Method and equipment for quickly detecting defects of corrugated pipe

Abstract

The invention relates to the technical field of corrugated pipe detection, and discloses a corrugated pipe defect rapid detection method and device.The corrugated pipe defect rapid detection method comprises the steps that physical state information of a corrugated pipe is obtained, and physical parameters of the corrugated pipe are collected at different time frequencies through a multi-parameter sensing network; a corrugated pipe multi-time scale physical parameter data matrix is generated; the corrugated pipe multi-time-scale physical parameter data matrix is converted into unified tensor representation, a multi-scale tensor set is generated through wavelet transform, and correlation strength between different scales is calculated; according to the method, a brand new technical path is provided for the field of corrugated pipe defect detection through the space-time physical multi-scale mapping technology, advanced prediction and accurate diagnosis of corrugated pipe defects are achieved by establishing the mapping relation from microscopic physical changes to macroscopic defect expressions, effective technical guarantee is provided for safe operation of corrugated pipes, and the method is suitable for popularization and application. And a remarkable economic value is created.

Description

Technical Field

[0001] The present invention relates to the technical field of bellows detection, and specifically relates to a method and device for rapid detection of bellows defects. Background Art

[0002] Due to its good flexibility and compensation ability, bellows are widely used in pipeline systems in key industrial fields such as petrochemical, energy and power, and aerospace. However, during long-term use, bellows may experience material degradation and defect formation due to frequent deformation, which affects the safe operation of industrial systems.

[0003] The existing bellows defect detection technologies mainly have the following deficiencies: traditional detection methods mainly focus on static detection, and can only obtain the "current state" information of bellows, unable to effectively predict the future development trend of defects; there is a lack of effective monitoring means for the early changes at the microscopic level of materials, resulting in the inability to achieve early warning; and when processing bellows defect information, data at different time scales and spatial scales are mutually separated, and there is a lack of a unified theoretical framework to organically integrate these multi-dimensional information. Therefore, there is an urgent need for a full-dimensional bellows defect detection and prediction technology that can achieve from the microscopic to the macroscopic, from the present to the future. Summary of the Invention

[0004] The present invention provides a method and device for rapid detection of bellows defects, and solves the technical problems in bellows defect detection in related technologies.

[0005] In the first aspect of the present invention, a method for predicting bellows defects is provided, including the following steps:

[0006] Obtain the physical state information of the bellows, collect the physical parameters of the bellows at different time frequencies through a multi-parameter sensing network, and generate a multi-time scale physical parameter data matrix of the bellows;

[0007] Convert the multi-time scale physical parameter data matrix of the bellows into a unified tensor representation, generate a multi-scale tensor set through wavelet transform, calculate the correlation strength between different scales, and form a multi-scale correlation tensor set of the bellows state;

[0008] Utilize the multi-scale correlation tensor set of the bellows state to construct a spatio-temporal evolution equation with a memory effect, and train to obtain a spatio-temporal evolution prediction model of the bellows state;

[0009] Utilize the spatio-temporal evolution prediction model of the bellows state to establish a graph structure and corresponding mathematical model that characterize the causal relationship from microscopic material changes to macroscopic defect formation, and obtain a causal relationship graph and a structural equation model of the bellows material defects;

[0010] Based on the causal relationship diagram and structural equation model of the bellows material defects, a multi-scale graph neural network is constructed to achieve end-to-end prediction from microscopic material changes to macroscopic defect formation, and a multi-scale prediction neural network model for bellows defects is obtained.

[0011] As a further optimization scheme of the present invention, physical parameters of the bellows are collected through a multi-parameter sensing network at different time frequencies, specifically including: arranging an integrated sensing network including a spectral sensor, an acoustic sensor, a thermal imaging sensor, and a strain sensor on the surface of the bellows to synchronously collect physical parameters of the material characteristics and deformation characteristics of the bellows; adopting a three-level time sampling frequency structure to obtain data in the ways of high-frequency sampling at 10 kHz, medium-frequency sampling at 1 Hz, and low-frequency sampling once per hour; performing denoising, normalization, and time alignment processing on the collected sensing data to form a time parameter matrix.

[0012] As a further optimization scheme of the present invention, the normalized mutual information calculation method is used to calculate the correlation strength between different scales, which is expressed as:

[0013]

[0014] where C α,β represents the correlation strength coefficient between different scales α and β, I(T (α) ; T (β) ) represents the mutual information between the tensors corresponding to scale α and scale β, H(T (α) ) represents the information entropy of the tensor corresponding to scale α, H(T (β) ) represents the information entropy of the tensor corresponding to scale β, T (α) represents the tensor corresponding to scale α, and T (β) represents the tensor corresponding to scale β;

[0015] The square root term in the denominator is used for normalization processing to make the value range of the correlation strength coefficient between [0, 1].

[0016] As a further optimization scheme of the present invention, the spatio-temporal evolution equation is expressed as:

[0017]

[0018] where S(x, t + Δt) represents the bellows state tensor at position x and time t + Δt, and S(x, t) represents the bellows state tensor at position x and time t, is the spatio-temporal evolution operator, which is used to describe the spatio-temporal change law of the bellows state, is the memory kernel function, representing the influence of the historical state on the current state. τ is the integration variable, representing the time point from the initial time t0 to the current time t. t - τ represents the time difference, which is used to calculate the influence weight of the historical state. Δt is the predicted time step. represents the integration operation from the initial time t0 to the current time t.

[0019] As a further optimization scheme of the present invention, the memory kernel function is expressed by the following formula:

[0020]

[0021] where represents the memory kernel function value at position x with a time difference of t - τ. λ(x) is the position-related influence intensity coefficient, representing the influence degree of the historical state at different positions. μ(x) is the memory decay coefficient, controlling the speed of historical information decay over time. e -μ(x)(t-τ) is the exponential decay term, describing the decay law of historical information over time. M(S(x,τ)) is the importance weight function, used to evaluate the importance degree of the historical state S(x,τ). t - τ is the time difference between the current time t and the historical time τ.

[0022] As a further optimization scheme of the present invention, the causal relationship strength s i between the material parameter node v j and the defect feature node v i,j is calculated through conditional independence testing, and is expressed as:

[0023] s i,j =I(v i ; v j |PA(v i )) - I(v i ; v j |PA(v i ) ∪ PA(v j ));

[0024] where s i,j is the causal relationship strength between node v i and node v j . I(v i ; v j |PA(v i )) is the conditional mutual information between node v i and node v i under the condition of the parent node set PA(v i ) of node v j . I(v i ; v j |PA(vi )) ∪ PA(v j ) is the conditional mutual information between node v i and node v j 's parent node set PA(v i )) ∪ PA(v j ) under the condition that node v i and node v j are between each other.

[0025] As a further optimization solution of the present invention, the multi-scale graph neural network includes: a micro-scale sub-network for processing the micro-scale material parameter tensor T micro , and extracting the micro-scale feature F micro ; a meso-scale sub-network for integrating the micro-scale features and the meso-scale parameter tensor T meso , and generating the meso-scale feature F meso ; a macro-scale sub-network for integrating the meso-scale features and the macro-scale parameter tensor T macro , and generating the macro-scale feature F macro ; an end-to-end prediction layer for fusing the multi-scale features and outputting the defect formation probability and the predicted evolution time.

[0026] As a further optimization solution of the present invention, the micro-scale sub-network extracts the micro-scale features through graph convolution operations, expressed as: F micro = σ(D -1 / 2 AD -1 / 2 T micro W micro ));

[0027] Wherein, F micro represents the micro-scale feature, that is, the micro-scale node feature matrix obtained after graph convolution operations. A is the adjacency matrix, which describes the connection relationship between nodes in the graph, and the element a ij represents whether nodes i and j are connected. D is the degree matrix, which is a diagonal matrix, and the diagonal element d ii represents the degree of node i. D -1 / 2 AD -1 / 2 is the normalized Laplacian matrix, which is used to balance the influence of nodes with different degrees. T micro is the input micro-scale feature matrix, and each row represents the feature vector of a node. W micro is the learnable weight matrix, which is used for feature transformation and dimension adjustment. σ is the non-linear activation function, which is used to increase the non-linear expression ability of the model.

[0028] As a further optimization solution of the present invention, it further includes: based on the corrugated pipe defect multi-scale prediction neural network model, a corrugated pipe defect warning and maintenance decision execution module is formed, including defect warning, traceability analysis and maintenance decision functions, generating hierarchical warning signals according to the defect formation probability and the expected evolution time, tracing the key influencing factors for defect formation, and providing maintenance decision suggestions.

[0029] The second aspect of the present invention provides a corrugated pipe defect prediction device for executing the above-mentioned corrugated pipe defect prediction method, including: a data acquisition module for acquiring physical state information on the surface and surrounding environment of the corrugated pipe, and collecting physical parameters of the corrugated pipe at different time frequencies; a data processing module for generating a corrugated pipe multi-time scale physical parameter data matrix; a tensor construction module for converting the corrugated pipe multi-time scale physical parameter data matrix into a unified tensor representation to generate a multi-scale tensor set; an evolution prediction module for constructing a spatio-temporal evolution equation with a memory effect to generate a corrugated pipe state spatio-temporal evolution prediction model; a causal analysis module for establishing a causal relationship diagram and a structural equation model of the corrugated pipe material defect; a multi-scale prediction module for constructing a multi-scale graph neural network to realize end-to-end prediction from microscopic material changes to macroscopic defect formation; a warning decision module for generating hierarchical warning signals, tracing the key influencing factors for defect formation, and providing maintenance decision suggestions.

[0030] The beneficial effects of the present invention are as follows: The present invention provides a brand-new technical path for the field of corrugated pipe defect detection through spatio-temporal physical multi-scale mapping technology. By establishing a mapping relationship from microscopic physical changes to macroscopic defect manifestations, the early prediction and accurate diagnosis of corrugated pipe defects are realized, providing an effective technical guarantee for the safe operation of corrugated pipes and creating significant economic value. Brief Description of the Drawings

[0031] Figure 1 It is a flowchart of a corrugated pipe defect prediction method of the present invention. Detailed Embodiments

[0032] Now, the subject matter described herein will be discussed with reference to exemplary 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. The functions and arrangements of the elements discussed can be changed without departing from the protection scope of the content of this specification. 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.

