Fluid filling pipeline guided wave modal tracking method based on optimal transmission distance

Abstract

The invention discloses a fluid filling pipeline guided wave modal tracking method based on an optimal transmission distance. The method comprises the following steps: firstly, calculating a characteristic solution by using a semi-analytical finite element method; secondly, introducing an optimal transmission distance (EMD) in an optimal transmission theory as modal similarity measurement, measuring modal similarity by calculating the minimum physical work of kinetic energy distribution rearrangement, and combining a section geometric geodesic distance to enhance physical interpretability; meanwhile, a continuous stabilization strategy based on wavenumber prediction is introduced to suppress mismatching; and finally, realizing global optimal modal matching by using a Hungary algorithm. According to the method, modal exchange errors can be effectively eliminated, tracking robustness is kept in a complex frequency dispersion area, and meanwhile, visual graphic interpretation of modal evolution can be provided.

Description

Technical Field

[0001] This invention relates to the field of non-destructive testing and structural health monitoring of pipeline structures, and in particular to an automatic modal tracking method for guided wave dispersion curves applicable to complex waveguide structures such as fluid-filled pipelines. Background Technology

[0002] Guided wave testing (GWT) has become an important method for screening and monitoring long-distance pipelines due to its advantages such as wide coverage of single-point excitation and ability to detect areas that are inaccessible underground or under cladding. In engineering implementation, accurately understanding the dispersion characteristics of the pipeline waveguide is a prerequisite for effective guided wave testing.

[0003] For ideal vacuum or free-boundary pipelines, their dispersion curves can be obtained analytically. However, actual industrial pipelines often transport liquids or gases (such as oil and gas pipelines), and the strong fluid-structure interaction (FSI) between the fluid and the pipe wall significantly alters the dispersion characteristics. Under fluid-filled conditions, the guided wave mode density increases sharply, and strong coupling effects exist between different mode families, leading to frequent mode veering, crossing, and mode splitting phenomena in the dispersion curve. At this point, analytical solutions become extremely difficult, typically requiring the use of numerical methods such as the semi-analytical finite element method (SAFE) to solve for the eigenvalues ​​at discrete frequency points, and then connecting these discrete solutions into a continuous dispersion curve using mode tracing techniques.

[0004] Existing automatic modal tracking methods are mainly divided into two categories, but both have limitations when dealing with fluid-filled pipes:

[0005] 1. Extrapolation-based methods: These methods rely on the local smoothness of eigenvalues, using Taylor's formula or Pad's formula for local approximation before extrapolation prediction. However, in regions of drastic modal evolution, such as the Veering region, the wavenumber changes at an extremely high rate with frequency, and even small frequency steps can lead to prediction failure and potential track breakage.

[0006] 2. Correlation-based methods: These methods rely on correlation indices between modal shapes, such as the Modal Assurance Criterion (MAC). However, MAC only quantifies the linear correlation between two vectors, and its value [0,1] lacks a clear physical boundary. When the modal shape changes significantly (e.g., during mode switching) or when different modes have partial similarities, the MAC calculation results are prone to ambiguity, leading to ID-Switch errors.

[0007] Furthermore, existing methods are mostly "black box" operations, only outputting tracking results and lacking an intuitive explanation of the physical mechanisms of modal evolution, making manual verification and engineering decision-making difficult. Therefore, there is an urgent need for an automatic modal tracking method that can adapt to the complex dispersion characteristics of fluid-filled pipes, has clear physical interpretability, and is robust. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a fluid-filled pipe guided wave mode tracking method based on optimal transmission distance, so as to solve the problems of tracking errors and lack of physical interpretability caused by drastic changes in mode shape when the existing technology is dealing with high mode density and strong fluid-structure interaction waveguides.

[0009] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: a guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance, comprising the following steps:

[0010] S1. Numerical Modeling and Characteristic Solution Acquisition: A numerical model of the fluid-filled pipe is constructed using the semi-analytical finite element method (SAFE). The model is scanned within a set frequency range to solve for the complex wave number and corresponding mode shape data at each discrete frequency point, and non-propagating modes are filtered out.

