplitude of the mode, is the displacement field, z ' is the axial coordinate of the point in the quasi-cylindrical coordinate system, Indicates from m =1 accumulated to m = M , e is a natural constant, exp is expressed as the power of e, and the following content is expressed as the power of e.

[0087] In guided wave nondestructive testing (GWT), the original signal is often a mixture of reflected, transmitted, and scattered components. Signal processing (such as time-frequency analysis and modal separation) can effectively distinguish the propagation characteristics of different modes, accurately extract the signal distortion characteristics caused by defects, and avoid interference caused by structural curvature and material differences.

[0088] The time domain signal of ultrasonic guided waves propagating in the structure can be expressed as:

[0089] (14);

[0090] in, A represents the amplitude, is the attenuation coefficient, d is the propagation distance, k is the wave number, f is the frequency, t For time, is the time domain signal, is pi, and cos is the cosine function.

[0091] The actual signal is formed by the superposition of multiple modes:

[0092] (15);

[0093] in, m is the guided wave mode, Indicates that all eligible m Add the corresponding terms, represents the amplitude in the m mode, is the attenuation coefficient in the m mode, is the wave number in mode m.

[0094] S6. Damage location is performed through reflection and transmission coefficients in time domain analysis:

[0095] (16);

[0096] in, Z 1 and Z 2 is the material impedance, R and T are the reflection coefficient and transmission coefficient.

[0097] The time difference :

[0098] (17);

[0099] in, d is the distance to the injury site, is the group velocity.

[0100] The short-time Fourier transform formula is:

[0101] (18);

[0102] in, is a discrete signal; is the window function, It represents the result of short-time Fourier transform, which is a function of time t and frequency f. is a complex exponential function, represents a signal variable, Represents a variable Integrate from negative infinity to positive infinity.

[0103] Injury location Expressed by group velocity and time difference:

[0104] (19);

[0105] in, Indicates the time difference.

[0106] The energy attenuation coefficient reflects the degree of material damage:

[0107] (20);

[0108] in, is the initial amplitude, A is the receiving amplitude.

[0109] This paper first solves the waveguide equations of the arched concrete-filled steel tube structure by establishing a numerical model, obtaining the dispersion curves of its phase velocity and energy velocity, and systematically analyzing the vibration dispersion characteristics of the structure. Subsequently, based on the finite element modal analysis method, the dominant modes with low dispersion characteristics are screened, while ensuring that the energy velocity of the selected mode at the corresponding frequency is significantly different from that of other modes. This facilitates the accurate identification and in-depth analysis of waveform signals in subsequent experiments. Through this comprehensive research method, it is possible to scientifically determine the effective modes suitable for structural health monitoring and their corresponding excitation frequency ranges.

[0110] After selecting the monitoring mode and initially defining the range of the excitation frequency, the present invention further refines the identification of the optimal excitation frequency. Using the acoustoelastic proportional boundary finite element method, the frequency-energy-velocity correlation curve and energy-velocity sensitivity distribution curve of the structure are systematically solved. By identifying the peak position of the energy-velocity sensitivity, the optimal excitation frequency parameters are precisely determined. This method achieves coupled optimization of excitation frequency selection and structural dynamic response, providing a theoretical basis and implementation benchmark for subsequent experimental research.

[0111] In summary, the method proposed in the present invention can be used to determine the most suitable excitation frequency and the corresponding mode.

[0112] In one embodiment, the placement of the guided wave sensor is designed based on the vibration mode diagram of the arched steel tube concrete arch structure and the optimal mode. Figure 7 shown.

[0113] Figure 7 The ultrasonic guided wave equipment in the test piece is responsible for generating and controlling the ultrasonic guided wave signal. It generates an electrical signal of specific frequency and amplitude through the internal circuit to simulate the excitation and propagation process of the ultrasonic guided wave in the test piece.

[0114] The computer is responsible for data processing and command control, sending parameters (such as excitation frequency and waveform) to the ultrasonic guided wave equipment, and receiving and analyzing detection data (such as time domain signals, guided wave mode group velocity and phase velocity).

[0115] The preamplifier amplifies the weak electrical signal output by the ultrasonic guided wave device, increases the signal strength, ensures that the subsequent oscilloscope can collect it clearly, and avoids detection errors caused by weak signals.

[0116] The oscilloscope observes and records the electrical signal waveform in real time, showing the time domain characteristics of ultrasonic guided wave propagation (such as amplitude and time difference), providing raw data for analyzing the interaction between guided waves and defects.

[0117] The test object was an arched concrete-filled steel tube specimen containing interfacial debonding defects. The purpose was to verify the ability of ultrasonic guided waves to identify structural damage. A ring of exciters and receivers was placed at each end of the arched concrete-filled steel tube. The exciters converted the electrical signals from the ultrasonic guided wave device into ultrasonic guided waves, which were then coupled to the surface of the arched concrete-filled steel tube specimen, simulating guided wave "transmission." The receivers captured the guided waves after propagation through the specimen, converted them into electrical signals, and transmitted them back, achieving guided wave "reception," completing the signal loop.

[0118] The detection process logic is as follows:

[0119] Signal generation: The computer sends instructions → the ultrasonic guided wave device generates electrical signals → the preamplifier enhances the signal.

[0120] Guided wave excitation: The exciter converts the electrical signal into ultrasonic guided waves, which are transmitted into the test piece and propagate along the arch structure.

[0121] Signal reception: The receiver captures the propagated waveguide and converts it back into an electrical signal → the oscilloscope displays the waveform → the signal is sent back to the computer for analysis.

[0122] Data analysis: The computer extracts the dispersion characteristics through time-frequency analysis (such as short-time Fourier transform), and combines it with theoretical / simulation data comparison to determine the damage of the specimen (such as the location and extent of the defect).

