On-line ultrasonic evaluation method for cross-linking degree of insulating material of extra-high voltage cable

Abstract

The application provides an online ultrasonic evaluation method for the crosslinking degree of an insulating material of an ultra-high voltage cable, comprising: collecting ultrasonic reflection signals covering a 0.5-15 MHz frequency band and a sampling rate not lower than 20 MHz and synchronously collecting process parameters, extracting multi-dimensional fractal features through variational mode decomposition; constructing a cross-scale causal knowledge graph based on molecular structures, crosslinking networks and process parameters, realizing fractal feature attribution distribution through a graph neural network, and quantitatively evaluating the contribution of causal paths to crosslinking degree prediction by using an improved SHAP value, and realizing a three-dimensional visual and interpretable report, wherein the application can dynamically optimize the knowledge graph, improve the accuracy of crosslinking degree prediction and the scientificity of process control, and enhance the evaluation interpretability and production adaptability.

Description

Technical Field

[0001] This invention relates to the field of intelligent power equipment condition assessment and material physical characteristic analysis technology, and in particular to an online ultrasonic assessment method for the crosslinking degree of insulation materials in ultra-high voltage cables. Background Technology

[0002] Existing technologies for assessing the crosslinking degree of ultra-high voltage cable insulation materials mainly include automated signal analysis methods based on deep learning and experience-based regression assessment methods based on expert knowledge. In recent years, with the improvement of online monitoring equipment and process data acquisition capabilities, mainstream technologies often employ deep neural network models to perform end-to-end fitting and crosslinking degree estimation on strong time-series data such as online ultrasonic signals. These methods, relying on multilayer convolutional neural networks and long short-term memory networks, can achieve high prediction accuracy and generalization ability under ultra-large datasets and are widely used in cable manufacturing lines and insulation material process optimization scenarios. However, the decision-making process of deep learning models is highly "black box," and their internal parameters are difficult to map to specific physical mechanisms, making the model results difficult to interpret and trace. This limits the application of crosslinking degree assessment results in safety-sensitive scenarios such as equipment reliability analysis, product quality traceability, and anomaly mechanism investigation. In contrast to deep learning models, current industry-standard empirical crosslinking degree analysis methods rely on manual feature engineering and limited physical models. These methods use experimentally measured structural and chemical parameters obtained through differential thermal analysis, wide-angle X-ray diffraction, and Fourier transform infrared spectroscopy, combined with statistical regression to establish crosslinking degree estimation models. While these methods offer some interpretability and engineering traceability, they struggle to adapt to the complex conditions of high-dimensional time-series signals in production lines, have limited feature space coverage, and are susceptible to performance failure due to environmental disturbances. The industry trend of online condition assessment for cable insulation materials shows that future assessment models need to possess high-precision predictive capabilities, physical traceability and interpretability, and production line adaptability. Currently, some intelligent methods such as graph neural networks and reinforcement learning for condition monitoring are being introduced, but most of them are difficult to deeply integrate with the multi-scale causal structure of materials science and lack engineering closed-loop interpretation mechanisms. Summary of the Invention

[0003] In order to solve the above-mentioned technical problems, the present invention provides an online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables.

[0004] The technical solution of this invention is implemented as follows: An online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables, comprising: S1: Collect online ultrasonic reflection signals and synchronous process parameters of ultra-high voltage cable insulation material on the continuous vulcanization production line. The ultrasonic signal sampling rate is not less than 20MHz and covers the 0.5–15MHz frequency band. The process parameters include temperature gradient, traction speed and irradiation dose, in order to obtain raw signal inputs with different operating conditions. S2: Perform variational mode decomposition preprocessing on each 10ms sliding window ultrasonic signal acquired in step S1 to separate 6 intrinsic mode functions, and calculate the Hurst exponent of rescaled range analysis, the box dimension of the box method, and the generalized fractal dimension spectrum width of each intrinsic mode function to generate a fractal feature set. S3: Based on the causal entities such as molecular chain entanglement density, cross-linking point spatial distribution, crystalline / amorphous region ratio and filler-matrix interface state of cable insulation materials, a cross-scale causal knowledge graph is constructed. The degree of cross-linking is the top-level target node, extending three layers of causal relationships downwards. Each causal edge is labeled with the type of source of experimental data, molecular dynamics simulation or expert experience, and confidence weight. S4: Input the fractal feature set generated in step S2 into the causal perception fractal embedding module designed based on the cross-scale causal knowledge graph constructed in step S3. This module is constrained by the causal edge weights of the knowledge graph through lightweight graph neural network aggregation operation and outputs the attribution distribution vector of each fractal feature in the causal graph. S5: Based on the attribution distribution vector output in step S4 and the cross-scale causal knowledge graph constructed in step S3, execute the causal path confidence backpropagation algorithm, and use the improved SHAP value that satisfies the causal graph transitive closure constraint to calculate the contribution of each causal path to the crosslinking degree prediction value. S6: Map the contribution obtained in step S5 to the cross-scale causal knowledge graph, construct a three-dimensional visualization coordinate framework, label the measured fractal values ​​and error propagation intervals based on the three-dimensional visualization coordinate framework, and integrate them with the predicted crosslinking degree to generate an interpretable evaluation report, including the predicted crosslinking degree and a three-dimensional visualization causal path diagram, where the X-axis represents the process → structure → chemical causal hierarchy, the Y-axis represents the fractal feature sensitivity ranking, and the Z-axis represents the path confidence. Each path is labeled with the measured fractal values ​​and error propagation intervals. S7: When the evaluation error of the new production line sample is greater than the preset threshold of 1.5%, the incremental update module of the causal graph based on the contribution threshold in step S5 is triggered. Only the causal edge association nodes with a contribution greater than 0.15 are fine-tuned with small samples, and the remaining graph parameters are frozen to maintain knowledge stability.

[0005] The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables provided by this invention has the following beneficial effects: (1) This invention significantly improves the accuracy and interpretability of crosslinking degree assessment for ultra-high voltage cable insulation materials by integrating fractal feature extraction of online ultrasonic signals with structured reasoning of cross-scale causal knowledge graphs. In the prior art, although deep learning-based prediction models can achieve high fitting accuracy, they lack explicit modeling of the multi-level internal mechanisms of process-structure-chemistry, making it difficult to support quality attribution analysis and process reverse optimization in engineering sites. In contrast, this invention constructs a three-layer causal knowledge graph with "crosslinking degree" as the core objective, formally expressing the physical causal relationship between macroscopic process parameters, mesoscopic structural features and microscopic chemical states. It also implements information aggregation under causal constraints in the fractal feature space through a lightweight graph neural network, enabling the model to not only output high-precision prediction values, but also trace the key paths affecting crosslinking degree from the physical mechanism level. This achieves a paradigm shift from "empirical fitting" to "mechanism guidance," greatly enhancing the credibility and decision support capabilities of industrial quality inspection systems.

[0006] (2) This invention proposes a causal-aware fractal embedding and path contribution tracing mechanism, which significantly improves the system's response sensitivity and adaptability to abnormal operating conditions. A causal path contribution calculation method based on improved SHAP values ​​is designed to accurately identify the key causal links that have the greatest impact on prediction deviations while satisfying the transitive closure constraint. When the prediction error exceeds a threshold, only local causal edge association nodes with contribution values ​​higher than the set threshold are fine-tuned with small samples, while the remaining graph structure and parameters remain frozen. This ensures the stability of existing knowledge and achieves fast, low-overhead online correction. This mechanism achieves an efficient knowledge update loop without introducing additional modal data or a complex credibility scoring system, significantly reducing the model's dependence on large-scale labeled data and high-performance computing power, and possesses good engineering practicality and deployability.