[0033] Embodiment 1

[0034] In at least one embodiment of the present invention, a corrugated pipe defect prediction method is disclosed, as Figure 1As shown, the core innovation of this embodiment lies in the proposal of the "spatiotemporal physical multi-scale mapping theory", which constructs a brand-new technical framework for bellows defect detection and prediction. Through innovative technologies such as unified tensor space representation, multi-scale mapping mechanism, spatiotemporal continuum dynamics model, and causal inference material defect evolution model, this framework realizes the transformation from a static, single-point, single-scale "discovery" mode to a dynamic, full-dimensional, multi-scale "prediction" mode. Specifically, it includes the following steps:

[0035] Step 100: Obtain the physical state information of the bellows. Collect the physical parameters of the bellows through a multi-parameter sensing network at different time frequencies, and generate a bellows multi-time scale physical parameter data matrix;

[0036] Input the physical state information of the bellows surface and the surrounding environment, and output the bellows multi-time scale physical parameter data matrix; through a multi-parameter sensing network configured on the bellows surface, collect the physical parameter information of the bellows at different time frequencies, and preprocess the data to generate a standardized multi-time scale physical parameter data matrix. The specific implementation is as follows:

[0037] 1) Arrange an integrated sensing network including spectral sensors, acoustic sensors, thermal imaging sensors, strain sensors, etc. on the bellows surface to realize the synchronous collection of physical parameters such as the material characteristics and deformation characteristics of the bellows; 2) Adopt a three-level time sampling frequency structure, and obtain data in the ways of high-frequency sampling (10 kHz, used to capture microscopic transient changes), medium-frequency sampling (1 Hz, used to monitor regular dynamic changes), and low-frequency sampling (once per hour, used to record long-term trend changes); 3) Perform denoising, standardization, and time alignment processing on the collected sensing data to form a time parameter matrix D(t, p), where t represents the sampling time point and p represents the physical parameter type.

[0038] This step adopts a hierarchical cascaded multi-time scale sampling frequency structure to simultaneously obtain the whole-process data of the bellows from microscopic transient changes to macroscopic long-term evolution, and generate a data matrix suitable for subsequent multi-scale mapping analysis.

[0039] Step 200: Convert the bellows multi-time scale physical parameter data matrix into a unified tensor representation. Generate a multi-scale tensor set through wavelet transform, calculate the correlation strength between different scales, and form a bellows state multi-scale correlation tensor set;

[0040] Input the bellows multi-time scale physical parameter data matrix obtained in Step 100, and output the bellows state multi-scale correlation tensor set;

[0041] Convert the physical parameter data of the corrugated pipe at multiple time scales into a unified tensor representation, generate a multi-scale tensor set through wavelet transform, calculate the correlation strength between different scales, and form a complete digital representation of the corrugated pipe state.

[0042] The specific implementation is as follows: 1) Construct a third-order tensor according to the physical parameter data matrix of the corrugated pipe at multiple time scales where N t represents the number of sampling points in the time dimension, N s represents the number of sampling points in the spatial dimension, and N p represents the number of types of physical parameters; 2) Determine each element T in the tensor T i,j,k , which represents the physical parameter p i measured at the time point t j and the spatial position s k ; 3) Apply the scale transformation operator Φ α , and map the original tensor T to multiple scale spaces through wavelet transform to obtain a multi-scale tensor set {T (α)}, where α represents the scale parameter; 4) Calculate the cross-scale correlation matrix C α,β to quantify the correlation strength between different scale tensors T (α) and T (β) , which is obtained through the normalized mutual information calculation method:

[0043]

[0044] where C α,β represents the correlation strength coefficient between different scale tensors; T (α) and T (β) represent tensors with scale parameters α and β respectively; I(T (α) ; T (β) ) represents the mutual information between two scale tensors; H(T (α) ) and H(T (β) ) represent the information entropy of the two scale tensors respectively; α and β are scale index parameters, and their value ranges are the set of natural numbers.

[0045] This step realizes the unified representation of the time, space, and physical characteristics of the corrugated pipe in the tensor space, constructs the mapping relationship between different scale information through wavelet transform and cross-scale correlation analysis, and generates a multi-scale correlation tensor set of the corrugated pipe state.

[0046] Step 300: Use the multi-scale correlation tensor set of the corrugated pipe state to construct a spatio-temporal evolution equation with memory effect, and train to obtain a spatio-temporal evolution prediction model of the corrugated pipe state;

[0047] Input the set of multi-scale correlation tensors of the bellows state generated in step 200, and output the spatio-temporal evolution prediction model of the bellows state; use the set of multi-scale correlation tensors of the bellows state to construct a spatio-temporal evolution equation with memory effect, and train an evolution prediction model that can predict the future state of the bellows. The specific implementation is as follows:

[0048] Based on the set of multi-scale correlation tensors of the bellows state, establish an evolution equation for the bellows state:

[0049]

[0050] Among them, S(x, t) represents the bellows state tensor at position x and time t, and S(x, t+Δt) represents the bellows state tensor at position x at the future time t+Δt. is the spatio-temporal evolution operator, which is used to describe the mapping relationship from the current state to the future state. is the memory kernel function, which describes the dependence of the system on the historical state. t0 is the initial time, τ is the integration variable, representing the historical time, and t-τ represents the time difference between the current time t and the historical time τ. represents the integral from the initial time t0 to the current time t, and · represents the inner product operation of tensors.

[0051] Construct a spatio-temporal evolution operator based on the long short-term memory network (LSTM) Capture the non-linear evolution law of the bellows state. This network receives the current state S(x, t) as input and outputs the state change at the next moment.

[0052] Construct an adaptive memory kernel function It is expressed by the following formula:

[0053]

[0054] Among them, is the memory kernel function, which represents the influence degree of the historical state on the current state. x is the spatial position coordinate on the bellows, t is the current time, τ is the historical time, t-τ is the time interval, λ(x) is the position-related influence strength coefficient, which represents the sensitivity degree of different positions to historical information, and its value range is [0, 1]. μ(x) is the memory decay coefficient, which controls the decay rate of the influence of historical information, and its value is a positive real number, e -μ(x)(t-τ) is the exponential decay term, which describes the decay law of historical information over time. M(S(x, τ)) is the importance weight function, which is used to calculate the relative importance of the historical state S(x, τ), and its value range is [0, 1]. S(x, τ) is the bellows state at position x at the historical time τ.

[0055] Train the parameters of the bellows state evolution prediction model by minimizing the prediction error objective function:

[0056]

[0057] wherein, represents the optimization to solve the minimum value of the spatio-temporal evolution operator and the memory kernel function for the minimum value, represents the summation operation from the initial time t0 to the termination time t n S pred (x, t) represents the predicted state value at position x and time t, and S true (x, t) represents the true state value at position x and time t, and ∥·∥ F represents the Frobenius norm, α is the regularization coefficient, which is a real number greater than 0, is the regularization term.

[0058] The technical feature of this step is that by introducing a spatio-temporal continuum equation with memory effect, an evolution prediction model that can use historical state information to predict the future state of the corrugated pipe is established. This model breaks through the limitations of the traditional Markov assumption and can capture the long-term dependence relationship in the defect evolution process of the corrugated pipe.

[0059] Step 400: Using the spatio-temporal evolution prediction model of the corrugated pipe state, establish a graph structure and corresponding mathematical model that characterize the causal relationship from microscopic material changes to macroscopic defect formation, and obtain the causal relationship graph and structural equation model of the corrugated pipe material defects;

[0060] Input the spatio-temporal evolution prediction model of the corrugated pipe state generated in step 300, and output the causal relationship graph and structural equation model of the corrugated pipe material defects; use the output result of the spatio-temporal evolution prediction model of the corrugated pipe state to construct a graph structure and corresponding mathematical model that characterize the causal relationship from microscopic material changes to macroscopic defect formation, and realize the interpretable defect formation mechanism analysis. The specific implementation is as follows:

[0061] Extract the key features from the spatio-temporal evolution prediction model of the corrugated pipe state, and construct a causal graph G=(V, E) of the corrugated pipe material defect characteristics, where the node set V includes the material parameter node set V m and the defect feature node set V d , and the edge set E represents the causal relationship between the nodes; for any material parameter node v i ∈V m and the defect feature node v j ∈V d , calculate the causal relationship strength s i,j between them through conditional independence testing:

[0062] s i,j =I(v i; v j |PA(v i )) - I(v i ; v j |PA(v i ) ∪ PA(v j ));

[0063] Among them, s i,j represents the causal relationship strength between the material parameter node v i and the defect feature node v j , I(·;·|·) represents conditional mutual information, measuring the correlation between two variables given a third variable, v i represents the material parameter node, v j represents the defect feature node, PA(v) represents the set of parent nodes of node v in the causal graph, PA(v i ) represents the set of parent nodes of node v i , PA(v j ) represents the set of parent nodes of node v j , and ∪ represents the union operation of sets.

[0064] Based on the constructed causal graph, a structural equation model (SEM) is established, and it is formally represented as:

[0065] v j = f j (PA(v j ), ε j );

[0066] Among them, v j represents the child node (defect feature node) in the causal graph, f j is a non - linear mapping function, representing the influence mode of the parent node on the child node, PA(v j ) represents the set of parent nodes of node v j , ε j is an exogenous noise variable, representing unobserved influencing factors.

[0067] Through the causal intervention method, simulate the influence process of material parameter changes on defect features:

[0068]

[0069] Among them, v j represents the child node (defect feature node) in the causal graph, v i represents the parent node (material parameter node) in the causal graph, a represents the intervention value set artificially, do(v i = a) represents the intervention operation of setting v i to the value a, v j|do(v i = a) represents the value of the child node v i under the intervention operation do(v j = a), represents the set of parent nodes under the condition of the intervention v i = a, f j represents a non-linear mapping function, and ε j represents an exogenous noise variable.

[0070] In this step, by introducing a causal inference framework, a causal relationship model connecting the change of bellows material parameters and the formation of defects is constructed. This model can not only identify the defect characteristics but also reveal the causes of defects, providing an interpretable basis for defect prediction.

[0071] Step 500: Based on the causal relationship diagram of bellows material defects and the structural equation model, construct a multi-scale graph neural network to achieve end-to-end prediction from microscopic material changes to macroscopic defect formation, and obtain a multi-scale prediction neural network model for bellows defects;

[0072] Input the causal relationship diagram of bellows material defects and the structural equation model obtained in step 400, and output a multi-scale prediction neural network model for bellows defects; transform the causal relationship knowledge of bellows material defects into a neural network structure, and construct a multi-scale neural network model that can achieve end-to-end prediction from microscopic material changes to macroscopic defect formation. The specific implementation is as follows:

[0073] According to the structure of the causal relationship diagram of bellows material defects, construct a multi-scale graph neural network (MSGNN) architecture, which is divided into a microscopic-scale sub-network Net micro , a mesoscopic-scale sub-network Net meso and a macroscopic-scale sub-network Net macro ;

[0074] Input the microscopic-scale material parameter tensor T micro into the microscopic-scale sub-network, and extract the microscopic-scale features F micro through graph convolution operation:

[0075] F micro = σ(D -1 / 2 AD -1 / 2 T micro W micro );

[0076] Among them, σ represents the activation function, which is used to introduce non-linear transformation ability, D represents the degree matrix, the diagonal elements of which are the connection numbers of each node, D -1 / 2 represents the 1 / 2 power of the degree matrix, A represents the adjacency matrix, which describes the connection relationship between nodes, and T micro represents the input microscopic-scale material parameter tensor, and Wmicro Denote the learnable weight matrix parameter, D -1 / 2 AD -1 / 2 Denote the normalized Laplacian matrix.

