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

Abstract

The present invention provides a cable bending fatigue life prediction method and system based on reinforcement learning, which relates to the technical field of cable life prediction. The method includes: collecting cable test sample data, calculating stress distribution field and strain distribution field, constructing a stress intensity factor calculation module, calculating crack propagation trajectory and rate, constructing a damage evolution tensor as a state feature, training the network based on a deep Q learning algorithm and using a Markov chain Monte Carlo method to quantify uncertainty, and establishing a credible interval and warning threshold.

Description

Technical Field

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

[0002] Cables are an important component of power and communication systems, and their bending fatigue life prediction is of great significance to ensuring the safe operation of equipment. Cables are subjected to mechanical stress during actual use, especially repeated bending, which leads to the accumulation of material fatigue damage and eventually fracture failure. Accurately predicting the bending fatigue life of cables is of great value in preventing sudden failures, formulating reasonable maintenance strategies, and extending service life.

[0003] Traditional cable bending fatigue life prediction methods 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 to estimate the life.

[0004] 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 fatigue life is predicted. However, existing technologies still have limited ability to accurately calculate the stress distribution within the cable, and are unable to fully capture the stress transfer and local stress concentration between different material layers. This leads to insufficient prediction accuracy, insufficient consideration of the cable fatigue damage evolution process, lack of dynamic monitoring and analysis capabilities of crack propagation paths and rates, difficulty in reflecting the accumulation law and nonlinear characteristics of fatigue damage, and lack of reliable uncertainty quantification and risk assessment mechanisms. It is impossible to provide credibility assessment and warning threshold setting for the prediction results, resulting in the difficulty of directly applying the prediction results to actual engineering decisions.

[0005] Therefore, a solution is urgently needed to solve the problems existing in the prior art. Summary of the Invention

[0006] The embodiments of the present invention provide a cable bending fatigue life prediction method and system based on reinforcement learning, which can at least solve some of the problems existing in the prior art.

[0007] A first aspect of an embodiment of the present invention provides a method for predicting cable bending fatigue life based on reinforcement learning, comprising:

[0008] Collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data, and calculate cable stress distribution field and strain distribution field based on the stress and strain data;

[0009] 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 factor of each stress monitoring point of the cable. The fatigue crack growth rate equation is established to calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable. The damage evolution tensor is constructed as the state feature input into the deep reinforcement learning network.

[0010] Calculate the action value function to iteratively train the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges;

[0011] The uncertainty of the deep reinforcement learning network output is quantified, a credible interval is established to divide the confidence level, and an adaptive warning threshold is constructed. When the predicted value of the cable fatigue life is less than the corresponding confidence level warning threshold, multi-dimensional warning information is output.

[0012] In an optional embodiment,

[0013] Collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data. Calculate the cable stress and strain distribution fields based on the stress and strain data, including:

[0014] Collecting cable bending fatigue life test sample data, the cable bending fatigue life test sample data including cable specification parameters, stress and 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;

[0015] Performing wavelet decomposition on the preprocessed sample data sequence to extract the time-frequency characteristics of the stress and strain data, and performing dimensionality reduction on the time-frequency characteristics to obtain a feature vector representing the stress and strain evolution law;

[0016] The stress distribution field and the strain distribution field of the cable are calculated based on the characteristic vector, where the stress distribution field and the strain distribution field include a normal component, a tangential component, and a radial component.

[0017] In an optional embodiment,

[0018] Based on the material fracture mechanics theory, 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 factor of each stress monitoring point of the cable. The fatigue crack growth rate equation is established, including:

[0019] The pre-acquired stress distribution field and strain distribution field are input into the stress intensity factor calculation module based on the material fracture mechanics theory. The mapping relationship between the stress distribution field and strain distribution field and the crack tip stress field is established, and the cracking type stress intensity factor and the sliding type stress intensity factor of the cable crack tip in the polar coordinate system are calculated respectively.

[0020] Calculate the crack propagation direction angle based on the cracking stress intensity factor and the sliding stress intensity factor, substitute the crack propagation direction angle into the equivalent stress intensity factor calculation formula to obtain the stress intensity factor of each stress monitoring point of the cable;

[0021] A fatigue crack growth rate equation including material constant term, stress intensity factor amplitude term, fatigue crack growth threshold correction term and fracture toughness correction term is established, and a quantitative relationship between crack growth rate and equivalent stress intensity factor is established.

[0022] In an optional embodiment,

[0023] Calculate the crack propagation trajectory and crack propagation rate at each monitoring point of the cable, and construct the damage evolution tensor as the state feature input deep reinforcement learning network including:

[0024] 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 maximum stress to obtain the crack growth trajectory at each monitoring point of the cable;

[0025] The position and range of the plastic zone at the crack tip are determined according to the crack propagation trajectory. The Schmidt factor of the plastic zone is calculated to determine the main slip system. The slip direction of the main slip system and the normal vector of the slip plane are used to obtain the dislocation slip system direction tensor through tensor product operation. The dislocation density tensor and the dislocation slip system direction tensor are constructed and tensor product operation is performed to obtain the local plastic strain tensor in the plastic zone.

[0026] The dislocation slip band density distribution is calculated, and the first correction coefficient is obtained by the ratio of the dislocation slip band density to the critical dislocation density. The second correction coefficient is obtained by the ratio of the local plastic strain tensor equivalent strain to the reference strain, and the dislocation slip band-local strain correlation function is constructed.

[0027] The damage correction term is obtained by performing a tensor product operation on the dislocation slip band-local strain correlation function and the initial damage tensor, and the damage evolution tensor is obtained by performing a tensor superposition operation on the second-order spatial derivative of the initial damage tensor.

[0028] In an optional embodiment,

[0029] Calculating the action value function to iteratively train the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges includes:

[0030] The action-value function is calculated 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.

[0031] Iteratively training the deep reinforcement learning network based on the updated action-value function, using the actual fatigue life data as a reward function, randomly sampling training data from an experience pool through an experience replay mechanism, and performing gradient backpropagation optimization on network parameters of the deep reinforcement learning network based on the training data;

[0032] Determine whether the loss function of the deep reinforcement learning network has converged. When the change of the loss function in a preset number of consecutive iterative trainings is less than a preset change threshold, the loss function is considered to have converged, and the iterative training is stopped to obtain the trained deep reinforcement learning network.

[0033] In an optional embodiment,

[0034] The uncertainty of the deep reinforcement learning network output is quantified, a credible interval is established to divide the confidence level, and an adaptive warning threshold is constructed. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, multi-dimensional warning information is output including:

[0035] Quantify the uncertainty of the deep reinforcement learning network output to obtain the uncertainty quantification result;

[0036] Based on the uncertainty quantification results, the mean and standard deviation of the cable fatigue life prediction values are calculated. The mean is used as the prediction center value, and the product of the standard deviation and the preset confidence coefficient is used as the interval radius to construct a credible interval and determine the first uncertainty threshold and the second uncertainty threshold. The confidence level is divided according to the relationship between the standard deviation and the first uncertainty threshold and the second uncertainty threshold:

[0037] The standard deviation is less than or equal to the first uncertainty threshold, which is the first level; the standard deviation is greater than the first uncertainty threshold and less than or equal to the second uncertainty threshold, which is the second level; and the standard deviation is greater than the second uncertainty threshold, which is the third level;

[0038] An adaptive warning threshold is constructed based on the credible interval and confidence level. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, multidimensional warning information including the cable fatigue life prediction value, credible interval, confidence level, and standard deviation is output.