[0011] S2. Constructing a physical-driven modal similarity metric: Introducing the optimal transmission distance (EMD) from optimal transmission theory as a similarity index; treating the kinetic energy distribution of each mode on the waveguide cross section as a probability distribution, and the geodesic distance between finite element mesh nodes as the transportation cost, calculating the minimum physical work required to rearrange the kinetic energy distribution of one mode into another mode, thereby quantifying the physical differences between modes;

[0012] S3. Introducing a continuity stabilization strategy: Based on the physical continuity of the dispersion curve, the wavenumber at the next discrete frequency point is predicted using Taylor series extrapolation. The deviation between the actual wavenumber and the predicted value of the candidate mode is calculated. This deviation is then normalized using the median of the characteristic wavenumber spacing at the current frequency layer, and a stabilization constraint term S is constructed. ij ;

[0013] S4. Global Optimization Allocation and Modal Connection: The EMD physical distance and stabilization constraint terms are weighted and fused to construct a comprehensive cost matrix; the modal tracking problem between adjacent frequency steps is modeled as a bipartite graph minimum weight matching problem model, and the Hungarian algorithm is used to solve it to determine the globally optimal modal correspondence, thereby connecting them to form a continuous dispersion curve.

[0014] As a preferred embodiment, the construction of the comprehensive cost matrix, which forms the final modal distance matrix D, is as follows:

[0015] Dij =EMD ij +λS ij

[0016] In the formula, the weighting coefficient λ is any value between 0.03 and 0.1;

[0017] The goal of constructing the bipartite graph minimum weight matching problem model is to minimize the total matching cost. The problem is solved using the Hungarian algorithm, yielding a Boolean matrix X, where X... ij =1 indicates that mode i and mode j belong to the same dispersion branch.

[0018] As a preferred embodiment, in step S2, the kinetic energy distribution is calculated by extracting the time-averaged kinetic energy E of the mode at the grid nodes. m The formula is Where ρ m Let ω be the node density, ω be the angular frequency, and Δ be the angular frequency. m The displacement amplitude is given; and after normalization, the probability distribution e(m) = E is obtained. m / ∑E n In the formula, E n Let represent the time-averaged kinetic energy of any finite element node n.

[0019] As a preferred embodiment, in step S2, the method for obtaining the geodesic distance is as follows: the finite element mesh of the pipe section is regarded as a weighted undirected graph, the edge weight is the Euclidean distance between nodes, the Dijkstra algorithm or the Floyd-Warshall algorithm is used to calculate the shortest path distance between any two nodes along the mesh surface, and dimensionless processing is performed.

[0020] As a preferred approach, Dijkstra's algorithm is used to calculate the shortest path distance between any two nodes m and n on the grid; this shortest path distance matrix is ​​then divided by its midpoint to obtain C. mn ;

[0021] Then solve the EMD problem: solve the following linear programming problem to find the optimal transfer matrix T:

[0022]

[0023] The constraint is energy conservation: and Matrix element T mn This represents the energy share of moving from node m in mode i to node n in mode j.

[0024] As a preferred embodiment, in step S3, the wavenumber at the next discrete frequency point is predicted using Taylor series extrapolation, and the deviation between the actual wavenumber and the predicted value of the candidate mode is calculated, specifically as follows:

[0025] Using the previous frequency step f n-1 and the current step f n The wavenumber is used to predict the next frequency step f using a first-order Taylor expansion. n+1 wavenumber:

[0026]

[0027] Calculate the actual wavenumber k of candidate mode j j (f n+1 The absolute deviation between the predicted value and the actual value

[0028] As a preferred embodiment, in step S3, the normalization method specifically involves: calculating the adjacent differences after sorting all modal wavenumbers of the target frequency layer, and taking the median of the non-zero differences as the feature spacing δk. char The wavenumber prediction bias is normalized by division using this characteristic spacing.

[0029] As a preferred approach, step S5 is also included: Visualizing the modal evolution mechanism: using the optimal transmission scheme matrix generated when calculating EMD in step S2, it is analyzed as an energy flow field, and the energy migration path of the mode during frequency change is visualized.

[0030] The beneficial effects of this invention are:

[0031] High robustness: The EMD metric is based on the redistribution cost of physical quantities (kinetic energy), which is naturally robust to drastic shape changes during mode transitions compared to the MAC method that simply compares vector shapes. Combined with a stabilization strategy based on median normalization, it significantly reduces identity switching errors and maintains extremely high tracking accuracy even with sparse frequency step sizes.

