Cable bending fatigue life prediction method and system based on reinforcement learning

Abstract

The invention provides a cable bending fatigue life prediction method and system based on reinforcement learning, and relates to the technical field of cable life prediction, and the method comprises the steps: collecting cable test sample data, calculating a stress distribution field and a strain distribution field, constructing a stress intensity factor calculation module, and calculating a crack propagation track and rate. A damage evolution tensor is constructed as a state feature, a network is trained based on a deep Q learning algorithm, uncertainty is quantified by adopting a Markov chain Monte Carlo method, and a credible interval and an early warning threshold are established.

Description

Technical Field

[0001] The present invention relates to the technical field of cable life prediction, and particularly to a method and system for predicting the bending fatigue life of a cable based on reinforcement learning. Background Art

[0002] As an important part of power and communication systems, the prediction of the bending fatigue life of cables is of great significance for ensuring the safe operation of equipment. During actual use, cables are subjected to mechanical stress, especially repeated bending, which leads to the accumulation of fatigue damage in the material and eventually results in fracture failure. Accurately predicting the bending fatigue life of cables is of great value for preventing sudden failures, formulating reasonable maintenance strategies, and extending the service life. Traditional methods for predicting the bending fatigue life of cables mainly rely on empirical formulas and experimental curve fitting. By conducting fatigue tests on a large number of samples, stress-life curves or strain-life curves are established for life estimation. With the development of computer technology, finite element analysis and numerical simulation methods have been applied to cable fatigue analysis. By constructing a mechanical model of the cable, the stress distribution of the cable under different load conditions is simulated, and then the fatigue life is predicted. However, the existing technologies still have limited ability to accurately calculate the internal stress distribution of the cable, cannot comprehensively capture the stress transfer between different material layers and local stress concentration phenomena, resulting in insufficient prediction accuracy, insufficient consideration of the fatigue damage evolution process of the cable, lack of dynamic monitoring and analysis capabilities for crack propagation paths and rates, difficulty in reflecting the accumulation law and non-linear characteristics of fatigue damage, and lack of a reliable uncertainty quantification and risk assessment mechanism, making it impossible to provide credibility evaluation and warning threshold setting for the prediction results, and resulting in difficulties in directly applying the prediction results to actual engineering decisions. Therefore, there is an urgent need for a solution to solve the problems existing in the prior art. Summary of the Invention

[0003] Embodiments of the present invention provide a method and system for predicting the bending fatigue life of a cable based on reinforcement learning, which can at least solve some of the problems existing in the prior art.

[0004] In a first aspect of an embodiment of the present invention, a method for predicting the bending fatigue life of a cable based on reinforcement learning is provided, including: Collecting cable bending fatigue life test sample data including cable specification parameters, stress-strain data, and actual fatigue life data, and calculating the cable stress distribution field and strain distribution field according to the stress-strain data; Based on the theory of material fracture mechanics, a stress intensity factor calculation module is constructed. The stress distribution field and strain distribution field are input into the stress intensity factor calculation module to calculate the stress intensity factors at each stress monitoring point of the cable. A fatigue crack growth rate equation is established to calculate the crack growth trajectory and crack growth rate at each monitoring point of the cable. A damage evolution tensor is constructed as the state feature and input into the deep reinforcement learning network; The action value function is calculated to iteratively train the deep reinforcement learning network, and the actual fatigue life data is used as the reward function until the loss function converges; Quantify the output uncertainty of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, and construct an adaptive warning threshold. When the predicted fatigue life value of the cable is less than the warning threshold corresponding to the confidence level, multi-dimensional warning information is output.

[0005] In an alternative embodiment, Collect the cable bending fatigue life test sample data including cable specification parameters, stress-strain data and actual fatigue life data. Calculate the stress distribution field and strain distribution field of the cable according to the stress-strain data, including: Collect the cable bending fatigue life test sample data, which includes cable specification parameters, stress-strain data and actual fatigue life data. Preprocess the cable bending fatigue life test sample data through an adaptive filter to obtain a preprocessed sample data sequence; Perform wavelet decomposition on the preprocessed sample data sequence, extract the time-frequency features of the stress-strain data, and reduce the dimension of the time-frequency features to obtain a feature vector representing the stress-strain evolution law; Calculate the stress distribution field and strain distribution field of the cable based on the feature vector. The stress distribution field and strain distribution field include normal components, tangential components and radial components.

[0006] In an alternative embodiment, Based on the theory of material fracture mechanics, a stress intensity factor calculation module is constructed. The stress distribution field and strain distribution field are input into the stress intensity factor calculation module to calculate the stress intensity factors at each stress monitoring point of the cable. Establish a fatigue crack growth rate equation, including: Input the pre-acquired stress distribution field and strain distribution field into the stress intensity factor calculation module constructed based on the theory of material fracture mechanics, establish the mapping relationship between the stress distribution field and strain distribution field and the crack tip stress field, and calculate the opening mode stress intensity factor and sliding mode stress intensity factor in the polar coordinate system of the cable crack tip respectively; Calculate the crack growth direction angle according to the opening mode stress intensity factor and sliding mode stress intensity factor, and substitute the crack growth direction angle into the equivalent stress intensity factor calculation formula to obtain the stress intensity factors at each stress monitoring point of the cable; Establish a fatigue crack growth rate equation that includes a material constant term, a stress intensity factor amplitude term, a fatigue crack growth threshold correction term, and a fracture toughness correction term, and establish a quantitative relationship between the crack growth rate and the equivalent stress intensity factor.

[0007] In an alternative embodiment, Calculating the crack growth trajectory and crack growth rate of each monitoring point of the cable, and constructing a damage evolution tensor as the state feature to input into the deep reinforcement learning network includes: Substitute the stress intensity factor into the fatigue crack growth rate equation to obtain the crack growth rate of each monitoring point of the cable, and integrate along the maximum stress direction to obtain the crack growth trajectory of each monitoring point of the cable; Determine the position and range of the crack tip plastic zone according to the crack growth trajectory, calculate the Schmid factor of the plastic zone to determine the main slip system, and obtain the dislocation slip system direction tensor through the tensor product operation of the slip direction and the slip plane normal vector of the main slip system; Construct a dislocation density tensor and perform a tensor product operation with the dislocation slip system direction tensor to obtain a local plastic strain tensor in the plastic zone; Calculate the dislocation slip band density distribution, obtain the first correction coefficient by taking the ratio of the dislocation slip band density to the critical dislocation density, obtain the second correction coefficient by taking the ratio of the equivalent strain of the local plastic strain tensor to the reference strain, and construct a dislocation slip band-local strain correlation function; Perform a tensor product operation on the dislocation slip band-local strain correlation function and the initial damage tensor to obtain a damage correction term, and perform a tensor superposition operation with the second-order spatial derivative term of the initial damage tensor to obtain a damage evolution tensor.

[0008] In an alternative embodiment, Iteratively train the deep reinforcement learning network by calculating the action value function, and use the actual fatigue life data as the reward function until the loss function converges, including: Use the deep Q-learning algorithm to calculate the action value function, and based on the double-network structure of the target network and the training network, iteratively update the action value function based on the temporal difference algorithm; Iteratively train the deep reinforcement learning network based on the updated action value function, use the actual fatigue life data as the reward function, randomly sample training data from the experience pool through the experience replay mechanism, and optimize the network parameters of the deep reinforcement learning network based on the training data through gradient backpropagation; Judge whether the loss function of the deep reinforcement learning network converges. When the change amount of the loss function is less than the preset change threshold in continuous preset number of iterative trainings, it is considered that the loss function converges, stop the iterative training, and obtain the trained deep reinforcement learning network.

[0009] In an alternative embodiment, Quantify the output uncertainty of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, and construct an adaptive warning threshold. When the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information including: Quantify the output of the deep reinforcement learning network to obtain the uncertainty quantification result; Calculate the mean and standard deviation of the predicted value of the cable fatigue life according to the uncertainty quantification result. Take the mean as the predicted central value, and take the product of the standard deviation and the preset confidence coefficient as the interval radius to construct a confidence interval and determine the first uncertainty threshold and the second uncertainty threshold. Divide the confidence level according to the size relationship between the standard deviation and the first uncertainty threshold and the second uncertainty threshold: The standard deviation less than or equal to the first uncertainty threshold is the first level, greater than the first uncertainty threshold and less than or equal to the second uncertainty threshold is the second level, and greater than the second uncertainty threshold is the third level; Construct an adaptive warning threshold based on the confidence interval and the confidence level. When the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information including the predicted value of the cable fatigue life, the confidence interval, the confidence level, and the standard deviation.