[0007] (3) This invention employs physical-driven variational mode decomposition combined with multidimensional fractal feature modeling to fully exploit the nonlinear dynamic characteristics in ultrasonic reflection signals, providing a highly sensitive non-destructive characterization method for the evolution of the internal structure of materials. By performing VMD decomposition on the 10ms sliding window signal and extracting the Hurst exponent, box dimension, and generalized fractal dimension spectrum of each IMF component, a 9-dimensional fractal feature space is constructed, which can finely distinguish the differences in microscopic inhomogeneity and energy dissipation modes of materials under different cross-linking states. These features serve as input anchors for the causal map, giving the model a high degree of sensitivity to hidden quality problems such as early defects and local heterogeneity. Combined with the output of a three-dimensional visualization interpretable report, it not only presents the final prediction results but also intuitively displays the confidence, sensitivity ranking, and error propagation range of each causal path, enabling technicians to quickly locate the root cause of the problem in the XYZ multidimensional view, greatly improving the efficiency of human-machine collaborative diagnosis and the level of quality control. Attached Figure Description

[0008] Figure 1 This is a flowchart of the online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to the present invention; Figure 2 This is a sub-flowchart of the online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to the present invention; Figure 3 This is another sub-flowchart of the online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to the present invention. Detailed Implementation

[0009] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0010] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0011] like Figure 1 As shown, this invention provides an online ultrasonic evaluation method for the crosslinking degree of insulation materials in ultra-high voltage cables, specifically including: S1: Collect online ultrasonic reflection signals and synchronous process parameters of ultra-high voltage cable insulation material on the continuous vulcanization production line. The ultrasonic signal sampling rate is not less than 20MHz and covers the 0.5–15MHz frequency band. The process parameters include temperature gradient, traction speed and irradiation dose, in order to obtain raw signal inputs with different operating conditions. S2: Perform variational mode decomposition preprocessing on each 10ms sliding window ultrasonic signal acquired in step S1 to separate 6 intrinsic mode functions, and calculate the Hurst exponent of rescaled range analysis, the box dimension of the box method, and the generalized fractal dimension spectrum width of each intrinsic mode function to generate a fractal feature set. S3: Based on the causal entities such as molecular chain entanglement density, cross-linking point spatial distribution, crystalline / amorphous region ratio and filler-matrix interface state of cable insulation materials, a cross-scale causal knowledge graph is constructed. The degree of cross-linking is the top-level target node, extending three layers of causal relationships downwards. Each causal edge is labeled with the type of source of experimental data, molecular dynamics simulation or expert experience, and confidence weight. S4: Input the fractal feature set generated in step S2 into the causal perception fractal embedding module designed based on the cross-scale causal knowledge graph constructed in step S3. This module is constrained by the causal edge weights of the knowledge graph through lightweight graph neural network aggregation operation and outputs the attribution distribution vector of each fractal feature in the causal graph. S5: Based on the attribution distribution vector output in step S4 and the cross-scale causal knowledge graph constructed in step S3, execute the causal path confidence backpropagation algorithm, and use the improved SHAP value that satisfies the causal graph transitive closure constraint to calculate the contribution of each causal path to the crosslinking degree prediction value. S6: Map the contribution obtained in step S5 to the cross-scale causal knowledge graph, construct a three-dimensional visualization coordinate framework, label the measured fractal values ​​and error propagation intervals based on the three-dimensional visualization coordinate framework, and integrate them with the predicted crosslinking degree to generate an interpretable evaluation report, including the predicted crosslinking degree and a three-dimensional visualization causal path diagram, where the X-axis represents the process → structure → chemical causal hierarchy, the Y-axis represents the fractal feature sensitivity ranking, and the Z-axis represents the path confidence. Each path is labeled with the measured fractal values ​​and error propagation intervals. S7: When the evaluation error of the new production line sample is greater than the preset threshold of 1.5%, the incremental update module of the causal graph based on the contribution threshold in step S5 is triggered. Only the causal edge association nodes with a contribution greater than 0.15 are fine-tuned with small samples, and the remaining graph parameters are frozen to maintain knowledge stability.

[0012] Step S1: Collect online ultrasonic reflection signals and synchronous process parameters of ultra-high voltage cable insulation material on a continuous vulcanization production line. The ultrasonic signal sampling rate is no less than 20MHz and covers the 0.5–15MHz frequency band. The process parameters include temperature gradient, traction speed, and irradiation dose, to obtain raw signal inputs that are differentiated under multiple operating conditions. Specifically, this includes: S1.1: Perform ultrasonic probe positioning treatment on the surface of ultra-high voltage cable insulation material on the continuous vulcanization production line to determine the optimal acoustic coupling position and generate a sensor arrangement scheme; For the outer surface area of ​​ultra-high voltage cable insulation material on the continuous vulcanization production line, a laser ranging method (parameters: laser wavelength 650nm, ranging accuracy ±0.1mm) is used to realize the spatial geometric coordinate acquisition function of the insulation material surface; Furthermore, a three-dimensional surface reconstruction algorithm (parameter: point cloud density of no less than 10 points per square millimeter) is used to realize the digital modeling of the surface morphology of the insulating material and obtain the surface micro-arc distribution data results; Furthermore, based on the ultrasonic sound field simulation algorithm (parameter: simulation mesh cell side length 0.5mm), the acoustic coupling efficiency of different probe positions on the surface of the insulating material is predicted, and a position-coupling coefficient comparison table is generated; Furthermore, by employing a multi-objective optimization method (parameters: the objective function includes maximizing the coupling coefficient and probe installation stability constraints), the optimal probe position is automatically selected, and a set of position coordinates is output. By using a sensor arrangement generation process, the above set of position coordinates is transformed into a sensor arrangement scheme to achieve the expected technical effect of positioning the probe on a continuous vulcanization production line. For example, in a continuous vulcanization production line test scenario, a triangulation sensor with a laser wavelength of 650nm was selected, with a ranging accuracy controlled within ±0.1mm and a data acquisition speed of 1000 times / second. Coordinate scanning was performed on the outer circumferential surface of an insulating material with a diameter of 120mm, resulting in a point cloud density of 12 points per square millimeter. A surface morphology model was generated using a 3D surface reconstruction algorithm, and the average micro-radian of the surface was analyzed to be 0.02rad. This model was input into ultrasonic sound field simulation software, with the probe frequency set to 5MHz. The coupling coefficient for different placement positions was calculated, with the highest position coefficient being 0.93. Using a multi-objective optimization algorithm, under the conditions that the coupling coefficient is greater than 0.9 and the installation structure stability coefficient is greater than 0.8, coordinate sets with circumferential position angles of 45°, 135°, and 225° were selected to form a three-point placement scheme. After actual installation, this scheme significantly reduced ultrasonic signal energy attenuation and improved signal amplitude stability, meeting the coupling requirements for subsequent high-frequency (0.5–15MHz) acquisition. S1.2: Configure the ultrasonic acquisition system parameters based on the sensor layout scheme to set a sampling rate of no less than 20MHz and a frequency band covering 0.5–15MHz, and output the acquisition parameter configuration file; Based on the sensor layout scheme data generated in step S1.1, the system parameter planning method (parameters: sensor spatial distribution matrix, coupling medium type, position coordinate accuracy ±0.1mm) is used to set the signal link structure of the ultrasonic acquisition system to ensure that the layout matches the sound field coverage. Furthermore, by using a frequency response calibration algorithm (parameters: target frequency range 0.5–15MHz, target sampling rate ≥20MHz), the reference frequency of the main sampling module frequency synthesizer is set, and a frequency band coverage control signal is obtained for hardware frequency tuning. Furthermore, a quantization sampling accuracy control method (parameters: analog-to-digital converter (ADC) bit width ≥ 14 bits, oversampling coefficient > 2) is adopted to optimize the quantization resolution of the ultrasonic reflection signal and generate a sampling accuracy configuration vector as the ADC calibration input. Furthermore, by using a signal-to-noise ratio optimization algorithm (parameters: target signal-to-noise ratio > 45dB, adjustable range of preamplifier gain 0–40dB), the coupling optimization of analog front-end gain and digital filter window length is achieved, and noise immunity performance indicators are generated for subsequent signal integrity detection. The system configuration file generation module integrates the frequency synthesizer settings, analog-to-digital converter sampling accuracy vector, and front-end gain and window parameter coupling optimization results into an acquisition parameter configuration file, achieving stable operation of the ultrasonic acquisition system at a sampling rate of no less than 20MHz and covering the 0.5–15MHz frequency band. For example, in a scenario where ultra-high voltage cable insulation material is collected in a continuous vulcanization production line, the sensor spatial distribution matrix is ​​an 8×4 array, the coupling medium is glycerol, and the position coordinate accuracy is controlled within ±0.05mm. The frequency response calibration algorithm sets the target frequency range to 0.5–15MHz and the sampling rate to 25MHz. The sampling period formula is expressed in MathML as follows: ,in The sampling period is in seconds. The analog-to-digital converter (ADC) uses a 16-bit width and an oversampling factor of 4. A sampling accuracy configuration vector is generated for ADC initialization. The front-end gain is set to 28dB, and the digital filter window length is set to 512 sampling points. The signal-to-noise ratio (SNR) calculated by the SNR optimization algorithm is approximately 48.7dB, which meets the design target. The final output acquisition parameter configuration file achieved a stable sampling rate of ≥25MHz and complete 0.5–15MHz frequency band coverage during actual acquisition. It maintained a significantly improved signal quality under multiple operating conditions (temperature gradient 35–60℃, traction speed 1.5–2.3m / min, and irradiation dose 12–20kGy), providing high-quality input for subsequent signal processing. S1.3: Use the acquisition parameter configuration file to trigger the multi-channel synchronous acquisition device to obtain ultrasonic reflection signals and process parameter data streams including temperature gradient, traction speed, and irradiation dose, forming the raw signal dataset; S1.4: Perform real-time integrity verification on the original signal dataset to detect signal distortion or missing data and generate a signal quality assessment report; S1.5: Perform data storage operations based on the signal quality assessment report to save valid multi-condition differentiated original signal inputs and output the original signal input set for subsequent analysis.

