Equipment and method for detecting fatigue life of corrugated pipe

Abstract

The invention relates to the technical field of corrugated pipe detection, and discloses corrugated pipe fatigue life detection equipment and a corrugated pipe fatigue life detection method, and the corrugated pipe fatigue life detection method comprises the following steps: building an acoustic-electric topological coupling detection unit through an acoustic metamaterial electromagnetic impedance topological coupling model; constructing a sensor network with topology protection boundary characteristics; obtaining a topological characteristic data set of the state of the corrugated pipe through a topological protection boundary sensing equation; generating a spatial distribution mapping graph of corrugated pipe damage; inputting the topological characteristic data set and the spatial distribution mapping graph into a topological characteristic spectrum pattern recognition algorithm, and outputting the type and severity of the fatigue damage of the corrugated pipe; according to the invention, a series of technical problems in corrugated pipe fatigue damage detection are innovatively solved through the deep coupling acoustic metamaterial and electromagnetic impedance technology and introduction of a physical cellular automaton theory and a topology protection mechanism.

Description

Technical Field

[0001] The present invention relates to the technical field of bellows detection, and more specifically, it relates to an apparatus and a detection method for detecting the fatigue life of bellows. Background Art

[0002] In high - requirement industrial environments such as aerospace, nuclear power, and chemical industries, bellows are widely used as key elastic components. However, their fatigue damage can cause serious safety hazards. Therefore, it is crucial to perform high - precision real - time monitoring and positioning of bellows fatigue damage.

[0003] Currently, there are many deficiencies in the existing bellows monitoring systems: When using the traditional electromagnetic impedance detection method, if full - coverage monitoring is to be achieved, a large number of sensors need to be densely arranged, which makes the system complexity and the monitoring range show a linear or super - linear growth relationship; in a complex industrial environment, the sensing network is easily affected by interference and local failures, resulting in unstable monitoring results; for minor fatigue damage, such as micro - cracks and material microstructure degradation, the positioning accuracy of the existing monitoring systems is limited, and it is difficult to achieve early warning; the existing systems cannot effectively distinguish and identify different types of fatigue damage modes.

[0004] In summary, there is an urgent need to develop a bellows fatigue damage monitoring method that can achieve high coverage, high precision, and high reliability with the minimum system complexity, and this method must have the ability to resist complex environmental interference and local failures. Summary of the Invention

[0005] The present invention provides a method for detecting the fatigue life of bellows, including:

[0006] Based on the geometric parameters and material property data of the bellows, construct an acoustic - electric topological coupling detection unit through an acoustic metamaterial electromagnetic impedance topological coupling model;

[0007] Organize multiple acoustic - electric topological coupling detection units according to the physical cellular automaton model to construct a sensing network with topological protection boundary characteristics;

[0008] Apply an excitation signal to the bellows, collect electromagnetic impedance response data, and obtain a topological feature data set of the bellows state through the topological protection boundary sensing equation;

[0009] Input the topological feature data set into an improved self - organizing mapping algorithm to generate a spatial distribution mapping diagram of bellows damage;

[0010] Input the topological feature data set and the spatial distribution mapping diagram into a topological feature spectrum pattern recognition algorithm to output the type and severity of bellows fatigue damage.

[0011] In a preferred embodiment, the acoustic metamaterial electromagnetic impedance topological coupling model includes: an acoustic resonator, and the calculation formula for its resonance frequency is as follows:

[0012]

[0013] where f r is the resonance frequency of the acoustic resonator; c is the sound wave velocity; S is the cavity opening area; V is the cavity volume; L is the equivalent length of the cavity opening;

[0014] The calculation formula for the resonance frequency of the electromagnetic impedance unit is as follows:

[0015]

[0016] where f e is the resonance frequency of the electromagnetic impedance unit; B is the inductance value; C is the capacitance value;

[0017] The acoustic-electric coupling mechanism, and the calculation formula for its coupling coefficient is as follows:

[0018]

[0019] where κ is the coupling coefficient value between the acoustic and electromagnetic systems; d 33 is the piezoelectric coefficient of the piezoelectric material; A is the area of the piezoelectric sheet; t p is the thickness of the piezoelectric sheet.

[0020] In a preferred embodiment, the steps for constructing a sensing network with topological protection boundary characteristics include:

[0021] The topological protection boundary condition, and the calculation formula is as follows:

[0022]

[0023] where is the state vector of the i-th unit in the boundary region ; Ψ0 is a basic state vector value; e is the natural constant; j is the imaginary unit, satisfying j 2 = -1; φ(s) is the phase function varying with the boundary parameter s; S is the boundary parameter, and the value of φ(S) changes with the change of S; is the boundary region;

[0024] The interaction rule between units, and the calculation formula is as follows:

[0025] g ij (Ψ i , Ψ j ) = c ij (Ψ j - Ψ i ) + dij (Ψ j ×Ψ i );

[0026] Among them, g ij (Ψ i , Ψ j ) is a function describing the mutual coupling relationship between the i-th unit and the j-th unit; c ij is the linear coupling coefficient; d ij is the non-linear coupling coefficient; Ψ i is the state vector of the i-th unit; Ψ j is the state vector of the j-th unit; (Ψ j - Ψ i ) reflects the difference in the state vectors of unit j and unit i; the "×" in (Ψ j × Ψ i ) represents a specific vector operation for the calculation of the non-linear coupling part;

[0027] Execute network evolution iteration, and the calculation formula is as follows:

[0028]

[0029] Among them, is the state vector of the i-th unit at time t + Δt; is the state vector of the i-th unit at time t; Δt is the time interval; is the rate of change of the state vector Ψ i of the i-th unit with respect to time t at time t.

[0030] In a preferred embodiment, the calculation formula for topological protection boundary sensing is as follows:

[0031]

[0032] Among them, Z eff (ω) is the effective electromagnetic impedance of the network; Z0(ω) is the reference electromagnetic impedance; κ i is the acousto-electric coupling coefficient of the i-th unit; L i is the inductance value; ω i is the resonant frequency; ω is the excitation frequency; j is the imaginary unit, satisfying j 2 = -1.

[0033] In a preferred embodiment, the steps of obtaining the topological feature dataset of the bellows state include: applying an excitation signal to the bellows within a preset frequency range and performing frequency scanning, and collecting the complex impedance data at each frequency point; calculating the topological invariant for the collected frequency impedance spectrum data, and the calculation formula is as follows:

[0034]

[0035] Among them, v is the calculated topological invariant; is the coefficient part in the formula; is the line integral along the closed path C; dω is the infinitesimal change in frequency ω; is the operator for differentiating with respect to frequency ω; ln(Ze ff (ω)) where Z eff (ω) is the effective electromagnetic impedance of the network;

[0036] The formula for calculating the topological deviation is as follows:

[0037] Δν = (ν - νe f );

[0038] Among them, Δv is the calculated topological deviation; ν is the topological invariant obtained from the above calculation; v ref is the reference state topological invariant value of the lossless corrugated pipe.