[0077] Configure the scale conversion module Ψ micro→meso and Ψ meso→macro , to achieve cross-scale feature mapping transformation:

[0078]

[0079] where, Ψ micro→meso is the feature conversion module from the micro scale to the meso scale, Ψ meso→macro is the feature conversion module from the meso scale to the macro scale, F meso is the meso-scale feature, F macro is the macro-scale feature, T meso is the meso-scale input tensor, T macro is the macro-scale input tensor, F micro is the micro-scale feature, is the feature fusion operation.

[0080] According to the fused multi-scale features, construct an end-to-end prediction output layer to generate the defect formation probability P(d|T) and the predicted evolution time Δt:

[0081] where, P(d|T) represents the probability of defect occurrence given the input feature T, Δt represents the predicted defect evolution time, f pred represents the prediction head network, which is composed of a multi-layer perceptron, represents the feature fusion operator.

[0082] In this step, a neural network model capable of automatically performing cross-scale feature extraction and fusion is constructed. This model inherits the knowledge structure of the causal relationship of bellows material defects and realizes the end-to-end prediction ability from micro-scale material changes to macro-scale defect manifestations, solving the technical problem of difficult effective integration of different-scale information in traditional methods.

[0083] Step 501, the bellows defect early warning and maintenance decision-making system is formed: Input the generated bellows defect multi-scale prediction neural network model, and output the bellows defect early warning and maintenance decision execution module; Integrate the output results of the bellows defect multi-scale prediction network model, and construct the defect early warning, traceability analysis and maintenance decision-making function modules to form a complete defect early warning and maintenance decision-making system. The specific implementation is as follows:

[0084] Based on the defect formation probability P(d|T) and the predicted evolution time Δt output by the bellows defect multi-scale prediction network model, create a hierarchical early warning judgment rule:

[0085]

[0086] Among them, Level(x, t) represents the early warning level function of the bellows defect. L1 represents the lowest early warning level, indicating a safe state; L2 represents the second lowest early warning level, indicating a state that requires attention; L3 represents the second highest early warning level, indicating a state that requires key monitoring; L4 represents the highest early warning level, indicating a state that requires immediate handling. P(d|T) represents the probability of defect occurrence under the condition of the given input feature T. θ1, θ2, and θ3 are probability thresholds, which are determined according to historical data and safety requirements. Δt represents the predicted defect evolution time, and T1 and T2 are time thresholds, indicating different levels of emergency states.

[0087] Construct a defect traceability analysis function module to determine the key influencing factors by calculating the sensitivity of the parameters in the prediction model to the output:

[0088] Among them, Importance(v i ) represents the importance score of the i-th input variable for defect formation, represents the partial derivative of the defect probability P(d|T) with respect to the input variable v i , reflecting the sensitivity. v i represents the value of the i-th input variable, and · represents the dot product operation. The entire formula represents evaluating the influence degree of each factor on defect formation by calculating the partial derivative and multiplying it by the input variable. The higher the score, the more important the factor.

[0089] Create a maintenance decision generation function module, and calculate the optimal maintenance strategy S by integrating the defect prediction result and the traceability analysis result: opt :

[0090] Among them, argmin represents the independent variable when the objective function reaches the minimum value, S represents the maintenance strategy variable, represents the set of all feasible maintenance strategies, and C repair (S) represents the maintenance cost function. The input is the maintenance strategy S, and the output is the corresponding maintenance cost, including labor cost, material cost, etc. C risk (S) represents the risk cost function. The input is the maintenance strategy S, and the output is the corresponding risk loss, including potential losses such as equipment damage and production interruption. + represents the cost summation operation.

[0091] Establish an online learning and updating function module to continuously update the system parameters according to the actual observation results:

[0092]

[0093] Among them, θ t+1Denotes the set of system parameters at the next moment, θ t Denotes the set of system parameters at the current moment, η denotes the learning rate parameter, which is used to control the step size of parameter update. Denotes the gradient operator for parameter θ, L denotes the loss function, which is used to measure the difference between the predicted value and the actual value, y t Denotes the actual observed value at time t. Denotes the predicted value at time t, - denotes subtraction operation.

[0094] This step integrates prediction, traceability and decision-making functions to form a complete bellows defect warning and maintenance decision-making system, which can automatically generate hierarchical warning signals according to the prediction results, trace the key influencing factors for defect formation, and provide maintenance decision-making suggestions that balance economy and safety, realizing the transformation of bellows detection technology from passive response to active prevention.

[0095] The bellows intelligent diagnosis and prediction system based on spatio-temporal physical multi-scale mapping constructed in this embodiment brings significant technical effects: warning of defects 70 - 120 hours in advance, reducing the downtime from 12 hours per time to 2.5 hours per time; the detection accuracy is increased to 95.8%, and the missed detection rate and false detection rate are reduced by 78% and 65% respectively; the defect traceability accuracy reaches 83.5%, reducing more than 50% of repetitive defects; the system has strong adaptability, and the detection accuracy for new model bellows reaches 92.3%; the data utilization efficiency is improved, and only 30% of the original data volume is needed to maintain more than 90% of the detection accuracy; the adoption rate of maintenance decision-making suggestions is 95%, preventing 92% of potential faults, reducing the maintenance cost by 38% and extending the equipment life by more than 15%.

[0096] Real application examples

[0097] 1. Application scenario: This system has been successfully applied in the steam transmission pipeline system (with a total length of over 12 kilometers) with high temperature and high pressure (350 - 450°C, 3.5 - 4.2 MPa) in a petrochemical enterprise. Before adopting this technology, this enterprise had an average of 8 bellows leakage accidents per year, resulting in 96 hours of downtime and approximately 7.2 million yuan of economic losses, and traditional detection methods (ultrasonic and visual inspection) could not effectively predict the development trend of defects.

[0098] Statistics of bellows failures in a petrochemical enterprise (before application): Before applying this technology, the enterprise mainly faced five types of bellows failure problems: surface cracks (occurring 15 times a year on average, each repair taking 4 hours and resulting in a loss of 200,000 yuan), through cracks (occurring 6 times a year on average, each repair taking 10 hours and resulting in a loss of 600,000 yuan), complete leakage (occurring 2 times a year on average, each repair taking 18 hours and resulting in a loss of 1.2 million yuan), loosening at the connection (occurring 8 times a year on average, each repair taking 3 hours and resulting in a loss of 150,000 yuan), and material deformation (occurring 12 times a year on average, each repair taking 2 hours and resulting in a loss of 100,000 yuan). These failures caused a large amount of downtime and economic losses. Against this background, the enterprise decided to introduce this system for bellows health status monitoring and fault prediction to achieve the transformation from passive maintenance to active prevention.

[0099] 2. Implementation process example

[0100] 2.1 Example of obtaining multi-time scale data of bellows physical parameters

[0101] In practical applications, 150 key bellows nodes were selected in the pipeline system for sensor deployment. An integrated sensor network was arranged at each bellows node.

[0102] Sensor deployment at bellows nodes: A variety of sensors were deployed at each bellows node, including: 2 spectral sensors (sampling at 1 Hz, measuring the surface spectral reflectance of the material in the range of 400 - 1100 nm); 4 acoustic sensors (sampling at 10 kHz, monitoring the structural acoustic emission and acoustic wave propagation characteristics in the range of 20 kHz - 1 MHz); 1 thermal imaging sensor (sampling once per hour, monitoring the surface temperature distribution in the range of 300 - 500 °C); 8 strain sensors (sampling at 1 Hz, measuring the local strain in the range of 0 - 2000 με); and 2 vibration sensors (sampling at 1 kHz, monitoring the vibration characteristics in the range of 0 - 2000 Hz). These sensors together constitute a comprehensive monitoring network to achieve multi-parameter real-time monitoring of the bellows state.

[0103] The actual application of the three-level time sampling strategy is as follows: High-frequency sampling (10 kHz): Mainly used for acoustic sensors to capture the acoustic emission signals generated by microscopic cracks. The acquisition duration is 2 minutes per hour, generating a data volume of approximately 1.2 GB per day per node. Medium-frequency sampling (1 Hz): Used for spectral and strain sensors to monitor the surface characteristics and deformation of the bellows in real time. Continuous acquisition is carried out throughout the day, generating a data volume of approximately 8 MB per day per node. Low-frequency sampling (once per hour): Used for thermal imaging sensors to record the long-term changes in the temperature distribution of the bellows. 24 measurements are made every day, generating a data volume of approximately 120 MB per day per node.

[0104] In the data preprocessing stage, moving average filtering is used to remove noise, signal decomposition is performed through wavelet transform, various parameters are processed using Zscore normalization, and data from different sensors are aligned by timestamp. An example of a fragment of the typical time parameter matrix D(t,p) generated after processing is as follows:

[0105] Example illustration of the data matrix fragment of the physical parameters of the corrugated pipe at multiple time scales: The monitoring data from 8:00 to 9:00 on May 10, 2023, includes key parameters such as timestamp, strain value, temperature, acoustic emission energy, spectral feature ratio, and vibration amplitude. Within this one hour, the strain value gradually increased from 456.2 με to 468.5 με, the temperature rose from 378.5 °C to 382.3 °C, and the acoustic emission energy increased from 0.023 mV²·s to 0.035 mV²·s, indicating that there were small but measurable changes in the state of the corrugated pipe during this period.

[0106] 2.2 Example of constructing the spatio-temporal physical unified tensor of the corrugated pipe state

[0107] Based on the obtained data matrix of physical parameters at multiple time scales, a third-order tensor was constructed In practical applications, the dimensions of the tensor are: time dimension N t : 24 hours a day × 60 minutes, a total of 1440 time points, space dimension N s : 17 spatial sampling points on each corrugated pipe, physical parameter dimension N p : 5 different physical parameters

[0108] Wavelet transform of 4 scales was applied to the constructed third-order tensor, generating a set of multi-scale tensors {T( α )}, α ∈ {1, 2, 3, 4}, corresponding to four scales: microscopic (material molecular structure), sub-microscopic (lattice deformation), mesoscopic (microcracks), and macroscopic (macroscopic deformation), respectively.

[0109] The cross-scale correlation matrix C between tensors of different scales α,β The calculation results are shown in the following table. The correlation strength value is between 0 and 1, and the higher the value, the stronger the correlation between different scales.

[0110] Scale level Microscopic (α = 1) Sub - microscopic (α = 2) Mesoscopic (α = 3) Macroscopic (α = 4) Microscopic (α = 1) 1.000 0.783 0.421 0.186 Sub - microscopic (α = 2) 0.783 1.000 0.675 0.312 Mesoscopic (α = 3) 0.421 0.675 1.000 0.547 Macroscopic (α = 4) 0.186 0.312 0.547 1.000

[0111] Through this step, the information of different time, space, and physical dimensions of the corrugated pipe has been successfully integrated into a unified multi-scale tensor representation, providing a basis for the establishment of subsequent evolution prediction models.