[0013] Step S2: The 10ms sliding window ultrasonic signal acquired in step S1 is preprocessed using variational mode decomposition to separate six intrinsic mode functions (EMFs). The rescaled range analysis Hurst exponent, box-counting dimension, and generalized fractal dimension spectral width of each EMF are calculated to generate a fractal feature set. Specifically, this includes: S2.1: Perform variational mode decomposition preprocessing on each 10ms sliding window ultrasonic signal acquired in step S1, and separate 6 intrinsic mode functions based on the adaptive center frequency optimization algorithm to obtain the time-frequency localization representation of the signal components in each frequency band; Each 10ms sliding window ultrasonic signal acquired in step S1 is input to the variational mode decomposition processing module. An adaptive center frequency optimization algorithm (parameters: center frequency iteration step size 0.1MHz, initial center frequency set covering 0.5–15MHz frequency band) is used to realize the multi-mode decomposition function of non-stationary signal components. Furthermore, by using the signal spectrum energy distribution estimation method (parameters: sliding window length 1024-point FFT, window function type Hanning window), the frequency range of each narrowband component is initially determined, and this range is used as the initial value of the center frequency to input the adaptive optimization algorithm to obtain the initial decomposition mode set; Furthermore, an improved variational mode decomposition iterative formula is used to perform mode separation of the signal. The objective function constrained by Lagrange multipliers is used to minimize the bandwidth of each mode, with the mode bandwidth converging to less than 0.2 MHz. The Lagrange multiplier λ is set to 2000. The mode update term in each iteration is calculated using the following formal expression:

[0014] in, For the k-th modal component, To input ultrasound signals, This is the bandwidth penalty coefficient; Furthermore, the rules are updated through adaptive center frequency. This enables dynamic adjustment of the center frequency of each modal cycle, where... Let be the center frequency of the k-th mode. The center frequency obtained in the new iteration, The update factor is set to 0.25 to ensure that the center frequency converges to the region where the signal energy is concentrated. Through the above processing method, the 10ms sliding window signal from the previous step is transformed into a set of intrinsic mode functions within the coverage of 6 frequency bands, realizing the accurate extraction of time-frequency localization representation and providing stable input for subsequent fractal feature analysis; For example, under the operating conditions of a continuous vulcanization production line, the ultrasonic reflection signal with a sampling rate of 20MHz and an initial center frequency distribution of [0.8MHz, 2.5MHz, 5.0MHz, 8.0MHz, 11.0MHz, 14.0MHz] was subjected to the above-mentioned adaptive center frequency optimized variational mode decomposition processing. FFT spectral energy analysis showed that the fourth mode was concentrated in the 7.9–8.2MHz range, and the center frequency of this mode was adjusted from 8.0MHz to 8.15MHz after two rounds of iteration. The second mode was concentrated in the 2.4–2.6MHz range, and was adjusted from 2.5MHz to 2.48MHz after iteration. The bandwidth of all modes was less than 0.2MHz at convergence. The six intrinsic mode functions obtained were finally verified by time-frequency plots to show a non-overlapping narrowband distribution. The fractal features generated based on these modes maintained a stable trend under the condition of increased noise level, which significantly improved the anti-interference ability and accuracy of feature analysis. S2.2: Based on the 6 intrinsic mode functions output by S2.1, rescaled range analysis is performed on each intrinsic mode function to calculate the Hurst exponential eigenvalue of each intrinsic mode function, so as to generate a 3D Hurst exponential eigenvector. Based on the six intrinsic mode function signal sequences output in step S2.1, the rescaled range analysis method (parameters: the sliding window length l varies from 5% to 20% of the signal length, and the step size is set according to logarithmic intervals) is used to quantify the fluctuation characteristics of the target signal at different time scales. The process is segmented using a sliding window, and the cumulative deviation from the sequence is calculated within each segment. Furthermore, the time series was scaled using the ratio of range to standard deviation, and the scale-statistic relationship curve data was obtained. Furthermore, the least squares method was used to perform linear fitting of the scale-statistic relationship curve in a double logarithmic coordinate system. The parameters were set to exclude scale values ​​less than three times the sampling period from the fitting interval, and the fitting slope results were generated. Furthermore, the Hurst exponent H is set as the equivalent value of the above-mentioned fitting slope and the theoretical model, and is calculated using the following formula:

[0015] in, The range of the sample. The standard deviation of the sample is 1. The length of the sliding window; This calculation yields the Hurst exponent value for each intrinsic mode function, forming an initial Hurst exponent vector of length 6. Furthermore, frequency band clustering is performed on the initial Hurst exponent vector (parameter: the clustering strategy is to group low-frequency, mid-frequency and high-frequency modes into one class respectively), to calculate the composite statistical value of the three frequency bands and generate a 3-dimensional Hurst exponent feature vector; By using rescaled range analysis and frequency band clustering, the intrinsic mode signal features from the previous step are transformed into 3D Hurst exponent feature data that reflects long-range correlation and fractal characteristics, thereby enabling a scale-dependent characterization of the non-stationary dynamic processes inside the insulating material. For example, in the online testing scenario of ultra-high voltage cable insulation material produced on a continuous vulcanization production line, a sliding window length l is set from 50 to 200 points for the acquired intrinsic mode functions of the first frequency band, with a step size taking the logarithmic sequence {50, 70, 100, 140, 200}. The cumulative deviation of each window is calculated, and the ratio of the range R to the standard deviation S is obtained. In a double logarithmic coordinate system, for... and Least squares linear fitting yielded a slope of 0.85, which was set as the Hurst exponent for this mode. The mode functions of the third and fifth frequency bands were processed in the same way, yielding Hurst exponents of 0.62 and 0.77, respectively. The Hurst exponents of the three frequency bands were combined to form a 3D feature vector [0.85, 0.62, 0.77]. In subsequent modules, this feature vector was mapped using causal graph embedding to establish a correlation with the corresponding structural parameter nodes, significantly improving the adaptability of the crosslinking degree assessment model to different operating conditions and demonstrating sensitive response characteristics to changes in process parameters in experimental verification. S2.3: The box-counting method is applied to calculate the fractal dimension of the 6 intrinsic mode functions output by S2.1. The box-counting eigenvalues ​​of each intrinsic mode function are determined by the mesh cover density analysis to generate a 3D box-counting eigenvector. S2.4: Based on the six intrinsic mode functions output by S2.1, perform generalized fractal dimension spectrum analysis and use the multifractal detrending fluctuation algorithm to calculate the eigenvalue of the generalized fractal dimension spectrum width of each intrinsic mode function to generate a 3D generalized fractal dimension spectrum width eigenvector. S2.5: Perform feature aggregation processing on the 3D Hurst exponent feature vector generated in S2.2, the 3D box dimension feature vector generated in S2.3, and the 3D generalized fractal dimension spectral width feature vector generated in S2.4 to generate a structured feature set containing 9-dimensional fractal features, which will be used as input data for the subsequent causal perception fractal embedding module.