[0039] In a preferred embodiment, the core update rule of the improved self-organizing mapping algorithm is calculated as follows:

[0040]

[0041] Among them, is the state vector of the i-th mapping unit at time t + 1; is the state vector of the i-th mapping unit at time t; η is the learning rate; h(d(i, m)) is the neighborhood function; d(i, m) is the distance from unit i to the best matching unit m; E is the feature vector of the input damage signal;

[0042] The formula for calculating the neighborhood function is as follows:

[0043]

[0044] Among them, h(d(i, m)) is the neighborhood function; exp is the exponential function; σ(t) is the neighborhood radius that decays with time, which determines the range of action of the neighborhood function, and σ(t) is the neighborhood radius that decays with time; as time t increases, the gradual decrease of σ(t) means that the influence range of the neighborhood function gradually shrinks.

[0045] In a preferred embodiment, the topological feature spectrum pattern recognition algorithm includes the following steps:

[0046] Construct the comprehensive feature spectrum calculation formula as follows:

[0047] F = (Δv1, Δv2,..., Δv K , Ψ m1 , Ψm2 ,..., Ψ mL ) T ;

[0048] where F is the comprehensive feature spectrum; T represents the transpose operation, which converts a row vector into a column vector; Δv1, Δv2, Δv k are the topological deviation values in different frequency intervals, k is the index of different frequency intervals, k = 1, 2,..., K, and these values reflect the degree of difference in topological characteristics between the corrugated pipe state and the non-damaged state in different frequency intervals; Ψ m1 , Ψ m2 , Ψ mL are all the feature components of the best matching unit in the self-organizing map, m is the best matching unit, l represents the index of the feature components of this best matching unit, l = 1, 2..., L, Ψ m1 , Ψ m2 , Ψ mL are the feature components of the best matching unit corresponding to l = 1, l = 2, and l = L respectively; select the pattern with the highest similarity as the recognition result;

[0049] The calculation formula for the finally recognized damage pattern is as follows:

[0050] p * = argmax p Sim(F, F p );

[0051] where p * is the finally recognized damage pattern; argmaxp is among all possible damage patterns p; Sim(F, F p ) is the similarity function between the comprehensive feature spectrum F and a certain damage pattern F p in the damage pattern library;

[0052] The calculation formula for the damage severity index is as follows:

[0053]

[0054] where S is the damage severity index; α is the first weight coefficient, used to adjust the weight of ||F - F ref || W in the calculation of the damage severity index S; β is the second weight coefficient, used to adjust the weight in the calculation of the damage severity index S; F is the comprehensive feature spectrum constructed above; F ref is the reference comprehensive feature spectrum; ||F - F ref || W represents the weighted distance between F and F ref ; W is the weight matrix; is the gradient norm of the comprehensive feature spectrum F.

[0055] In a preferred embodiment, the similarity calculation of the damage pattern adopts an improved cosine similarity calculation formula as follows:

[0056]

[0057] F is the constructed comprehensive feature spectrum vector; W is the feature weight matrix; F T is the transpose of F, which converts the original row vector into a column vector; is the weighted norm of F, which is used to measure the magnitude of F; is F p 's weighted norm, which is used to measure the magnitude of F p ; Sim(F, F p ) is the similarity between the input feature vector F and the p-th mode feature vector F in the damage pattern library p .

[0058] In a preferred embodiment, before the step of constructing a sensing network with topological protection boundary characteristics, it further includes: optimizing the topological structure design according to the structural characteristics and usage environment of the bellows, determining the spatial layout of the acoustic-electric topological coupling detection unit; determining the optimal number of acoustic-electric coupling units through predictive performance simulation so that it can achieve full coverage with the lowest system complexity.

[0059] In a preferred embodiment, a bellows fatigue damage detection device includes:

[0060] An acoustic-electric topological coupling detection unit construction module: used to construct an acoustic-electric topological coupling detection unit based on the geometric parameters and material property data of the bellows;

[0061] A topological protection sensing network construction module: used to organize multiple acoustic-electric topological coupling detection units according to the physical cellular automaton model to construct a sensing network with topological protection boundary characteristics;

[0062] A topological feature extraction module: used to apply an excitation signal to the bellows, collect electromagnetic impedance response data, and obtain a topological feature data set of the bellows state through the topological protection boundary sensing equation;

[0063] A damage space mapping module: used to input the topological feature data set into an improved self-organizing mapping algorithm to generate a spatial distribution mapping diagram of the bellows damage;

[0064] A damage identification and classification module: used to input the topological feature data set and the spatial distribution mapping diagram into the topological feature spectrum pattern recognition algorithm to output the type and severity of the bellows fatigue damage.

[0065] The beneficial effects of the present invention are as follows:

[0066] System complexity reduction: Under the guidance of the physical cellular automaton theory, the layout of the acoustic-electric coupling units is carried out, so that the system complexity increases sub-linearly with the coverage range. Only one-fifth of the number of sensors required by the traditional method is needed to achieve 100% monitoring coverage rate, effectively reducing the hardware cost and complexity.

[0067] Improved damage mode recognition ability: By adopting the pattern recognition method based on the topological feature spectrum, the present invention can distinguish 12 different fatigue damage modes, and the recognition accuracy rate is as high as 97%. In contrast, the traditional method can only distinguish 3 to 5 damage types, and the accuracy rate is less than 85%. The present invention has achieved a qualitative breakthrough.

[0068] Enhanced self-adaptive ability of the sensing network: The system of the present invention has the ability of self-learning and adaptation, and can automatically adjust the detection parameters according to the environmental changes and damage evolution, solving the problem that the traditional fixed-threshold method needs manual intervention for recalibration under different environmental conditions. Description of the Drawings

[0069] Figure 1 is a flowchart of a method for detecting the fatigue life of a corrugated pipe according to the present invention. Detailed Embodiments

[0070] Now, the subject matter described herein will be discussed with reference to example embodiments. It should be understood that discussing these embodiments is only to enable those skilled in the art to better understand and thus implement the subject matter described herein. Without departing from the protection scope of the content of this specification, changes can be made to the functions and arrangements of the elements discussed. Each example can omit, substitute, or add various processes or components as needed. Additionally, the features described in some examples can also be combined in other examples.

[0071] In at least one embodiment of the present invention, a method for detecting the fatigue life of a corrugated pipe is disclosed, as Figure 1 shown, including the following steps:

[0072] Step100, based on the geometric parameters and material property data of the corrugated pipe, construct an acoustic-electric topological coupling detection unit through the acoustic metamaterial electromagnetic impedance topological coupling model;

[0073] The input data of Step100 includes the geometric parameters and material property data of the corrugated pipe, specifically the diameter D, wall thickness t, corrugation height h, corrugation pitch p of the corrugated pipe, and the elastic modulus E, Poisson's ratio v, and density ρ of the material. Based on these parameters, a detection unit is constructed using the acoustic metamaterial electromagnetic impedance topological coupling model, which mainly includes the following steps:

[0074] Step101. Determine the parameters of the acoustic resonant cavity according to the geometric parameters of the corrugated pipe. The calculation formula for the resonant frequency is as follows:

[0075]

[0076] Among them, f r is the resonant frequency of the acoustic resonant cavity, which is a frequency value that measures the resonance of the acoustic resonant cavity under specific conditions. This frequency plays an important role in determining the electrical parameters of the electromagnetic impedance unit subsequently; c is the sound wave velocity, which is the speed at which sound propagates in a specific medium. This velocity value affects the calculation result of the resonant frequency; S is the cavity opening area, that is, the area size at the opening of the acoustic resonant cavity. This area parameter participates in the calculation of the resonant frequency and has a direct impact on the value of the resonant frequency; V is the cavity volume, which refers to the size of the internal space of the acoustic resonant cavity and is one of the important parameters for calculating the resonant frequency; L is the equivalent length of the cavity opening, which is equivalent to the length of the cavity opening under a specific calculation model and also affects the calculation result of the resonant frequency. The output result is a set of parameters of the acoustic resonant cavity adapted to the corrugated pipe structure, including the cavity size and the resonant frequency.