[0032] High physical interpretability: The introduction of geodesic distance and kinetic energy distribution gives the similarity metric a clear physical meaning. In particular, by visualizing the optimal transport scheme, it is possible to intuitively demonstrate how energy migrates from the inner wall to the outer wall or rotates circumferentially, revealing the intrinsic physical mechanism of mode switching and making the tracking process transparent.

[0033] Global optimality: The Hungarian algorithm is used instead of the traditional greedy (nearest neighbor) algorithm, which ensures that in the dense modal region, the overall cost of all modal matching between frequency layers is minimized, avoiding tracking interruption or chaos caused by local conflicts.

[0034] High industrial application value and scenario adaptability: This method is particularly suitable for on-site inspection of in-service liquid-filled pipelines such as oil and gas pipelines and heating pipelines. It can overcome the dispersion analysis problem caused by strong fluid-structure interaction, provide an accurate wave velocity reference for long-distance guided wave screening, and significantly reduce false alarms and missed alarms. Its extremely high robustness and automation capabilities make it easy to integrate into portable inspection equipment or internal inspection robots. It can generate reliable curves without human intervention, greatly reducing the technical threshold. At the same time, this method can be extended to the health monitoring of complex waveguide structures such as submarine composite pipes, buried pipes, and irregularly shaped steel rails. It can also intuitively reveal modal characteristics through energy visualization function, assist engineers in optimizing excitation frequency and probe selection, and guide the formulation of optimal inspection process. Attached Figure Description

[0035] Figure 1 This is an overall flowchart of the method of the present invention.

[0036] Figure 2 This is a schematic diagram of the principle of discrete EMD metric calculation in this invention; (a) shows the definition of geodesic distance on the pipe cross-section grid, and (b) shows the visualization of the optimal transport scheme for intermodal kinetic energy rearrangement.

[0037] Figure 3 This diagram illustrates the continuous stabilization strategy, showing the wavenumber prediction, bias calculation, and characteristic spacing normalization process.

[0038] Figure 4 The diagram shows the dispersion curves of the L(0,3) and L(0,4) modes when they change direction in the embodiments of the present invention, as well as the modal radial kinetic energy distribution diagrams of four typical stages.

[0039] Figure 5 For the corresponding Figure 3 A visualization of energy transfer in the mid-mode turning region, showing the radial component (left column) and tangential component (right column) of the energy flow.

[0040] Figure 6 The results show a comparison between the method of this invention and existing methods; (a)-(e) show the dispersion curve tracking effect under different strategies, and (f) shows the identity switching rate (R) under different frequency step sizes. SW Indicator comparison. Detailed Implementation

[0041] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0042] Automatic tracking of guided wave dispersion curves in water-filled steel pipes

[0043] This embodiment uses a steel pipe with an outer diameter of 219.1 mm and a wall thickness of 14.3 mm, filled with water, with a free boundary on the outside. The density of the steel is 7800 kg / m³. 3Young's modulus 210 GPa, Poisson's ratio 0.3; water density 1000 kg / m³ 3 The speed of sound is 1500 m / s.

[0044] like Figure 1 As shown, the method of the present invention specifically includes the following steps:

[0045] Step S1: Numerical Modeling and Characteristic Solution Acquisition

[0046] The above-mentioned water-filled pipe was modeled using the semi-analytical finite element method (SAFE).

[0047] 1.1. Discretization: The cross-section of the pipe is discretized into second-order triangular elements. The solid domain follows the elastic dynamics equations, and the fluid domain follows the acoustic wave equations. At the interface, the two satisfy the conditions of displacement continuity and stress equilibrium.

[0048] 1.2. Solving for eigenvalues: Sweep the frequency range of 0-20kHz and solve for the characteristic equation. in Φ is the complex wave number, and Φ is the mode shape vector.

[0049] 1.3. Filtering: Using criteria Remove non-propagating modes (spurious modes) that decay too quickly, and retain physically propagating modes.

[0050] Step S2: Calculate modal similarity based on EMD

[0051] In order to quantize frequency f n Mode i at point i and the next frequency f n+1 The difference between modes j at point j is used to calculate the optimal transmission distance (EMD) between them.