[0039] In an optional embodiment,

[0040] The uncertainty quantification results of the deep reinforcement learning network output include:

[0041] According to the material mechanics theory, the cable stress-strain constraint conditions are constructed to establish the stress tensor and strain tensor correlation equation, and the crack growth rate and stress intensity factor amplitude correlation equation are established as physical constraint conditions;

[0042] Construct the target distribution function and the proposed distribution function to calculate the acceptance probability of the new sampling point, calculate the constraint violation metric of the new sampling point under the physical constraint conditions, and determine whether the new sampling point is a valid sampling point based on the relationship between the constraint violation metric and the preset allowable threshold;

[0043] The degree of freedom parameter is calculated by fitting the effective sampling points with Student distribution. The tail weight parameter, skewness parameter, scale parameter, location parameter and shape parameter are calculated by describing the heavy-tail characteristics of the effective sampling points with generalized hyperbolic distribution. The joint probability distribution function is constructed to establish a multidimensional dependency structure.

[0044] The mean and variance of the effective sampling points are calculated, the sampling convergence and sampling effectiveness are evaluated, and the uncertainty distribution characteristics of the effective sampling points are determined as the quantitative results of the cable fatigue life uncertainty.

[0045] A second aspect of an embodiment of the present invention provides a cable bending fatigue life prediction system based on reinforcement learning, comprising:

[0046] The first unit is used to collect cable specification parameters, stress and strain data, and actual fatigue life data of cable bending fatigue life test sample data, and calculate the cable stress distribution field and strain distribution field based on the stress and strain data;

[0047] The second unit is used to build a stress intensity factor calculation module based on material fracture mechanics theory, 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 the fatigue crack growth rate equation, calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable, and construct the damage evolution tensor as the state feature input deep reinforcement learning network;

[0048] The third unit is used to calculate the action value function for iterative training of the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges;

[0049] The fourth unit is used to quantify the uncertainty of the deep reinforcement learning network output, establish a credible interval to divide the confidence level, and construct an adaptive warning threshold. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, it outputs multi-dimensional warning information.

[0050] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including:

[0051] 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 aforementioned method.

[0052] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0053] In the present invention, by integrating material fracture mechanics theory with deep reinforcement learning technology, it is possible to capture the crack propagation trajectory and rate at the microscopic level, and use the damage evolution process as the state feature of reinforcement learning, thereby achieving accurate prediction of cable fatigue life and improving prediction accuracy. The Markov chain Monte Carlo method is used to quantify the uncertainty of the prediction results, construct a credible interval of the prediction results, and design an adaptive warning threshold based on the confidence level, making the warning mechanism more reliable and effectively reducing the prediction risk. By using actual fatigue life data as a reward function to guide model learning, it is possible to automatically extract key features and optimize the prediction strategy, thereby improving the generalization ability and adaptability of the model. At the same time, the output multi-dimensional warning information provides a comprehensive basis for cable maintenance decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the process of a cable bending fatigue life prediction method based on reinforcement learning according to an embodiment of the present invention;

[0055] Figure 2 This is a distribution diagram of the Schmidt factor in the plastic zone of the crack tip of the cable bending fatigue life prediction method based on reinforcement learning in an embodiment of the present invention;

[0056] Figure 3 This is an uncertainty analysis diagram of cable fatigue life prediction of a cable bending fatigue life prediction method based on reinforcement learning in an embodiment of the present invention;

[0057] Figure 4 This is a three-dimensional distribution characteristic diagram of cable fatigue life uncertainty in the cable bending fatigue life prediction method based on reinforcement learning in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0059] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0060] Figure 1 FIG. 1 is a flow chart of a cable bending fatigue life prediction method based on reinforcement learning according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0061] Collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data, and calculate cable stress distribution field and strain distribution field based on the stress and strain data;

[0062] 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 factor of each stress monitoring point of the cable. The fatigue crack growth rate equation is established to calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable. The damage evolution tensor is constructed as the state feature input into the deep reinforcement learning network.

[0063] Calculate the action value function to iteratively train the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges;

[0064] The uncertainty of the deep reinforcement learning network output is quantified, a credible interval is established to divide the confidence level, and an adaptive warning threshold is constructed. When the predicted value of the cable fatigue life is less than the corresponding confidence level warning threshold, multi-dimensional warning information is output.

[0065] In an optional embodiment,

[0066] Collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data. Calculate the cable stress and strain distribution fields based on the stress and strain data, including:

[0067] Collecting cable bending fatigue life test sample data, the cable bending fatigue life test sample data including cable specification parameters, stress and 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;

[0068] Performing wavelet decomposition on the preprocessed sample data sequence to extract the time-frequency characteristics of the stress and strain data, and performing dimensionality reduction on the time-frequency characteristics to obtain a feature vector representing the stress and strain evolution law;

[0069] The stress distribution field and the strain distribution field of the cable are calculated based on the characteristic vector, where the stress distribution field and the strain distribution field include a normal component, a tangential component, and a radial component.

[0070] Before the cable bending fatigue life test begins, the test equipment, including a bending fatigue testing machine, high-precision strain gauges, a data acquisition system, and a computer processing system, is prepared. Test cable samples of different specifications are selected, including copper core cables with diameters of 0.5mm, 1.0mm, 1.5mm, and 2.0mm, and insulation layer thicknesses of 0.2mm, 0.3mm, 0.5mm, and 0.7mm, respectively. The cable samples are installed in the bending fatigue testing machine, with bending radii set to 5, 10, and 15 times the cable diameter, bending frequencies set to 0.5Hz, 1Hz, and 2Hz, and a preset upper limit of 106 bends.

[0071] Strain gauges are placed at key locations on the cable surface, including the bend center and at ±5mm, ±10mm, and ±15mm from the center, for a total of seven measurement points. Stress and strain data are collected using high-precision strain gauges with a sampling frequency of 100Hz to ensure data accuracy. The stress and strain time series data generated at each test point, along with the corresponding actual fatigue life data (number of cycles to failure), are recorded and stored.

[0072] The collected raw data contains noise and outliers, so an adaptive filter is used for preprocessing. Using a minimum mean square error adaptive algorithm, the filter order is set to 64, the step size parameter μ is set to 0.01, and the convergence coefficient is set to 0.98. The adaptive filter is used to suppress noise in the stress and strain time series data at each measurement point, filtering out high-frequency noise and electromagnetic interference. For example, for a 1.0 mm diameter cable with a bend radius of 10 times the diameter, the strain signal at the center point fluctuates from the original ±0.35% range to a stable ±0.32% range after filtering, improving the signal-to-noise ratio by approximately 15%.

[0073] Wavelet decomposition is performed on the preprocessed sample data sequence to extract the time-frequency characteristics of the stress and strain data. The Daubechies wavelet function (db6) is used to perform a five-layer decomposition of the signal, obtaining the corresponding low-frequency approximate coefficients and high-frequency detail coefficients. Wavelet energy characteristics, statistical moment characteristics, and spectral characteristics are extracted from the stress and strain time series data at each measurement point. For example, in the third layer of wavelet decomposition for a 1.5mm diameter cable, the stress fluctuation characteristics are primarily concentrated in the 2-5Hz frequency band, accounting for 68.4% of the total energy, reflecting the main stress distribution pattern during the cable bending process.

[0074] Principal component analysis (PCA) is used to reduce the dimensionality of time-frequency features. Features derived from wavelet decomposition are used to construct a feature matrix, calculate the covariance matrix, and determine the eigenvalues and eigenvectors. The first few principal components with cumulative contributions exceeding 90% are selected as the eigenvectors after dimensionality reduction. Typically, the first three to five principal components can represent over 95% of the data variability. For example, for a 2.0 mm diameter cable sample, the cumulative contribution of the first four principal components reaches 93.7%. The first principal component represents the strain characteristics in the cable's central bending area, with a contribution of 56.2%. The second principal component represents the strain propagation characteristics, with a contribution of 21.3%.