[0123] Among them, the material properties of the arched steel tube concrete arch structure are shown in Table 1 below:

[0124] Table 1 Material properties of arched steel tube concrete arch structure

[0125]

[0126] Therefore, the present invention adopts the above-mentioned arched steel tube concrete bridge detection method based on the dispersion characteristics of ultrasonic guided waves, uses multi-physics field coupling simulation technology to establish a guided wave propagation model, integrates material anisotropy and interface contact effects, and uses electromagnetic ultrasonic array sensors to improve signal acquisition efficiency. The deep learning dispersion compensation algorithm is introduced to break through the technical bottlenecks of traditional modal separation and signal decoupling, forming a complete technical system integrating theoretical modeling, simulation optimization and experimental verification. This method provides a high-precision, highly adaptable engineering solution for arch bridge structural health monitoring, significantly improving the reliability and practicality of damage identification in complex curvature structures.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves, characterized in that: The following steps are involved: S1. Establish a rotating coordinate system based on the arched steel tube concrete arch structure; S2. Use the semi-analytical finite element method to establish the wave characteristic equation of the arched steel tube concrete and obtain the guided wave dispersion characteristic equation of the arched steel tube concrete; S3. Calculate the theoretical wave number, phase velocity, and group velocity dispersion curves of the arched steel tube concrete, analyze the vibration dispersion characteristics of the guided wave mode at different frequencies, and determine the optimal monitoring mode and excitation frequency range; S4. Construct a three-dimensional finite element model of the arched steel tube concrete structure according to S1, S2 and S3, and draw a simulation dispersion curve diagram in combination with the finite element modeling; S5. Conduct ultrasonic guided wave testing experiments on arched steel tube concrete structures according to S3 and S4, and derive experimental data; S6, processing the experimental data derived from S5, and comparing and analyzing the experimental data with the simulation and theoretical data; The rotation coordinate system in S1 is as follows: Any point in the Cartesian coordinate system Quasi-cylindrical coordinate system It is expressed as shown in formula (1): （1）； in, represents the coordinates of a Cartesian coordinate system point, Indicates arrival The perpendicular distance of the axis is the radial coordinate, express and The angle with respect to the positive direction of the axis is the azimuth. is the axial coordinate of the point in the quasi-cylindrical coordinate system, is the polar coordinate radius, is the central angle; In S2, the semi-analytical finite element method is used to establish the wave characteristic equation of the arched steel tube concrete. The mathematical model of the semi-analytical finite element method is applicable to the stress wave propagating in the waveguide medium in a vacuum. This method is applicable to any complex cross-section. Considering the finite element unit is composed of Small quadrilaterals on the plane and The curved edges in the direction; Strain and simple harmonic displacement The relationship is expressed as: （2）； Where L is the differential operator, express and The angle with respect to the positive direction of the axis is the azimuth. is the axial coordinate of the point in the quasi-cylindrical coordinate system, 、 、 Differential operator in direction, Express Seek derivation, Express Derivative; The strain matrix is ​​sorted as follows: （3）； Where, 、 is the strain matrix, N Expressed as a shape function, 、 Indicates and Form function in direction; For viscoelastic waveguide media, the matrix C is a complex matrix to describe the damping characteristics of the material. When the damping is neglected, the material stiffness matrix C is: （4）； Where C is the material stiffness matrix, E is the elastic modulus, is Poisson's ratio; The material constitutive relationship is: （5）； Where, is stress; For strain; The wave dispersion characteristic equation of the arched steel tube concrete is obtained, as shown in formula (6): （6）； Where, is the circular frequency; 、 and is the system stiffness matrix; M is the system mass matrix; is the global node displacement vector; is the wave number; Is an imaginary number.

2. The method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves according to claim 1 is characterized in that: In S3, the theoretical wave number, phase velocity, and group velocity dispersion curves of the arched steel tube concrete arch structure are calculated based on the wave characteristic equation of the arched steel tube concrete arch structure. The formulas for solving the group velocity and phase velocity are as follows: （7）； （8）； Where, is the phase velocity; is the group velocity; is the right eigenvector; is the left eigenvector.

3. The method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves according to claim 2, characterized in that: In S3, the low-dispersion bending mode is selected as the optimal monitoring mode according to the vibration dispersion characteristics, and the optimal excitation frequency range is determined to be 0.5~2.5kHz.

4. The method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves according to claim 3 is characterized in that: In S4, a three-dimensional finite element model of the arched concrete-filled steel tube is constructed based on S1, S2, and S3, and the material properties, boundary conditions, and structural interface debonding defects are defined; Among them, the material properties include steel density, steel Young's modulus, steel Poisson's ratio, concrete density, concrete Young's modulus and concrete Poisson's ratio; The simulated wave number, phase velocity and group velocity dispersion curves are extracted and compared with the theoretical solution in S3 to verify the accuracy of the model.

5. The method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves according to claim 4 is characterized in that: In S5, an electromagnetic ultrasonic array sensor was used to collect time domain signals and extract measured dispersion characteristics in the ultrasonic guided wave detection experiment. Ultrasonic guided waves were emitted to the arched steel tube concrete specimen, and experimental data including propagation distance, amplitude and time difference were recorded at the same time.

6. The method for detecting arched steel tube concrete bridges based on the dispersion characteristics of ultrasonic guided waves according to claim 5, characterized in that: In S6, damage location is performed through reflection and transmission coefficients in time-frequency analysis, and the degree of material damage is reflected by the energy attenuation coefficient. The experimental data are compared with simulation and theoretical data, and the accuracy of the theoretical model is verified by error analysis.

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