[0077] Step102. Determine the electrical parameters of the electromagnetic impedance unit based on the resonant frequency. The calculation formula for the resonant frequency of the electromagnetic impedance unit circuit is as follows:

[0078]

[0079] Among them, f e is the resonant frequency of the electromagnetic impedance unit circuit, which determines the resonance characteristics of the electromagnetic impedance unit in the circuit; L is the inductance value, which is a physical quantity that measures the ability of an inductor element to store magnetic field energy. The size of the inductance value affects the level of the circuit resonant frequency; C is the capacitance value, which is a physical quantity that characterizes the ability of a capacitor to hold charge. The capacitance value and the inductance value jointly determine the resonant frequency of the circuit. The output result is the LC circuit parameters that match the acoustic resonant frequency.

[0080] Step103. The calculation formula for the acoustic-electric coupling coefficient is as follows:

[0081]

[0082] Among them, κ is the acoustic-electric coupling coefficient, which is used to measure the degree of mutual coupling between the acoustic system and the electromagnetic system. This coefficient value reflects the intensity of energy conversion and mutual interaction between the two systems; d 33 is the piezoelectric coefficient of the piezoelectric material, which is a parameter that describes the ability of the piezoelectric material to generate strain under the action of an electric field or generate an electric field under the action of stress. Its numerical size directly affects the acoustic-electric coupling coefficient; A is the area of the piezoelectric sheet, that is, the area of the thin piezoelectric material sheet. This area parameter participates in the calculation of the acoustic-electric coupling coefficient and affects the value of the coupling coefficient; tp is the thickness of the piezoelectric sheet, which refers to the thickness dimension of the thin piezoelectric material sheet and is also one of the important parameters for calculating the acoustic-electric coupling coefficient; the output result is the coupling coefficient value between the acoustic and electromagnetic systems.

[0083] The final output result is the structure of the acoustic-electric topological coupling detection unit, which includes the parameters and physical connection relationships of the resonant cavity, LC circuit, and piezoelectric coupling layer. Different from traditional single physical field detection elements, this detection unit can simultaneously respond to changes in acoustic and electromagnetic characteristics and generate a composite response signal with high sensitivity to the fatigue damage of the bellows.

[0084] Step200, organize multiple acoustic-electric topological coupling detection units according to the physical cellular automaton model to construct a sensing network with topological protection boundary characteristics;

[0085] Taking the acoustic-electric topological coupling detection unit structure data generated in Step100 as the input, use the physical cellular automaton model to organize multiple units to form a network. This model represents each acoustic-electric coupling unit as a computing unit with local interaction rules, and its state evolution follows the non-linear coupling equation. The calculation formula is as follows:

[0086]

[0087] Among them, is the change rate of the state vector Ψ of the i-th unit with respect to time t; Ψ i is the state vector of the i-th unit; f i is the internal dynamics function; i is the sum of the interactions between unit i and all neighbor units j; g is the coupling function; N(i) is the neighbor set of unit i. ij is the coupling function; N(i) is the neighbor set of unit i.

[0088] The steps for constructing a sensing network with topological protection boundary characteristics include the following:

[0089] Step201, input the parameters of the acoustic-electric coupling unit, and calculate the topological protection boundary condition. The calculation formula is as follows:

[0090]

[0091] Among them, is the state vector of the i-th unit in the boundary region ; is the boundary region, that is, the range of the region at the edge in the network structure; Ψ0 is a reference state vector, and φ(s) is the phase function that changes with the boundary parameter S. S is the parameter used to describe the boundary characteristics, and the change of φ(s) will affect the phase characteristics of the boundary unit state vector; the output result is the set of boundary condition parameters that meet the topological protection characteristics.

[0092] Step 202. Determine the calculation formula for the interaction rule between units according to the boundary condition parameters as follows:

[0093] g ij (Ψ i , Ψ j ) = c ij (Ψ j - Ψ i ) + d ij (Ψ j × Ψ i );

[0094] Among them, g ij (Ψ i , Ψ j ) is a function describing the mutual coupling relationship between the i-th unit and the j-th unit; c ij is the linear coupling coefficient; d ij is the non-linear coupling coefficient; Ψ i is the state vector of the i-th unit; Ψ j is the state vector of the j-th unit; (Ψ j - Ψ i ) reflects the difference in the state vectors of unit j and unit i; the "×" in (Ψ j × Ψ i ) represents a specific vector operation for the calculation of the non-linear coupling part.

[0095] Step 203. Perform the network evolution iteration calculation with the following formula:

[0096]

[0097] Among them, is the state vector of the i-th unit at time t + Δt; is the state vector of the i-th unit at time t; Δt is the time interval; is the change rate of the state vector of the i-th unit at time t; the output result is the unit state distribution map in the network stable state, which characterizes the network structure with topological protection characteristics.

[0098] The final output result is the data of the sensing network structure with topological protection boundary characteristics, including the unit spatial arrangement, unit state distribution, and connection relationship between units; different from the traditional sensing network, this network structure has dynamic adaptive characteristics and non-linear coupling characteristics, showing boundary state protection properties similar to quantum topological materials and having a high immunity to local faults and external disturbances.

[0099] Step 300, apply an excitation signal to the corrugated pipe, collect the electromagnetic impedance response data, and obtain the topological feature dataset of the corrugated pipe state through the topological protection boundary sensing equation.

[0100] Taking the topological protection sensing network structure data constructed in Step 200 and the corrugated pipe to be detected as inputs, measure and analyze the electromagnetic impedance response through the topological protection boundary sensing equation. The effective electromagnetic impedance calculation formula is as follows:

[0101]

[0102] Among them, Z eff (ω) is the effective electromagnetic impedance of the network; Z0(ω) is the reference electromagnetic impedance; κ i is the acoustic-electric coupling coefficient of the i-th unit; L i is the inductance value; ω i is the resonant frequency; ω is the excitation frequency; j is the imaginary unit.

[0103] Step 301, apply an excitation signal to the corrugated pipe and perform a frequency scan with a step size of Δω within the preset frequency range (ω min , ω max ), collect the complex impedance Z eff (ω) data at each frequency point, and output the frequency impedance spectrum data; during this process, ω min is the lower limit value of the preset frequency range, which determines the lowest frequency at which the frequency scan starts; ω max is the upper limit value of the preset frequency range, which specifies the highest frequency at which the frequency scan ends; Δω is the step size of the frequency scan, that is, a fixed value by which the excitation frequency ω is increased each time. By changing the excitation frequency ω step by step with this step size, the complex impedance Z eff (ω) data at different frequency points can be systematically collected.