[0016] like Figure 2As shown, step S3 involves constructing a cross-scale causal knowledge graph based on causal entities such as the molecular chain entanglement density, crosslinking point spatial distribution, crystalline / amorphous region ratio, and filler-matrix interface states of the cable insulation material. This graph extends three layers of causal relationships downwards, with crosslinking degree as the top-level target node. Each causal edge is labeled with experimental data, molecular dynamics simulations, or expert experience sources, along with their confidence weights. Specifically, this includes: S3.1: Based on the molecular chain entanglement density, crosslinking point spatial distribution, crystalline region to amorphous region ratio, and filler matrix interface state causal entity data of cable insulation materials, define the bottom node set of the knowledge graph, and initialize the knowledge graph structure with the degree of crosslinking as the top target node to form the basic node layer of the cross-scale causal knowledge graph. Based on the fractal feature set generated in step S2 and the measured data of the microstructure of cable insulation materials, a causal entity extraction method was adopted (parameter: molecular chain entanglement density). Spatial distribution function of crosslinking points crystalline / amorphous region ratio Filler-matrix interface state parameters This enables the initialization definition of the underlying nodes of a cross-scale causal knowledge graph. Furthermore, through the entity attribute parsing algorithm (parameters: data source label, measurement standardization coefficient, structural hierarchy coding rules), the attribute fields of each causal entity are structured, and a node attribute matrix is ​​obtained, which is used for binding the physical parameters of the graph nodes; Furthermore, by using a unique node identifier generation method (parameters: entity type code, data collection batch index, measurement timestamp), cross-scale causal knowledge graph node IDs are assigned, and a node index table is generated for subsequent causal edge connection operations. Furthermore, by using the top-level target node setting method of the graph (parameters: target variable = degree of cross-linking, measurement method = differential scanning calorimetry combined with infrared spectroscopy), the degree of cross-linking node is implanted as the top-level target node into the graph structure, and target node anchoring records are generated to establish causal path direction constraints from the top level to each bottom level node; Furthermore, through a node-level mapping algorithm, the step-like cross-scale connection structure between the top-level target node and the bottom-level nodes is declared, forming a cross-scale causal knowledge graph basic node layer containing the top-level and bottom-level structures, thereby realizing global node layout and hierarchical connection. By defining the underlying node set and initializing the top-level node as described above, the results of the previous step are transformed into structured node layer data that can be used to construct causal relationships, thereby realizing the basic structure construction of a cross-scale causal knowledge graph. For example, in a polyethylene-insulated ultra-high voltage cable on a continuous vulcanization production line, differential scanning calorimetry (DSC) was used to measure the crystalline region ratio. The value is 0.62, and the molecular chain entanglement density is analyzed by small-angle neutron scattering. for The average spacing of crosslinking points was statistically analyzed using three-dimensional microtomography. The wavelength was 15.8 nm, and the filler-matrix interface state parameters were measured using atomic force microscopy with interface analysis. The value is 0.18. A causal entity extraction method is used to extract the causal entity. , , and Load the data into the entity parsing module to generate a node attribute matrix. Using a unique node identifier generation method, define this batch of samples as a set of node IDs N001~N004, and label each node with its type code (structure / chemical / interface). Set the target node for crosslinking degree T000 and measure the crosslinking degree value. The calculation formula, obtained by combining differential scanning calorimetry and infrared spectroscopy, is as follows:

[0017] in, This represents the overall enthalpy change of the sample. For the enthalpy change in the amorphous region, The enthalpy change of the crystalline region is used as the top-level node. A step-by-step cross-scale connection is established between this cross-linking target node and N001~N004. The resulting basic node layer shows high consistency matching in the simulation structure evaluation, which significantly improves the accuracy and physical correlation of subsequent causal edge construction. S3.2: Based on the experimental data of macroscopic process parameters such as temperature gradient and vulcanization time in the continuous vulcanization production line, the first layer of causal relationship is constructed, which associates macroscopic process parameters with molecular chain mobility, generates the first layer of causal edge set, and labels the source type as experimental data and initial confidence weight, so as to establish a causal mapping from process parameters to molecular behavior. Based on the temperature gradient data stream and vulcanization time records output by the real-time monitoring system of the continuous vulcanization production line, a parameter normalization algorithm is used (parameter: minimum value - maximum value scaling factor). =0.95), to achieve the standardization of the comparability of macroscopic process parameters under different production line conditions; Furthermore, by using a time series correlation analysis algorithm (parameter: sliding window length = 50 points), the dynamic correlation between temperature gradient and vulcanization time series is calculated, and a process parameter correlation matrix dataset is obtained. Furthermore, a molecular dynamics parameter inversion algorithm (parameter: time step) is employed. This allows for the calculation of the mean square displacement (MSD) characteristics of molecular chains under different macroscopic process conditions, and the generation of a set of quantitative indicators of molecular chain mobility. Furthermore, a causal edge generation algorithm is used (parameter: initial edge weight). The temperature gradient and the normalized index of sulfidation time are mapped to the nodes corresponding to the mean square displacement of the molecular chain to generate the first layer of causal edge set and obtain the initial causal weight matrix data. Furthermore, a source type labeling module (parameters: experimental data identifier E, simulation data identifier M) is used to add "experimental data" source labeling information to the first-level causal edge set, forming a causal relationship set with source attributes; Initialize using the confidence weight algorithm (parameter: weighting coefficients) =0.7), transforming the initial causal weight matrix obtained in the previous step into an initial set of confidence weights that satisfy the topological constraints of the knowledge graph, thus initially establishing the causal mapping structure from process parameters to molecular chain mobility; For example, in the implementation of a continuous vulcanization production line, the temperature gradient data output by the temperature sensor array ranges from -15℃ / m to +20℃ / m, and the vulcanization time ranges from 180s to 240s. A normalization algorithm is used to standardize the temperature gradient to [0,1] and the vulcanization time to the [0,1] interval. The mean of the normalized temperature gradient is 0.62, and the mean of the vulcanization time is 0.58. Based on sliding window correlation analysis, the Pearson correlation coefficient between the temperature gradient and the vulcanization time is calculated to be 0.83, forming a 2×2 process parameter correlation matrix. Molecular dynamics inversion technology is used, with a time step... Simulations were performed on the mean square displacement of molecular chains under different combinations of vulcanization time and temperature gradient. The results showed that the mean square displacement of molecular chains reached [value missing] under the condition of longest vulcanization time and positive temperature gradient. The macroscopic process parameter nodes and molecular chain mean square displacement nodes are connected by a causal edge construction algorithm. The initial edge weight is set to 0.5, and the source type is labeled as "experimental data". After confidence weight initialization, the weight range of the first layer of causal edge set is finally adjusted to [0.45, 0.58], realizing the causal mapping from two types of macroscopic process parameters, temperature gradient and vulcanization time, to molecular chain mobility. The structure satisfies the logical consistency and traceability of cross-scale causal knowledge graphs. S3.3: Based on the experimental data of crystallinity measured by differential scanning calorimetry and mesoscopic structural parameters of full width at half maximum measured by wide-angle X-ray diffraction, a second-layer causal relationship is constructed. The mesoscopic structural parameters are associated with the cross-linking network topology parameters such as the average spacing between cross-linking points and the entanglement density. A second-layer causal edge set is generated and the source type is labeled as experimental data and confidence weight, so as to establish a causal chain from structural parameters to network characteristics. Based on the crystallinity Xc data measured by differential scanning calorimetry (DSC) and the full width at half maximum (FWHM) data measured by wide-angle X-ray diffraction (WAXD), a mesoscopic structural parameter analysis algorithm (parameters: test temperature range -60℃ to 200℃, heating rate 10℃ / min, diffraction scanning range 5°–50°) is used to realize the standardized preprocessing function of structural parameters. Furthermore, by using a structural parameter normalization processing algorithm (parameter: minimum-maximum normalization), the crystallinity and half-peak width data output by different detection platforms are compared and analyzed under the same dimension, and a normalized data matrix of mesoscopic structure is obtained. Furthermore, the Pearson correlation coefficient calculation method (parameter: sample size n≥30) is applied to evaluate the linear correlation between crystallinity and the average distance Lc between crosslinking points, and a correlation coefficient matrix is ​​generated. Furthermore, a multiple linear regression algorithm (parameter: least squares iterations ≤ 500) is applied to realize the relationship between FWHM and entanglement density. A multivariate fit analysis was performed to obtain the set of regression coefficients. Regression equation. In the figure, a is the regression coefficient corresponding to the half-peak width, and b is a constant term obtained by fitting the training samples; Furthermore, a causal edge weighting algorithm (parameter: weight range 0.1–0.9) is used to realize weighted connections between mesoscopic structural parameter nodes and cross-linked network topology parameter nodes, and to generate a second-layer causal edge set; By using the causal chain mapping process, the mesoscopic structure standardized data matrix from the previous step is transformed into the corresponding causal edge set data, thereby achieving the expected technical effect of constructing causal chains from structural parameters to cross-linking network characteristics. For example, in a sample set of a continuous vulcanization production line, the crystallinity measured by DSC ranged from 0.45 to 0.65, and the FWHM measured by WAXD ranged from 0.20 to 0.32 radians. The crystallinity and FWHM data were normalized to their minimum and maximum values, resulting in matrix elements ranging from 0 to 1. The linear correlation between crystallinity and the average distance between crosslinking points (range 0.8 nm–1.5 nm) was calculated using the Pearson correlation coefficient. With a sample size of n=50, the correlation coefficient was calculated to be 0.82. Multiple linear regression was then applied to fit the FWHM and entanglement density (range 0.8 nm–1.5 nm). The relationship between the two factors is used to obtain the regression coefficients. ,constant Based on the weight allocation algorithm, the weight of the causal edge between the crystallinity node and the node with the average spacing between crosslinking points is set to 0.85, and the weight of the causal edge between the FWHM node and the entanglement density node is set to 0.78, generating a complete set of second-layer causal edges. In subsequent applications of causal knowledge graphs, this set enables high-confidence construction of causal chains between structure and network characteristics, significantly improving the model's generalization ability and interpretability under different operating conditions. S3.4: Based on experimental data of microscopic chemical parameters such as the C=S bond intensity ratio measured by Fourier transform infrared spectroscopy and the T2 relaxation time measured by nuclear magnetic resonance, a third-layer causal relationship is constructed, which associates the microscopic chemical parameters with the chemical type of the crosslinking point and the spatial heterogeneity of the crosslinking point, generates a third-layer causal edge set, and labels the source type as experimental data and confidence weight, so as to complete the causal path from microscopic mechanism to crosslinking characteristics; Based on experimental data such as the C=S bond intensity ratio measured by Fourier transform infrared spectroscopy (FTIR) and the T2 relaxation time measured by nuclear magnetic resonance (NMR), a high-resolution spectral analysis algorithm (parameter: wavenumber resolution) was employed. With a signal-to-noise ratio greater than 100, baseline correction and peak fitting processing of microscopic chemical feature signals are achieved. Furthermore, by using the absorption peak area normalization method (parameter: spectral integral interval is...), (corresponding to the C=S bond absorption region), to realize the quantitative calculation of the C=S bond strength ratio and obtain the corresponding chemical bond ratio data; Furthermore, a spin-spin relaxation curve fitting algorithm is employed (parameters: exponential decay fitting function, fitting accuracy). This allows for the precise extraction of the T2 relaxation time and the generation of chemical kinetic response time indices at crosslinking points. Furthermore, using a chemical bond type discrimination model (parameters: the support vector machine classification kernel function is a radial basis kernel, and the training samples are no less than 500 sets), the classification and identification of chemical types such as C=S, polysulfides, and carbon-carbon are realized, and the set of chemical types of crosslinking points is obtained; Furthermore, spatial heterogeneity statistical analysis was conducted (parameters: the crosslinking point coordinates statistical sample is no less than 200, and the distance standard deviation is calculated using the following formula):

[0018] in, The number of crosslinking point samples. The spacing between individual crosslinking points, The average distance between crosslinking points. (Standard deviation of spatial heterogeneity at crosslinking points) to achieve quantitative assessment of the uniformity of spatial distribution of crosslinking points and generate spatial heterogeneity parameter data; By using a causal relationship mapping process, the chemical bond ratio data and T2 relaxation time index from the previous step are transformed into a set of causal edges related to the chemical type of crosslinking points and the spatial heterogeneity of crosslinking points, thereby achieving the expected technical effect of constructing a causal path from microscopic mechanism to crosslinking characteristics. For example, during the production of ultra-high voltage AC cable insulation materials, FTIR spectral data (wavenumber resolution) of samples collected during the vulcanization stage are analyzed. Integration interval After baseline correction and peak fitting, the C=S bond strength was calculated to be 0.82, and the normalized ratio was 0.154 based on the total absorption peak area. Solid-state NMR data from the same sample were collected, and the T2 relaxation time was found to be 36.5 ms after exponential decay fitting, with a fitting accuracy of [insert accuracy here]. The value was 0.995. After being input into the support vector machine chemical type classification model, it was identified as a polysulfide bond type. The crosslinking point coordinates of this sample under a scanning electron microscope were statistically analyzed. With a sample size N of 254, the average interval was... The value is 5.62 nm. Substituting this into the formula, the standard deviation of spatial heterogeneity is calculated. The value is 0.47 nm. The ratio 0.154, T2=36.5 ms, chemical type label, and multi-point spacing σ value are used to establish the edge of the third-level causal relationship. The causal weight is set to 0.92 based on the consistency of experimental data and the confidence of model classification. Finally, a high-confidence causal chain from microscopic chemical parameters to cross-linking characteristic nodes is formed, which enhances the traceability of the cross-linking degree assessment model to the physicochemical mechanism. S3.5: Based on the set of all causal edges in the knowledge graph, perform a weighted fusion calculation of source type labeling and confidence weight. The source type includes experimental data, molecular dynamics simulation or expert experience. The confidence weight is determined based on data consistency, expert scoring and simulation verification to generate a complete cross-scale causal knowledge graph, providing a structured basis for subsequent causal path tracing.