[0075] The eigenvectors were input into a finite element analyzer to establish a cable bending fatigue model. The cable model employed a multilayer structure, consisting of a metal conductor core, an insulation layer, and an outer sheath. Physical parameters were assigned to each material layer. For example, the Young's modulus of the copper core was 110 GPa, with a Poisson's ratio of 0.34; the Young's modulus of the insulation layer (PVC) was 3.5 GPa, with a Poisson's ratio of 0.38. Hexahedral elements were used for meshing, with increased mesh density in the central bending region and an element size set to 1 / 20 of the cable diameter.

[0076] The stress and strain distribution fields of the cable were calculated using a stress-strain constitutive equation solver. During the solution process, the updated Lagrangian method was used to address large deformation problems, and the Newton-Raphson iterative algorithm was employed to solve the nonlinear equations. The iterative accuracy was set to 10-6, and the maximum number of iterations was 50. Based on the stress-strain boundary conditions determined by the eigenvectors, the stress and strain distribution fields at each point in the cable were calculated, including normal, tangential, and radial components. The calculation results show that for a 1.0 mm diameter cable with a bending radius of 10 times the diameter, the maximum normal stress of the conductor core at the bend center reached 78.5 MPa, the maximum tangential stress was 32.7 MPa, and the maximum radial stress was 25.6 MPa. The corresponding maximum normal strain was 0.31%, the maximum tangential strain was 0.16%, and the maximum radial strain was 0.12%.

[0077] In this embodiment, the cable bending fatigue life test sample data is preprocessed by an adaptive filter, which can effectively remove measurement noise and abnormal interference, improve the data quality of subsequent analysis, and use wavelet decomposition to extract the time-frequency characteristics of stress and strain data, which can simultaneously obtain time domain and frequency domain information. It can more comprehensively characterize the dynamic evolution characteristics of stress and strain 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 and strain state inside the cable.

[0078] In an optional embodiment,

[0079] Based on the material fracture mechanics theory, 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 factor of each stress monitoring point of the cable. The fatigue crack growth rate equation is established, including:

[0080] The pre-acquired stress distribution field and strain distribution field are input into the stress intensity factor calculation module based on the material fracture mechanics theory. The mapping relationship between the stress distribution field and strain distribution field and the crack tip stress field is established, and the cracking type stress intensity factor and the sliding type stress intensity factor of the cable crack tip in the polar coordinate system are calculated respectively.

[0081] Calculate the crack propagation direction angle based on the cracking stress intensity factor and the sliding stress intensity factor, substitute the crack propagation direction angle into the equivalent stress intensity factor calculation formula to obtain the stress intensity factor of each stress monitoring point of the cable;

[0082] A fatigue crack growth rate equation including material constant term, stress intensity factor amplitude term, fatigue crack growth threshold correction term and fracture toughness correction term is established, and a quantitative relationship between crack growth rate and equivalent stress intensity factor is established.

[0083] Based on the stress distribution field and strain distribution field data, mapping transformation is performed in the stress intensity factor calculation module. The Williams series expansion method is used to transform the original data and 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 coefficient is determined through iterative calculation. Utilizing the symmetry and antisymmetry of the stress field, the stress components corresponding to the cracking type and the sliding type are extracted respectively, and an accurate mapping relationship between the stress distribution and the singular field at the crack tip is established.

[0084] During the stress intensity factor calculation phase, singularities are addressed through extrapolation. Multiple concentric circular paths are established around the crack tip, and stress components are extracted along each path. The stress components along each path are integrated and averaged to obtain path-independent integral values. A path integral method based on the strain energy release rate is employed, combining displacement and stress field information to calculate the stress intensity factors for cracking and sliding, respectively. To improve accuracy, the results from multiple paths are weighted averaged, with the weight coefficient decaying exponentially with path distance.

[0085] The crack propagation direction is determined, and the objective function is established based on the maximum tangential stress criterion. The stress field in the mixed mode is decomposed into radial and tangential components through polar coordinate transformation. A grid search method is used to find the point with the maximum tangential stress in the fan-shaped area centered on the crack tip. To avoid local optimal solutions, multiple initial search points are set, and the search process is optimized using the gradient descent method. The direction angle corresponding to the maximum tangential stress obtained from the search is substituted into the equivalent stress intensity factor calculation formula. The equivalent stress intensity factor of each monitoring point is calculated through tensor transformation and stress superposition principle.

[0086] A fatigue crack growth rate equation is established, using piecewise functions to describe the characteristics of different growth stages. A weighting function is introduced to embed threshold and fracture toughness correction terms into the basic equation. For the threshold correction term, a gradual transition function is used to describe the crack growth behavior in the near-threshold region, ensuring prediction accuracy in the low stress intensity factor region. The fracture toughness correction term uses a nonlinear function to characterize the rapid increase in crack growth rate as it approaches the fracture toughness. During the solution process, a numerical integration method with an adaptive step size is used to cumulatively calculate the crack growth amount. By dynamically adjusting the integration step size, both computational accuracy and solution efficiency are guaranteed.

[0087] Multiple error controls are implemented during the solution process. Independent error control metrics are set for truncation error in series expansion, discretization error in path integrals, and convergence error in azimuth search. During data processing, a sliding window method is used to smooth intermediate calculation results, reducing the impact of numerical fluctuations on the final result. Furthermore, singular points and transition points during the calculation process are identified and specially handled to ensure the robustness of the algorithm under various operating conditions.

[0088] For example, a certain type of power cable with a 20 mm cross-sectional diameter, a 2 mm outer sheath thickness, and a complex multilayer structure was studied. Stress distribution data was obtained through bending fatigue testing, and 12 stress monitoring points were placed on the cable surface. A Williams series expansion to the eighth order was used to establish a stress field mapping relationship. A polar coordinate system was established at the crack tip, and the calculated stress intensity factor for the cracking type was the square root of 25 MPa·m, while the stress intensity factor for the sliding type was the square root of 15 MPa·m.

[0089] Based on the maximum tangential stress criterion, the crack propagation angle was calculated to be 70 degrees. Substituting this angle into the calculation formula yielded an equivalent stress intensity factor of 32 MPa·m². Taking into account the characteristics of this cable material, the fatigue crack growth rate equation was set to the negative power of ten, the threshold correction term to the square root of 8 MPa·m², and the fracture toughness correction term to the square root of 85 MPa·m². This equation shows that under cyclic loading, when the stress intensity factor amplitude is 30 MPa·m², the crack growth rate is 0.002 mm per cycle.

[0090] In this embodiment, the Williams series expansion method is used to establish the mapping relationship between the stress distribution field and the strain distribution field and the crack tip stress field, which can accurately describe the stress distribution characteristics of the crack tip. By calculating the cracking type and sliding type stress intensity factors respectively, the mixed mode fracture characteristics of the cable under complex load conditions are fully reflected, which is more in line with the actual working conditions than the single mode fracture analysis. The crack propagation direction angle is calculated based on the maximum tangential stress criterion, which can accurately predict the crack propagation path. The fatigue crack propagation rate equation is established through the improved Paris fracture criterion, and the fatigue crack propagation threshold value correction term and the fracture toughness correction term are introduced to overcome the prediction deviation of the traditional Paris formula in low stress and high stress areas.