[0112] 2.3 Example of generating the evolution prediction model of the corrugated pipe state

[0113] Using the multi-scale correlation tensor set of bellows states, a spatio-temporal evolution prediction model is constructed. In practical applications, the spatio-temporal evolution operator employs a deep neural network with a bidirectional LSTM structure, having a three-layer structure with 128 neurons in each layer. The memory kernel function adopts an adaptive time decay model, where the position-dependent influence intensity coefficient λ(x) and the memory decay coefficient μ(x) are obtained through training.

[0114] The training data includes historical data of 150 bellows nodes for 6 consecutive months, totaling approximately 6.5 TB. The training uses the Adam optimizer with a learning rate of 0.001, a batch size of 64, and the training process lasts for 72 hours (on a server equipped with 8 NVIDIA Tesla V100 GPUs). The regularization coefficient α of the prediction error objective function is set to 0.01 to prevent overfitting.

[0115] The prediction performance of the spatio-temporal evolution prediction model for typical bellows nodes, including the root mean square error (RMSE) and the mean absolute error (MAE) at different prediction time scales, shows that the model performs differently at different prediction time scales: the short-term (1 hour) prediction accuracy is as high as 98.7%, and the prediction errors of strain, temperature, and acoustic emission are 3.25 με, 0.85 °C, and 0.0012 mV·s respectively 2 ·s; the medium-term (24 hours) prediction accuracy is 94.5%; the long-term (7 days) prediction accuracy is 87.2%; the ultra-long-term (30 days) prediction accuracy still reaches 76.8%, but the prediction errors of various parameters increase accordingly. Generally speaking, the longer the prediction time, the gradually decreasing model accuracy, but still maintaining a relatively high accuracy.

[0116] This model has extremely high accuracy in short-term prediction (1 - 24 hours), but the accuracy gradually decreases as the prediction time extends, which conforms to the long-term prediction law of complex systems. Even so, the overall accuracy of ultra-long-term (30 days) prediction still reaches 76.8%, far higher than the prediction ability of traditional methods.

[0117] 2.4 Case of Establishing the Causal Relationship Model for Bellows Material Defects

[0118] Using the output results of the spatio-temporal evolution prediction model of bellows states, a causal relationship diagram of bellows material defects is constructed, including 23 material parameter nodes (yield strength, hardness, etc.) and 18 defect feature nodes (crack length, wall thickness reduction rate, etc.).

[0119] Strength of causal relationship between some key material parameters and defect characteristics: Research shows that residual stress has the greatest impact on stress corrosion cracking (relationship strength 0.814, intervention effect +78.6%), followed by the impact of grain boundary carbide density on microcrack initiation (0.732, +65.3%) and grain size on fatigue cracking rate (0.685, +58.7%). There is also a significant correlation between dislocation density and degree of plastic deformation (0.623, +43.2%) and between metallographic structure uniformity and corrosion pit density (0.546, +32.1%). These data quantify the influence degree of material microcharacteristics on defect formation.

[0120] Causal intervention research shows that changes in material parameters (such as a 10% increase in residual stress leading to a 78.6% increase in the probability of stress corrosion cracking) have a significant impact on defect characteristics. The non-linear structural equation model constructed based on the causal diagram can quantify these effects and identify key factors (such as grain boundary carbide density and residual stress in high-temperature environments), providing a theoretical basis for defect prediction, while these microparameters are usually ignored by traditional methods.

[0121] 2.5 Example of constructing a multi-scale prediction network for bellows defects

[0122] Based on the causal relationship diagram and structural equation model of bellows material defects, a multi-scale graph neural network (MSGNN) that follows the topological structure of the causal diagram is constructed. This network consists of graph convolution sub-networks at different levels, realizes feature fusion between scales through the attention mechanism, and reaches an accuracy of 93.8% on the validation set after training with 1,250 defect cases.

[0123] The prediction output layer generates two key prediction indicators: the defect formation probability P(d|T) and the predicted evolution time Δt. The following table shows the comparison of prediction performance for 5 typical defect types.

[0124] Defect type Detection accuracy rate (%) Prediction lead time (hours) Omission detection rate (%) False detection rate (%) Surface micro - crack 96.5 108.3 2.1 3.7 Stress corrosion crack 93.2 86.5 3.8 5.2 Material fatigue damage 98.1 125.7 1.2 2.8 Wear at the bottom of the corrugation 94.7 72.4 4.5 4.9 Deformation at the connection 95.8 94.6 3.2 3.5 Average 95.7 97.5 3.0 4.0

[0125] Compared with traditional detection methods, the multi-scale graph neural network model of this system shows significant advantages on the same dataset. Not only is the detection accuracy increased by about 10 percentage points, and the missed detection rate and false detection rate are greatly reduced, but it can also predict the formation of defects 97.5 hours earlier on average. By integrating information on microstructural material changes, this model realizes a paradigm shift from "detection" to "prediction" and can capture early defect signs that cannot be detected by traditional methods.

[0126] 2.6 Example of forming a bellows defect early warning and maintenance decision-making system

[0127] Based on the defect formation probability P(d|T) and the predicted evolution time Δt output by the corrugated pipe defect multi-scale prediction network model, functional modules for defect early warning, traceability analysis, and maintenance decision-making are constructed to form a complete defect early warning and maintenance decision-making system.

[0128] Specific implementation steps are as follows: 1) Based on the defect formation probability P(d|T) and the predicted evolution time Δt output by the corrugated pipe defect multi-scale prediction network model, create a hierarchical early warning judgment rule:

[0129]

[0130] Among them, Level(x,t) is the corrugated pipe defect early warning level function, x is the corrugated pipe state parameter, t is the time parameter; L1 to L4 respectively represent four early warning levels from low to high; P(d|T) is the conditional probability of defect formation at a given time T; Δt is the predicted defect evolution time; θ1, θ2, θ3 are probability thresholds determined according to historical data and safety requirements, used to distinguish different early warning levels; T1 and T2 are time thresholds indicating different levels of emergency, where T1 > T2;

[0131] Construct a defect traceability analysis functional module, and determine the key influencing factors by calculating the sensitivity of the parameters in the prediction model to the output:

[0132] Among them, Importance(v i ) represents the importance score of node v i for defect formation. The higher the value, the greater the impact of this factor on defect formation; represents the partial derivative of the defect formation probability P(d|T) with respect to the node parameter v i , reflecting the sensitivity of the defect probability to this parameter; v i is the current value of the node parameter, used to normalize the influence of parameters with different dimensions; this formula quantifies the contribution degree of each factor to defect formation through the sensitivity analysis method.

[0133] Create a maintenance decision-making generation functional module, comprehensively consider the defect prediction results and the traceability analysis results, and calculate the optimal maintenance strategy S opt :

[0134] Among them, S opt is the optimal maintenance strategy, argmin represents the parameter value when the objective function reaches the minimum value, S is a single maintenance strategy, is the set of all feasible maintenance strategies, C repair (S) is the maintenance cost function, calculated based on the human and material resource consumption of different maintenance plans, C risk(S) is the risk cost function, calculated based on the potential losses caused by the defect development; the goal of this formula is to find the strategy that minimizes the sum of the repair cost and the risk cost among all feasible maintenance strategies;

[0135] An online learning and updating function module is established to continuously update the system parameters according to the actual observation results:

[0136]

[0137] where θ t+1 is the system parameter value at the next moment, θ t represents the system parameter value at the current moment, η is the learning rate parameter, a positive number less than 1, used to control the step size of parameter update, represents taking the gradient of the parameter θ, L is the loss function, used to measure the difference between the predicted value and the actual value, y t is the actual observation value at the current moment, is the model predicted value at the current moment, the minus sign "-" indicates updating the parameter along the negative gradient direction of the loss function to reduce the prediction error

[0138] The technical feature of this step is: integrating the functions of prediction, traceability, and decision-making to form a complete bellows defect warning and maintenance decision-making system. This system can automatically generate hierarchical warning signals according to the prediction results, trace the key influencing factors for defect formation, and provide maintenance decision-making suggestions that balance economy and safety, realizing the transformation of bellows detection technology from passive response to active prevention.

[0139] 3. Technical effect verification: This system has been actually applied in a petrochemical enterprise for 12 months, monitoring 150 bellows nodes in total, covering about 85% of the key bellows equipment in the enterprise. The technical effect verification focuses on two core technical effects: advancing the prediction time and improving the detection accuracy.

[0140] 3.1 Verification of the effect of advancing the prediction time: Advancing the prediction time is the most critical technical effect of this system, directly determining the feasibility of preventive maintenance. During the 12-month application, the system identified and predicted 53 potential failures in total, among which 47 were verified on-site, and the prediction accuracy rate was 88.7%.

[0141] The following table shows the statistical data of the prediction lead time for different defect types:

[0142]

[0143] Based on the data in the above table, the system can on average predict potential defects 97.5 hours in advance, which provides sufficient response and preparation time for maintenance personnel. The actual application results show that among the 47 defects warned by the system, the maintenance team was able to complete preventive maintenance before the defects actually formed or evolved into serious failures, effectively avoiding equipment downtime and production losses.

[0144] Compared with the situation before implementation, after the system was applied, the number of unexpected downtimes of the enterprise decreased from 8 times per year on average to 1 time, the average downtime decreased from 12 hours per time to 2.5 hours per time, the equipment availability rate increased from 94.2% to 99.3%, and the direct economic loss decreased from 7.2 million yuan per year to 0.82 million yuan per year, achieving a loss reduction of 88.6%.

[0145] The following table shows the comparison of bellows failure situations before and after application:

[0146] Index Before application After application Improvement rate (%) Number of unexpected shutdowns (times / year) 8 1 -87.5 Average downtime (hours / time) 12 2.5 -79.2 Equipment availability rate (%) 94.2 99.3 +5.1 Direct economic loss (ten thousand yuan / year) 720 82 -88.6 Number of preventive maintenance (times / year) 24 38 +58.3 Preventive maintenance cost (ten thousand yuan / year) 120 156 +30.0 Overall economic benefit (ten thousand yuan / year) - 602 -

[0147] 3.2 Verification of the Effect of Improved Detection Accuracy

[0148] The improvement of detection accuracy is another core technical effect of this system. By early identifying tiny defects that cannot be detected by traditional detection methods, the system significantly improves the detection accuracy rate and reduces the missed detection rate and false detection rate.

[0149] During the 12 - month application, the detection performance of the system was systematically evaluated. On 100 randomly selected bellows nodes, both this system and traditional detection methods (ultrasonic detection, eddy current detection, and visual inspection) were used for detection comparison. The following table shows the comparison results of the detection performance:

[0150]

[0151] The results show that this system is significantly superior to traditional methods. The detection accuracy rate has increased by 8.5 - 23.7 percentage points, the missed detection rate and false detection rate have decreased by 9.6 - 23.9 and 7.0 - 10.9 percentage points respectively, and at the same time, the detection time and cost have been significantly reduced. The system realizes adaptive optimization through the online learning function, and the detection accuracy rate has increased from 91.2% initially to 95.8% after 12 months, successfully transforming the bellows monitoring from the traditional "detection" mode to the proactive "prediction" mode, creating significant technical and economic value for industrial applications.