[0010] In an alternative embodiment, Quantifying the output of the deep reinforcement learning network to obtain the uncertainty quantification result includes: Construct the cable stress-strain constraint condition according to the theory of mechanics of materials, establish the correlation equation between the stress tensor and the strain tensor, and establish the correlation equation between the crack growth rate and the stress intensity factor amplitude as the physical constraint condition; Construct the target distribution function and the proposal distribution function to calculate the acceptance probability of the new sampling point, calculate the constraint violation measure of the new sampling point under the physical constraint condition, and determine whether the new sampling point is a valid sampling point according to the size relationship between the constraint violation measure and the preset tolerance threshold; Use the student distribution to fit the valid sampling points to calculate the degree of freedom parameter, describe the heavy-tailed characteristics of the valid sampling points through the generalized hyperbolic distribution to calculate the tail heaviness parameter, skewness parameter, scale parameter, position parameter and shape parameter, and construct the joint probability distribution function to establish the multi-dimensional dependence structure; Calculate the mean and variance of the valid sampling points, evaluate the sampling convergence and sampling effectiveness to determine the uncertainty distribution characteristics of the valid sampling points, and use them as the uncertainty quantification results of the cable fatigue life.

[0011] In the second aspect of the embodiments of the present invention, a cable bending fatigue life prediction system based on reinforcement learning is provided, including: The first unit is used to collect the sample data of the cable bending fatigue life test, including cable specification parameters, stress-strain data and actual fatigue life data, and calculate the cable stress distribution field and strain distribution field according to the stress-strain data; The second unit is used to construct a stress intensity factor calculation module based on the material fracture mechanics theory, input the stress distribution field and strain distribution field into the stress intensity factor calculation module, calculate the stress intensity factors at each stress monitoring point of the cable, establish a fatigue crack growth rate equation, calculate the crack growth trajectory and crack growth rate at each monitoring point of the cable, and construct a damage evolution tensor as the state feature to input into the deep reinforcement learning network; The third unit is used to calculate the action value function to iteratively train the deep reinforcement learning network, and use the actual fatigue life data as the reward function until the loss function converges; The fourth unit is used to quantify the output uncertainty of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, construct an adaptive warning threshold, and when the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information.

[0012] In the third aspect of the embodiments of the present invention, an electronic device is provided, including: A processor and a memory for storing processor-executable instructions, wherein the processor is configured to call the instructions stored in the memory to execute the method described above.

[0013] In the fourth aspect of the embodiments of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored, and when the computer program instructions are executed by a processor, the method described above is implemented.

[0014] In the present invention, by integrating the material fracture mechanics theory and the deep reinforcement learning technology, it is possible to capture the crack growth trajectory and rate from the microscopic level, use the damage evolution process as the state feature of the reinforcement learning, realize the accurate prediction of the cable fatigue life, improve the prediction accuracy, use the Markov chain Monte Carlo method to quantify the uncertainty of the prediction results, construct the confidence interval of the prediction results, and design an adaptive warning threshold based on the confidence level, making the warning mechanism more reliable, effectively reducing the prediction risk. By using the actual fatigue life data as the reward function to guide the model learning, it can automatically extract key features and optimize the prediction strategy, improve the generalization ability and adaptability of the model, and at the same time, the output multi-dimensional warning information provides a comprehensive basis for the cable maintenance decision. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic flow chart of the cable bending fatigue life prediction method based on reinforcement learning according to the embodiments of the present invention; Figure 2Distribution diagram of Schmidt factor in the plastic zone at the crack tip of the cable bending fatigue life prediction method based on reinforcement learning according to the embodiments of the present invention; Figure 3 Analysis diagram of the uncertainty of cable fatigue life prediction of the cable bending fatigue life prediction method based on reinforcement learning according to the embodiments of the present invention; Figure 4 Three-dimensional distribution characteristic diagram of the uncertainty of cable fatigue life of the cable bending fatigue life prediction method based on reinforcement learning according to the embodiments of the present invention. Detailed implementation manners

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0017] The technical solutions of the present invention will be described in detail below with specific embodiments. These specific embodiments may be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0018] Figure 1 Schematic flow diagram of the cable bending fatigue life prediction method based on reinforcement learning according to the embodiments of the present invention, as Figure 1 shown, the method includes: Collect cable bending fatigue life test sample data of cable specification parameters, stress-strain data, and actual fatigue life data, and calculate the cable stress distribution field and strain distribution field according to the stress-strain data; Based on the material fracture mechanics theory, construct a stress intensity factor calculation module, input the stress distribution field and strain distribution field into the stress intensity factor calculation module, calculate the stress intensity factors of each stress monitoring point of the cable, establish a fatigue crack growth rate equation, calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable, and construct a damage evolution tensor as the state feature to input into the deep reinforcement learning network; Calculate the action value function to iteratively train the deep reinforcement learning network, and use the actual fatigue life data as the reward function until the loss function converges; Quantify the output uncertainty of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, construct an adaptive warning threshold, and when the cable fatigue life prediction value is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information.

[0019] In an alternative implementation manner, Collect the cable bending fatigue life test sample data of cable specification parameters, stress-strain data and actual fatigue life data. Calculate the cable stress distribution field and strain distribution field according to the stress-strain data, including: Collect the cable bending fatigue life test sample data. The cable bending fatigue life test sample data includes cable specification parameters, stress-strain data and actual fatigue life data. Preprocess the cable bending fatigue life test sample data through an adaptive filter to obtain a preprocessed sample data sequence. Perform wavelet decomposition on the preprocessed sample data sequence, extract the time-frequency characteristics of the stress-strain data, and reduce the dimension of the time-frequency characteristics to obtain a feature vector representing the stress-strain evolution law. Calculate the stress distribution field and strain distribution field of the cable based on the feature vector. The stress distribution field and strain distribution field include normal components, tangential components and radial components.

[0020] Before the cable bending fatigue life test starts, prepare the test equipment including a bending fatigue testing machine, a high-precision strain gauge, a data acquisition system and a computer processing system. Select test cable samples of different specifications, including copper core cables with diameters of 0.5 mm, 1.0 mm, 1.5 mm and 2.0 mm, and the insulation layer thicknesses are 0.2 mm, 0.3 mm, 0.5 mm and 0.7 mm respectively. Install the cable samples on the bending fatigue testing machine, set the bending radius to 5 times, 10 times and 15 times the cable diameter, the bending frequency to 0.5 Hz, 1 Hz and 2 Hz, and the preset upper limit of the bending times to 10^6 times.

[0021] Arrange strain gauges at key positions on the cable surface, including the bending center point, ±5 mm, ±10 mm and ±15 mm from the center point, a total of 7 measurement points. Collect the stress-strain data through a high-precision strain gauge, and set the sampling frequency to 100 Hz to ensure data accuracy. The stress-strain time series data generated at each test point and the corresponding actual fatigue life data (the number of cycles before bending failure) are recorded and stored.

[0022] There are noises and outliers in the collected original data, and an adaptive filter is used for preprocessing. Use the least mean square error adaptive algorithm, set the filter order to 64, the step size parameter μ to 0.01, and the convergence coefficient to 0.98. For the stress-strain time series data of each measurement point, perform noise suppression through an adaptive filter to filter out high-frequency noises and electromagnetic interferences. For example, for a 1.0 mm diameter cable with a bending radius of 10 times the diameter, the strain signal at the center point fluctuates in the original range of ±0.35%, and after filtering, it stabilizes in the range of ±0.32%, and the signal-to-noise ratio is increased by about 15%.

[0023] Perform wavelet decomposition on the preprocessed sample data sequence to extract the time-frequency characteristics of the stress-strain data. Use the Daubechies wavelet function (db6) to decompose the signal into 5 layers to obtain the corresponding low-frequency approximation coefficients and high-frequency detail coefficients. For the stress-strain time-series data at each measurement point, extract wavelet energy characteristics, statistical moment characteristics, spectral characteristics, etc. For example, for a cable with a diameter of 1.5 mm, in the 3rd layer of wavelet decomposition, the stress fluctuation characteristics are mainly concentrated in the frequency band of 2 - 5 Hz, accounting for 68.4% of the total energy, reflecting the main stress distribution law of the cable during the bending process.