[0091] In an optional embodiment,

[0092] Calculate the crack propagation trajectory and crack propagation rate at each monitoring point of the cable, and construct the damage evolution tensor as the state feature input deep reinforcement learning network including:

[0093] 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 maximum stress to obtain the crack growth trajectory at each monitoring point of the cable;

[0094] The position and range of the plastic zone at the crack tip are determined according to the crack propagation trajectory. The Schmidt factor of the plastic zone is calculated to determine the main slip system. The slip direction of the main slip system and the normal vector of the slip plane are used to obtain the dislocation slip system direction tensor through tensor product operation. The dislocation density tensor and the dislocation slip system direction tensor are constructed and tensor product operation is performed to obtain the local plastic strain tensor in the plastic zone.

[0095] The dislocation slip band density distribution is calculated, and the first correction coefficient is obtained by the ratio of the dislocation slip band density to the critical dislocation density. The second correction coefficient is obtained by the ratio of the local plastic strain tensor equivalent strain to the reference strain, and the dislocation slip band-local strain correlation function is constructed.

[0096] The damage correction term is obtained by performing a tensor product operation on the dislocation slip band-local strain correlation function and the initial damage tensor, and the damage evolution tensor is obtained by performing a tensor superposition operation on the second-order spatial derivative of the initial damage tensor.

[0097] The obtained stress intensity factor is input into the fatigue crack growth rate equation, and the crack growth rate at each monitoring point on the cable is numerically calculated. Using a numerical integration algorithm with an adaptive step size, the crack growth rate is integrated along the direction of maximum principal stress to obtain the crack growth trajectory at each monitoring point. The calculation step size is dynamically adjusted during the integration process, and the step size is refined in areas where the crack growth rate varies dramatically to ensure calculation accuracy.

[0098] Based on the crack propagation trajectory, the boundaries of the plastic deformation region at the crack tip are determined using the plastic zone estimation criterion. Within the defined plastic zone, crystal orientation data is obtained through diffraction analysis, and a transformation relationship between the crystal coordinate system and the specimen coordinate system is established. Schmidt factors are calculated for all possible slip systems within the plastic zone, and the most easily activated principal slip system is identified, taking into account the coupling effect of crystal orientation and applied stress state. The slip direction vector of the principal slip system and the slip plane normal vector are used to construct a complete dislocation slip system direction tensor field.

[0099] Within a defined plastic region, a dislocation density tensor field is constructed based on dislocation dynamics theory. The dislocation density evolution equation is established, taking into account the processes of dislocation generation, annihilation, and accumulation. This constructed dislocation density tensor is then multiplied with the previously obtained dislocation slip system direction tensor to obtain a strain tensor field representing the local plastic deformation. The calculations consider the effects of crystal anisotropy and dislocation interactions.

[0100] Based on the obtained local plastic strain tensor field, the density distribution of dislocation slip bands is calculated using continuum mechanics methods. By setting a critical dislocation density threshold and calculating the ratio of the actual dislocation density to the critical density, a first correction factor reflecting the degree of dislocation accumulation is obtained. Simultaneously, the ratio of the equivalent strain of the local plastic strain tensor to the material reference strain is calculated to obtain a second correction factor representing the degree of plastic deformation. Based on these correction factors, a coupling function is constructed that accurately describes the relationship between dislocation slip bands and local strain.

[0101] The constructed dislocation slip band-local strain correlation function is multiplied by the initial damage state tensor of the material to obtain a damage correction term that accounts for the influence of microscopic mechanisms. The spatial second-order derivative of the initial damage tensor is also calculated to characterize the gradient effect of damage. The damage correction term and the spatial derivative term are combined through tensor superposition to obtain a complete tensor field for damage evolution.

[0102] For example, a certain type of copper-core power cable was used as the research object. Eight stress monitoring points were arranged during a bending fatigue test. After obtaining the stress intensity factor through a pre-calculation, the crack growth rate at each monitoring point was calculated using an improved crack growth rate equation. The initial integration step size was selected as one-tenth the size of the plastic zone at the crack tip, and this step size was dynamically adjusted during the crack growth process using an adaptive algorithm.

[0103] Within the defined plastic zone, crystal orientation data was obtained using electron backscatter diffraction. Calculations revealed twelve potential slip systems within the plastic zone, and Schmidt factor analysis confirmed that the primary slip system resides on the octahedral slip planes of the crystal. The constructed dislocation density tensor field showed that the dislocation density reached its maximum at a distance of 0.2 mm from the crack tip to the surface.

[0104] Calculations and analysis show that dislocation slip bands are primarily distributed within a fan-shaped region 0.5 mm from the crack tip. The ratio of the measured dislocation density to the critical dislocation density of the material is used as the first correction factor, while the ratio of the calculated equivalent plastic strain to the material's yield strain is used as the second correction factor. A correlation function constructed using these two correction factors accurately describes the evolution of dislocation slip bands.

[0105] The resulting damage evolution tensor field shows that damage initiates in the high stress concentration region at the crack tip and gradually propagates along the dislocation slip band. The spatial distribution of the damage field exhibits a distinct anisotropic characteristic, which is consistent with the observed fatigue crack growth path.

[0106] In this embodiment, the plastic deformation region is determined by the crack propagation trajectory. On this basis, the crystal plasticity theory is introduced, and the main slip system is determined through Schmidt factor analysis. This achieves 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 microscopic dislocation motion and macroscopic plastic strain is established. The effects of dislocation density and plastic strain are respectively considered by two correction coefficients, achieving a scale transition from microscopic damage to macroscopic damage.

[0107] In existing technologies, macro-scale continuum damage mechanics models are often directly used, treating the material as a homogeneous continuous medium and ignoring the dislocation evolution and slip band formation processes at the microscale. This makes it difficult to accurately describe the local damage evolution characteristics of the material during fatigue, resulting in a large deviation between the predicted results and the actual situation.

[0108] The multi-scale coupling method of this embodiment breaks through the limitations of traditional single-scale models, can more accurately describe the damage evolution law of materials during fatigue, and realizes full-scale analysis from microscopic dislocation motion to macroscopic damage evolution. It overcomes the defect of traditional methods that ignore microscopic mechanisms and significantly improves the accuracy and reliability of fatigue damage prediction.

[0109] Figure 2 This is a diagram of the Schmidt factor distribution in the crack tip plastic zone of the cable bending fatigue life prediction method based on reinforcement learning in an 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.

[0110] 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 at 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 the 45° direction in front of the crack, with a width of about 0.15mm, which is highly consistent with the preferred slip area actually observed. The areas of different depths in the figure represent different Schmidt factor values, ranging from 0.2 to 0.48. Observations showed the distribution of three main slip systems: the octahedral slip system dominated in the high stress area, with a Schmidt factor value between 0.42 and 0.487; the cubic slip system was active in the area 0.3 mm below the crack tip, with a Schmidt factor value between 0.32 and 0.38; the unconventional slip system began to activate in the far field area (>0.5 mm from the crack tip), with a Schmidt factor value below 0.3.

[0111] The "butterfly wing"-like high Schmidt factor region around the crack tip indicates that plastic deformation is highly concentrated in this area, which is consistent with the deformation characteristics observed before microcrack formation in experiments. The Schmidt factor reaches a maximum of 0.487 at a distance of 0.23 mm from the crack tip, indicating the region most susceptible to microcrack initiation. The high Schmidt factor band at a 45° angle is approximately 0.15 mm wide, indicating the highest slip band density and the most likely path for fatigue crack propagation.