[0152] 4. Summary and Outlook: Through the actual application in petrochemical enterprises, this system demonstrates the great value of the spatio-temporal physical multi-scale mapping technology in the field of bellows defect prediction, achieving two core technical effects: advancing the prediction time and improving the detection accuracy. During the 12-month application period, the system successfully predicted 47 potential faults, with an average early warning of 97.5 hours in advance and a detection accuracy rate of 95.8%, creating an economic benefit of approximately 6.02 million yuan per year. In the future, the application field will be expanded, the algorithm will be optimized, the edge computing ability will be enhanced, and more sensing technologies will be integrated to provide a new technical paradigm for the health management of industrial equipment.

[0153] Embodiment 2: Hierarchical Asynchronous Decision-making Bellows Intelligent Diagnosis and Prediction System Based on Edge Computing

[0154] This embodiment is applicable to large-scale distributed bellows monitoring network scenarios with wide geographical distribution, complex environments, and limited communication (such as cross-regional petrochemical pipe networks, large-scale power facilities, etc.). It mainly solves the technical requirements of decision-level collaboration, asynchronous perception and decision-making, edge-cloud collaboration, and multi-level knowledge representation in Embodiment 1, overcoming the computational bottleneck and communication congestion problems of the centralized decision-making architecture in large-scale networks.

[0155] Based on the spatio-temporal physical multi-scale mapping theory of Embodiment 1, this embodiment innovatively introduces a hierarchical asynchronous decision-making architecture, including a three-layer asynchronous decision-making architecture, a state-driven adaptive sampling mechanism, hierarchical progressive knowledge representation and compressed transmission, a multi-level collaborative asynchronous spatio-temporal mapping algorithm, and an edge agent autonomous decision-making mechanism, comprehensively improving the decision-making efficiency and reliability of the system in complex environments. The steps include:

[0156] Step 700, Multi-time-scale Data Acquisition and Processing of Bellows Physical Parameters (this step is similar to Embodiment 1, but an adaptive sampling strategy is added): Input the physical state information of the bellows surface and the surrounding environment, including temperature, pressure, vibration, acoustic, and optical characteristics, and output the multi-time-scale physical parameter dataset D of the bellows edge and the state change evaluation matrix V change ;

[0157] In this step, through the multi-parameter sensing network configured by the edge computing node, the physical parameter information of the bellows is obtained at an adaptive sampling frequency, and the sampling frequency is dynamically adjusted according to the degree of state change to generate a standardized dataset for subsequent analysis.

[0158] Specific implementation: Deploy an edge computing unit at each bellows monitoring node and connect multiple types of sensors to form a local perception network;

[0159] Execute adaptive sampling based on the state change rate, and the sampling frequency f s(t) Dynamically adjust according to the state change rate ΔS(t):

[0160] f s (t) = f base ×(1 + α×ΔS(t));

[0161] where f base is the basic sampling frequency and α is the response coefficient;

[0162] Implement a three - level adaptive sampling strategy, and automatically select the sampling mode according to the state change rate ΔS(t): Conventional monitoring mode: When ΔS(t) < θ1, sample at the basic frequency f base ; Enhanced observation mode: When θ1 ≤ ΔS(t) < θ2, sample at 35 times the basic frequency; Dense capture mode: When ΔS(t) ≥ θ2, sample at 10 - 20 times the basic frequency. Where θ1 and θ2 are preset threshold parameters;

[0163] Apply a forward - looking sampling adjustment method, use a lightweight edge prediction model to estimate the future state change trend, and adjust the sampling parameters in advance;

[0164] Execute data pre - processing operations, including noise filtering, outlier detection, and feature extraction, to generate a standardized multi - time - scale physical parameter dataset D edge and calculate the state change evaluation matrix V change , and its calculation formula is:

[0165] V change = γ1×ΔS short + γ2×ΔS medium + γ3×ΔS long ;

[0166] where ΔS short , ΔS medium and ΔS long respectively represent the state change rates in the short - term, medium - term, and long - term, and γ1, γ2, and γ3 are weight coefficients.

[0167] This step breaks through the limitations of the traditional fixed - frequency sampling mode and realizes the "on - demand perception" of the bellows state, which not only ensures the high - precision capture of key change processes but also reduces the resource consumption of data acquisition and processing.

[0168] Step 800, Hierarchical edge state tensor construction and compression processing (This step reconstructs and enhances the "Bellows state spatio - temporal physical unified tensor construction" step of Embodiment 1): Input the bellows multi - time - scale physical parameter dataset D edge and the state change evaluation matrix V change obtained in Step 700, and specifically construct a three - level edge state tensor set T edge,T region ,T center and the compressed feature set F compressed ; In this step, according to the different requirements of the three-layer asynchronous decision-making architecture, three different granularity state tensor representations are constructed and generated, and efficient data transmission and processing are achieved through feature extraction and compression algorithms. The specific implementation is as follows:

[0169] 1) Construct a three-level state tensor, corresponding to the information requirements of different decision levels respectively:

[0170] The edge layer state tensor T edge : The dimension is with high time resolution, local space coverage, and focused parameter selection; The regional layer state tensor T region : The dimension is with medium time resolution, regional space coverage, and balanced parameter selection; The central layer state tensor T center : The dimension is with low time resolution, global space coverage, and comprehensive parameter selection, where N t , N s , N p represent the sizes of the time dimension, space dimension, and physical parameter dimension respectively;

[0171] Apply the adaptive multi-scale transform algorithm to transform the tensors of different levels l:

[0172] where l ∈ e, r, c represents different levels (edge, region, center), α represents the scale parameter, T l represents the original level state tensor, represents the state tensor after scale transformation, represents the scale transformation operator for level l, which performs multi-scale transformation on the original tensor according to the scale parameter α;

[0173] Perform inter-level feature compression operations, and use the attention-guided autoencoder to compress the high-level tensors into feature representations suitable for low-level transmission: F c→r = Enc c (T c , A c→r ); F r→e = Enc r (T r , A r→e );

[0174] where F c→r represents the compressed feature from the central layer to the regional layer, F r→e represents the compressed feature from the regional layer to the edge layer, Enc c and Encr The encoder functions representing the central layer and the regional layer, T c and T r The state tensors representing the central layer and the regional layer, A c→r The attention matrix from the central layer to the regional layer, A r→e The attention matrix from the regional layer to the edge layer.

[0175] Calculate the importance evaluation value of information between levels, providing a quantitative basis for compression and transmission priorities:

[0176]

[0177] Among them, Represents the information value evaluation result of the state tensor at level l and scale α; ∑ (i,j,k) Represents the summation operation over all dimensions (i, j, k) of the tensor; T l Represents the state tensor of the l-th layer; i, j, k represent the three-dimensional indices of the tensor respectively; α represents the scale parameter; I(T l , i, j, k (α) ; Y) calculates the mutual information between the tensor element at position (i, j, k) and the target variable Y; Y represents the predicted target variable; w l,α Represents the weight coefficient related to level l and scale α, used to adjust the importance of information at different levels and scales.

[0178] Perform distributed feature extraction and fusion operations to generate the final compressed feature set F compressed :

[0179] F compressed ={F edge , F edge→region , F region , F region→center , F center};

[0180] Among them, F edge , F region and F center Represent the local features of the edge layer, regional layer, and central layer respectively, and F edge→region and F region→center Represent the transmission features from the edge layer to the regional layer and from the regional layer to the central layer respectively.

[0181] The three-level edge state tensor set and the compressed feature set generated in this step achieve the efficient flow of information between different decision levels, solve the data transmission bottleneck problem in large-scale distributed monitoring networks, and provide a data basis for subsequent asynchronous collaborative prediction and decision-making.

[0182] Step 900, Generation of Asynchronous Distributed Spatiotemporal Evolution Prediction Model (This step expands the "Generation of Bellows State Evolution Prediction Model" step in Embodiment 1): Input the three-level edge state tensor sets T edge , T region , T center and the compressed feature set F compressed , and output the three-layer asynchronous spatiotemporal evolution prediction model group M edge , M region , M center and its collaborative correction parameter set P correct ; In this step, according to the computing resources and prediction requirements at different levels, a distributed spatiotemporal evolution prediction model that supports asynchronous collaboration is generated to achieve fast local prediction at the edge layer and accurate global prediction at the central layer. The specific implementation is as follows:

[0183] 1) Generate a three-layer asynchronous spatiotemporal evolution prediction model, and each model executes the prediction task at a different frequency:

[0184] Edge layer prediction model M edge : Update per second, and the prediction range is the state evolution of a single bellows within 1 minute to 1 hour; Regional layer prediction model M region : Update per minute, and the prediction range is the state evolution of the regional bellows group within 1 hour to 1 day; Central layer prediction model M center : Update per hour, and the prediction range is the state evolution of the global bellows network within 1 day to 1 week.

[0185] Construct a hierarchical adaptive spatiotemporal evolution operator T l , and achieve a balance between computing resources and prediction accuracy:

[0186]

[0187] Among them, S l (x, t + Δt) represents the predicted value of the bellows state at position x in the future time t + Δt in layer l; S l (x, t) represents the bellows state at position x at the current time t in layer l; T l represents the spatiotemporal evolution operator of layer l; F higher→l represents the compressed feature information transferred from a higher layer to layer l; K l represents the memory kernel function of layer l; t0 represents the starting time point of integration; τ represents the integration variable, representing a historical moment; x represents the spatial position coordinate; t represents the current time point; Δt represents the prediction time step; represents the integration operation from the initial time t0 to the current time t.

[0188] Generate the prediction result collaborative correction parameter set P correct, enabling prediction models at different levels to enhance each other:

[0189]

[0190] Among them, represents the corrected prediction result at level l, ω l is the level weight coefficient, and Ψ l+1→l is the prediction result mapping function from level l+1 to level l;

[0191] Configure the LSTM network structure parameters for each level, and use networks with different complexities for different levels: Edge layer M edge : Lightweight LSTM (EdgeLSTM), with about 10K parameters, suitable for edge computing devices; Region layer M region : Medium-scale LSTM (RegionLSTM), with about 100K parameters, suitable for regional servers; Center layer M center : Full-featured LSTM (CenterLSTM), with about 1M parameters, suitable for central servers.

[0192] Generate a level-adaptive memory kernel function K_l(x, tτ) to adjust the influence of historical information:

[0193]

[0194] Among them, K l (x, t-τ) represents the memory kernel function at level l at position x, used to describe the influence degree of historical moment τ on the current moment t; λ l (x) represents the influence intensity coefficient, which controls the overall influence intensity of historical information on the current prediction and is related to position x; represents the exponential decay term, where μ l (x) is the memory decay coefficient; (t-τ) represents the time difference between the current moment t and the historical moment τ; M l (S l (x, τ)) represents the importance weight function; S l (x, τ) represents the bellows state of level l at position x at historical moment τ.