[0052] 2.1. Define the probability distribution: Calculate the time-averaged kinetic energy of mode i at grid node m. To meet the input requirements of EMD, it is normalized to a probability distribution: In the formula, En represents the time-averaged kinetic energy of any finite element node n. This reflects the energy spatial distribution of the mode on the cross section.

[0053] 2.2. Defining Ground Distance: The finite element mesh is considered as a weighted undirected graph, with edge weights equal to the Euclidean distance between nodes. Dijkstra's algorithm is used to calculate the shortest path distance (i.e., geodesic distance) between any two nodes m and n on the mesh. This distance matrix is ​​then dimensionless by dividing by its midpoint, yielding C. mn .like Figure 2 As shown in (a), the geodesic distance accurately reflects the topology of the annular section and is superior to the straight-line Euclidean distance represented by the blue dashed line.

[0054] 2.3. Solving EMD: Solve the following linear programming problem to find the optimal transfer matrix T:

[0055]

[0056] The constraint is energy conservation: and Matrix element T mn This represents the energy share of moving from node m in mode i to node n in mode j.

[0057] Step S3: Continuous Stabilization Strategy

[0058] To overcome the problem that EMD may be overly sensitive to minute shape changes at extremely small frequency steps, physical constraints based on wavenumber continuity (such as...) are introduced. Figure 3 (As shown).

[0059] 3.1. Extrapolation prediction: using the previous frequency step f n-1 and the current step f n The wavenumber is used to predict the next frequency step f using a first-order Taylor expansion. n+1 wavenumber:

[0060]

[0061] 3.2. Deviation Calculation: Calculate the actual wavenumber k of candidate mode j. j (f n+1 The absolute deviation between the predicted value and the actual value

[0062] 3.3. Normalization: To give the deviation physical meaning and adapt it to the modal density of different frequency bands, the target frequency layer f is calculated. n+1 The set of adjacent differences after sorting all modal wavenumbers {δk} (p)}, take the median as the feature distance: δk char =median({δk (p) |δk (p) ≠0}).

[0063] 3.4. Calculate the stabilization term S ij :S ij =Δk ij / δk char .

[0064] Step S4: Construct the integrated distance and global allocation

[0065] 4.1. Constructing the cost matrix: Weighted fusion of EMD distance and stabilization term to form the final modal distance matrix D:

[0066] D ij =EMDij +λS ij (3)

[0067] In this embodiment, the weighting coefficient λ is preferably in the range of 0.03-0.1.

[0068] 4.2. Global Optimal Matching: Construct a bipartite graph matching model with the goal of minimizing the total matching cost. The problem is solved using the Hungarian algorithm, yielding a Boolean matrix X, where X... ij =1 indicates that mode i and mode j belong to the same dispersion branch.

[0069] Step S5: Performance Quantitative Evaluation and Visual Analysis

[0070] 5.1. Evaluation Indicator Definition (Identity Switching Rate R) SW ):

[0071] To quantitatively evaluate the accuracy and stability of the modal tracking algorithm, this embodiment introduces the ID-Switch Rate (R) metric. SW The calculation method is as follows: traverse each dispersion branch trajectory that serves as the ground truth, and check whether the mode IDs assigned between adjacent discrete frequency points have changed. If the assigned mode IDs change between two consecutive points, it is recorded as an ID switching event (IDSW). SW Defined as the ratio of the total number of ID switching events occurring across the entire frequency range to the total number of trajectory data points. R SW The higher the R value, the more frequent the identity switching in the tracking results, and the lower the accuracy; SW The lower the value, the more stable the tracking results and the higher the accuracy.

[0072] 5.2. Tracking accuracy verification results:

[0073] For the aforementioned water-filled steel pipe model, ablation experiments were conducted at different frequency discrete step lengths (100Hz, 300Hz, and 500Hz) for comparison. The results are as follows: Figure 6 As shown:

[0074] Existing technology (MAC-BNN): It adopts the traditional MAC combined with the bidirectional nearest neighbor algorithm, which results in frequent identity switching in the high-frequency region (12-20kHz) with dense modes, causing the dispersion curve to break and become disordered.