[0112] The Schmidt factor distribution diagram accurately predicts the dislocation slip starting point and preferred slip system, providing a key foundation for subsequent dislocation density tensor calculations and damage evolution predictions. Compared with traditional methods, this technical solution can more accurately capture the crystallographic characteristics and slip system activation within the plastic zone, explaining the deformation behavior of copper core cables during fatigue from a microscopic perspective. The spatial distribution characteristics of multiple slip systems provide a key basis for the subsequent construction of the dislocation density tensor and also reveal the microscopic plastic deformation mechanism of copper core materials during fatigue deformation.

[0113] In an optional embodiment,

[0114] Calculating the action value function to iteratively train the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges includes:

[0115] The action-value function is calculated 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.

[0116] Iteratively training the deep reinforcement learning network based on the updated action-value function, using the actual fatigue life data as a reward function, randomly sampling training data from an experience pool through an experience replay mechanism, and performing gradient backpropagation optimization on network parameters of the deep reinforcement learning network based on the training data;

[0117] Determine whether the loss function of the deep reinforcement learning network has converged. When the change of the loss function in a preset number of consecutive iterative trainings is less than a preset change threshold, the loss function is considered to have converged, and the iterative training is stopped to obtain the trained deep reinforcement learning network.

[0118] A dual-network computing architecture is established, with a target network and a training network constructed separately. Both networks share the same neural network structure, but differ in their parameter update strategies. The training network is responsible for real-time learning and adaptation, while the target network is used to generate stable target values. An experience buffer pool is set up to store state transition samples, including information such as the current state, executed actions, rewards received, and next state. During the action-value function calculation process, a soft update strategy is employed, setting a low update rate to ensure that the target network parameters slowly track those of the training network, thus avoiding drastic fluctuations in the value function estimate.

[0119] In temporal difference learning, a forward sweep approach is used to calculate the temporal difference error (TDE). Starting from the current state, the system advances a fixed number of steps forward, accumulating the rewards received. A discount factor is also considered, applying a weighted attenuation to future rewards. The TDE is calculated by comparing the actual cumulative rewards with the predicted action values. Based on this error term, the action-value function is iteratively updated to continuously optimize the estimated accuracy of the state-action value.

[0120] During the training of a deep reinforcement learning network, a reward function is constructed based on actual fatigue life data. Normalization is used to map the life data to an appropriate numerical range, and a reward signal is designed based on the deviation between the predicted and actual values. A priority sampling strategy is used to select training samples from the experience pool, assigning a higher sampling probability to samples with large temporal difference errors to improve learning efficiency. During the sampling process, importance weights are used to correct sampling biases to ensure unbiased parameter updates.

[0121] The gradient backpropagation algorithm is implemented to optimize network parameters. The gradient of the loss function with respect to the network output is calculated and then propagated layer by layer using the chain rule. During the gradient propagation process, gradient clipping is used to prevent gradient explosion, while a dropout mechanism is introduced to enhance the network's generalization capabilities. An adaptive learning rate adjustment strategy dynamically adjusts the parameter update step size based on gradient changes, ensuring convergence while improving training efficiency.

[0122] The training process is monitored by setting multiple convergence criteria. The loss function value after each training iteration is recorded, and the change in the loss function over multiple consecutive iterations is calculated. A sliding window method is used to smooth this change to reduce the impact of random fluctuations. The training process is considered converged when the smoothed change remains below a preset threshold over a predetermined number of iterations. Furthermore, model performance is evaluated using a validation set to prevent overfitting.

[0123] Throughout the training process, a dynamic balancing mechanism is implemented. Hyperparameters such as the experience pool size, batch size, and training frequency are adjusted to achieve a balance between exploration and exploitation. The network's predictive performance is regularly evaluated, and the model's generalization ability is verified through cross-validation. When convergence conditions are reached, the network parameters are saved, completing the training process for the deep reinforcement learning network.

[0124] For example, a fatigue life prediction model for a certain cable model was trained using a deep neural network consisting of four hidden layers, with 128, 256, 128, and 64 neurons in each layer, respectively. The experience pool was set to 10,000 samples, with 32 samples randomly sampled for training at each time. A learning rate of 0.001 and a discount factor of 0.95 were used.

[0125] During training, measured fatigue life data was normalized on a logarithmic scale, and a reward function based on prediction error was constructed. The target network parameters were updated every 100 iterations. The convergence criterion was set to a relative change in the loss function of less than 0.1 percent over 50 consecutive iterations. After approximately 2,000 training iterations, the loss function stabilized, indicating successful network training. The average prediction error on the test set was less than 5 percent, demonstrating good generalization performance.

[0126] In this embodiment, by constructing a dual network structure for deep reinforcement learning, stable optimization of the action value function is achieved. By introducing forward scanning and discount factors, long-term dependencies are accurately captured, and the prediction model's ability to express fatigue life evolution characteristics is improved. By assigning a higher sampling probability to important samples, the network's learning speed 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.

[0127] In an optional embodiment,

[0128] The uncertainty of the deep reinforcement learning network output is quantified, a credible interval is established to divide the confidence level, and an adaptive warning threshold is constructed. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, multi-dimensional warning information is output including:

[0129] Quantify the uncertainty of the deep reinforcement learning network output to obtain the uncertainty quantification result;

[0130] Based on the uncertainty quantification results, the mean and standard deviation of the cable fatigue life prediction values are calculated. The mean is used as the prediction center value, and the product of the standard deviation and the preset confidence coefficient is used as the interval radius to construct a credible interval and determine the first uncertainty threshold and the second uncertainty threshold. The confidence level is divided according to the relationship between the standard deviation and the first uncertainty threshold and the second uncertainty threshold:

[0131] The standard deviation is less than or equal to the first uncertainty threshold, which is the first level; the standard deviation is greater than the first uncertainty threshold and less than or equal to the second uncertainty threshold, which is the second level; and the standard deviation is greater than the second uncertainty threshold, which is the third level;

[0132] An adaptive warning threshold is constructed based on the credible interval and confidence level. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, multidimensional warning information including the cable fatigue life prediction value, credible interval, confidence level, and standard deviation is output.

[0133] Using the cable fatigue life predictions output by a deep reinforcement learning network as the foundational data, a Markov Chain Monte Carlo sampling framework was constructed. During the sampling initialization phase, independent probability distribution functions were set for each component of the damage evolution tensor. Based on material mechanics theory, physical parameters such as fracture toughness and yield strength were converted into constraints for the probability density function. These constraints were integrated into the probability density function using the Lagrange multiplier method, ensuring that the sampling process adhered to physical laws.

[0134] A stratified sampling strategy is used for parallel chain sampling. Multiple independently running Markov chains are set up, each with different initial temperature parameters. During the sampling process, the energy difference and state transition probability of adjacent samples are calculated to determine whether to accept a new sampling point. A temperature annealing mechanism is introduced to gradually reduce the sampling temperature as the number of iterations increases, thereby improving the local precision of the sampling. During the inter-chain interaction phase, the state exchange probability is calculated based on the difference in energy functions, enabling information exchange between chains with different temperatures.

[0135] The sampled data is processed using a non-Gaussian process regression approach. Kernel density estimation is used to construct a probability distribution model for the sample, and the kernel bandwidth parameter is dynamically adjusted to balance the smoothness and accuracy of the estimate. For data with significant non-normal distribution characteristics, polynomial expansion is used to approximate the true distribution. The skewness and kurtosis of the distribution are assessed by calculating the moments of the probability density function. Outlier detection is also implemented to identify and address outliers in the distribution.

[0136] A multi-layered evaluation system was established for convergence monitoring. Inter-chain variance was assessed by calculating the Gilman-Rubin statistic to analyze the degree of mixing within the sampling chains. The autocorrelation function was calculated to determine the effective sample size and eliminate highly correlated, redundant samples. Trend analysis was performed on the energy trajectory of each sampling chain to determine whether the sampling had reached a steady-state distribution. Segmented statistical methods were used to assess the stability of the sampling variance to ensure the reliability of the sampling results.