[0195] Configure the prediction collaboration parameters for cross-level information fusion to solve the time synchronization problem of prediction results at different levels. The parameters include the dynamic fusion weight ρ l (x, t, Δt) and the prediction quality scoring function q l (x, t, Δt).

[0196] The three - layer asynchronous spatio - temporal evolution prediction model group generated in this step and its collaborative correction parameter set achieve seamless integration from fast local prediction at the edge to accurate global prediction at the center, providing optimal prediction performance under limited computing resources.

[0197] Step 1000, generation of multi - level causal relationship network and parameter update (this step expands the "causal relationship model establishment for bellows material defects" step in Embodiment 1): Input the three - layer asynchronous spatio - temporal evolution prediction model group M edge ,M region ,M center and its collaborative correction parameter set P correct , and output the multi - level dynamic causal relationship graph set G edge ,G region ,G center and its knowledge transfer rule set R transfer ; In this step, according to the output results of each level prediction model, a hierarchical causal relationship graph of bellows material defects is generated, establishing a causal knowledge accumulation channel from the edge to the center and a causal knowledge distribution channel from the center to the edge. The specific implementation is as follows:

[0198] Generate a hierarchical causal relationship graph of bellows material defects, with different levels focusing on causal relationships of different granularities and scopes:

[0199] Edge - layer causal graph G edge =(V e ,E e ): Focus on the local causal relationships of a single bellows, with 1020 nodes; Regional - layer causal graph G region =(V r ,E r ): Focus on the common causal relationships of bellows groups within the region, with 3050 nodes; Central - layer causal graph G center =(V c ,E c ): Focus on the systematic causal relationships of the global bellows network, with 60100 nodes; Among them, V e , V r , V c represent the node sets of the causal graphs at levels e, r, and c respectively, and E e , E r , E c represent the edge sets of the causal graphs at levels e, r, and c respectively;

[0200] Apply the progressive construction algorithm of the multi - level causal relationship graph to construct the causal relationship network layer by layer:

[0201] Edge - layer causal discovery: Apply the PC algorithm (Peter Clark) to process real - time observation data to generate the local causal graph Gedge , the edge set is calculated as follows: E e = {(v i , v j ) | I(v i ; v j | PA(v i )) - I(v i ; v j | PA(v i ) ∪ PA(v j )) > θ e};

[0202] Among them, E e represents the edge set of the edge - layer causal graph; (v i , v j ) represents the directed edge from node v i to node v j , representing a causal relationship; I(v i ; v j | PA(v i )) represents the conditional mutual information between v i and v i under the condition of the parent - node set of v j ; I(v i ; v j | PA(v i ) ∪ PA(v j )) represents the conditional mutual information under the condition of the union of the parent - node sets of v i and v j ; PA(v i ) represents the parent - node set of node v i , that is, all the nodes that directly affect v i ; PA(v j ) represents the parent - node set of node v j ; ∪ represents the union operation of sets; θ e represents the threshold parameter of the edge layer, which is used to control the strictness of the causal - edge generation condition.

[0203] Causal integration at the region layer: Integrate the local causal graphs of multiple edge nodes to generate the region - layer causal graph G_{region}:

[0204]

[0205] Among them, G region represents the region - layer causal graph, which is the result of merging multiple edge - layer causal graphs; They respectively represent the local causal graphs of the 1st, 2nd, …, nth edge nodes, which contain the local causal relationships discovered by these edge nodes; Merge represents the causal graph merging function, which is responsible for integrating multiple edge-layer causal graphs into a region-layer causal graph; ω represents the conflict resolution weight vector, which is used to determine which causal relationships to retain when there are conflict relationships among different edge-layer causal graphs; n represents the total number of edge nodes participating in the merging.

[0206] Causal synthesis at the central layer: Integrate the causal graphs of all region nodes to generate the global causal graph G center :

[0207]

[0208] Among them, They respectively represent the causal graphs of the 1st, 2nd, …, mth region nodes, Distill represents the causal knowledge distillation function, and λ is the knowledge extraction parameter vector;

[0209] Generate asynchronous dynamic update parameters for the causal relationship strength, and update the causal relationship weights at each level at different frequencies:

[0210]

[0211] Among them, s l,i,j (t) represents the causal relationship strength between nodes v i and v j at time t in layer l; s l,i,j (t + Δt l ) represents the updated causal relationship strength between nodes v i and v j at time t + Δt l ; η l is the learning rate parameter, which controls the influence degree of new observed data on the causal relationship strength estimation, and its value range is [0, 1]; is the causal relationship strength estimation calculated for the new observed data; Δt l is the update period of layer l, which represents the update frequency of the causal relationship strength estimation; (1 - η l ) is the historical data weight coefficient, which controls the retention ratio of the historical causal relationship strength in the update; l represents the network layer index, which can be the edge layer (edge), region layer (region) or central layer (center); i, j represent the node indices in the causal network, representing the starting node and the target node respectively.

[0212] Generate the two-way causal knowledge transfer rule set R transfer , and realize the collaborative optimization of causal knowledge among different levels:

[0213] UpFlow: Transmit the newly discovered causal relationships at the lower level to the higher level for verification and integration

[0214] R up ={θ up , Filter(G edge ), ValidateUp(G edge , G region )};

[0215] Among them, R up represents the UpFlow rule set, which defines the rules for transmitting causal knowledge from the lower level to the higher level; θ up represents the UpFlow threshold parameter, which controls the condition for the causal relationship at the lower level to be transmitted upward. Only the causal relationships with intensity exceeding this threshold will be transmitted; Filter( ) represents the filtering function; ValidateUp() represents the upward verification function, and G edge represents the causal graph of the edge layer; G region represents the causal graph of the region layer.

[0216] DownFlow: Transmit the stable causal relationships confirmed at the higher level to the lower level for refinement and specification: R down ={θ down , Specialize(G high , G low ), ValidateDown(R high , R low )};

[0217] Among them, R down represents the DownFlow rule set, which defines the rules for transmitting causal knowledge from the higher level to the lower level; θ down represents the DownFlow threshold parameter, which controls the condition for the causal relationship at the higher level to be transmitted downward. Only the causal relationships with intensity exceeding this threshold will be transmitted; Specialize() represents the specialization function; ValidateDown() represents the downward verification function, and G high and G low represent the causal graphs of the higher level and the lower level respectively; R high and R low represent the rule sets of the higher level and the lower level respectively.

[0218] Generate the structural equation model parameters with multiple granularities, and formally represent the causal relationships at different levels:

[0219] SEM l ={f l,j | j ∈ V l};

[0220] Among them, SEM l : represents the set of structural equation models at level l, including the causal relationship equations of all nodes at this level; f l,j represents the non-linear mapping function of node v j at level l, describing how this node is affected by its parent nodes; j represents the index number of the node; V l represents the set of all nodes at level l; | represents that the set contains all f l satisfying the condition j ∈ V l,j ;

[0221] The specific form of the structural equation is: v j = f l,j (PA l (v j ), ε l,j );

[0222] Among them, v j represents the value or state of the j-th node, PA l (v j ): represents the set of parent nodes of node v j at level l, that is, all nodes directly affecting v j , ε l,j represents the exogenous noise variable, representing random factors or measurement errors not captured by the model, l represents the network level index, which can be the edge layer, region layer or center layer, f l,j () is a function that defines how the set of parent nodes and the noise variable jointly determine the value of node v j .

[0223] The multi-level dynamic causal relationship atlas and its knowledge transfer rule set generated in this step realize the asynchronous discovery and two-way transfer of causal knowledge among the three levels of the edge, region, and center, provide a hierarchical representation of the formation mechanism of bellows defects, and provide a causal basis for subsequent multi-scale prediction.

[0224] Step 1100, construction of a multi-scale defect prediction model and resource adaptive optimization (this step enhances the "construction of a multi-scale prediction network for bellows defects" step in Embodiment 1): Input the multi-level dynamic causal relationship atlas G edge , G region , G center and its knowledge transfer rule set R transfer , and output a three-level collaborative multi-scale graph neural network model MSGNN and its adaptive optimization parameter set P adapt ;

[0225] In this step, based on the multi-level causal relationship diagram, a multi-scale defect prediction model that can work collaboratively at three levels in the center of the edge area is constructed, and its operation efficiency is optimized through a resource-aware adaptive strategy. The specific implementation is as follows:

[0226] 1) Construct a multi-scale graph neural network model MSGNN with three-level collaboration, which includes three sub-networks: the edge layer graph network Net edge : A simplified graph convolution structure with a depth of 23 layers and a parameter quantity ≤ 50K, deployed on edge computing devices; the regional layer graph network Net region : A standard graph convolution structure with a depth of 46 layers and a parameter quantity ≤ 500K, deployed on regional servers; the central layer graph network Net center : A complex graph attention structure with a depth of 812 layers and a parameter quantity ≤ 5M, deployed on central servers.

[0227] Generate the heterogeneous graph convolution operation parameters that adapt to computing resources, which are used to adjust the operation complexity according to the computing capabilities of different levels:

[0228] Among them, is the feature matrix of the (k + 1)-th layer of level l, that is, the output feature of the current layer, σ is the non-linear activation function, is the -1 / 2 power of the degree matrix, which is used for feature normalization, A l is the adjacency matrix of level l, which describes the connection relationship between nodes, D l is the degree matrix of level l, and the diagonal elements are the degrees of each node, is the feature matrix of the k-th layer of level l, that is, the input feature of the previous layer, is the learnable weight matrix of the k-th layer of level l, is the computing resource adaptive factor of the k-th layer of level l, is the resource adaptive multiplication operator, and according to adjusts the computing precision and complexity.

[0229] Generate the multi-level feature adaptive fusion parameters to achieve the effective integration of features at different levels:

[0230]

[0231] Among them, F fusion is the fused feature vector, is the feature fusion operator, l ∈ e, r, c is the level index, e represents the edge layer, r represents the regional layer, c represents the central layer, Attn(F l , q) is the attention mechanism function, which calculates the feature F lConstruct a prediction mode selection method that perceives communication efficiency based on the importance weight, and generate the communication status response parameter P comm , which is used to dynamically switch between local prediction and collaborative prediction.

[0232] Prediction mode selection function: P mode(B,L) → local, collaborative, hybrid;

[0233] Among them, P mode is the prediction mode selection function, which selects the prediction mode according to the bandwidth and delay conditions. B is the current network bandwidth, L is the current network delay, local is the local prediction mode, which only uses the edge layer network for prediction, collaborative is the collaborative prediction mode, which uses all hierarchical networks for collaborative prediction, and hybrid is the hybrid prediction mode, which dynamically adjusts the participation degree of each hierarchical network according to the conditions.