[0104] Step 302, apply the topological invariant extraction algorithm to the collected frequency impedance spectrum data. The topological invariant calculation formula is as follows:

[0105]

[0106] Among them, v is the topological invariant, is a constant coefficient, 2π is a constant related to pi, and j is the imaginary unit; is the integral operation along the closed path C. C is the closed path in the frequency space; the selection of the integral path C is related to the specific detection requirements and topological analysis methods; dω is the infinitesimal change of the integral variable ω, ω is the excitation frequency; d is the symbol representing differentiation in calculus; ln(Z eff (ω)) where Z eff$(\omega)$ represents the effective electromagnetic impedance of the network; the output result is the numerical value of the topological invariant characterizing the current state of the corrugated pipe.

[0107] Step303, compare the calculated topological invariant $v$ with the reference state value $v$ of the non-damaged corrugated pipe ref The topological deviation calculation formula is as follows:

[0108] $\Delta v=(v - \nu_e$ f );

[0109] where $\Delta v$ is the numerical value of the topological deviation; $v$ is the topological invariant; $v$ ref is the reference state value of the non-damaged corrugated pipe; the output result is the numerical value of the topological deviation, which is highly sensitive to fatigue damage and insensitive to environmental interference.

[0110] The final output result is the topological feature dataset of the corrugated pipe. The topological feature dataset of the corrugated pipe refers to the set composed of the topological invariants and their deviation values in different frequency intervals, including the topological invariants and their deviation values in different frequency intervals; this dataset uses the concept of topological invariants in quantum topology physics to characterize the damage state of the corrugated pipe, and has the characteristics of being extremely insensitive to local interference and highly sensitive to fatigue damage, solving the contradiction between sensitivity and anti-interference ability in traditional detection methods.

[0111] Step400, input the topological feature dataset into the improved self-organizing map algorithm to generate the spatial distribution map of the corrugated pipe damage.

[0112] Taking the topological feature dataset of the corrugated pipe obtained in Step300 as the input, the improved self-organizing map (Self-0rganizingMap, SOM) algorithm is used to map the abstract acoustic-electric topological features to the specific spatial positions of the corrugated pipe; the calculation formula of the core update rule of this algorithm is as follows:

[0113]

[0114] where, is the state vector of the $i$-th mapping unit updated at time $t + 1$; is the state vector of the $i$-th mapping unit at time $t$; $\eta$ is the learning rate; $h(d(i, m))$ is the neighborhood function; $d(i, m)$ is the distance from unit $i$ to the best matching unit $m$; $E$ is the feature vector of the input damage signal.

[0115] The construction and training of the mapping network include the following steps:

[0116] Step401, input the topological feature dataset, and initialize $M\times N$ mapping units in the two-dimensional or three-dimensional space representing the corrugated pipe. The state vector of each unit Randomly assign initial values; the output result is the initialized mapping network structure; M×N is the number layout of mapping units in two - dimensional or three - dimensional space, where M and N are the number of units in two dimensions respectively; is the state vector of the i - th mapping unit during initialization, and its value is randomly assigned to provide an initial state for subsequent iterative updates.

[0117] Step402: For each input damage signal feature vector E, calculate the Euclidean distance between it and the state vector of each mapping unit. The output result is the index value and position coordinates of the best - matching unit. The formula for determining the best - matching unit is as follows:

[0118]

[0119] where, argmin i is to find the value of i that makes the following expression take the minimum value; is the Euclidean distance between the input damage signal feature vector E and the state vector of the i - th mapping unit at time t to quantify the similarity between the two.

[0120] Step403: According to the position of the best - matching unit, the formula for the neighborhood function is as follows:

[0121]

[0122] where, h(d(i, m)) is the neighborhood function; exp is the exponential function; d 2 (i, m) is the square of the distance d(i, m) from unit i to the best - matching unit m; σ 2 (t) is the square of the neighborhood radius σ(t) that changes with time t,

[0123] σ(t) is the neighborhood radius that decays with time, and its calculation formula is as follows:

[0124]

[0125] where, σ(t) is the neighborhood radius that decays with time; exp is the exponential function; σ0 is the initial neighborhood radius; τ σ is the parameter that controls the decay speed of the neighborhood radius σ(t) with time; t is the time variable.

[0126] Step404: Adjust the state vector of each mapping unit according to the update rule. The output result is the updated mapping network state, and at the same time, update the learning rate:

[0127]

[0128] where, η(t) is the learning rate at time t; η0 is the initial learning rate; τη It is a parameter for controlling the decay rate of the learning rate η(t) over time; t is the time variable; exp is the exponential function.

[0129] Step405, repeatedly execute sub-Steps 200 to 400 until the network converges. The condition for judging convergence is that the change amount of the state vector is less than the preset threshold or the maximum number of iterations is reached.

[0130] The final output result is the mapping diagram of the spatial distribution of bellows damage. This mapping diagram converts the abstract topological feature data into specific spatial position information on the bellows, realizing the precise positioning of damage; compared with the traditional self-organizing mapping algorithm, there is also a topological protection interaction between the mapping units in this embodiment, making the mapping process have stronger robustness and accuracy, and being able to locate fatigue damage on the bellows with an accuracy of ±0.3 mm.

[0131] Step500, input the topological feature data set and the spatial distribution mapping diagram into the topological feature spectrum pattern recognition algorithm, and output the type and severity of the bellows fatigue damage;

[0132] Taking the bellows topological feature data set obtained in Step300 and the damage spatial distribution mapping diagram generated in Step400 as inputs, use the topological feature spectrum pattern recognition algorithm to classify and identify the bellows fatigue damage and evaluate the severity; the specific implementation process includes:

[0133] Step501, receive the topological feature data and the spatial distribution mapping data, and construct the comprehensive feature spectrum calculation formula as follows:

[0134] F=(Δv1, Δv2,..., Δv K , Ψ m1 , Ψ m2 ,..., Ψ mL ) T ;

[0135] Among them, F is the comprehensive feature spectrum; T represents the transpose operation, that is, converting a row vector into a column vector; Δv1, Δv2, Δv k are the topological deviation values in different frequency intervals respectively, k is the index of different frequency intervals, k = 1, 2,..., K, and these values reflect the difference degree of the topological characteristics between the bellows state and the non-damaged state in different frequency intervals; Ψ m1 , Ψ m2 , Ψ mL are all the feature components of the best matching unit in the self-organizing mapping. m is the best matching unit, 1 represents the index of the feature component of this best matching unit, l = 1, 2..., L, Ψ m1 , Ψ m2 , Ψ mLThey are the best matching unit feature components corresponding to l = 1, l = 2, and l = L respectively; select the pattern with the highest similarity as the recognition result.

[0136] Step502, retrieve the matching pattern from the pre-established damage pattern library D = F1, F2,..., F P among them,

[0137] where F1 is the feature vector corresponding to the first pattern in the damage pattern library D, and this pattern corresponds to fatigue damage of a specific type and severity; F2 is the feature vector corresponding to the second pattern in the damage pattern library D, which also corresponds to fatigue damage of a specific type and severity; F P is the feature vector corresponding to the Pth pattern in the damage pattern library D, where the value range of P is from 1 to P, and each pattern corresponds to fatigue damage of a specific type and severity; each pattern corresponds to fatigue damage of a specific type and severity.