[0024] Perform dimensionality reduction on the time-frequency characteristics through principal component analysis. Construct a feature matrix from the characteristics obtained by wavelet decomposition, calculate the covariance matrix, and solve for the eigenvalues and eigenvectors. Select the first few principal components with a cumulative contribution rate exceeding 90% as the feature vectors after dimensionality reduction. Usually, the first 3 - 5 principal components can represent more than 95% of the data variability. For example, for a cable sample with a diameter of 2.0 mm, the cumulative contribution rate of the first 4 principal components reaches 93.7%. Among them, the first principal component represents the strain characteristics in the central bending region of the cable, with a contribution rate of 56.2%; the second principal component represents the strain propagation characteristics, with a contribution rate of 21.3%.

[0025] Input the feature vectors into the finite element analyzer to establish a cable bending fatigue model. The cable model adopts a multi-layer structure, including a metal conductor core, an insulating layer, and an outer sheath. Corresponding physical parameters are set for each layer of material. For example, the Young's modulus of the copper core is 110 GPa, and the Poisson's ratio is 0.34; the Young's modulus of the insulating layer (PVC material) is 3.5 GPa, and the Poisson's ratio is 0.38. The mesh is divided using hexahedral elements, and the mesh density in the central bending region is increased, with the element size set to 1 / 20 of the cable diameter.

[0026] Calculate the stress distribution field and strain distribution field of the cable through the stress-strain constitutive equation solver. During the solution process, use the updated Lagrangian method to handle large deformation problems, adopt the Newton-Raphson iterative algorithm to solve the nonlinear equations, set the iterative accuracy to 10 - 6, and the maximum number of iterations to 50. Based on the stress-strain boundary conditions determined by the feature vectors, calculate the stress distribution field and strain distribution field of each point on the cable, including normal components, tangential components, and radial components. The calculation results show that for a cable with a diameter of 1.0 mm under the condition of a bending radius of 10 times the diameter, the maximum normal stress at the conductor core of the bending center point reaches 78.5 MPa, the maximum tangential stress is 32.7 MPa, and the maximum radial stress is 25.6 MPa; the corresponding maximum normal strain is 0.31%, the maximum tangential strain is 0.16%, and the maximum radial strain is 0.12%.

[0027] In this embodiment, by preprocessing the sample data of the cable bending fatigue life test with an adaptive filter, the measurement noise and abnormal interference can be effectively removed, and the data quality for subsequent analysis can be improved. By using wavelet decomposition to extract the time-frequency characteristics of the stress-strain data, the time-domain and frequency-domain information can be obtained simultaneously, and the dynamic evolution characteristics of the stress-strain can be characterized more comprehensively than simple time-domain analysis or frequency-domain analysis. The calculation method based on the mechanical model has stronger physical significance than simple data fitting and can more accurately reflect the stress-strain state inside the cable.

[0028] In an alternative embodiment, Based on the theory of material fracture mechanics, a stress intensity factor calculation module is constructed. The stress distribution field and the strain distribution field are input into the stress intensity factor calculation module to calculate the stress intensity factors at each stress monitoring point of the cable. The established fatigue crack growth rate equation includes: The pre-acquired stress distribution field and strain distribution field are input into the stress intensity factor calculation module constructed based on the theory of material fracture mechanics to establish the mapping relationship between the stress distribution field and the strain distribution field and the stress field at the crack tip, and calculate the mode I stress intensity factor and the mode II stress intensity factor in the polar coordinate system at the crack tip of the cable respectively; Calculate the crack propagation direction angle according to the mode I stress intensity factor and the mode II stress intensity factor, and substitute the crack propagation direction angle into the formula for the equivalent stress intensity factor to obtain the stress intensity factors at each stress monitoring point of the cable; Establish a fatigue crack growth rate equation including material constant terms, stress intensity factor amplitude terms, fatigue crack growth threshold correction terms, and fracture toughness correction terms, and establish the quantitative relationship between the crack growth rate and the equivalent stress intensity factor.

[0029] Based on the stress distribution field and strain distribution field data, a mapping transformation is performed in the stress intensity factor calculation module. The Williams series expansion method is used to perform coordinate transformation on the original data to establish a polar coordinate system with the crack tip as the origin. The stress field is expressed in polar coordinate form through Fourier series expansion, and the number of expansion terms is dynamically adjusted until the convergence error is less than the preset threshold. During the series expansion process, the least squares method is used to optimize and solve each coefficient, and the series coefficients are determined through iterative calculation. By using the symmetry and anti-symmetry of the stress field, the stress components corresponding to mode I and mode II are extracted respectively to establish an accurate mapping relationship between the stress distribution and the singular field at the crack tip.

[0030] In the stage of solving the stress intensity factor, the singularity problem is handled by extrapolation. Multiple concentric circle paths are established around the crack tip, and stress components are extracted along each path. The stress components on each path are integrated and averaged to obtain the path-independent integral value. The path integral method based on the strain energy release rate is used to combine the displacement field and stress field information to calculate the cracking type and sliding type stress intensity factors respectively. In order to improve the calculation accuracy, the calculation results of multiple paths are weighted averaged, and the weight coefficient decays exponentially with the path distance.

[0031] Determine the crack propagation direction and establish the objective function based on the maximum tangential stress criterion. Decompose the stress field in the mixed mode into radial and tangential components through polar coordinate transformation. In the fan-shaped area centered on the crack tip, the grid search method is used to find the maximum tangential stress point. In order to avoid local optimal solutions, multiple initial search points are set, and the search process is optimized by combining the gradient descent method. Substitute the direction angle corresponding to the maximum tangential stress obtained by the search into the equivalent stress intensity factor calculation formula, and calculate the equivalent stress intensity factor of each monitoring point through tensor transformation and stress superposition principle.

[0032] The fatigue crack growth rate equation is established, and the piecewise function is used to describe the characteristics of different growth stages. The threshold value correction term and the fracture toughness correction term are embedded in the basic equation by introducing the weight function. For the threshold value correction term, a gradual transition function is used to describe the crack growth behavior in the near-threshold area to ensure the prediction accuracy in the low stress intensity factor area. The fracture toughness correction term uses a nonlinear function to characterize the rapid growth characteristics of the crack growth rate when it is close to the fracture toughness. In the solution process, the numerical integration method with adaptive step size is used to accumulate the crack extension amount. By dynamically adjusting the integration step size, both the calculation accuracy and the solution efficiency are guaranteed.

[0033] Multiple error controls are implemented during the solution process. Independent error control indicators are set for the truncation error of series expansion, the discrete error of path integral, the convergence error of direction angle search, etc. During data processing, the sliding window method is used to smooth the intermediate calculation results to reduce the impact of numerical fluctuations on the final results. At the same time, the singular points and jump points in the calculation process are identified and specially processed to ensure the robustness of the algorithm under various working conditions.

[0034] For example, a certain type of power cable is used as the research object. The cable has a cross-sectional diameter of 20 mm, an outer sheath thickness of 2 mm, and a complex multi-layer structure. The stress distribution field data is obtained through bending fatigue test, and 12 stress monitoring points are arranged on the cable surface. The Williams series is expanded to the eighth order to establish a stress field mapping relationship. A polar coordinate system is established at the crack tip, and the cracking type stress intensity factor is calculated to be the square root of 25 MPa·m, and the sliding type stress intensity factor is calculated to be the square root of 15 MPa·m.

[0035] Based on the maximum tangential stress criterion, the crack propagation direction angle is calculated to be 70 degrees. Substituting this direction angle into the calculation formula, the equivalent stress intensity factor is obtained as the square root of 32 MPa·m. Considering the characteristics of the cable material of this model, the material constant is set to 10^(-10) in the fatigue crack propagation rate equation, the threshold value correction term is the square root of 8 MPa·m, and the fracture toughness correction term is the square root of 85 MPa·m. Through this equation, under cyclic loading, when the stress intensity factor amplitude is the square root of 30 MPa·m, the crack propagation rate is 0.002 mm per cycle.

[0036] In this embodiment, the Williams series expansion method is used to establish the mapping relationship between the stress distribution field, strain distribution field and the crack tip stress field, which can accurately describe the stress distribution characteristics at the crack tip. By calculating the opening mode and sliding mode stress intensity factors respectively, the mixed mode fracture characteristics of the cable under complex loading conditions are comprehensively reflected, which is more in line with the actual working conditions compared with the single mode fracture analysis. Based on the maximum tangential stress criterion, the crack propagation direction angle is calculated to accurately predict the crack propagation path. By improving the Paris fracture criterion to establish the fatigue crack propagation rate equation and introducing the fatigue crack propagation threshold value correction term and fracture toughness correction term, the prediction deviation of the traditional Paris formula in the low stress and high stress regions is overcome.