[0137] Statistical features are extracted from the processed sampled data. The sample mean is calculated using a weighted average method and used as the predicted central value. The standard deviation is calculated using an improved maximum likelihood estimation method to improve the robustness of parameter estimation. A credible interval is constructed by multiplying the preset confidence factor by the standard deviation. During interval construction, skewness of the distribution is considered and asymmetric adjustments are made to the interval boundaries.

[0138] A dual-threshold grading mechanism is established to categorize forecast results. Historical data analysis is used to determine baseline values for the two uncertainty thresholds, and a dynamic update mechanism is established. Based on the comparison of the standard deviation with the thresholds, forecast confidence is divided into three levels. Corresponding early warning criteria are established for each level, forming a complete tiered early warning system.

[0139] An adaptive weighting approach is employed to construct warning thresholds. Credible interval information and confidence level information are weighted and combined to generate warning thresholds. The weighting coefficients are dynamically adjusted based on the uncertainty of the forecast, improving the sensitivity and reliability of the warning. When the forecast value falls below the threshold, the warning mechanism is triggered, simultaneously activating the multi-dimensional information integration module.

[0140] Early warning information is integrated using the Analytic Hierarchy Process (AHP). Predicted values are normalized to unify the dimensions of different indicators. Information such as the predicted central value, credible interval range, confidence level, and standard deviation are organized according to a predefined format to form a structured early warning report. The importance of each dimension is determined using an information entropy weighting method, highlighting key early warning indicators. A hierarchical display strategy is employed during the release of early warning information to ensure that important information is prioritized.

[0141] Implement a dynamic early warning tracking mechanism. Continuously monitor the changing trends of forecast results and analyze the temporal evolution of early warning indicators using a sliding window approach. Raise the warning level when multiple consecutive forecast results trigger the warning condition. Simultaneously, record warning history and establish a warning event database to provide data support for subsequent optimization of early warning strategies.

[0142] For example, an uncertainty analysis of fatigue life prediction for a certain type of power cable was conducted. A sampling framework consisting of five parallel Markov chains was constructed, with each chain sampling 1,000 points. The sampling step size was set to 0.01, and the Gilles Rubin diagnostic criterion was used to monitor sampling convergence. After approximately 10,000 iterations, all five sampling chains reached convergence.

[0143] Based on the sampling results, the fatigue life predictions were calculated to have a mean of 10,000 cycles and a standard deviation of 500 cycles. A confidence level of 95% was set, and a credible interval of plus or minus two standard deviations from the predicted center was constructed. The first uncertainty threshold was set to 300 cycles, and the second uncertainty threshold to 600 cycles. When the standard deviation reached 400 cycles, the predictions were classified as belonging to the second confidence level.

[0144] The warning threshold for this confidence level is set at 8,000 cycles. Since the current predicted value is below the warning threshold, a warning message is output: the predicted life is 10,000 cycles, the credible interval is 9,000 to 11,000 cycles, the confidence level is level 2, and the standard deviation is 400 cycles. This warning information provides a reliable basis for engineering maintenance decisions.

[0145] In this embodiment, physical constraints are introduced to ensure that the sampling results meet the laws of material mechanics, thereby improving the physical rationality of the prediction. An adaptive interval estimation method based on standard deviation is adopted, and the credible interval is dynamically adjusted in combination with the confidence coefficient. The credible interval and confidence level are organically combined to achieve dynamic adjustment of the warning threshold.

[0146] Existing technologies often directly adopt deterministic forecasting methods or use simple statistical models for uncertainty analysis. These methods ignore the physical constraints in the forecasting process and fail to accurately quantify the impact of multiple sources of uncertainty. Fixed threshold criteria are used, lacking the ability to dynamically assess forecast reliability, which can easily lead to blindness and lag in early warnings.

[0147] This embodiment introduces physical constraints to ensure that the sampling results meet the laws of material mechanics, thereby improving the physical rationality of the prediction. By introducing a dual-threshold grading mechanism, it achieves refined management of the prediction results and provides differentiated processing strategies for prediction results with different reliability levels. It can adaptively adjust the early warning strategy according to the uncertainty level of the prediction, significantly improving the accuracy and timeliness of the early warning, effectively responding to prediction tasks under complex working conditions, and providing strong technical support for the safe operation and maintenance of the cable system.

[0148] Figure 3 This figure shows the uncertainty analysis of cable fatigue life prediction for a reinforcement learning-based cable bending fatigue life prediction method according to an embodiment of the present invention. It demonstrates the uncertainty analysis results of cable fatigue life prediction using the Markov Chain Monte Carlo method combined with physical constraints and non-Gaussian process regression. The horizontal axis represents the fatigue life prediction value, ranging from 1000 to 11000 cycles; the vertical axis represents the probability density, ranging from 0 to 1.0.

[0149] The central black curve shows the probability distribution of the predicted lifetime, which exhibits distinct non-Gaussian characteristics. The distribution is centered at 10,000 cycles (indicated by the central vertical dashed line), representing the predicted expected value μ. The standard deviation σ of the predictions is 400 cycles, as indicated by the horizontal arrows pointing right from the center. Based on this standard deviation, a credible interval is constructed around the predicted central value, ranging from 9,500 cycles (μ - σ) to 10,500 cycles (μ + σ), indicated by the two vertical dashed lines on the left and right.

[0150] The vertical gray solid line on the left side of the figure, at 8000 cycles, represents the warning threshold. When the predicted lifespan falls below this value, the warning mechanism is triggered. The figure also shows two horizontal dashed lines, representing the boundaries of the uncertainty thresholds used to determine the confidence level of the prediction results. When the standard deviation falls between these two lines, such as the current prediction's standard deviation of 400 cycles, the prediction results are classified as medium confidence.

[0151] This precise uncertainty quantification method not only provides point predictions for fatigue life but also defines the uncertainty range of the prediction using credible intervals. It also assigns confidence levels to the predictions based on the standard deviation, forming a comprehensive prediction and early warning system. Compared to traditional methods, the Markov Chain Monte Carlo method, combined with physical constraints, significantly improves prediction accuracy and reliability, providing a more scientific basis for cable fatigue life assessment and maintenance decisions.

[0152] In an optional embodiment,

[0153] The uncertainty quantification results of the deep reinforcement learning network output include:

[0154] According to the material mechanics theory, the cable stress-strain constraint conditions are constructed to establish the stress tensor and strain tensor correlation equation, and the crack growth rate and stress intensity factor amplitude correlation equation are established as physical constraint conditions;

[0155] Construct the target distribution function and the proposed distribution function to calculate the acceptance probability of the new sampling point, calculate the constraint violation metric of the new sampling point under the physical constraint conditions, and determine whether the new sampling point is a valid sampling point based on the relationship between the constraint violation metric and the preset allowable threshold;

[0156] The degree of freedom parameter is calculated by fitting the effective sampling points with Student distribution. The tail weight parameter, skewness parameter, scale parameter, location parameter and shape parameter are calculated by describing the heavy-tail characteristics of the effective sampling points with generalized hyperbolic distribution. The joint probability distribution function is constructed to establish a multidimensional dependency structure.

[0157] The mean and variance of the effective sampling points are calculated, the sampling convergence and sampling effectiveness are evaluated, and the uncertainty distribution characteristics of the effective sampling points are determined as the quantitative results of the cable fatigue life uncertainty.