[0138] Calculate the similarity between the input feature and each pattern in the pattern library through the improved cosine similarity. The calculation formula is as follows:

[0139]

[0140] where F is the constructed comprehensive feature spectrum vector; W is the feature weight matrix; F T is the transpose of F, converting the original row vector into a column vector; is the weighted norm of F, used to measure the magnitude of F; is F p 's weighted norm, used to measure the magnitude of F p ; Sim(F, F p ) is the similarity between the input feature vector F and the feature vector F p of the pth pattern in the damage pattern library.

[0141] Step503, determine the damage type based on the similarity value, and select the pattern with the highest similarity as the recognition result. The calculation formula is as follows:

[0142] p * = argmax p Sim(F, F p );

[0143] where argmax p is to find the value of p when Sim(F, F p ) takes the maximum value; p * is the index of the pattern with the highest similarity to the input feature vector F finally determined; the output result is the type identification of the bellows fatigue damage, including different forms of fatigue damage such as cracks, creep, and corrosion.

[0144] Step 504. According to the identified damage type, the severity index calculation formula is as follows:

[0145]

[0146] Where S is the severity index; α is the fifth weight coefficient, used to adjust ||F - F ref || W in calculating the weight in the damage severity index S; β is the sixth weight coefficient, used to adjust in calculating the weight in the damage severity index S; F represents the constructed comprehensive feature spectrum vector; F ref is the feature vector in the non-destructive reference state; is the norm of the spatial gradient of the feature vector F, used to measure the degree of change of the feature in space.

[0147] The final output result is the type and severity of the bellows fatigue damage, including the damage type, damage location coordinates, severity value, and predicted remaining life. By using the stability and distinctiveness of topological features and combining the precise positioning ability of spatial mapping, 12 different fatigue damage modes can be identified, and the identification accuracy rate reaches 97%, providing a scientific basis for the preventive maintenance and life management of bellows.

[0148] This method is applied to the fatigue damage detection of bellows in the secondary loop system of nuclear power plants. The bellows in this system are under high pressure, high temperature, and frequent thermal cycling conditions, and are prone to fatigue damage. In this environment, conventional detection methods face challenges such as severe electromagnetic interference, high-temperature environment limitations, and limited detection coverage.

[0149] We select a high-temperature alloy bellows with a diameter of 80 mm and a wall thickness of 1.2 mm in the secondary loop system of a certain nuclear power plant as the detection object. This bellows needs to be subjected to fatigue damage detection and evaluation after 30 months of operation.

[0150] Bellows parameter and construction of acoustic-electric topological coupling detection unit;

[0151] The geometric parameters and material property data of the detected bellows are shown in the following table:

[0152] Parameter Symbol Value Unit Outer diameter D 80 mm Wall thickness t 1.2 mm Corrugation height h 12 mm Corrugation pitch p 8 mm Elastic modulus E 195 GPa Poisson's ratio v 0.32 - Density ρ 8.2 <![CDATA[g / cm 3 >

[0153] The parameters of the acoustic-electric topological coupling detection unit are shown in the following table:

[0154] Parameter type Parameter name Symbol Value Unit Acoustic parameter Resonator volume V 2.5 <![CDATA[cm 3 > Orifice area S 1.0 <![CDATA[cm 2 > Equivalent orifice length L 0.8 cm Sound wave velocity c 343 m / s Resonant frequency <![CDATA[f r > 5.4 kHz Electrical parameter Inductance value L 4.7 mH Capacitance value C 0.18 μF Circuit resonant frequency <![CDATA[f e > 5.4 kHz Acoustic-electric coupling Piezoelectric coefficient d33 425 pC / N Piezoelectric patch area A 0.8 <![CDATA[cm 2 > Piezoelectric patch thickness <![CDATA[t p > 0.6 mm Acoustic-electric coupling coefficient k 0.57 -

[0155] Construction of Topological Protection Sensing Network: Based on the above acoustic-electric topological coupling detection unit, a topological protection sensing network is constructed. In this example, 12 acoustic-electric topological coupling detection units are actually applied and organized according to the physical cellular automaton model to form a circumferential coverage of the corrugated pipe.

[0156] The main parameters of the topological protection sensing network are shown in the following table:

[0157] Parameter Symbol Value Description Number of detection units N 12 Circumferentially uniformly distributed Linear coupling coefficient matrix <![CDATA[c ij > 0.45-0.78 Non-zero values only exist in adjacent units Nonlinear coupling coefficient matrix <![CDATA[d ij > 0.12-0.28 Non-zero values only exist in adjacent units Boundary phase function φ(s) <![CDATA[2πs / L b > <![CDATA[L b is the boundary perimeter]]> Evolution time step Δt 0.01 Normalized unit Number of iterations - 500 Required to reach steady state

[0158] Comparison between traditional network methods and topological protection networks (under the same coverage rate) is shown in the following table:

[0159]

[0160] Topological Feature Extraction: Based on the constructed topological protection sensing network, an excitation signal is applied to the corrugated pipe and frequency scanning is carried out to obtain topological feature data. In the example, frequency scanning of the corrugated pipe is carried out in the range of 2 to 10 kHz with a step size of 50 Hz.

[0161] An example of frequency impedance spectrum data (partial frequency points) is shown in the following table:

[0162] Frequency (kHz) <![CDATA[||Z eff ||(Ω)]]> <![CDATA[∠Z eff (°)]]> Topological eigenvalue 2.0 168.4 -25.7 0.012 3.0 205.7 -38.2 0.035 4.0 312.5 -42.6 0.057 5.0 526.8 -65.3 0.128 5.4 1243.6 -78.9 0.215 6.0 478.3 62.7 0.185 7.0 312.7 43.5 0.065 8.0 236.9 32.1 0.037 9.0 195.4 18.7 0.023 10.0 172.8 12.3 0.018

[0163] By processing the above frequency impedance spectrum data through the topological protection boundary sensing equation, topological invariants and topological deviations are extracted to obtain a topological feature data set. In this example, the fatigue damage of the corrugated pipe is mainly concentrated near a welding area, and the topological feature data shows obvious anomalies in this area.

[0164] The comparison of topological deviations under different working conditions is shown in the following table:

[0165]

[0166] Damage Spatial Mapping and Identification Classification: Based on the obtained topological feature data set, an improved self-organizing mapping algorithm is used to generate a spatial distribution mapping diagram of the corrugated pipe damage and carry out fatigue damage classification and identification.

[0167] The parameter settings of the damage spatial mapping are shown in the following table:

[0168] Parameter Symbol Value Description Mapping grid size M×N 60×20 Covering the circumferential and axial directions of the corrugated pipe Initial learning rate η0 0.6 - Learning rate decay time constant 150 Unit of number of iterations Initial neighborhood radius σ0 8.0 Grid unit Neighborhood radius decay time constant τσ 100 Unit of number of iterations Convergence threshold - 0.001 Change in state vector Maximum number of iterations - 1000 -

[0169] The fatigue damage identification result (area 3) is shown in the following table:

[0170] Damage type Similarity value Recognition result Accuracy rate Microcrack (axial) 0.873 Yes 97.3％ Microcrack (circumferential) 0.452 No - Creep damage 0.325 No - Corrosion damage 0.156 No - Wear damage 0.107 No - Fatigue initiation point 0.215 No -

[0171] Upon identification, axial microcracks were found in Region 3, located at the 7th corrugation of the bellows, with an angular position of 225°, a damage length of approximately 2.8 mm, a depth of approximately 0.35 mm, and a severity index of 43.6 (on a 0 to 100 scale); based on this result, the predicted remaining safe operating time is 18 months.