[0037] In an alternative embodiment, Calculating the crack propagation trajectories and crack propagation rates of each monitoring point of the cable, and constructing the damage evolution tensor as the state feature to input into the deep reinforcement learning network includes: Substitute the stress intensity factor into the fatigue crack propagation rate equation to obtain the crack propagation rate of each monitoring point of the cable, and integrate along the maximum stress direction to obtain the crack propagation trajectories of each monitoring point of the cable; Determine the position and range of the plastic zone at the crack tip according to the crack propagation trajectory, calculate the Schmid factor of the plastic zone to determine the main slip system, and obtain the dislocation slip system direction tensor through the tensor product operation of the slip direction and the slip plane normal vector of the main slip system; construct the dislocation density tensor and perform the tensor product operation with the dislocation slip system direction tensor to obtain the local plastic strain tensor of the plastic zone; Calculate the dislocation slip band density distribution, obtain the first correction coefficient by taking the ratio of the dislocation slip band density to the critical dislocation density, obtain the second correction coefficient by taking the ratio of the equivalent strain of the local plastic strain tensor to the reference strain, and construct the dislocation slip band - local strain correlation function; Perform the tensor product operation of the dislocation slip band - local strain correlation function and the initial damage tensor to obtain the damage correction term, and perform the tensor superposition operation with the second-order spatial derivative term of the initial damage tensor to obtain the damage evolution tensor.

[0038] The obtained stress intensity factors are input into the fatigue crack growth rate equation, and the crack growth rates at each monitoring point of the cable are obtained through numerical calculation. An adaptive-step numerical integration algorithm is used to integrate the crack growth rate along the direction of the maximum principal stress to obtain the crack growth trajectories at each monitoring point. The calculation step is dynamically adjusted during the integration process, and the step is refined in the region where the crack growth rate changes violently to ensure the calculation accuracy.

[0039] Based on the obtained crack growth trajectories, the plastic zone estimation criterion is used to determine the boundary of the plastic deformation region at the crack tip. In the determined plastic zone, crystal orientation data are obtained through diffraction analysis methods, and the conversion relationship between the crystal coordinate system and the specimen coordinate system is established. The Schmid factor is calculated for all possible slip systems in the plastic zone, and considering the coupling effect of crystal orientation and applied stress state, the most easily activated primary slip system is identified. The slip direction vector and slip plane normal vector of the primary slip system are used for tensor product operation to construct a complete dislocation slip system direction tensor field.

[0040] In the determined plastic region, a dislocation density tensor field is constructed based on the dislocation dynamics theory. Considering the generation, annihilation, and accumulation processes of dislocations, a dislocation density evolution equation is established. The constructed dislocation density tensor is subjected to tensor product operation with the dislocation slip system direction tensor obtained previously to obtain a strain tensor field characterizing local plastic deformation. The influence of crystal anisotropy and dislocation interaction is considered during the calculation process.

[0041] According to the obtained local plastic strain tensor field, the density distribution of dislocation slip bands is calculated using the method of continuum mechanics. By setting a critical dislocation density threshold, the ratio of the actual dislocation density to the critical density is calculated to obtain the first correction coefficient reflecting the degree of dislocation accumulation. At the same time, the ratio of the equivalent strain of the local plastic strain tensor to the reference strain of the material is calculated to obtain the second correction coefficient characterizing the degree of plastic deformation. Based on the correction coefficients, a coupling function that can accurately describe the relationship between dislocation slip bands and local strain is constructed.

[0042] The constructed dislocation slip band-local strain correlation function is subjected to tensor product operation with the initial damage state tensor of the material to obtain a damage correction term considering the influence of microscopic mechanisms. At the same time, the spatial second derivative of the initial damage tensor is calculated to characterize the gradient effect of damage. Through tensor superposition operation, the damage correction term and the spatial derivative term are combined to obtain a complete damage evolution tensor field.

[0043] Exemplarily, a certain type of copper-core power cable is taken as the research object, and eight stress monitoring points are arranged in the bending fatigue test. After obtaining the stress intensity factors through the previous calculation, the improved crack growth rate equation is used to calculate the growth rates at each monitoring point. The initial integration step size is selected as one-tenth of the size of the plastic zone at the crack tip and is dynamically adjusted during the expansion process through an adaptive algorithm.

[0044] In the determined plastic zone, crystal orientation data is obtained by electron backscatter diffraction. It is calculated that there are a total of twelve potential slip systems in the plastic zone, and the main slip system is determined to be located on the octahedral slip plane of the crystal through Schmidt factor analysis. The constructed dislocation density tensor field shows that the dislocation density reaches the maximum value at a distance of 0.2 mm from the crack tip to the surface.

[0045] Through calculation and analysis, the dislocation slip bands are mainly distributed in the fan-shaped area 0.5 mm away from the crack tip. The ratio of the actually measured dislocation density to the critical dislocation density of the material is used as the first correction coefficient, and the ratio of the calculated equivalent plastic strain to the yield strain of the material is used as the second correction coefficient. The correlation function constructed by the two correction coefficients accurately describes the evolution characteristics of the dislocation slip bands.

[0046] The obtained damage evolution tensor field shows that damage initiates from the high stress concentration area at the crack tip and gradually expands along the direction of the dislocation slip bands. The spatial distribution of the damage field exhibits obvious anisotropic characteristics, which is in good agreement with the actually observed fatigue crack propagation path.

[0047] In this embodiment, the plastic deformation region is determined through the crack propagation trajectory. On this basis, the crystal plasticity theory is introduced, and the main slip system is determined through Schmidt factor analysis, realizing an effective mapping from the macroscopic stress field to the activation of the microscopic slip system. By constructing the dislocation density tensor and the dislocation slip system direction tensor, a quantitative relationship between the microscopic dislocation motion and the macroscopic plastic strain is established. The influence of the dislocation density and the plastic strain is considered respectively through the two correction coefficients, realizing the scale transition from microscopic damage to macroscopic damage; In the prior art, a continuous damage mechanics model at the macroscopic scale is usually directly adopted, regarding the material as a homogeneous continuous medium, ignoring the dislocation evolution and the formation process of slip bands at the microscopic scale, and it is difficult to accurately describe the local damage evolution characteristics of the material during fatigue, resulting in a large deviation between the prediction results and the actual situation; The multi-scale coupling method in this embodiment breaks through the limitations of the traditional single-scale model, can more accurately describe the damage evolution law of the material during fatigue, realizes the full-scale analysis from microscopic dislocation motion to macroscopic damage evolution, overcomes the defect of ignoring the microscopic mechanism in the traditional method, and significantly improves the accuracy and reliability of fatigue damage prediction.

[0048] Figure 2 This is the Schmidt factor distribution diagram of the crack tip plastic zone of the cable bending fatigue life prediction method based on reinforcement learning in the embodiment of the present invention, presenting the simulation results of the Schmidt factor distribution in the crack tip plastic zone of the copper core power cable.

[0049] The plastic zone takes the crack tip as the origin and shows a detailed distribution within the range of 0.8mm×0.6mm. The crystal orientation data obtained by electron backscatter diffraction technology show that a clear Schmidt factor gradient distribution is formed in this area. The maximum Schmidt factor value of 0.487 appears 0.23mm to the upper right of the crack tip, indicating that dislocation slip is most likely to occur at this position. A high Schmidt factor band (value>0.42) is formed in front of the crack along the 45° direction, with a width of about 0.15mm, which is highly consistent with the preferential slip area actually observed. The different depths of the areas in the figure represent different Schmidt factor values, ranging from 0.2 to 0.48. Observations show the distribution of three main slip systems: the octahedral slip system dominates the high stress area, and its Schmidt factor value is between 0.42-0.487; the cubic slip system is active in the area 0.3mm below the crack tip, and the Schmidt factor value is between 0.32-0.38; the unconventional slip system begins to activate in the far field area (>0.5mm from the crack tip), and the Schmidt factor value is less than 0.3.

[0050] The "butterfly wing"-shaped high Schmidt factor area around the crack tip indicates that plastic deformation is highly concentrated in this area, which is consistent with the deformation characteristics observed before the formation of microcracks in the experiment. At 0.23mm from the crack tip, the Schmidt factor reaches a maximum value of 0.487, which is the area where microcracks are most likely to initiate. The width of the high Schmidt factor band in the 45° direction is about 0.15mm. This area is the area with the highest slip band density and the most likely path for fatigue cracks to extend.