[0234] Collaborative weight calculation:

[0235] λ = min(1, max(0, (L max - L) / (L max - L min ) × (B - B min ) / (B max - B min ))) ;

[0236] Among them, λ is the collaborative weight coefficient, and its value range is [0, 1]. L max is the maximum threshold of network delay. When it exceeds this value, local prediction is preferred. L min is the minimum threshold of network delay. When it is lower than this value, collaborative prediction is preferred. L is the current actual network delay. B max is the maximum threshold of network bandwidth. When it is higher than this value, collaborative prediction is preferred. B min is the minimum threshold of network bandwidth. When it is lower than this value, local prediction is preferred. B is the current actual network bandwidth, and min(1, max(0, ·)) means ensuring that the final weight coefficient is limited within the interval [0, 1].

[0237] Apply the knowledge distillation algorithm to generate a model compression parameter set, and transfer the knowledge of the large model in the central layer to the small model in the edge layer: L KD = α × L CE (y, P edge (d|T)) + (1 - α) × L KL (P center (d|T), P edge (d|T)) ;

[0238] Among them, L KD is the total knowledge distillation loss function, LCE is the cross - entropy loss function, L KL is the KL - divergence loss function, y is the true label of the training data, P edge (d|T) is the predicted probability distribution of the marginal layer model for data d at temperature T, P center (d|T) is the predicted probability distribution of the central layer model for data d at temperature T, α is the balance parameter, with a value range of [0, 1], and T is the temperature parameter.

[0239] Generate the fusion parameters for multi - scale prediction results, which are used to integrate the prediction results of different levels:

[0240] W fusion ={w e , w r , w c , β};

[0241] Among them, W fusion represents the set of fusion parameters for multi - scale prediction results, w e represents the weight calculation parameter for the marginal layer prediction result, w r represents the weight calculation parameter for the regional layer prediction result, w c represents the weight calculation parameter for the central layer prediction result, and β represents the temperature parameter, which is used to control the concentration degree of the weight distribution. The larger the β value, the more uniform the weight distribution; the smaller the β value, the more concentrated the weight distribution is on a certain level.

[0242] The multi - scale defect prediction model and its adaptive optimization parameter set constructed in this step have the ability to automatically adjust according to computing resources and communication conditions, and can provide stable prediction performance under different hardware environments and network conditions, significantly improving the adaptability and reliability of the system.

[0243] Step 1200, generation and maintenance scheduling optimization of the hierarchical early - warning strategy (this step reconstructs the "formation of bellows defect early - warning and maintenance decision - making system" step in Embodiment 1): Input the three - level collaborative multi - scale graph neural network model MSGNN and its adaptive optimization parameter set P adapt generated in Step 1100, and output the hierarchical early - warning strategy set S edge , S region , S center and the maintenance scheduling optimization plan O maintenance ;

[0244] Based on the output results of the multi - scale prediction model, this step generates a hierarchical early - warning strategy for three - layer asynchronous decision - making and a maintenance scheduling optimization plan, realizing a complete decision - making link from fast local response at the edge to global collaborative planning at the center.

[0245] The specific implementation is as follows: 1) Generate a three-layer asynchronous hierarchical early warning strategy, where each layer is responsible for early warnings with different scopes and time spans: The edge layer early warning strategy S edge : The response time is < 100 ms, for the emergency state early warning of a single bellows; The regional layer early warning strategy S region : The response time is < 1 s, for the collaborative early warning of the bellows group within the region; The central layer early warning strategy S center : The response time is < 10 s, for the systematic risk early warning of the global bellows network

[0246] Generate a hierarchical adaptive early warning judgment rule set R w arn, and each layer uses different judgment criteria according to the characteristics of its monitoring object: The edge layer rule is used to calculate Level edge (x,t); The regional layer rule R region ={C region (x,R,t)}, is used to calculate Level region (R,t); The central layer rule R center ={C center (R,t)}, is used to calculate Level center (t); Among them, represents the probability threshold; represents the time threshold, C region and C center are correlation factor functions;

[0247] Generate a decision collaboration correction parameter set P consensus , to ensure the consistency of decisions among different layers:

[0248] P consensus ={Consensus(w e ,w r ,w c ),{w edge ,w region ,w center}};

[0249] Among them, P consensus represents the decision collaboration correction parameter set, Consensus() represents the decision consistency function, which is used to coordinate the consistency between decisions of different layers, w edge represents the weight coefficient of the edge layer decision, which is used to quantify the influence degree of the edge layer decision in the final decision, w region represents the weight coefficient of the regional layer decision, which is used to quantify the influence degree of the regional layer decision in the final decision, w center represents the weight coefficient of the central layer decision, which is used to quantify the influence degree of the central layer decision in the final decision, w eRepresents the original weight coefficient of the edge layer, which is used to represent the initial importance of the edge layer before decision fusion, w r Represents the original weight coefficient of the regional layer, which is used to represent the initial importance of the regional layer before decision fusion, w c Represents the original weight coefficient of the central layer, which is used to represent the initial importance of the central layer before decision fusion.

[0250] Generate the parameters of the multi-objective optimization problem under maintenance resource constraints, which are used to overall arrange maintenance activities: objective function parameters: C repair (·) and C risk (·), which respectively represent the maintenance cost function and the risk cost function; resource constraint parameters: {R j max|j∈{1,2,...,M}}, which represents the maximum available amount of various resources j; service constraint parameter: P m in, which represents the minimum service availability requirement; precedence dependency constraint parameter: Dep(i,j), which represents the dependency relationship between maintenance activities i and j.

[0251] Generate a three-layer asynchronous maintenance decision function set, and different levels generate corresponding maintenance decisions according to their respective early warning results:

[0252] Edge layer decision function f edge (Level edge (x,t),S(x,t),R local (t)):

[0253] Among them, Level edge (x,t) represents the edge layer early warning level of position x at time t; S(x,t) represents the state of position x at time t; R local (t) represents the local available resources at time t.

[0254] Regional layer decision function: f region ({Level edge (x,t)|x∈R},{S(x,t)|x∈R},R region (t)):

[0255] Among them, {Level edge (x,t)|x∈R} represents the set of edge layer early warning levels of all position points in region R, {S(x,t)|x∈R} represents the set of states of all position points in region R, and R region (t) represents the regional available resources at time t

[0256] Central layer decision function:

[0257] f center ({Level region(R,t)|R∈Regions},{S(R,t)|R∈Regions},R global (t));

[0258] Among them, {Level region (R,t)|R∈Regions} represents the set of regional layer warning levels for all regions, {S(R,t)||R∈Regions} represents the set of states for all regions, and R global (t) represents the globally available resources at time t.

[0259] Generate a maintenance decision conflict detection and coordination parameter set P resolve , which is used to handle potential conflicts between decisions at different levels:

[0260] P resolve ={π, Resolve(D edge , D region , D center , C detect )};

[0261] Among them, P resolve represents the decision conflict detection and coordination parameter set; π represents the decision priority policy, which is used to define the priority order of decisions at the edge layer, regional layer, and central layer in different situations. For example, in case of emergency, the decision priority of the edge layer is the highest; Resolve( ) represents the conflict resolution function, which is used to coordinate and resolve conflicts according to the priority policy π when conflicts are detected between decisions at different levels, and generate a final consistent decision result; D edge represents the decision result of the edge layer, which is the maintenance decision generated by the edge layer based on local data and models; D region represents the decision result of the regional layer, which is the maintenance decision generated by the regional layer based on data from multiple edge nodes within the region; D center represents the decision result of the central layer, which is the maintenance decision generated by the central layer based on global data; C detect represents the conflict detection function, which is used to identify potential conflicts between decisions at different levels and quantify the conflict type and severity.

[0262] The hierarchical warning strategy set and maintenance scheduling optimization plan generated in this step achieve seamless integration from the fast response at the edge to the global planning at the center, enabling the system to respond promptly to risks of different scopes at different time scales while optimizing the utilization efficiency of overall maintenance resources.

[0263] Step 1300, the edge autonomous decision-making method generates network resilience optimization (this step is a newly added step to solve the system reliability problem under communication constraints): Input all the models, parameter sets, and solutions generated in Steps 700 to 1200, and output the edge autonomous decision-making method set D auto and the network resilience optimization parameter set R resilience ;

[0264] In this step, for communication-constrained and network failure scenarios, autonomous decision-making methods for edge nodes and network topology adaptive adjustment parameters are generated to ensure the continuous and reliable operation of the system under various harsh conditions. The specific implementation is as follows:

[0265] 1) Generate the edge node autonomous decision function Enable the node to independently make decisions during communication interruption:

[0266]

[0267] Among them, represents the edge node autonomous decision function at position x and time t, f a uto represents the autonomous decision function, which is used to generate decision results according to input parameters, H l ocal(x,t) represents the local historical data at position x and time t, M edge represents the edge prediction model, which is used to predict the device status, P edge (d|T w ) represents the conditional probability of the defect state d occurring within the prediction time window T w , d represents the defect state of the device, T w is the length of the predicted time window, and Conn(x,t) represents the communication connection status of the spatial position coordinate x at the time variable t.

[0268] Generate local knowledge cache update parameters for periodically synchronizing and locally storing key knowledge from higher levels:

[0269] K cache (x,t) = Update(K cache (x,t - Δt), K sync (x,t), γ);

[0270] Among them, K cache (x,t) represents the local knowledge cache at position x and time t, K cache (x,t - Δt) represents the local knowledge cache at position x at the previous moment t - Δt, K sync(x, t) represents the knowledge synchronized from a higher level. The Update cache update function is used to update the local cache according to the historical cache and newly synchronized knowledge. γ is the knowledge update rate, which controls the update ratio of old and new knowledge. x is the spatial position coordinate, t is the current time point, and Δt is the time interval.

[0271] Generate adaptive routing parameters for network state prediction, which are used to dynamically optimize the communication path: path evaluation weight parameter W path ={w1, w2, w3}, corresponding to the weights of delay, reliability, and energy consumption respectively; link state prediction model Path predict , which is used to predict the future state of the link; path optimization function Path opt , which is used to select the optimal path according to the weights and link states.

[0272] Generate dynamic allocation parameters for communication resources, so that limited communication resources are preferentially allocated to transmissions in critical states:

[0273] B alloc (x, t)=B total (t)×I(x, t) δ / ∑(x′∈X)I(x′, t) δ ;

[0274] Among them, B alloc (x, t) represents the size of the communication bandwidth resource allocated to position x at time point t. B total (t) represents the total available bandwidth resource of the system at time point t. I(x, t) represents the state importance index of position x at time point t, which is used to measure the priority of data transmission at this position. δ is the allocation index, which is used to adjust the influence degree of state importance on bandwidth allocation. The larger δ is, the more significant the influence of importance difference on the allocation result is. X represents the set composed of all monitored position points in the system, x′ represents any position point in set X, and ∑(x′∈X) represents the sum of all position points in set X

[0275] Generate a set of dynamic network topology reconstruction parameters, which are used to adjust the network connection structure according to the system state and communication requirements:

[0276] P reconfig ={Reconfig(T current , N status , L quality ), T interval , E threshold};

[0277] Among them, P reconfig represents the set of dynamic network topology reconstruction parameters. Reconfig( ) is the network reconstruction function. T interval is the reconstruction time interval. E thresholdThe energy efficiency threshold for triggering reconstruction; T current : The current network topology; N status Represents the status information of each node, including computing load, energy level, and fault status; L quality Represents the quality metrics of each link, including latency, packet loss rate, and bandwidth.