[0158] A constraint system is constructed based on the theory of material mechanics. A correlation between the stress tensor and the strain tensor is established, taking into account constitutive parameters such as the material's elastic modulus and Poisson's ratio, and extending the theory of linear elasticity to include plastic deformation. Within the framework of fracture mechanics, a mapping relationship between the crack growth rate and the stress intensity factor amplitude is established, accounting for the fatigue threshold and the boundary effects of fracture toughness. Tensor operations are used to unify these constraint equations into a single coordinate system, forming a complete set of physical constraints.

[0159] In constructing a Markov chain sampling strategy, a state transition mechanism is designed using a random walk maximum likelihood algorithm. A target distribution function reflecting physical properties is constructed, using stress state, strain level, and crack growth characteristics as distribution parameters. A highly adaptable suggested distribution function is also designed, ensuring sampling efficiency through adaptive adjustments. For each new sampling point, its acceptance probability relative to the current state is calculated, and its satisfaction with physical constraints is evaluated.

[0160] The constraint violation metric is calculated using a multi-level evaluation strategy. The conformance of the stress-strain relationship is checked, and the deviation between the stress and strain tensors is calculated. The crack growth behavior is evaluated for compliance with fracture mechanics criteria, and the error in the growth rate compared to theoretical predictions is calculated. The violation levels at each level are combined in a weighted manner to produce an overall constraint violation metric. The validity of the sampling point is determined by comparing it with a preset tolerance threshold.

[0161] During the distribution fitting phase, a Student distribution is fitted to valid sampling points. An iterative optimization algorithm is used to estimate the degrees of freedom parameters, and the maximum likelihood method is used to improve the accuracy of parameter estimation. A generalized hyperbolic distribution is used to describe the heavy-tailed characteristics of the data, and the method of moments is used to estimate the characteristic parameters of the distribution, including tail weight, skewness, scale, location, and shape parameters. A joint probability distribution function is constructed, establishing a multidimensional dependency structure to achieve an organic integration of different distribution characteristics.

[0162] During the fitting process, a segmented optimization strategy was employed to improve fitting accuracy. Different weight coefficients were applied to different intervals of the data, with a particular focus on the fitting performance in the tail region. Cross-validation was used to assess the stability of the fitting results, and parameters were fine-tuned and optimized as necessary. Furthermore, the temporal correlation of the data was considered, and time weighting was introduced in parameter estimation to increase the model's sensitivity to recent data.

[0163] A multi-verification mechanism is used to evaluate the convergence of sampling results. The ratio of inter-chain variance to intra-chain variance is calculated, and the degree of convergence is determined by setting a dynamic threshold. Energy changes in the sampling trajectory are also monitored to assess whether the sampling process has reached a stable state. Sampling effectiveness is assessed by calculating the proportion of valid sampling points to total sampling points, and the sampling strategy is dynamically adjusted based on the sampling efficiency metric.

[0164] Determine the characteristics of the uncertainty distribution through comprehensive analysis. Transform the characteristic parameters of the Student distribution and the generalized hyperbolic distribution into interpretable uncertainty indicators, including the distribution's central tendency, degree of dispersion, skewness, and tail behavior. By combining these indicators, a complete uncertainty description is constructed, providing a foundation for subsequent reliability assessment.

[0165] For example, a certain type of overhead conductor with a cross-sectional diameter of 25 mm was used as the research object. Based on material mechanics theory, an elastoplastic constitutive equation was constructed, with the elastic modulus set at 110 GPa and the yield strength set at 300 MPa. For the fracture mechanics constraints, the fatigue threshold was set at the square root of 8 MPa-m, and the fracture toughness was set at the square root of 85 MPa-m.

[0166] Sampling was performed using five parallel Markov chains, each with a different initial temperature. Ten thousand sampling iterations yielded eight thousand valid sampling points. A Student distribution fit yielded 4.5 degrees of freedom, a tail weight parameter of 2.8, and a skewness parameter of 0.3 for the generalized hyperbolic distribution. The ratio of the inter-chain to intra-chain variance was 1.05, and the effective sampling rate reached 80%, indicating convergence and high sampling efficiency. The determined uncertainty distribution exhibited a slightly right-skewed characteristic, with a heavy tail.

[0167] In this embodiment, a complete physical constraint system is formed by establishing stress-strain constraints and crack extension constraints. A random walk maximum likelihood algorithm is used to construct a Markov chain, and a constraint violation metric is introduced to screen sampling points. A hybrid model of the Student distribution and the generalized hyperbolic distribution is introduced, breaking through the limitations of the traditional normal distribution assumption.

[0168] In existing technologies, simple probabilistic statistical methods are often used to analyze cable fatigue life uncertainty, ignoring the physical constraints of material mechanics and fracture mechanics. These methods often assume that data follows a normal distribution, making it difficult to accurately describe the non-normal distribution characteristics commonly found in actual projects. In particular, predictions of extreme events can be subject to significant deviations.

[0169] This embodiment not only ensures that the prediction results meet the basic laws of mechanics, but also can accurately reflect the damage evolution characteristics of the material during the fatigue process, significantly improves the effectiveness of sampling, avoids the generation of a large number of invalid sampling points in traditional random sampling methods, and uses the generalized hyperbolic distribution to characterize the heavy-tail characteristics, thereby 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.

[0170] Figure 4 This is a three-dimensional distribution characteristic diagram of cable fatigue life uncertainty in the cable bending fatigue life prediction method based on reinforcement learning in an embodiment of the present invention. It shows the constructed three-dimensional distribution characteristics of cable fatigue life uncertainty and intuitively presents the complex relationship between stress level, strain level and life distribution probability density through a three-dimensional topological surface.

[0171] 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 a probability density of 0.82. The distribution exhibits a distinct asymmetry. The orange right tail (high life region) shows a slight ductility with a skewness parameter of 0.3, consistent with the observed slight skewness of cable fatigue life towards long life. The yellow left tail (low life region) exhibits a steeper downward trend with a tail weight parameter of 2.8, reflecting the sharp increase in cable failure probability under high stress conditions. In the purple region, where stress approaches the green yield strength reference plane (300 MPa), the distribution surface exhibits a distinct abrupt change, consistent with the physical mechanism of the material transitioning from elastic to plastic deformation. The blue fracture toughness boundary (K_IC = 85 MPa·m^0.5) marks the critical state of crack growth, beyond which the distribution rapidly decays to zero. This technical solution successfully characterizes the uncertainty characteristics of cable fatigue life in the range of (4.5~6.0)×10^6 cycles by combining the Student's t distribution (degrees of freedom parameter 4.5) with the multidimensional dependency structure of the generalized hyperbolic distribution. The shape parameter 2.3 further accurately describes the geometric characteristics of the distribution.

[0172] Compared with the traditional two-dimensional statistical distribution, the three-dimensional topological expression more comprehensively reflects the influence of physical constraints (stress-strain relationship and crack propagation behavior) on fatigue life distribution, providing a more reliable theoretical basis for cable safety assessment and maintenance decisions.

[0173] A second aspect of an embodiment of the present invention provides a cable bending fatigue life prediction system based on reinforcement learning, comprising:

[0174] The first unit is used to collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data, and calculate the stress distribution field and strain distribution field of the cable based on the stress and strain data;

[0175] 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 factor of each stress monitoring point of the cable, and establish a fatigue crack growth rate equation according to the Paris fracture criterion, substitute the stress intensity factor 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 input it into the deep reinforcement learning network as a state feature;

[0176] A third unit is configured to calculate an action-value function using a deep Q-learning algorithm according to the state characteristics, iteratively train a deep reinforcement learning network based on the action-value function, and use the actual fatigue life data as a reward function until the loss function converges, thereby obtaining a trained deep reinforcement learning network;

[0177] The fourth unit is used to quantify the uncertainty of the output of the deep reinforcement learning network through the Markov chain Monte Carlo method, establish a credible interval based on the uncertainty quantification result, and divide the confidence of the cable fatigue life prediction value into three levels. Based on the credible interval and confidence level, an adaptive warning threshold is constructed. When the cable fatigue life prediction value is less than the warning threshold corresponding to the confidence level, multi-dimensional warning information is output.