[0051] The Schmidt factor distribution diagram can accurately predict the dislocation slip starting point and the preferred slip system, providing a key basis for the subsequent calculation of the dislocation density tensor and the prediction of damage evolution. Compared with traditional methods, this technical solution can more accurately capture the crystallographic characteristics and slip system activation in the plastic zone, and explain the deformation behavior of copper core cables during fatigue from a microscopic mechanism. The spatial distribution characteristics of multiple slip systems provide a key basis for the construction of the subsequent dislocation density tensor, and also reveal the microscopic plastic deformation mechanism of copper core materials during fatigue deformation.

[0052] In an optional embodiment, Calculating the action value function to iteratively train the deep reinforcement learning network, using the actual fatigue life data as the reward function until the loss function converges includes: The action value function is calculated by using a deep Q learning algorithm, and the action value function is iteratively updated based on a temporal difference algorithm by constructing a dual network structure of a target network and a training network; Iteratively train the deep reinforcement learning network based on the updated action value function, use the actual fatigue life data as the reward function, randomly sample training data from the experience pool through the experience replay mechanism, and optimize the network parameters of the deep reinforcement learning network by gradient backpropagation based on the training data; Judge whether the loss function of the deep reinforcement learning network converges. When the change amount of the loss function is less than the preset change threshold in consecutive preset numbers of iterative trainings, it is considered that the loss function converges, and stop the iterative training to obtain the trained deep reinforcement learning network.

[0053] Establish a dual-network computing architecture, and construct a target network and a training network respectively. The two networks have the same neural network structure, but different parameter update strategies. The training network is responsible for immediate learning and adaptation, while the target network is used to generate stable target values. By setting up an experience buffer pool to store state transition samples, including information such as the current state, executed action, obtained reward, and next state. During the calculation of the action value function, adopt a soft update strategy, and make the target network parameters slowly track the training network parameters by setting a small update rate to avoid drastic fluctuations in the value function estimation.

[0054] In temporal difference learning, calculate the temporal difference error in a forward scanning manner. Each time, start from the current state, advance a fixed number of steps forward, and accumulate the obtained reward values. At the same time, consider the influence of the discount factor to weight and decay future rewards. By comparing the difference between the actually obtained cumulative reward and the predicted action value, obtain the temporal difference error. Based on this error term, iteratively update the action value function to continuously optimize the estimation accuracy of the state-action value.

[0055] During the training process of the deep reinforcement learning network, construct a reward function based on the actual fatigue life data. Map the life data to an appropriate numerical range through normalization processing, and design the reward signal according to the deviation between the predicted value and the actual value. Adopt a priority sampling strategy to select training samples from the experience pool, assign a higher sampling probability to samples with larger temporal difference errors, and improve the learning efficiency. During the sampling process, correct the sampling bias through importance weights to ensure the unbiasedness of parameter updates.

[0056] Implement the gradient backpropagation algorithm to optimize the network parameters. Calculate the gradient of the loss function with respect to the network output, and then transmit the gradient information layer by layer through the chain rule. During the gradient propagation process, adopt gradient clipping technology to prevent gradient explosion, and at the same time introduce the dropout mechanism to enhance the generalization ability of the network. Through the adaptive learning rate adjustment strategy, dynamically adjust the parameter update step size according to the gradient change, and improve the training efficiency while ensuring convergence.

[0057] Monitor the training process by setting multiple convergence criteria. Record the loss function values after each iterative training, and calculate the change in the loss function over consecutive multiple iterations. Use the sliding window method to smooth the change amount and reduce the influence of random fluctuations. When the smoothed change amount is always less than the preset threshold in consecutive preset number of iterations, it is determined that the training process converges. At the same time, evaluate the model performance through the validation set to prevent overfitting.

[0058] During the entire training process, implement a dynamic balance mechanism. Achieve a balance between exploration and exploitation by adjusting hyperparameters such as the size of the experience pool, batch size, and training frequency. Regularly evaluate the prediction performance of the network and verify the generalization ability of the model through cross-validation methods. When the convergence condition is reached, save the network parameters to complete the training process of the deep reinforcement learning network.

[0059] Exemplarily, train a fatigue life prediction model for a certain type of cable, construct a deep neural network with four hidden layers, and the number of neurons in each layer is 128, 256, 128, and 64 respectively. Set the capacity of the experience pool to 10,000 samples, and randomly sample 32 samples for training each time. Use a learning rate of 0.001 and a discount factor of 0.95.

[0060] During the training process, normalize the actually measured fatigue life data according to the logarithmic scale, and construct a reward function based on the prediction error. Update the target network parameters every 100 iterations. Set the convergence criterion as the relative change amount of the loss function being less than 0.1% in consecutive 50 iterations. After about 2,000 iterations of training, the loss function tends to be stable, and the network successfully completes the training. Finally, the prediction error on the test set is on average within 5%, showing good generalization performance.

[0061] In this embodiment, through constructing a dual-network structure for deep reinforcement learning, the stable optimization of the action value function is realized. By introducing forward scanning and discount factors, long-term dependencies are accurately captured, and the expression ability of the prediction model for the evolution characteristics of fatigue life is improved. By assigning higher sampling probabilities to important samples, the learning speed of the network for key features is accelerated. It can not only accurately describe the fatigue damage evolution process, but also has high computational efficiency and practicality, providing reliable technical support for cable fatigue life assessment.

[0062] In an alternative implementation, Quantify the output uncertainty of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, construct an adaptive early warning threshold. When the predicted value of the cable fatigue life is less than the early warning threshold corresponding to the confidence level, output multi-dimensional early warning information including: Quantify the output of the deep reinforcement learning network to obtain the uncertainty quantification result; Calculate the mean and standard deviation of the predicted value of the cable fatigue life according to the uncertainty quantification results. Take the mean as the predicted central value, and take the product of the standard deviation and the preset confidence coefficient as the interval radius to construct a confidence interval and determine the first uncertainty threshold and the second uncertainty threshold. Divide the confidence level according to the size relationship between the standard deviation and the first uncertainty threshold and the second uncertainty threshold: The standard deviation less than or equal to the first uncertainty threshold is the first level, greater than the first uncertainty threshold and less than or equal to the second uncertainty threshold is the second level, and greater than the second uncertainty threshold is the third level; Construct an adaptive warning threshold based on the confidence interval and the confidence level. When the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information including the predicted value of the cable fatigue life, the confidence interval, the confidence level, and the standard deviation.

[0063] Take the predicted value of the cable fatigue life output by the deep reinforcement learning network as the basic data and construct a Markov chain Monte Carlo sampling framework. In the sampling initialization stage, set independent probability distribution functions for each component of the damage evolution tensor. Based on the theory of material mechanics, convert physical parameters such as fracture toughness and yield strength into constraint conditions of the probability density function. Integrate these constraint conditions into the probability density function by the Lagrange multiplier method to ensure that the sampling process satisfies the physical laws.

[0064] Adopt a stratified sampling strategy for parallel chain sampling. Set multiple independently running Markov chains, and each chain is equipped with different initial temperature parameters. During the sampling process, decide whether to accept a new sampling point by calculating the energy difference and state transition probability between adjacent samples. Introduce a temperature annealing mechanism to gradually reduce the sampling temperature as the number of iterations increases, improving the local fineness of the sampling. In the inter-chain interaction stage, calculate the state exchange probability based on the energy function difference to achieve information exchange between chains at different temperatures.

[0065] Combine the non-Gaussian process regression method to process the sampling data. Construct a probability distribution model of the sample through kernel density estimation, dynamically adjust the kernel function bandwidth parameter, and balance the smoothness and accuracy of the estimation. For data with obvious non-normal distribution characteristics, use the polynomial expansion method to approximate the true distribution. Evaluate the skewness and kurtosis characteristics of the distribution by calculating the moments of the probability density function. At the same time, implement outlier detection to identify and process the outliers in the distribution.

[0066] In the convergence monitoring stage, a multi-layer evaluation system is established. The between-chain variance is evaluated by calculating the Gelman-Rubin statistic to analyze the mixing degree of the sampling chains. The autocorrelation function is calculated to determine the effective sample size, and highly correlated redundant samples are removed. The trend of the energy trajectory of each sampling chain is analyzed to judge whether the sampling reaches a steady-state distribution. The stability of the sampling variance is evaluated by the piecewise statistical method to ensure the reliability of the sampling results.

[0067] Based on the processed sampling data, the extraction of statistical characteristic quantities is carried out. The weighted average method is used to calculate the sample mean as the prediction central value. The standard deviation is calculated by an improved maximum likelihood estimation method to improve the robustness of parameter estimation. The preset confidence coefficient is multiplied by the standard deviation to construct a confidence interval. During the interval construction process, the skewness characteristics of the distribution and the asymmetric adjustment of the interval boundaries are considered.