[0172] This example mainly verified two main technical effects: anti-interference ability and reduced system complexity;

[0173] The detection performances under different noise environments and sensing unit failure conditions are compared in the following table:

[0174] Operating condition Detection accuracy rate of this method Detection accuracy rate of traditional method Improvement ratio Noise-free environment 97.8％ 93.5％ 4.6％ Noise environment (-20dB) 97.5％ 87.2％ 11.8％ Noise environment (-10dB) 96.2％ 62.5％ 53.9％ Noise environment (-5dB) 93.8％ 41.3％ 127.1％ Noise environment (0dB) 91.6％ 25.7％ 256.4％ 10% of the sensing units fail 96.7％ 68.4％ 41.4％ 20% of the sensing units fail 95.2％ 41.8％ 127.8％ 30% of the sensing units fail 92.8％ 22.3％ 316.1％

[0175] Under extreme conditions of high noise environment (0 dB) and high failure rate (30% sensing unit failure), this method can still maintain a detection accuracy of over 90%, while the detection accuracy of the traditional method drops to less than 30%. This proves the superior anti-interference ability of this method based on the topological protection mechanism.

[0176] This method achieves physical immunity, does not rely on digital filtering or signal processing algorithms, but resists interference from the physical level through the topological protection boundary characteristics, enabling the system to still maintain high performance in harsh environments.

[0177] The complexities under different system coverage ranges are compared in the following table:

[0178]

[0179] The comparison of the growth of system complexity with the coverage range: The traditional method shows linear growth (complexity n), while this method shows sub-linear growth (n is the number of bellows). In large-scale applications, this method can reduce system complexity and cost.

[0180] Benefiting from the physical cellular automata theory and topological protection boundary characteristics, this method realizes the non-linear relationship between the monitoring coverage range and system complexity, fundamentally solving the contradiction between coverage density and system complexity in the traditional method. In large-scale industrial applications, it can achieve a reduction of about 85% in system complexity without sacrificing monitoring accuracy and reliability.

[0181] In an embodiment of the present invention, for realizing the asynchronous collaborative monitoring of a group of bellows for distributed elastic consensus, a method for detecting the fatigue life of bellows further includes:

[0182] Step600, receiving the geometric parameters and material property data of the bellows, and constructing an acoustic-electric topological coupling detection unit with distributed processing capabilities;

[0183] Basic detection unit structure: Receive the cross-sectional profile data of the corrugated pipe and the acoustic-electric characteristic parameters of the material, and construct the basic acoustic-electric coupling detection unit by the same method;

[0184] Edge computing module construction: Receive the system resource constraint data and configure the calculation parameter set of each detection unit as follows:

[0185] C i =P i ,M i ,S i ,E i ;

[0186] Among them, C i is the calculation configuration set of detection unit i; P i is the processing capacity parameter; M i is the storage capacity parameter; S i is the scheduling priority parameter; E i is the energy efficiency parameter.

[0187] Hierarchical communication interface construction: Receive the network topology data and configure the communication parameter set of each detection unit; The communication interface configuration set is as follows:

[0188] I i =B i ,L i ,T i ,R i ;

[0189] Among them, I i is the communication interface configuration set of detection unit i; B i is the bandwidth parameter; L i is the communication delay parameter; T i is the type of transmission protocol (used to specify the rules and methods for data transmission between detection units); R j is the reliability level.

[0190] Output the distributed acoustic-electric topology coupling detection unit construction data packet, including the basic detection structure parameters, the calculation configuration data set and the communication interface configuration data set, for subsequent construction of the hierarchical asynchronous decision network.

[0191] Step700, receive the distributed acoustic-electric topology coupling detection unit construction data packet and construct a hierarchical network structure that supports multi-time scale decision-making;

[0192] Three-level network structure construction: Receive the detection unit location distribution data and the calculation ability parameters. The three-layer functional network parameters are as follows:

[0193] N=U1,U2,U3;

[0194] Among them, N is the overall network structure; U1, U2, and U3 are the fast response layer, the coordination control layer, and the strategy planning layer respectively; the output is the network topology structure diagram and the hierarchical division data table.

[0195] Asynchronous scheduling strategy generation: Receive the response time data of each detection unit, and apply the multi-time scale Markov decision process calculation formula as follows:

[0196]

[0197] Among them, π i (s) is the optimal scheduling strategy of detection unit i in state S; R(s, a) is the immediate reward value obtained by executing action a; γ is the discount factor; P(s1s, a) is the state transition probability matrix; V(s′) is the value function of state s′; the output is the asynchronous scheduling strategy parameter table.

[0198] Node role switching rule generation: Receive the performance monitoring data of the detection unit, and the fitness score calculation formula is as follows:

[0199] Q i (t) = w1C i (t) + w2N i (t) + w3S i (t) + w4E i (t);

[0200] Among them, Q i (t) is the fitness score of detection unit i at time t; C i (t) is the computing resource status value, which reflects the available situation of the computing resources of detection unit i at time t; N i (t) is the network connection status value, which reflects the network connection status of detection unit i at time t; S i (t) is the sensor health status value, which indicates the health degree of the sensors equipped by detection unit i at time t; E i (t) is the energy level value; w1 is the 7th weight coefficient, which is used to adjust the relative importance of the computing resource status value C i (t) in the calculation of the fitness score Q i (t); w2 is the 8th weight coefficient, which is used to adjust the relative importance of the network connection status value N i (t); w3 is the 9th weight coefficient, which is used to adjust the relative importance of the sensor health status value S i (t); w4 is the 10th weight coefficient, which is used to adjust the relative importance of the energy level value E i (t); the output is the dynamic role switching rule data set.

[0201] Output hierarchical asynchronous decision network configuration package, including network topology structure diagram, asynchronous scheduling policy parameter table and dynamic role switching rule data set, for subsequent implementation of distributed elastic consensus.

[0202] Step800, receive the hierarchical asynchronous decision network configuration package and the initial state data of the detection unit, and execute the distributed decision cooperation algorithm;

[0203] Execute the elastic consensus algorithm, receive the initial state evaluation values of each detection unit, and the Byzantine fault-tolerant consensus calculation formula is as follows:

[0204]

[0205] Among them, V i (t + 1) is the Byzantine fault-tolerant consensus; V i (t) is the estimated value of the bellows state by the detection unit i at time t; W ij (t) is the weighting coefficient of the influence of the detection unit j on the detection unit i; N i is the neighbor set of the detection unit i; after calculation by this formula, output the consensus protocol parameter matrix.

[0206] Trust evaluation calculation, receive historical decision data, and the trust degree calculation formula between detection units is as follows:

[0207] T ij (t + 1) = M·T ij (t) + (1 - M)·F(D ij (t));

[0208] Among them, T ij (t + 1) is the trust degree between detection units; T ij (t) is the trust degree value of the detection unit i to the detection unit j at time t, reflecting the trust degree of i to j at time t; M is the historical trust weight factor; F(·) is the trust evaluation function; D ij (t) is the decision difference measurement value between the detection units i and j at time t; after calculation by this formula, output the dynamic trust relationship matrix.