[0178] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including:

[0179] 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 aforementioned method.

[0180] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0181] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0182] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, 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 cable bending fatigue life prediction method based on reinforcement learning, characterized by: include: Collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data, and calculate cable stress distribution field and strain distribution field based on the stress and 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 factor of each stress monitoring point of the cable. The fatigue crack growth rate equation is established to calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable. The damage evolution tensor is constructed as the state feature input into the deep reinforcement learning network, including: The pre-acquired stress distribution field and strain distribution field are input into the stress intensity factor calculation module based on the material fracture mechanics theory. The mapping relationship between the stress distribution field and strain distribution field and the crack tip stress field is established, and the cracking type stress intensity factor and the sliding type stress intensity factor of the cable crack tip in the polar coordinate system are calculated respectively. Calculate the crack propagation direction angle based on the cracking stress intensity factor and the sliding stress intensity factor, substitute the crack propagation direction angle into the equivalent stress intensity factor calculation formula to obtain the stress intensity factor of each stress monitoring point of the cable; Establish a fatigue crack growth rate equation that includes material constant terms, stress intensity factor amplitude terms, fatigue crack growth threshold correction terms, and fracture toughness correction terms, and establish a quantitative relationship between crack growth rate and equivalent stress intensity factor; 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 maximum stress to obtain the crack growth trajectory at each monitoring point of the cable; The position and range of the plastic zone at the crack tip are determined according to the crack propagation trajectory. The Schmidt factor of the plastic zone is calculated to determine the main slip system. The slip direction of the main slip system and the normal vector of the slip plane are used to obtain the dislocation slip system direction tensor through tensor product operation. The dislocation density tensor and the dislocation slip system direction tensor are constructed and tensor product operation is performed to obtain the local plastic strain tensor in the plastic zone. The dislocation slip band density distribution is calculated, and the first correction coefficient is obtained by the ratio of the dislocation slip band density to the critical dislocation density. The second correction coefficient is obtained by the ratio of the local plastic strain tensor equivalent strain to the reference strain, and the dislocation slip band-local strain correlation function is constructed. The damage correction term is obtained by performing a tensor product operation on the dislocation slip band-local strain correlation function and the initial damage tensor, and the damage evolution tensor is obtained by performing a tensor superposition operation on the second-order spatial derivative of the initial damage tensor. Calculate the action value function to iteratively train the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges; The uncertainty of the deep reinforcement learning network output is quantified, a credible interval is established to divide the confidence level, and an adaptive warning threshold is constructed. When the predicted value of the cable fatigue life is less than the corresponding confidence level warning threshold, multi-dimensional warning information is output.

2. The method according to claim 1, characterized in that Collect cable bending fatigue life test sample data including cable specification parameters, stress and strain data, and actual fatigue life data. Calculate the cable stress and strain distribution fields based on the stress and strain data, including: Collecting cable bending fatigue life test sample data, the cable bending fatigue life test sample data including cable specification parameters, stress and 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 to extract the time-frequency characteristics of the stress and strain data, and performing dimensionality reduction on the time-frequency characteristics to obtain a feature vector representing the stress and strain evolution law; The stress distribution field and the strain distribution field of the cable are calculated based on the characteristic vector, where the stress distribution field and the strain distribution field include a normal component, a tangential component, and a radial component.

3. The method according to claim 1, characterized in that Calculating the action value function to iteratively train the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges includes: The action-value function is calculated 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 training the deep reinforcement learning network based on the updated action-value function, using the actual fatigue life data as a reward function, randomly sampling training data from an experience pool through an experience replay mechanism, and performing gradient backpropagation optimization on network parameters of the deep reinforcement learning network based on the training data; Determine whether the loss function of the deep reinforcement learning network has converged. When the change of the loss function in a preset number of consecutive iterative trainings is less than a preset change threshold, the loss function is considered to have converged, and the iterative training is stopped to obtain the trained deep reinforcement learning network.

4. The method according to claim 1, wherein The uncertainty of the deep reinforcement learning network output is quantified, a credible interval is established to divide the confidence level, and an adaptive warning threshold is constructed. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, multi-dimensional warning information is output including: Quantify the uncertainty of the deep reinforcement learning network output to obtain the uncertainty quantification result; Based on the uncertainty quantification results, the mean and standard deviation of the cable fatigue life prediction values are calculated. The mean is used as the prediction center value, and the product of the standard deviation and the preset confidence coefficient is used as the interval radius to construct a credible interval and determine the first uncertainty threshold and the second uncertainty threshold. The confidence level is divided according to the relationship between the standard deviation and the first uncertainty threshold and the second uncertainty threshold: The standard deviation is less than or equal to the first uncertainty threshold, which is the first level; the standard deviation is greater than the first uncertainty threshold and less than or equal to the second uncertainty threshold, which is the second level; and the standard deviation is greater than the second uncertainty threshold, which is the third level; An adaptive warning threshold is constructed based on the credible interval and confidence level. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, multidimensional warning information including the cable fatigue life prediction value, credible interval, confidence level, and standard deviation is output.

5. The method according to claim 4, characterized in that The uncertainty quantification results of the deep reinforcement learning network output include: According to the material mechanics theory, the cable stress-strain constraint conditions are constructed to establish the stress tensor and strain tensor correlation equation, and the crack growth rate and stress intensity factor amplitude correlation equation are established as physical constraint conditions; Construct the target distribution function and the proposed distribution function to calculate the acceptance probability of the new sampling point, calculate the constraint violation metric of the new sampling point under the physical constraint conditions, and determine whether the new sampling point is a valid sampling point based on the relationship between the constraint violation metric and the preset allowable threshold; The degree of freedom parameter is calculated by fitting the effective sampling points with Student distribution. The tail weight parameter, skewness parameter, scale parameter, location parameter and shape parameter are calculated by describing the heavy-tail characteristics of the effective sampling points with generalized hyperbolic distribution. The joint probability distribution function is constructed to establish a multidimensional dependency structure. The mean and variance of the effective sampling points are calculated, the sampling convergence and sampling effectiveness are evaluated, and the uncertainty distribution characteristics of the effective sampling points are determined as the quantitative results of the cable fatigue life uncertainty.

6. A cable bending fatigue life prediction system based on reinforcement learning, used to implement the method according to any one of claims 1 to 5, characterized in that: include: The first unit is used to collect cable specification parameters, stress and strain data, and actual fatigue life data of cable bending fatigue life test sample data, and calculate the cable stress distribution field and strain distribution field based on the stress and strain data; The second unit is used to build a stress intensity factor calculation module based on material fracture mechanics theory, 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 the fatigue crack growth rate equation, calculate the crack growth trajectory and crack growth rate of each monitoring point of the cable, and construct the damage evolution tensor as the state feature input deep reinforcement learning network; The third unit is used to calculate the action value function for iterative training of the deep reinforcement learning network, using actual fatigue life data as the reward function until the loss function converges; The fourth unit is used to quantify the uncertainty of the deep reinforcement learning network output, establish a credible interval to divide the confidence level, and construct an adaptive warning threshold. When the cable fatigue life prediction value is less than the corresponding confidence level warning threshold, it outputs multi-dimensional warning information.

7. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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