[0068] A double-threshold grading mechanism is set up to achieve the grading of prediction results. The benchmark values of the two uncertainty thresholds are determined through historical data analysis, and a dynamic update mechanism is established. According to the comparison results of the standard deviation and the thresholds, the prediction confidence is divided into three levels. For different levels, corresponding early warning criteria are established respectively to form a complete grading early warning system.

[0069] In the construction of the early warning threshold, an adaptive weight method is adopted. The confidence interval information and the confidence level information are weighted and combined to generate the early warning threshold. The weight coefficient is dynamically adjusted according to the prediction uncertainty to improve the sensitivity and reliability of the early warning. When the predicted value is lower than the threshold, the early warning mechanism is triggered, and at the same time, the multi-dimensional information integration module is activated.

[0070] The integration of early warning information adopts the analytic hierarchy process. The predicted values are normalized to unify the dimensions of different indicators. Information such as the prediction central value, the confidence interval range, the confidence level, and the standard deviation is organized in a predetermined format to form a structured early warning report. The importance of information in each dimension is determined by the information entropy weight method to highlight the key early warning indicators. When the early warning information is released, a hierarchical display strategy is adopted to ensure the priority transmission of important information.

[0071] A dynamic early warning tracking mechanism is implemented. Continuously monitor the change trend of the prediction results, and analyze the time evolution characteristics of the early warning indicators by the sliding window method. When the early warning conditions are triggered by the prediction results for multiple consecutive times, the early warning level is increased. At the same time, the early warning history is recorded, and an early warning event database is established to provide data support for the subsequent optimization of the early warning strategy.

[0072] Exemplarily, an uncertainty analysis of the fatigue life prediction of a certain type of power cable is carried out. A sampling framework consisting of five parallel Markov chains is constructed, and each chain samples one thousand sample points. The sampling step size is set to 0.01, and the sampling convergence is monitored by the Gelman-Rubin diagnostic criterion. After about ten thousand iterations, all five sampling chains reach the convergence state.

[0073] Based on the sampling results, the calculated mean value of the fatigue life prediction is ten thousand cycles, and the standard deviation is five hundred cycles. The confidence coefficient is set to 95%, and a confidence interval of plus or minus two standard deviations from the predicted central value is constructed. The first uncertainty threshold is set to three hundred cycles, and the second uncertainty threshold is set to six hundred cycles. When the standard deviation is four hundred cycles, the prediction result belongs to the second confidence level.

[0074] The warning threshold corresponding to this confidence level is set to eight thousand cycles. Since the current predicted value is lower than the warning threshold, a warning message is output: the predicted life is ten thousand cycles, the confidence interval is nine thousand to eleven thousand cycles, the confidence level is the second level, and the standard deviation is four hundred cycles. This warning message provides a reliable basis for engineering maintenance decisions.

[0075] In this embodiment, by introducing physical constraint conditions, it is ensured that the sampling results satisfy the material mechanics law, improving the physical rationality of the prediction. An adaptive interval estimation method based on the standard deviation is adopted, and the confidence interval is dynamically adjusted in combination with the confidence coefficient, organically combining the confidence interval and the confidence level, and realizing the dynamic adjustment of the warning threshold; In the prior art, usually a deterministic prediction method is directly adopted, or a simple statistical model is used for uncertainty analysis, ignoring the physical constraint conditions in the prediction process, and unable to accurately quantify the influence of multi-source uncertainties. A fixed threshold criterion is adopted, lacking the ability to dynamically evaluate the prediction reliability, which is prone to lead to blindness and lag in early warning; In this embodiment, by introducing physical constraint conditions, it is ensured that the sampling results satisfy the material mechanics law, improving the physical rationality of the prediction. By introducing a double-threshold grading mechanism, the refined management of the prediction results is realized, providing differentiated processing strategies for prediction results with different reliability levels, and being able to adaptively adjust the early warning strategy according to the uncertainty level of the prediction, significantly improving the accuracy and timeliness of the early warning, and being able to effectively handle the prediction tasks under complex working conditions, providing strong technical support for the safe operation and maintenance of the cable system.

[0076] Figure 3This is the uncertainty analysis diagram of the cable fatigue life prediction for the cable bending fatigue life prediction method based on reinforcement learning in the embodiments of the present invention, which shows the uncertainty analysis results of the cable fatigue life prediction based on the Markov chain Monte Carlo method combined with physical constraints and non-Gaussian process regression. In the figure, the horizontal axis represents the predicted fatigue life, ranging from 1000 to 11000 cycles; the vertical axis represents the probability density, ranging from 0 to 1.0.

[0077] The central black curve presents the probability distribution of the predicted life, showing obvious non-Gaussian distribution characteristics. The center of the distribution is located at 10000 cycles (marked by the central vertical dashed line), which is the predicted expected value μ. The predicted standard deviation σ is 400 cycles, which is visually represented by the horizontal arrow segment to the right from the center. Based on this standard deviation, a confidence interval is constructed on both sides of the predicted central value, ranging from 9500 cycles (μ - σ) to 10500 cycles (μ + σ), marked by the two vertical dashed lines on the left and right.

[0078] The vertical gray solid line on the left side of the figure is located at 8000 cycles, representing the warning threshold. When the predicted life is lower than this value, the warning mechanism will be triggered. The figure also shows two horizontal dashed lines, representing the boundary lines of the uncertainty threshold, which are used to determine the confidence level of the prediction result. When the standard deviation is between these two lines, such as the current predicted standard deviation of 400 cycles, the prediction result belongs to the medium confidence level.

[0079] The accurate uncertainty quantification method not only provides the point prediction value of the fatigue life, but also gives the uncertainty range of the prediction through the confidence interval, and grades the confidence of the prediction result according to the size of the standard deviation, forming a complete prediction and warning system. Compared with the traditional method, the Markov chain Monte Carlo method combined with physical constraints significantly improves the prediction accuracy and reliability, providing a more scientific basis for cable fatigue life assessment and maintenance decision-making.

[0080] In an alternative embodiment, The uncertainty quantification of the output of the deep reinforcement learning network to obtain the uncertainty quantification result includes: Construct the cable stress-strain constraint condition according to the material mechanics theory, establish the correlation equation between the stress tensor and the strain tensor, and establish the correlation equation between the crack growth rate and the stress intensity factor amplitude as the physical constraint condition; Construct the target distribution function and the proposal distribution function to calculate the acceptance probability of the new sampling point, calculate the constraint violation measure of the new sampling point under the physical constraint condition, and determine whether the new sampling point is an effective sampling point according to the relationship between the constraint violation measure and the preset tolerance threshold; The degree of freedom parameter is calculated by fitting the effective sampling points with the Student's distribution. The heavy-tailed characteristics of the effective sampling points are described by the generalized hyperbolic distribution to calculate the tail heaviness parameter, skewness parameter, scale parameter, location parameter, and shape parameter, and a joint probability distribution function is constructed to establish a multi-dimensional dependence structure. The mean and variance of the effective sampling points are calculated, and the sampling convergence and sampling effectiveness are evaluated to determine the uncertainty distribution characteristics of the effective sampling points, which are used as the quantification results of the uncertainty of the cable fatigue life.

[0081] Based on the theory of mechanics of materials, a system of constraint conditions is constructed. The correlation between the stress tensor and the strain tensor is established, and constitutive parameters such as the elastic modulus and Poisson's ratio of the material are considered, and the linear elastic theory is extended to the case considering plastic deformation. In the framework of fracture mechanics, the mapping relationship between the crack propagation rate and the amplitude of the stress intensity factor is established, and the boundary effects of the fatigue threshold value and fracture toughness are considered. Through tensor operations, these constraint equations are unified in the same coordinate system to form a complete set of physical constraint conditions.

[0082] In the construction of the Markov chain sampling strategy, the state transition mechanism is designed by the random walk maximum likelihood algorithm. A target distribution function reflecting the physical characteristics is constructed, with the stress state, strain level, and crack propagation characteristics as distribution parameters. At the same time, a more adaptable proposal distribution function is designed, and the sampling efficiency is ensured through adaptive adjustment. For each new sampling point, its acceptance probability relative to the current state is calculated, and its satisfaction degree with respect to the physical constraints is evaluated.

[0083] The calculation of the constraint violation metric adopts a multi-level evaluation strategy. The compliance of the stress-strain relationship is checked, and the deviation between the stress tensor and the strain tensor is calculated. Whether the crack propagation behavior satisfies the fracture mechanics criterion is evaluated, and the error between the propagation rate and the theoretical prediction is calculated. The violation degrees at each level are combined by weighting to obtain the overall constraint violation metric. By comparing with the preset allowable threshold, the effectiveness of the sampling points is determined.