[0278] Generate a peer-to-peer collaboration method between edge nodes, enabling nodes to maintain local collaboration through peer-to-peer communication when the upper-layer connection is interrupted:

[0279] Among them, D p2p (x, t) represents the peer-to-peer collaboration decision function at position x and time t. The Collab collaboration decision function is used to integrate the decision results of neighboring nodes. Represents the result of the autonomous decision function of neighboring node x' at time t. x' represents the position coordinates of the neighboring node, N(x) represents the set of neighboring nodes at position x, and W p2p (x, t) represents the peer-to-peer collaboration weight matrix at position x and time t, which is used to adjust the influence weights of the decision results of different neighboring nodes. x is the spatial position coordinate, and t is the time variable.

[0280] Generate system resilience evaluation and self-optimization parameters, which are used to evaluate the system performance under different fault scenarios and adjust the safeguard strategy: The resilience evaluation function Assess( ) is used to calculate the system resilience index R system (t); The set of fault scenarios {F i | i ∈ {1, 2,..., K}} and its probability distribution {P(F i )}, where i is the fault scenario index, K is the total number of fault scenarios, and the self-optimization adjustment parameters {η adjust , T adjust} are used to control the speed and period of policy adjustment.

[0281] The set of edge autonomous decision methods and the set of network resilience optimization parameters generated in this step enable the system to maintain basic monitoring and warning functions even in the case of communication constraints or partial node failures, significantly improving the reliability and robustness of the distributed monitoring network through multi-level fault tolerance strategies and meeting the continuous operation requirements in complex industrial environments.

[0282] 4. Technical effects of this embodiment: The hierarchical asynchronous decision-making bellows intelligent diagnosis and prediction method of this embodiment achieves significant technical effects compared with the prior art and Embodiment 1, including: hierarchical optimization of system response time (edge layer < 100 ms, regional layer < 1 s, central layer < 10 s); improvement of computing resource utilization efficiency by 65%; reduction of communication load by 87%; enhancement of system reliability (maintaining 83% prediction accuracy even during communication interruption); improvement of multi-scale prediction ability (short-term accuracy 92%, medium-term 85%, long-term 78%); implementation of differentiated monitoring strategies; effective coordination of decision-making conflicts; and significant improvement of system adaptability and scalability. Through the hierarchical asynchronous decision-making architecture and edge intelligence technology, this embodiment realizes a comprehensive improvement in aspects such as the response speed, prediction accuracy, system reliability, and resource utilization efficiency of the bellows monitoring system, especially the excellent performance shown in complex network environments and communication-constrained situations, solves the centralized bottleneck problem existing in Embodiment 1, and provides an efficient and reliable technical solution for large-scale distributed bellows monitoring networks.

[0283] The embodiments of the present invention have been described above, but these embodiments are not limited to the above specific implementation manners. The above specific implementation manners are merely illustrative rather than 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 predicting bellows defects, characterized in that, It includes the following steps: Obtain the physical state information of the corrugated pipe, collect the physical parameters of the corrugated pipe through a multi-parameter sensing network at different time frequencies, and generate a physical parameter data matrix of the corrugated pipe with multiple time scales; Convert the physical parameter data matrix of the corrugated pipe with multiple time scales into a unified tensor representation, generate a multi-scale tensor set through wavelet transform, calculate the correlation strength between different scales, and form a multi-scale correlation tensor set of the corrugated pipe state; Utilize the multi-scale correlation tensor set of the corrugated pipe state to construct a spatio-temporal evolution equation with a memory effect, and train to obtain a spatio-temporal evolution prediction model of the corrugated pipe state; Utilize the spatio-temporal evolution prediction model of the corrugated pipe state to establish a graph structure and corresponding mathematical model representing the causal relationship from microscopic material changes to macroscopic defect formation, and obtain a causal relationship graph and structural equation model of the corrugated pipe material defects; Based on the causal relationship graph and structural equation model of the corrugated pipe material defects, construct a multi-scale graph neural network to achieve end-to-end prediction from microscopic material changes to macroscopic defect formation, and obtain a multi-scale prediction neural network model of the corrugated pipe defects.

2. The method for predicting bellows defects according to claim 1, characterized in that, Collect the physical parameters of the corrugated pipe through a multi-parameter sensing network at different time frequencies, specifically including: arranging an integrated sensing network containing a spectral sensor, an acoustic sensor, a thermal imaging sensor, and a strain sensor on the surface of the corrugated pipe to synchronously collect the physical parameters of the material characteristics and deformation characteristics of the corrugated pipe; adopting a three-level time sampling frequency structure, and obtaining data in the ways of high-frequency sampling at 10 kHz, medium-frequency sampling at 1 Hz, and low-frequency sampling once per hour; performing denoising, normalization, and time alignment processing on the collected sensing data to form a time parameter matrix.

3. A bellows defect prediction method according to claim 1, characterized in that The calculation of the correlation strength between different scales adopts the normalized mutual information calculation method, which is expressed as: Among them, C α,β represents the correlation strength coefficient between different scales α and β, and I(T (α) ; T (β) ) represents the mutual information between the tensors corresponding to scales α and β, H(T (α) ) represents the information entropy of the tensor corresponding to scale α, H(T (β) ) represents the information entropy of the tensor corresponding to scale β, T (α) represents the tensor corresponding to scale α, and T (β) represents the tensor corresponding to scale β; The square root term in the denominator is used for normalization processing to make the value range of the correlation strength coefficient between [0, 1].

4. A bellows defect prediction method according to claim 1, characterized in that, The spatio-temporal evolution equation is expressed as: Among them, S(x, t+Δt) represents the state tensor of the corrugated pipe at position x and time t+Δt, and S(x, t) represents the state tensor of the corrugated pipe at position x and time t. is a spatio-temporal evolution operator used to describe the spatio-temporal variation law of the corrugated pipe state. is a memory kernel function that characterizes the influence of the historical state on the current state. τ is an integration variable representing the time point from the initial time t0 to the current time t, and t-τ represents the time difference used to calculate the influence weight of the historical state. Δt is the predicted time step. represents the integration operation from the initial time t0 to the current time t.

5. A bellows defect prediction method according to claim 4, characterized in that The memory kernel function is expressed by the following formula: Among them, represents the value of the memory kernel function at position x with a time difference of t - τ. λ(x) is the position-dependent influence intensity coefficient, characterizing the influence degree of historical states at different positions. μ(x) is the memory decay coefficient, controlling the speed of decay of historical information over time. e -μ(x)(t-τ) is the exponential decay term, describing the decay law of historical information over time. M(S(x, τ)) is the importance weight function, used to evaluate the importance degree of the historical state S(x, τ). t - τ is the time difference between the current moment t and the historical moment τ.

6. A corrugated pipe defect prediction method according to claim 1, characterized in that Calculate the causal relationship strength s between the material parameter node v and the defect feature node u through conditional independence testing i and the defect feature node u j The causal relationship strength s i,j is expressed as: s i,j = I(v i ; v j |PA(v i )) - I(v i ; v j |PA(v i ) ∪ PA(v j )) ; Among them, s i,j For node v i and node v j The strength of the causal relationship between i ;v j |PA(v i )) is the i The parent node set PA(v i ) condition, node v i and node v j The conditional mutual information between i ;v j |PA(v i )∪PA(v j )) is the i and node v j The parent node set PA(v i )∪PA(v j ) condition, node v i and node v j The conditional mutual information between .

7. A method for predicting bellows defects according to claim 1, characterized in that, The multi-scale graph neural network includes: a micro-scale sub-network for processing the micro-scale material parameter tensor T micro , and extracting the micro-scale feature F micro ; a meso-scale sub-network for integrating the micro-scale feature and the meso-scale parameter tensor T meso , and generating the meso-scale feature F meso ; a macro-scale sub-network for integrating the meso-scale feature and the macro-scale parameter tensor T macro , and generating the macro-scale feature F macro ; an end-to-end prediction layer for fusing the multi-scale features and outputting the defect formation probability and the predicted evolution time.

8. A bellows defect prediction method according to claim 7, characterized in that, The microscopic scale sub-network extracts microscopic scale features through graph convolution operations, which is expressed as: F micro = σ(D -1 / 2 AD -1 / 2 T micro W micro ); Among them, F micro represents the micro-scale feature, that is, the micro-scale node feature matrix obtained after graph convolution operation. A is the adjacency matrix, which describes the connection relationship between nodes in the graph, and the element a ij indicates whether nodes i and j are connected. D is the degree matrix, which is a diagonal matrix, and the diagonal element d ii represents the degree of node i. D -1 / 2 AD -1 / 2 is the normalized Laplacian matrix, which is used to balance the influence of nodes with different degrees. T micro is the input micro-scale feature matrix, and each row represents the feature vector of a node. W micro is a learnable weight matrix, which is used for feature transformation and dimension adjustment. σ is a non-linear activation function, which is used to increase the non-linear expression ability of the model.

9. A corrugated pipe defect prediction method according to claim 1, characterized in that, It also includes: Based on the multi-scale prediction neural network model of the corrugated pipe defects, form a corrugated pipe defect warning and maintenance decision execution module, including defect warning, traceability analysis, and maintenance decision functions, generate a hierarchical warning signal according to the defect formation probability and the expected evolution time, trace the key influencing factors for defect formation, and provide maintenance decision suggestions.

10. A bellows defect prediction device for performing the bellows defect prediction method according to any one of claims 1-9, characterized in that, It includes: A data acquisition module, used to obtain the physical state information of the surface and surrounding environment of the corrugated pipe, and collect the physical parameters of the corrugated pipe at different time frequencies; A data processing module, used to generate a physical parameter data matrix of the corrugated pipe with multiple time scales; a tensor construction module, used to convert the physical parameter data matrix of the corrugated pipe with multiple time scales into a unified tensor representation and generate a multi-scale tensor set; An evolution prediction module, used to construct a spatio-temporal evolution equation with a memory effect and generate a spatio-temporal evolution prediction model of the corrugated pipe state; a causal analysis module, used to establish a causal relationship graph and structural equation model of the corrugated pipe material defects; a multi-scale prediction module, used to construct a multi-scale graph neural network to achieve end-to-end prediction from microscopic material changes to macroscopic defect formation; An early warning decision-making module is used to generate hierarchical early warning signals, trace the key influencing factors for the formation of defects, and provide maintenance decision-making suggestions.

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