[0075] The method of this invention (EMD-Hun-Stabilized): R at a fine step size of 100Hz SW The value drops to 0%, meaning all modes are correctly connected without any identity switching errors. Even with a large step size (sparse sampling) of 500Hz, R... SWIt remains below 0.5%.

[0076] This demonstrates that the EMD physical metric and continuity stabilization strategy introduced in this invention significantly improves the robustness of the algorithm in complex fluid-structure interaction environments.

[0077] 5.3. Visual analysis of modal steering mechanism:

[0078] To further verify the physical effectiveness of the method of the present invention in handling complex fluid-structure interaction, a typical modal turning region in a water-filled steel pipe, namely the frequency band in which longitudinal modes L(0,3) and L(0,4) interact, was selected, and the transmission matrix T calculated in step 2 was used for visualization analysis.

[0079] like Figure 4 As shown in (a), the dispersion curves of the L(0,3) and L(0,4) modes are illustrated. The two curves approach each other and then change direction in the frequency range of approximately 18kHz to 20kHz. Four characteristic stages are marked in the figure, and the corresponding modal energy distributions are as follows: Figure 4 As shown in (b):

[0080] In stage ①, energy is mainly concentrated on the inner wall of the pipe, exhibiting typical interface wave characteristics. As the frequency increases into stages ② and ③, the energy center of gravity shifts outward. By stage ④, the energy distribution has been completely reconstructed, mainly concentrated on the outer wall of the pipe. This indicates that the modal shape changes are extremely drastic in the modal transition region. Traditional methods, lacking a clear decision-making basis, still rely on intuition and experience for direct analysis of modal shape changes during manual inspection.

[0081] By utilizing the EMD optimal transmission scheme of the present invention, the energy flow between adjacent frequency steps can be decomposed into radial flow and tangential flow. Figure 5 The evolution of radial and tangential energy flows in the four stages described above is illustrated. In the radial energy flow diagram, red represents outward flow along the radius, and blue represents inward flow along the radius. In the tangential energy flow diagram, red represents counterclockwise flow, and blue represents clockwise flow.

[0082] Phase ① (Stable propagation): such as Figure 5 As shown in (a), the cross-section exhibits uniform and low-intensity blue specks. This indicates that the energy flow is mainly characterized by weak inward compression, which is a typical steady state of the longitudinal modes in a fluid-filled pipe under the influence of fluid load, with no obvious signs of modal abrupt change.

[0083] Phase ② (Instability Initiation): such as Figure 5As shown in (b), the flow pattern begins to break down as the cutoff frequency of the L(0,4) mode approaches. The previously uniform blue inward flow weakens, and red scattered points representing outward flow begin to appear in local regions. It is noteworthy that this instability began before the L(0,4) mode officially appeared, indicating that the L(0,3) mode had already begun to adjust its energy distribution in advance to adapt to the upcoming mode competition.

[0084] Phase ③ (Intense Restructuring): such as Figure 5 As shown in (c), this is the core region of mode transition. The figure is filled with high-intensity red scattering points, covering the entire pipe cross-section. This indicates that kinetic energy is undergoing a large-scale radial outward migration, meaning that energy is being "transported" from the inner wall to the outer wall with minimal physical cost to complete the transition. Figure 4 The mode reconstruction observed in (b).

[0085] Phase 4 (Restoration to Stability): such as Figure 5 As shown in (d), once the mode exchange is complete, the system returns to equilibrium. The high-intensity red outflow disappears, replaced by a low-intensity blue inflow similar to stage ①. This indicates that the L(0,3) mode has stabilized and continues to propagate in the new physical form (i.e., the outer wall waveguide mode).

[0086] Through the above Figure 4 and Figure 5 Through joint analysis, this invention intuitively reveals the physical mechanism behind the mode switching phenomenon, namely the directional migration of energy. This visualization capability is unavailable from traditional MAC correlation analysis, demonstrating that this method is based on the accurate capture of the laws governing the evolution of waveguide structures to implement tracking decisions.

[0087] The above embodiments are merely illustrative of the principles and effects of the present invention, as well as some examples of its application, and are not intended to limit the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these modifications and improvements are all within the scope of protection of the present invention.