[0084] In the distribution fitting step, the effective sampling points are fitted with the Student's distribution. An iterative optimization algorithm is used to estimate the degree of freedom parameter, and the maximum likelihood method is used to improve the accuracy of parameter estimation. At the same time, the generalized hyperbolic distribution is used to describe the heavy-tailed characteristics of the data, and the characteristic parameters of the distribution, including the tail heaviness, skewness, scale, location, and shape parameters, are estimated by the method of moments. A joint probability distribution function is constructed to establish a multi-dimensional dependence structure, realizing the organic integration of different distribution characteristics.

[0085] During the fitting process, a piecewise optimization strategy is adopted to improve the fitting accuracy. Different weight coefficients are used for different intervals of the data, with a focus on the fitting effect in the tail region. The stability of the fitting results is evaluated through cross-validation, and the parameters are fine-tuned and optimized if necessary. At the same time, considering the temporal correlation of the data, time weights are introduced in parameter estimation to enhance the sensitivity of the model to recent data.

[0086] A multiple verification mechanism is used to evaluate the convergence of the sampling results. The ratio of between-chain variance to within-chain variance is calculated, and the convergence degree is judged by setting a dynamic threshold. At the same time, the energy change of the sampling trajectory is monitored to evaluate whether the sampling process reaches a steady state. The evaluation of sampling effectiveness is achieved by calculating the proportion of effective sampling points in the total sampling points, and the sampling strategy is dynamically adjusted in combination with the sampling efficiency index.

[0087] The characteristics of the uncertainty distribution are determined through comprehensive analysis. The characteristic parameters of the Student's distribution and the generalized hyperbolic distribution are transformed into interpretable uncertainty indicators, including the central tendency, dispersion degree, skewness characteristics, and tail behavior of the distribution. Through the combination of these indicators, a complete uncertainty description is constructed, providing a basis for subsequent reliability assessment.

[0088] Exemplarily, a certain type of overhead conductor is taken as the research object, with a cross-sectional diameter of twenty-five millimeters. Based on the theory of material mechanics, an elastoplastic constitutive equation is constructed, with the elastic modulus set at 110 GPa and the yield strength at 300 MPa. In the fracture mechanics constraint, the fatigue threshold is set at the square root of 8 MPa·m, and the fracture toughness is set at the square root of 85 MPa·m.

[0089] Five parallel Markov chains are used for sampling, and different initial temperatures are set for each chain. Through 10,000 sampling iterations, 8,000 effective sampling points are obtained. The Student's distribution fitting results in a degree of freedom of 4.5, the tail heaviness parameter of the generalized hyperbolic distribution is 2.8, and the skewness parameter is 0.3. The ratio of between-chain variance to within-chain variance is 1.05, and the effective sampling rate reaches 80%, indicating that the sampling process has converged and has a high sampling efficiency. The determined uncertainty distribution shows a slightly right-skewed characteristic and a heavy-tailed property.

[0090] In this embodiment, by establishing stress-strain constraint conditions and crack propagation constraint conditions, a complete physical constraint system is formed. The random walk maximum likelihood algorithm is used to construct a Markov chain, and a constraint violation metric is introduced for sampling point screening. A mixed model of the Student's distribution and the generalized hyperbolic distribution is introduced, breaking through the limitations of the traditional normal distribution assumption; In the prior art, when analyzing the uncertainty of cable fatigue life, simple probability statistical methods are usually adopted, ignoring the physical constraints of material mechanics and fracture mechanics. It often assumes that the data follows a normal distribution, making it difficult to accurately describe the non-normal distribution characteristics commonly existing in actual engineering, especially there are large deviations in the prediction of extreme value events. This embodiment not only ensures that the prediction results satisfy the basic mechanical laws, but also can accurately reflect the damage evolution characteristics of the material during the fatigue process, significantly improving the effectiveness of sampling, avoiding the generation of a large number of invalid sampling points in the traditional random sampling method, using the generalized hyperbolic distribution to characterize the heavy-tailed characteristics, achieving an accurate description of the fatigue life distribution characteristics, significantly improving the accuracy and reliability of the prediction, and providing a more accurate theoretical basis for decision-making in engineering practice.

[0091] Figure 4 This is the three-dimensional distribution characteristic diagram of the cable fatigue life uncertainty of the cable bending fatigue life prediction method based on reinforcement learning in the embodiment of the present invention, showing the constructed three-dimensional distribution characteristics of the cable fatigue life uncertainty, and intuitively presenting the complex relationship between the stress level, strain level and life distribution probability density through the three-dimensional topological surface.

[0092] The figure clearly shows the multi-level contour structure of the probability distribution. The red peak region is located at a stress of 250 MPa and a strain of 0.8%, corresponding to a fatigue life of 5.2×10^6 cycles, and the probability density reaches 0.82. The distribution shows an obvious asymmetric characteristic. The orange right tail (high-life region) shows a slight extension characteristic, and the skewness parameter is 0.3, which is in line with the actual observed characteristic that the cable fatigue life is slightly biased towards the long-life direction; while the yellow left tail (low-life region) shows a steeper downward trend, and the tail heaviness parameter is 2.8, reflecting the sharp increase in the cable failure probability under high stress conditions. In the purple region where the stress is close to the green yield strength reference surface (300 MPa), obvious mutation characteristics appear on the distribution surface, which is consistent with the physical mechanism of the material changing from elastic deformation to plastic deformation. The blue fracture toughness interface (K_IC = 85 MPa·m^0.5) marks the critical state of crack propagation, and the distribution rapidly decays to zero after exceeding this interface. This technical solution successfully characterizes the uncertainty characteristics of the cable fatigue life in the range of (4.5~6.0)×10^6 cycles through the multi-dimensional dependence structure of the student t-distribution (degree of freedom parameter 4.5) combined with the generalized hyperbolic distribution, and the shape parameter 2.3 further accurately describes the geometric characteristics of the distribution.

[0093] Compared with the traditional two-dimensional statistical distribution, the three-dimensional topological expression more comprehensively reflects the influence of physical constraint conditions (stress-strain relationship and crack propagation behavior) on the fatigue life distribution, providing a more reliable theoretical basis for cable safety assessment and maintenance decision-making.

[0094] In a second aspect of the embodiments of the present invention, there is provided a cable bending fatigue life prediction system based on reinforcement learning, including: A first unit, configured to collect cable bending fatigue life test sample data including cable specification parameters, stress-strain data, and actual fatigue life data, and calculate the stress distribution field and strain distribution field of the cable according to the stress-strain data; A second unit, configured to construct a stress intensity factor calculation module based on the material fracture mechanics theory, input the stress distribution field and strain distribution field into the stress intensity factor calculation module, calculate the stress intensity factors of each stress monitoring point of the cable, establish a fatigue crack growth rate equation according to the Paris fracture criterion, substitute the stress intensity factors into the fatigue crack growth rate equation, calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable, construct a damage evolution tensor based on the crack growth trajectory and crack growth rate, and use it as a state feature to input into a deep reinforcement learning network; A third unit, configured to calculate an action value function by using a deep Q-learning algorithm according to the state feature, iteratively train the deep reinforcement learning network based on the action value function, use the actual fatigue life data as a reward function until the loss function converges, and obtain a trained deep reinforcement learning network; A fourth unit, configured to perform uncertainty quantification on the output of the deep reinforcement learning network by using the Markov chain Monte Carlo method, establish a confidence interval according to the uncertainty quantification result, divide the confidence level of the cable fatigue life prediction value into three levels, construct an adaptive warning threshold based on the confidence interval and confidence level, and output multi-dimensional warning information when the cable fatigue life prediction value is less than the warning threshold corresponding to the confidence level.

[0095] In a third aspect of the embodiments of the present invention, there is provided an electronic device, including: A processor and a memory for storing processor-executable instructions, wherein the processor is configured to call the instructions stored in the memory to execute the method described above.

[0096] In a fourth aspect of the embodiments of the present invention, there is provided a computer-readable storage medium, on which computer program instructions are stored, and when the computer program instructions are executed by a processor, the method described above is implemented.