[0209] Multi-level information aggregation: receive the data of each level of detection units and perform hierarchical aggregation operations;

[0210] Fast response layer: receive the original detection data and aggregate to generate real-time anomaly detection results;

[0211] Coordination control layer: receive the anomaly detection results and aggregate to generate a damage trend analysis report;

[0212] Policy planning layer: receive the trend analysis report and aggregate to generate a system-level risk assessment report;

[0213] Distributed collaborative perception data packet, including a consensus protocol parameter matrix, a dynamic trust relationship matrix, and a multi-level information aggregation result set, for subsequent resource scheduling and priority management.

[0214] Step900, receive the distributed collaborative perception data packet and the system resource status data, and calculate the optimal resource allocation plan:

[0215] Resource allocation plan calculation: Receive the list of available resources and the bellows status data. The utility maximization calculation formula is as follows:

[0216] A(t)=argmax z U(S(t), R(t), z);

[0217] Among them, A(t) is the optimal resource allocation plan at time t; U(·) is the resource utility function; S(t) is the bellows group status matrix, which records the overall status information of the bellows group at time t, and this information will affect the decision-making of resource allocation; R(t) is the available resource vector; z is the candidate allocation plan, that is, the possible resource allocation method. Different candidate allocation plans are evaluated through the resource utility function U(·) to find the optimal resource allocation plan A(t); output the resource allocation strategy table.

[0218] Task priority calculation; Receive the damage assessment data and the bellows importance data. The task priority calculation formula is as follows:

[0219] P i (t)=y1·U i (t)+y2·C i (t)+y3·D i (t);

[0220] Among them, P i (t) is the task priority value of the detection unit i; U i (t) is the damage urgency value; C i (t) is the bellows criticality index; D i (t) is the damage severity value; y1 is the 11th weight coefficient, used to adjust the relative importance of the damage urgency value U i (t) in the calculation of the task priority value P i (t); y2 is the 12th weight coefficient, used to adjust the relative importance of the bellows criticality index C i (t); y3 is the 13th weight coefficient, used to adjust the relative importance of the damage severity value D i (t); Output the task priority ranking table.

[0221] Communication route calculation: Receive the network congestion status data. The path optimization calculation formula is as follows:

[0222]

[0223] Among them, R* is the optimal routing scheme; R is the set of all possible routing schemes; is the sum of the delay values of all links (i, j) in the routing scheme R; P is the balance parameter; max (i，j) C ij is the maximum value among the congestion degree values of all links (i, j) in the routing scheme R; argmin R is to find the routing scheme in the routing scheme set R that minimizes the value of the following expression, that is, the optimal routing scheme R * .

[0224] Output the resource scheduling optimization data packet, including the resource allocation policy table, the task priority sorting table, and the communication routing configuration table, for subsequent collaborative perception and decision fusion.

[0225] Step1000, receive the resource scheduling optimization data packet and the multi-level information aggregation result set, perform decision fusion and risk assessment; collaborative perception data integration; receive the damage knowledge data of each detection unit, and the calculation formula of the knowledge fusion algorithm is as follows:

[0226]

[0227] Among them, K i (t + 1) is knowledge fusion; K i (t) is the damage knowledge base data of detection unit i at time t; is the knowledge fusion operator; F is the function of the federated learning algorithm, and this function takes the damage knowledge base data of the neighbor detection unit set as input and performs specific federated learning calculation processing; N i is the neighbor set of detection unit i, that is, the set of other detection units directly associated with detection unit i in the network topology; output the updated data of the distributed knowledge base.

[0228] Multi-level decision fusion calculation: receive the decision results of each level of detection units, and the calculation formula of the weighted fusion formula is as follows:

[0229]

[0230] Among them, D final is the final decision result vector; l is the level index; is the decision result of detection unit i in level l, which reflects the judgment made by detection unit i for bellows monitoring in the l-th level; L1 is the set of detection units in level l; α l is the 14th weight coefficient; β iis the reliability weight of the detection unit i; output the fusion decision result report.

[0231] System risk assessment calculation: Receive the fusion decision result and the bellows topological relationship data. The risk propagation assessment calculation formula is as follows:

[0232]

[0233] where R sys (t) is the system-level risk assessment result; D i (t) is the decision result of the detection unit i; C i is the criticality index of the bellows i; T is the bellows group topological structure matrix; G represents the risk propagation assessment function, taking T and T as inputs, and obtaining the system-level risk assessment result R sys (t) through specific calculation rules; output the system risk assessment report. G represents the risk propagation assessment function.

[0234] Output the comprehensive result set of the bellows group monitoring, including the distributed knowledge base update data, the fusion decision result report, and the system risk assessment report, providing a comprehensive assessment basis for the safety monitoring of the bellows group.

[0235] The above describes the embodiments of the present invention. However, these embodiments are not limited to the above specific implementation manners. The above specific implementation manners are merely illustrative and not restrictive. Under the inspiration of this embodiment, those of ordinary skill in the art can also make more equivalent embodiments in various forms, all of which fall within the protection scope of this embodiment.

Claims

1. A method for detecting the fatigue life of a corrugated pipe, characterized in that, Including: Based on the geometric parameters and material property data of the corrugated pipe, an acoustic-electric topological coupling detection unit is constructed through an acoustic metamaterial electromagnetic impedance topological coupling model; Multiple acoustic-electric topological coupling detection units are organized according to the physical cellular automaton model to construct a sensing network with topological protection boundary characteristics; An excitation signal is applied to the corrugated pipe, electromagnetic impedance response data is collected, and a topological feature data set of the corrugated pipe state is obtained through the topological protection boundary sensing equation; The topological feature data set is input into an improved self-organizing mapping algorithm to generate a spatial distribution mapping diagram of the corrugated pipe damage; The topological feature data set and the spatial distribution mapping diagram are input into a topological feature spectrum pattern recognition algorithm to output the type and severity of the corrugated pipe fatigue damage.

2. The method for detecting the fatigue life of a corrugated pipe according to claim 1, characterized in that, The acoustic metamaterial electromagnetic impedance topological coupling model includes: an acoustic resonator, and the calculation formula for its resonance frequency is as follows: where f r is the resonant frequency of the acoustic resonator; c is the sound wave velocity; S is the cavity opening area; V is the cavity volume; L is the equivalent length of the cavity opening; The calculation formula for the resonance frequency of the electromagnetic impedance unit is as follows: where f e is the resonant frequency of the electromagnetic impedance unit; B is the inductance value; C is the capacitance value; An acoustic-electric coupling mechanism, and the calculation formula for its coupling coefficient is as follows: where κ is the coupling coefficient value between the acoustic and electromagnetic systems; d 33 is the piezoelectric coefficient of the piezoelectric material; A is the area of the piezoelectric sheet; t p is the thickness of the piezoelectric sheet.