Claims

1. A guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance, comprising the following steps: S1. Numerical Modeling and Characteristic Solution Acquisition: A numerical model of the fluid-filled pipe is constructed using the semi-analytical finite element method (SAFE). The model is scanned within a set frequency range to solve for the complex wave number and corresponding mode shape data at each discrete frequency point, and non-propagating modes are filtered out. S2. Constructing a physical-driven modal similarity metric: Introducing the optimal transmission distance (EMD) from optimal transmission theory as a similarity index; treating the kinetic energy distribution of each mode on the waveguide cross section as a probability distribution, and the geodesic distance between finite element mesh nodes as the transportation cost, calculating the minimum physical work required to rearrange the kinetic energy distribution of one mode into another mode, thereby quantifying the physical differences between modes; S3. Introduce a continuous stabilization strategy: Based on the physical continuity of the dispersion curve, use Taylor series extrapolation to predict the wavenumber at the next discrete frequency point, and calculate the deviation between the actual wavenumber and the predicted value of the candidate mode. The deviation is then normalized using the median of the current frequency layer characteristic wavenumber spacing to construct a stabilization constraint term S. ij ; S4. Global Optimization Allocation and Modal Connection: The EMD physical distance and stabilization constraint terms are weighted and fused to construct a comprehensive cost matrix; the modal tracking problem between adjacent frequency steps is modeled as a bipartite graph minimum weight matching problem model, and the Hungarian algorithm is used to solve it to determine the globally optimal modal correspondence, thereby connecting them to form a continuous dispersion curve.

2. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 1, characterized in that: The construction of the comprehensive cost matrix, which forms the final modal distance matrix D, is as follows: D ij =EMD ij +λS ij In the formula, the weighting coefficient λ is any value between 0.03 and 0.1; The goal of constructing the bipartite graph minimum weight matching problem model is to minimize the total matching cost. The problem is solved using the Hungarian algorithm, yielding a Boolean matrix X, where X... ij =1 indicates that mode i and mode j belong to the same dispersion branch.

3. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 1, characterized in that: In step S2, the kinetic energy distribution is calculated by extracting the time-averaged kinetic energy E of the mode at the grid nodes. m The formula is Where ρ m Let ω be the node density, ω be the angular frequency, and Δ be the angular frequency. m The displacement amplitude is given; and after normalization, the probability distribution e(m) = E is obtained. m / ∑E n In the formula, E n Let represent the time-averaged kinetic energy of any finite element node n.

4. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 1, characterized in that: In step S2, the method for obtaining the geodesic distance is as follows: the finite element mesh of the pipe section is regarded as a weighted undirected graph, the edge weight is the Euclidean distance between nodes, the Dijkstra algorithm or the Floyd-Warshall algorithm is used to calculate the shortest path distance between any two nodes along the mesh surface, and dimensionless processing is performed.

5. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 4, characterized in that: Dijkstra's algorithm is used to calculate the shortest path distance between any two nodes m and n on the grid; this shortest path distance matrix is ​​then divided by its midpoint to obtain C. mn ; Then solve the EMD problem: solve the following linear programming problem to find the optimal transfer matrix T: The constraint is energy conservation: and Matrix element T mn This represents the energy share of moving from node m in mode i to node n in mode j.

6. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 1, characterized in that: In step S3, the wavenumber at the next discrete frequency point is predicted using Taylor series extrapolation, and the deviation between the actual wavenumber and the predicted value of the candidate mode is calculated, specifically as follows: Using the previous frequency step f n-1 and the current step f n The wavenumber is used to predict the next frequency step f using a first-order Taylor expansion. n+1 wavenumber: Calculate the actual wavenumber k of candidate mode j j (f n+1 The absolute deviation between the predicted value and the actual value 7. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 1, characterized in that: In step S3, the normalization method specifically involves: calculating the adjacent differences after sorting all modal wavenumbers in the target frequency layer, and taking the median of the non-zero differences as the feature spacing δk. char The wavenumber prediction bias is normalized by division using this characteristic spacing.

8. The guided wave mode tracking method for fluid-filled pipes based on optimal transmission distance as described in claim 1, characterized in that: It also includes step S5. Visualizing the modal evolution mechanism: using the optimal transmission scheme matrix generated when calculating EMD in step S2, it is analyzed as an energy flow field, and the energy migration path of the mode during the frequency change process is visualized.

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