[0097] The present invention can be a method, device, system, and / or computer program product. The computer program product may include a computer-readable storage medium, on which computer-readable program instructions for executing various aspects of the present invention are loaded.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the bending fatigue life of a cable based on reinforcement learning, characterized in that Including: Collecting the cable bending fatigue life test sample data of cable specification parameters, stress-strain data and actual fatigue life data, and calculating the cable stress distribution field and strain distribution field according to the stress-strain data; Based on the material fracture mechanics theory, constructing a stress intensity factor calculation module, inputting the stress distribution field and strain distribution field into the stress intensity factor calculation module, calculating the stress intensity factors of each stress monitoring point of the cable, establishing a fatigue crack growth rate equation, calculating the crack growth trajectory and crack growth rate of each monitoring point of the cable, and constructing a damage evolution tensor as the state feature to input into the deep reinforcement learning network; Calculating the action value function to iteratively train the deep reinforcement learning network, and using the actual fatigue life data as the reward function until the loss function converges; Quantifying the output uncertainty of the deep reinforcement learning network, establishing a confidence interval to divide the confidence level, constructing an adaptive warning threshold, and when the predicted cable fatigue life value is less than the warning threshold corresponding to the confidence level, outputting multi-dimensional warning information.

2. The method according to claim 1, characterized in that Collecting the cable bending fatigue life test sample data of cable specification parameters, stress-strain data and actual fatigue life data, and calculating the cable stress distribution field and strain distribution field includes: Collecting the cable bending fatigue life test sample data, where the cable bending fatigue life test sample data includes cable specification parameters, stress-strain data and actual fatigue life data, and preprocessing the cable bending fatigue life test sample data through an adaptive filter to obtain a preprocessed sample data sequence; Performing wavelet decomposition on the preprocessed sample data sequence, extracting the time-frequency features of the stress-strain data, and reducing the dimension of the time-frequency features to obtain a feature vector characterizing the stress-strain evolution law; Calculating the cable stress distribution field and strain distribution field based on the feature vector, where the stress distribution field and strain distribution field include normal components, tangential components and radial components.

3. The method according to claim 1, characterized in that, Based on the material fracture mechanics theory, constructing a stress intensity factor calculation module, inputting the stress distribution field and strain distribution field into the stress intensity factor calculation module, calculating the stress intensity factors of each stress monitoring point of the cable, and establishing a fatigue crack growth rate equation includes: Inputting the pre-acquired stress distribution field and strain distribution field into the stress intensity factor calculation module constructed based on the material fracture mechanics theory, establishing a mapping relationship between the stress distribution field and strain distribution field and the crack tip stress field, and respectively calculating the opening mode stress intensity factor and the sliding mode stress intensity factor in the polar coordinate system of the cable crack tip; Calculating the crack growth direction angle according to the opening mode stress intensity factor and the sliding mode stress intensity factor, substituting the crack growth direction angle into the equivalent stress intensity factor calculation formula to obtain the stress intensity factors of each stress monitoring point of the cable; Establishing a fatigue crack growth rate equation including material constant terms, stress intensity factor amplitude terms, fatigue crack growth threshold correction terms and fracture toughness correction terms, and establishing a quantitative relationship between the crack growth rate and the equivalent stress intensity factor.

4. The method according to claim 1, wherein Calculating the crack growth trajectory and crack growth rate of each monitoring point of the cable, and constructing a damage evolution tensor as the state feature to input into the deep reinforcement learning network includes: Substitute the stress intensity factor into the fatigue crack growth rate equation to obtain the crack growth rate at each monitoring point of the cable, and integrate along the direction of the maximum stress to obtain the crack growth trajectory at each monitoring point of the cable; Determine the position and range of the plastic zone at the crack tip according to the crack growth trajectory, calculate the Schmid factor of the plastic zone to determine the primary slip system, and obtain the dislocation slip system direction tensor through the tensor product operation of the slip direction and the normal vector of the slip plane of the primary slip system; construct the dislocation density tensor and perform the tensor product operation with the dislocation slip system direction tensor to obtain the local plastic strain tensor in the plastic zone; Calculate the density distribution of the dislocation slip band, obtain the first correction coefficient by taking the ratio of the dislocation slip band density to the critical dislocation density, obtain the second correction coefficient by taking the ratio of the equivalent strain of the local plastic strain tensor to the reference strain, and construct the dislocation slip band-local strain correlation function; Perform the tensor product operation on the dislocation slip band-local strain correlation function and the initial damage tensor to obtain the damage correction term, and perform the tensor superposition operation with the second-order spatial derivative term of the initial damage tensor to obtain the damage evolution tensor.

5. The method according to claim 1, characterized in that Calculate the action value function for iterative training of the deep reinforcement learning network, and use the actual fatigue life data as the reward function until the loss function converges, including: Use the deep Q-learning algorithm to calculate the action value function. By constructing a dual-network structure of the target network and the training network, the action value function is iteratively updated based on the temporal difference algorithm; Based on the updated action value function, perform iterative training on the deep reinforcement learning network. Use the actual fatigue life data as the reward function, randomly sample training data from the experience pool through the experience replay mechanism, and optimize the network parameters of the deep reinforcement learning network based on the training data through gradient backpropagation; Judge whether the loss function of the deep reinforcement learning network converges. When the change amount of the loss function is less than the preset change threshold in continuous preset number of iterative trainings, it is considered that the loss function converges, stop the iterative training, and obtain the trained deep reinforcement learning network.

6. The method according to claim 1, characterized in that, Quantify the output uncertainty of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, construct an adaptive warning threshold, and when the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information including: Quantify the output of the deep reinforcement learning network to obtain the uncertainty quantification result; Calculate the mean and standard deviation of the predicted value of the cable fatigue life according to the uncertainty quantification result, use the mean as the prediction central value, use the product of the standard deviation and the preset confidence coefficient as the interval radius to construct a confidence interval and determine the first uncertainty threshold and the second uncertainty threshold, and divide the confidence level according to the size relationship between the standard deviation and the first uncertainty threshold and the second uncertainty threshold: The standard deviation less than or equal to the first uncertainty threshold is the first level, greater than the first uncertainty threshold and less than or equal to the second uncertainty threshold is the second level, and greater than the second uncertainty threshold is the third level; Construct an adaptive warning threshold based on the confidence interval and confidence level. When the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information including the predicted value of the cable fatigue life, the confidence interval, the confidence level, and the standard deviation.

7. The method according to claim 6, characterized in that, The uncertainty quantification of the output of the deep reinforcement learning network includes: Construct the stress-strain constraint condition of the cable according to the theory of material mechanics, establish the correlation equation between the stress tensor and the strain tensor, and establish the correlation equation between the crack propagation rate and the amplitude of the stress intensity factor as the physical constraint condition; Construct the target distribution function and the proposal distribution function to calculate the acceptance probability of the new sampling point, calculate the constraint violation measure of the new sampling point under the physical constraint condition, and determine whether the new sampling point is a valid sampling point according to the relationship between the constraint violation measure and the preset tolerance threshold; Use the Student's distribution to fit the valid sampling points to calculate the degrees of freedom parameter, describe the heavy-tailed characteristics of the valid sampling points through the generalized hyperbolic distribution to calculate the tail heaviness parameter, skewness parameter, scale parameter, location parameter and shape parameter, and construct the joint probability distribution function to establish the multi-dimensional dependence structure; Calculate the mean and variance of the valid sampling points, evaluate the sampling convergence and sampling effectiveness to determine the uncertainty distribution characteristics of the valid sampling points, and use them as the uncertainty quantification results of the cable fatigue life.

8. A cable bending fatigue life prediction system based on reinforcement learning, which is used to implement the method described in any one of the foregoing claims 1-7, and is characterized in that, Including: The first unit is used to collect the cable bending fatigue life test sample data of the cable specification parameters, stress-strain data and actual fatigue life data, and calculate the cable stress distribution field and strain distribution field according to the stress-strain data; The second unit is used to construct a stress intensity factor calculation module based on the theory of material fracture mechanics, input the stress distribution field and strain distribution field into the stress intensity factor calculation module, calculate the stress intensity factor of each stress monitoring point of the cable, establish a fatigue crack propagation rate equation, calculate the crack propagation trajectory and crack propagation rate of each monitoring point of the cable, and construct a damage evolution tensor as the state feature and input it into the deep reinforcement learning network; The third unit is used to calculate the action value function and iteratively train the deep reinforcement learning network until the actual fatigue life data converges to the loss function as the reward function; The fourth unit is used to quantify the uncertainty of the output of the deep reinforcement learning network, establish a confidence interval to divide the confidence level, construct an adaptive warning threshold, and when the predicted value of the cable fatigue life is less than the warning threshold corresponding to the confidence level, output multi-dimensional warning information.

9. An electronic device, characterized in that, Including: A processor; A memory for storing instructions executable by the processor; Wherein, the processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, the method according to any one of claims 1 to 7 is implemented.

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