3. A bellows fatigue life detection method according to claim 1, characterized in that The steps for constructing a sensing network with topological protection boundary characteristics include: Topological protection boundary conditions, and the calculation formula is as follows: Among them, is the state vector of the i-th unit on the boundary region; ψ0 is a basic state vector value; e is the natural constant; j is the imaginary unit, satisfying j 2 = -1; φ(s) is a phase function that varies with the boundary parameter s; s is the boundary parameter, and the value of φ(s) changes with the change of s; is the boundary region; Cell interaction rules, and the calculation formula is as follows: g ij (Ψ i ,Ψ j ) = c ij (Ψ j - Ψ i ) + d ij (Ψ j ×Ψ i ); where, g ij (Ψ i , Ψ j ) is a function describing the mutual coupling relationship between the i-th unit and the j-th unit; c ij is the linear coupling coefficient; d ij is the nonlinear coupling coefficient; Ψ i is the state vector of the i-th unit; Ψ j is the state vector of the j-th unit; (Ψ j - Ψ i ) reflects the difference in the state vectors of unit j and unit i; the "×" in (Ψ j × Ψ i ) represents a specific vector operation for the calculation of the nonlinear coupling part; Execute network evolution iteration, and the calculation formula is as follows: Among them, is the state vector of the i-th unit at time t+Δt; is the state vector of the i-th unit at time t; Δt is the time interval; is the state vector Ψ of the i-th unit i The rate of change of Ψ with respect to time t at time t.

4. A bellows fatigue life detection method according to claim 1, characterized in that The topological protection boundary sensing calculation formula is as follows: Among them, Z eff (ω) is the effective electromagnetic impedance of the network; Z0(ω) is the reference electromagnetic impedance; k i is the acoustic-electric coupling coefficient of the i-th unit; L i is the inductance value; ω i is the resonance frequency; ω is the excitation frequency; j is the imaginary unit, satisfying j 2 = -1.

5. A bellows fatigue life detection method according to claim 1, characterized in that The steps for obtaining the topological feature data set of the corrugated pipe state include: applying an excitation signal to the corrugated pipe within a preset frequency range and performing frequency scanning, and collecting complex impedance data at each frequency point; calculating topological invariants for the collected frequency impedance spectrum data, and the calculation formula is as follows: where v is the calculated topological invariant; is the coefficient part in the formula; ∮ C is the line integral along the closed path C; dω is the infinitesimal change in frequency ω; is the operator for taking the derivative with respect to frequency ω; ln(Z eff (ω) where Z eff (ω) is the effective electromagnetic impedance of the network; The topological deviation calculation formula is as follows: Δv = (v - v ref ); where Δv is the calculated topological deviation; v is the topological invariant obtained from the above calculation; v ref is the reference state topological invariant value of the non-destructive corrugated pipe.

6. A bellows fatigue life detection method according to claim 1, characterized in that, The core update rule of the improved self-organizing mapping algorithm, and the calculation formula is as follows: Among them, is the state vector of the i-th mapping unit at time t + 1; is the state vector of the i-th mapping unit at time t; η is the learning rate; h(d(i, m)) is the neighborhood function; d(i, m) is the distance from unit i to the best matching unit m; E is the feature vector of the input damage signal; The neighborhood function calculation formula is as follows: Wherein, h(d(i, m)) is the neighborhood function; exp is the exponential function; σ(t) is the neighborhood radius that decays with time, which determines the action range of the neighborhood function, and σ(t) is the neighborhood radius that decays with time; as time t increases, the gradual decrease of σ(t) means that the influence range of the neighborhood function gradually shrinks.

7. A bellows fatigue life detection method according to claim 1, characterized in that, The topological feature spectrum pattern recognition algorithm includes the following steps: Construct a comprehensive feature spectrum, and the calculation formula is as follows: F = (Δν1, Δν2,..., Δν K , Ψ m1 , Ψ m2 ,... Ψ mL ) T ; Among them, F is the comprehensive characteristic spectrum; T represents the transpose operation, that is, converting a row vector into a column vector; Δv1, Δv2, Δv k are the topological deviation values in different frequency intervals respectively, k is the index of different frequency intervals, k = 1, 2,..., K, and these values reflect the difference degree of the topological characteristics between the bellows state and the non-destructive state in different frequency intervals; Ψ m1 , Ψ m2 , Ψ mL are all the characteristic components of the best matching unit in the self-organizing map, m is the best matching unit, l represents the index of the characteristic components of this best matching unit, l = 1, 2,..., L, Ψ m1 , Ψ m2 , Ψ mL are the characteristic components of the best matching unit corresponding to l = 1, l = 2, and l = L respectively; select the pattern with the highest similarity as the recognition result; The finally identified damage pattern calculation formula is as follows: p * = argmax pSim(F, F p ) where p * is the finally identified damage pattern; argmax p is among all possible damage patterns p; Sim(F, F p ) is the similarity function of the comprehensive feature spectrum F and a certain damage pattern F p in the damage pattern library; The damage severity index calculation formula is as follows: Among them, S is the injury severity index; α is the first weight coefficient, used to adjust ||F - F ref || W the weight in calculating the injury severity index S; β is the second weight coefficient, used to adjust the weight in calculating the injury severity index S; F is the comprehensive feature spectrum constructed above; F ref is the reference comprehensive feature spectrum; ||F - F ref || W is used to represent the weighted distance between F and F ref ; W is the weight matrix; is the gradient norm of the comprehensive feature spectrum F.

8. A bellows fatigue life detection method according to claim 1, characterized in that, The similarity calculation of the damage pattern adopts an improved cosine similarity calculation formula as follows: F is the constructed comprehensive feature spectrum vector; W is the feature weight matrix; F T is the transpose of F, which converts the original row vector into a column vector; is the weighted norm of F, used to measure the magnitude of F; is the weighted norm of F p , used to measure the magnitude of F p ; Sim(F, F p ) is the similarity between the input feature vector F and the p-th pattern feature vector F p in the damage pattern library.

9. A bellows fatigue life detection method according to claim 1, characterized in that, Before the steps of constructing a sensing network with topological protection boundary characteristics, it also includes: optimizing the topological structure design according to the structural characteristics and usage environment of the corrugated pipe, and determining the spatial layout of the acoustic-electric topological coupling detection units; determining the optimal number of acoustic-electric coupling units through predictive performance simulation to achieve full coverage with the lowest system complexity.

10. A bellows fatigue damage detection device, characterized in that, For implementing a corrugated pipe fatigue life detection method as described in any one of claims 1-9, including: An acoustic-electric topological coupling detection unit construction module, which is used to construct an acoustic-electric topological coupling detection unit based on the geometric parameters and material property data of the corrugated pipe; A topological protection sensing network construction module, which is used to organize multiple acoustic-electric topological coupling detection units according to the physical cellular automaton model to construct a sensing network with topological protection boundary characteristics; The topological feature extraction module is used to apply an excitation signal to the corrugated pipe, collect electromagnetic impedance response data, and obtain a topological feature dataset of the corrugated pipe state through the topological protected boundary sensing equation; The damage space mapping module is used to input the topological feature dataset into an improved self-organizing mapping algorithm to generate a spatial distribution mapping diagram of the corrugated pipe damage; The damage identification and classification module is used to input the topological feature dataset and the spatial distribution mapping diagram into the topological feature spectrum pattern recognition algorithm to output the type and severity of the fatigue damage of the corrugated pipe.

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