[0019] like Figure 3 As shown, step S4 involves inputting the fractal feature set generated in step S2 into a causal-aware fractal embedding module designed based on the cross-scale causal knowledge graph constructed in step S3. This module, through a lightweight graph neural network aggregation operation constrained by the causal edge weights of the knowledge graph, outputs the attribution distribution vector of each fractal feature in the causal graph. Specifically, this includes: S4.1: Based on the cross-scale causal knowledge graph constructed in step S3, a causal-aware fractal embedding module is designed. This module adopts a lightweight graph neural network architecture, and its aggregation operation is constrained by the causal edge weights in the knowledge graph in order to establish a dynamic mapping relationship between fractal features and causal entities. The input data is the node set and causal edge weight matrix of the cross-scale causal knowledge graph constructed in step S3, and the execution object is the 9-dimensional fractal feature set and associated node mapping rules formed in step S2. A lightweight graph neural network design method (parameters: 3 layers, 64 hidden units per layer, and ReLU activation function) is used to define the overall architecture of the causal perception fractal embedding module. Furthermore, a graph convolution algorithm (parameters: neighbor sampling number 3, normalization coefficient based on causal edge confidence weight) is used to achieve node feature aggregation and obtain preliminary mapping weight distribution data between fractal features and causal entities. Furthermore, a message passing mechanism with causal weight constraints is adopted (parameters: message function is the weighted sum of neighbor features, weight source is the causal edge confidence value) to achieve directed propagation of node information across scales and generate hierarchical sensitive embedding representations; Furthermore, through a multi-layer embedding representation fusion algorithm (parameters: fusion strategy is skip connection and inter-layer weighted average), the fractal features are mapped to knowledge graph nodes at multiple levels to achieve a comprehensive expression, and an embedding vector matrix is ​​generated; By using a lightweight graph neural network structure with causal weight constraints, the fractal feature input obtained in the previous step is transformed into dynamically embedded data distributed across a cross-scale causal knowledge graph, thereby realizing the ability of fractal features to attribute physical mechanisms in causal entities. For example, in an application scenario of an ultra-high voltage cable production line, the input is a 9-dimensional fractal feature set, including Hurst exponent feature vectors of 0.72, 0.68, and 0.75, box dimension feature vectors of 1.42, 1.46, and 1.40, and generalized fractal spectrum width feature vectors of 0.18, 0.21, and 0.19. The initial state of the corresponding knowledge graph node is standardized with zero mean and unit variance. The lightweight graph neural network is set to 3 layers, with 64 hidden units in each layer. Convolutional aggregation uses a causal edge weight matrix. In this matrix, the weight of the edge between a certain process parameter and molecular chain mobility is 0.83, the weight of the edge between a certain structural parameter and the average spacing of crosslinking points is 0.79, and the weight of the edge between a certain chemical parameter and the spatial heterogeneity of crosslinking points is 0.88. In the first-layer aggregation, the neighbor sampling number is 3, the normalization coefficient is the reciprocal of the input node degree, and the aggregation function is a weighted sum. The second layer uses skip connections, directly adding the first-layer output to the input to retain low-order information. The third layer performs inter-layer weighted averaging to fuse the outputs of each layer, with a weight ratio of 0.4:0.35:0.25. In the output embedding vector matrix, a certain fractal feature has an embedding value of 0.57 in the top-level process parameter node, an embedding value of 0.62 in the meso-structure node, and an embedding value of 0.66 in the micro-chemistry node. After normalization, an attribution distribution vector is formed. The peak of this vector corresponds to the chemical level node, indicating that the correlation between this feature and the micro-chemical mechanism is significantly improved in multi-condition evaluation, supporting subsequent causal path tracing and contribution calculation. S4.2: Input the fractal feature set generated in step S2 into the causal-aware fractal embedding module to generate a feature embedding representation; S4.3: Perform node initialization processing on the feature embedding representation, mapping the fractal features to the initial state vectors of the corresponding nodes in the cross-scale causal knowledge graph; S4.4: Based on the causal edge weights of the knowledge graph, perform graph neural network aggregation operation on the initial state vector to calculate the weighted sum of neighbor information to obtain the updated node feature vector; Based on the initial state vector output in step S4.3, a weighted neighbor aggregation algorithm (parameters: causal edge weight matrix W, node feature vector set H) is used to realize the information fusion of physical dependencies between nodes in a cross-scale causal knowledge graph. Furthermore, by using a normalized weighting function (parameters: degree matrix D, weight matrix W), the proportional influence of neighbor node features is controlled, and the neighbor influence coefficient matrix N of each node is obtained; Furthermore, graph convolution operations (parameters: N, initial state vector H) are used to achieve a linear combination of neighbor information and its own features, and to generate a node feature update vector U after one aggregation. Furthermore, the nonlinear activation function ReLU (parameter: U) is used to achieve a nonlinear mapping of updated node features and generate an enhanced node state vector E. Furthermore, through the residual connection mechanism (parameters: E, H), structural fusion is achieved by preserving the original fractal features while introducing neighbor information, and the final updated node feature vector F is generated; By using weighted neighbor aggregation and nonlinear mapping, the initial state vector of the previous step is transformed into an updated node feature vector containing causal adjacency information, thereby realizing the dynamic attribution capability of fractal features on cross-scale causal knowledge graphs. For example, in one embodiment, the initial state vector H output in step S4.3 is a 9-dimensional fractal feature, with each feature initialized to a node at three different levels in the knowledge graph. The weight matrix W is set according to the confidence weights calculated in step S3.5; in this example, W is a 9×9 matrix with elements ranging from 0.15 to 0.92. The degree matrix D is obtained by calculating the sum of the weights of the causal edges associated with each node and is used for neighbor influence normalization. The formula for calculating the normalization weighting function is as follows:

[0020] in, For degree matrix, This is the weight matrix. The inverse of the degree matrix is ​​used to normalize the influence of neighbor features. The formula for calculating the graph convolutional layer is:

[0021] in, Update the node feature vector after one aggregation. Let be the initial state vector. The neighbor influence coefficient matrix, This indicates the introduction of the residual mechanism. In this embodiment, the ReLU activation function performs an element-wise nonlinear transformation on U, suppressing negative values ​​and preserving the positive values ​​to obtain E. Subsequently, E and H are residually fused to obtain F. After this layer of processing, the node features, while maintaining the fractal characteristics, absorb the weighted information of associated causal entities, significantly improving the hierarchical correlation of the attribution distribution. The node state vector exhibits stronger physical traceability in the downstream multi-layer information propagation. S4.5: Based on the updated node feature vectors and the topological structure data of the cross-scale causal knowledge graph, an attribution distribution vector is generated through multi-layer information propagation of a lightweight graph neural network, and the attribution distribution of each fractal feature in the cross-scale causal knowledge graph is output.

[0022] Step S5: Based on the attribution distribution vector output in step S4 and the cross-scale causal knowledge graph constructed in step S3, the causal path confidence backpropagation algorithm is executed. An improved SHAP value satisfying the causal graph transitive closure constraint is used to calculate the contribution of each causal path to the predicted crosslinking degree. Specifically, this includes: S5.1: Based on the structural topology data of the cross-scale causal knowledge graph constructed in step S3, a causal path confidence backpropagation algorithm is constructed. This algorithm defines the path selection mechanism and backpropagation rules. The set of causal edge confidence weights and the hierarchical relationship matrix of the cross-scale causal knowledge graph are input. By aggregating the weights of experimental data, molecular dynamics simulations, or expert experience source types labeled with causal edge source types, a path confidence threshold screening function is generated. The causal path confidence backpropagation algorithm definition file is output, which includes the path selection rule with the highest confidence and the backpropagation termination condition, providing an algorithmic basis for subsequent path selection. Based on the structural topology data of the cross-scale causal knowledge graph constructed in step S3, the path set is initially generated using the graph traversal analysis method (parameters: node hierarchy relation matrix, causal edge confidence weight set); Furthermore, through the causal edge weight aggregation algorithm (parameter: set of source type weight coefficients, including experimental data weights)... Molecular dynamics simulation weights Weight of expert experience This allows for the calculation of the global confidence value for each path, and the obtaining of the comprehensive confidence quantification result for each path. Furthermore, a path confidence threshold filtering function is used to generate the filter (parameter: confidence threshold). The system uses a weight normalization constant K to construct a high-confidence path filtering function and generates a function form with an adjustable threshold for subsequent filtering actions. Furthermore, a backpropagation rule generation algorithm (parameters: path topology sequence, edge weight decay factor β, backtracking depth limit dmax) is applied to perform layer-by-layer backpropagation calculation of path confidence and generate the cumulative confidence value for each node; in this process, the path confidence... The following formula can be used for calculation:

[0023] in, Let be the weight value of the causal edge from layer i to layer j in the path. This represents the total number of levels in the path. Furthermore, an algorithm is defined through a path selection mechanism to combine the confidence ranking results with a threshold filtering function to generate a set of high-confidence paths that meet the conditions, and outputs a path selection table verified by backpropagation rules. By using the causal path confidence backpropagation algorithm, the structural topology data and weight set of the previous step are transformed into executable path selection rules and backtracking termination conditions, thereby achieving the structured output of high-confidence path sets. For example, in an ultra-high voltage cable insulation material evaluation scenario, in the causal edge weight set data of the input knowledge graph, the edge weight from experimental data sources is set to 0.85, the edge weight from molecular dynamics simulation sources is set to 0.75, and the edge weight from expert experience sources is set to 0.65. The hierarchical relationship matrix represents a three-layer causal path structure. When executing the edge weight aggregation algorithm, the parameters... =0.5、 =0.3、 =0.2, the overall confidence level of a certain path is calculated. =0.812. When constructing the path confidence threshold filtering function, set... =0.8, filter out the set of paths with a confidence level ≥ 0.8. Apply the backpropagation rule generation algorithm, setting a decay factor. =0.95, backtracking depth limit =3, calculate the cumulative confidence of nodes by backpropagating layer by layer along the three-layer structure, and obtain a set of 3 high-confidence causal paths. The output path selection table includes path identifier, node sequence and cumulative confidence, which provides input basis for path screening and contribution calculation in S5.3; S5.2: Based on the transitive closure constraints of the cross-scale causal knowledge graph constructed in step S3, construct an improved SHAP value calculation module; input the transitive closure constraint equations of the causal graph and the basic framework of the standard SHAP value, use the graph topological consistency constraints to correct the standard SHAP value, and generate a contribution calculation kernel function that satisfies the transitive closure constraints; output the improved SHAP value calculation module, which includes constrained contribution calculation rules and an error propagation interval mapping table to ensure that the contribution calculation maintains logical consistency with the causal graph structure; Based on the transitive closure constraints of the cross-scale causal knowledge graph constructed in step S3, a graph constraint parsing algorithm (parameters: node hierarchy relation matrix, causal edge weight set) is used to realize the structured expression of the transitive closure equation system and generate a set of constraint parameters that can be used for contribution calculation. Furthermore, by using the standard SHAP value calculation framework (parameters: sample feature vector, model predicted value), the unconstrained contribution of features to the predicted value is calculated, and the original SHAP value vector is obtained. Furthermore, by utilizing the graph topology consistency constraint correction algorithm (parameters: transitive closure equation system, original SHAP value vector), path-by-path correction processing of the original SHAP values ​​is achieved, and a set of constrained SHAP values ​​that satisfies the causal hierarchical transitive closure condition is generated. Furthermore, a constrained contribution kernel function construction method (parameters: constrained SHAP value set, causal edge weight distribution) is adopted to define the formula of the contribution kernel function, specifically including:

[0024] in, Represents the set of constrained SHAP values. The value of the path, This indicates the weight of the causal edge corresponding to the path. For the first The identifier of the path; Furthermore, the error propagation interval mapping algorithm (parameters: constrained SHAP value set, path error coefficient matrix) is used to calculate the error interval of each path contribution and generate an error propagation interval mapping table. By using the improved SHAP value calculation module, the transitive closure constraint conditions of the previous step are combined with the standard SHAP value framework and transformed into path contribution data and error range that satisfy the logical consistency of the causal graph, so as to achieve the expected technical effect of quantifiable output of path sensitivity. For example, in an embodiment of constructing an improved SHAP value calculation module, the input condition is a knowledge graph of a certain ultra-high voltage cable insulation material, whose node hierarchy relation matrix is ​​12×12, and the causal edge weight set ranges from 0.15 to 0.92. The transitive closure equation system is generated by a graph constraint parsing algorithm and contains 48 constraint relations. The feature vector input of the standard SHAP value calculation framework has a dimension of 9, corresponding to the fractal feature set in step S2, and the model predicts a crosslinking degree of 78.3. The original SHAP value vector has a length of 9 and a value in the range of -0.012 to 0.087. The topology consistency constraint correction algorithm uses the transitive closure equation system as the correction basis to adjust the three paths in the original SHAP value that do not satisfy the hierarchical transitivity to the consistency range of 0.025 to 0.033. The contribution kernel function is calculated according to the formula, and the contribution of the i-th path is... when The values ​​are 0.025, 0.033, and 0.029 respectively. When the scalar values ​​are 0.88, 0.75, and 0.81, the calculation results are as follows: The output is approximately 0.029. The error coefficient recorded in the error propagation interval mapping table on this path is 0.0044. After error propagation calculation, the final contribution interval of this path is 0.029 ± 0.0044, ensuring the interpretability and structural consistency of the evaluation results. S5.3: Apply the causal path confidence backpropagation algorithm constructed in step S5.1 to the attribution distribution vector output in step S4 for path selection processing to filter the top 3 causal paths with the highest confidence; perform a confidence threshold filtering operation based on the node activation intensity sequence of the attribution distribution vector to generate a set of high-confidence causal paths; perform a reverse tracing operation along the hierarchical relationship of the knowledge graph to backtrack to the original fractal feature nodes; generate a causal path identifier sequence and a feature attribution mapping relationship table as the input basis for contribution calculation; Based on the attribution distribution vector output in step S4, the causal path confidence backpropagation algorithm (parameters: path confidence threshold filtering function, hierarchical relationship matrix) constructed in step S5.1 is used to realize the path filtering function for each attribution node in the cross-scale causal knowledge graph. Furthermore, by using the node activation intensity sequence analysis method of attribution distribution vector (parameter: node activation intensity threshold), the importance of nodes is quantitatively evaluated, and a preliminary high-confidence causal path index set is obtained. Furthermore, a path confidence threshold filtering algorithm (parameters: confidence ranking rule, number of filters = 3) is adopted to extract the set of high confidence paths and generate the top three causal path identification data with the highest confidence. Furthermore, by using the knowledge graph hierarchical relationship reverse tracing method (parameter: process-structure-chemistry hierarchical relationship matrix), the mapping association of the selected high-confidence causal path is reversed along the graph back to the original fractal feature node, and the back-tracing mapping relationship from the path to the fractal feature is generated; Furthermore, a feature attribution mapping generation algorithm (parameters: node ID, causal edge weight set) is used to construct a structured mapping table between causal path identifier sequences and fractal features; Through the above processing method, the attribution distribution vector of the previous step is transformed into a causal path identifier sequence and a feature attribution mapping relationship table, so as to provide structured and computable input data for the subsequent improved SHAP value contribution calculation module. For example, in the online evaluation scenario of ultra-high voltage cable insulation materials, the attribution distribution vector length is 9, corresponding to 3 dimensions for each of the 3 types of fractal features; the node activation intensity threshold is set to 0.65, the path confidence threshold is set to 0.72, and the number of filters is fixed at 3. First, the activation intensity sequence of the 9 attribution nodes is calculated, and the node importance index is calculated using an exponentially weighted smoothing function. ,in Let i be the weight of the i-th node. This is the attribution value. Nodes with an importance index ≥ 0.65 are selected to form a preliminary path set. A path confidence threshold filtering function is then applied. ,in Let j be the confidence weight of path segment j. For segment relevance coefficients, paths with C ≥ 0.72 were selected, and the top three were ranked. A reverse lookup was performed along the three-layer relationship matrix of the knowledge graph (process → structure → chemistry) to obtain the original fractal feature IDs corresponding to the three paths (e.g., box dimension - process temperature gradient → structural crystallinity → proportion of polysulfide bonds). Finally, a causal path identifier sequence (path index, node sequence) and a feature attribution mapping table (feature dimension, mapping path, causal edge weight) were generated for subsequent contribution calculation. Verification results show that the selected paths all have significant physical mechanism support and improve the stability of the subsequent explanation model. S5.4: Based on the causal path identifier sequence generated in step S5.3 and the improved SHAP value calculation module constructed in step S5.2, perform causal path contribution calculation processing; input the causal path identifier sequence, feature attribution mapping relationship table and crosslinking degree prediction benchmark data, apply the constrained contribution calculation kernel function of the improved SHAP value calculation module to perform path sensitivity analysis; generate a set of contribution values ​​of each causal path to the crosslinking degree prediction value, including path contribution quantification index and error propagation interval parameters; Based on the causal path identifier sequence generated in step S5.3 and the improved SHAP value calculation module constructed in step S5.2, the path sensitivity analysis function is realized by using the constrained contribution calculation kernel function (parameters: transitive closure constraint equation set, characteristic attribution mapping relationship table, and crosslinking degree prediction value benchmark). Furthermore, a weighted combination method of predicting residuals using node attribution strength and crosslinking degree (parameter: residual weight coefficient) is employed. Path confidence weight This allows for the initial contribution estimation of a single causal path and the generation of a sequence of candidate contribution values. Furthermore, the graph topology consistency constraint function (parameters: graph hierarchy relation matrix L, edge weight matrix W) embedded in the improved SHAP value calculation module is applied to realize the structured correction of candidate contribution values ​​and generate a set of consistent contribution values ​​that satisfy cross-scale causal logic. Furthermore, based on the error propagation interval mapping table (parameter: path length) Node variance ), calculate the error propagation amplitude of each contribution value It generates path analysis records that include contribution metrics and corresponding error ranges; By using the constrained kernel function processing method described above, the causal path identification sequence from the previous step is transformed into contribution data that can be used to evaluate accuracy and interpretability, thereby improving the robustness and reliability of the crosslinking degree prediction model under multiple working conditions. For example, in an evaluation sample of a continuous vulcanization production line, the three causal paths with the highest confidence levels are selected and labeled as P1, P2, and P3, respectively. Let the feature attribution mapping table show that P1 has a Hurst index of 0.82, P2 has a box dimension of 1.45, and P3 has a... The value is 0.27, the predicted degree of crosslinking is based on a baseline of 78.3, and the corresponding residual is... The initial contribution is set to 1.0. A constrained contribution kernel function is used to calculate the initial contribution of P1:

[0025] in =0.4, =1.0, =0.6, =0.82, and the initial contribution is calculated to be 0.87. The initial values ​​for P2 and P3 are calculated using the same method, resulting in 0.91 and 0.76 respectively. A graph topology consistency constraint function is introduced. The initial values ​​were corrected so that the contributions of the three paths were adjusted to 0.85, 0.89, and 0.74, respectively. Based on the error propagation interval mapping table, the following calculations were performed. The values ​​are 0.03, 0.04, and 0.02, respectively. The final output contribution set is {P1:[0.85,±0.03],P2:[0.89,±0.04],P3:[0.74,±0.02]}. The physical mechanism and fractal feature sensitivity of each path are marked in the interpretable report to achieve logical tracing of the crosslinking degree prediction value and improve its credibility. S5.5: Format the set of contribution values ​​generated in step S5.4 to generate structured contribution output data; based on the path contribution quantification index and error propagation interval parameter of the contribution value set, perform data standardization to generate a standardized causal path contribution dataset, which includes path identifier, contribution value, error propagation interval and physical mechanism description, for use in generating the interpretable evaluation report in step S6.

[0026] Step S6: Map the contribution obtained in step S5 to the cross-scale causal knowledge graph, construct a three-dimensional visualization coordinate framework, label the measured fractal values ​​and error propagation intervals based on the three-dimensional visualization coordinate framework, and integrate them with the predicted crosslinking degree to generate an interpretable evaluation report, including the predicted crosslinking degree and a three-dimensional visualization causal path diagram, where the X-axis represents the process → structure → chemical causal hierarchy, the Y-axis represents the fractal feature sensitivity ranking, and the Z-axis represents the path confidence. Each path is labeled with the measured fractal value and error propagation interval. Specifically, this includes: S6.1: Perform structured reading and processing on the contribution values ​​and path confidence data of each causal path output by S5 to generate a standardized causal path dataset; S6.2: Based on the standardized causal path dataset generated in S6.1 and the cross-scale causal knowledge graph constructed in S3, X-axis mapping is performed on the process parameter level, structural parameter level and chemical parameter level, Y-axis mapping is performed on the fractal feature sensitivity ranking, and Z-axis mapping is performed on the path confidence to construct a three-dimensional visualization coordinate framework. Based on the standardized causal path dataset generated by S6.1, a hierarchical node mapping algorithm (parameters: process-level coding rules, structure-level coding rules, and chemical-level coding rules) is used to realize the mapping function of causal path nodes to the three-dimensional coordinate X-axis, and the causal parameters of different levels are summarized into three major categories of coordinate indices: process, structure, and chemistry. Furthermore, by using the fractal feature sensitivity ranking algorithm (parameters: feature sensitivity evaluation matrix, ranking threshold 0.05), the fractal features involved in the causal path are quantitatively ranked and mapped on the Y-axis, and a fractal feature sensitivity sequence data table is obtained. Furthermore, a confidence level numerical normalization method (parameters: normalization interval [0,1], minimum confidence level cutoff value 0.1) is used to perform numerical transformation on the path confidence in the standardized causal path dataset, generating a set of confidence coordinate values ​​adapted to the Z-axis; Furthermore, based on the three-dimensional coordinate construction module (parameters: X-axis hierarchical index table, Y-axis sensitivity sequence, Z-axis confidence coordinate value set), coordinate point fusion processing is performed to combine the process level, fractal feature sensitivity ranking value and confidence coordinate value of each causal path to generate a three-dimensional spatial positioning matrix; The spatial positioning matrix is ​​transformed into three-dimensional structural data for subsequent visualization rendering through a three-dimensional coordinate frame generation algorithm, thereby achieving the expected technical effect of building a three-dimensional visualization coordinate frame. For example, in an evaluation path for ultra-high voltage cable insulation materials, the process level code is set to 0, the structural level code to 1, and the chemical level code to 2, forming an X-axis mapping index table. Fractal feature sensitivity ranking is performed from high to low based on the improved SHAP contribution value of each feature in the sensitivity evaluation matrix. The ranking value corresponding to the Hurst exponent eigenvalue sensitivity of 0.78 is set as the Y-axis coordinate 0, the box dimension eigenvalue sensitivity of 0.65 corresponds to the ranking value 1, and the generalized fractal dimension spectrum width eigenvalue sensitivity of 0.53 corresponds to the ranking value 2. In the confidence mapping process, the original path confidence is 0.87, which is normalized and retained as the Z-axis coordinate value of 0.87. X=1 (structural level), Y=0 (highest Hurst exponent sensitivity), and Z=0.87 (high confidence) are combined into a three-dimensional coordinate point and added to the three-dimensional spatial positioning matrix. The above process is repeated for multiple paths, eventually forming a visualization framework containing N three-dimensional coordinates. In the subsequent generation of dynamic causal path visualization primitives in S6.3, this framework can be directly called to complete spatial positioning and rendering, realizing the construction of an interpretable and evaluable visualization foundation. S6.3: Using the three-dimensional visualization coordinate framework constructed in S6.2, spatial positioning and annotation processing is performed on the measured fractal values ​​and error propagation intervals corresponding to each causal path to generate dynamic causal path visualization primitives; S6.4: Integrate the dynamic causal path visualization primitives generated by S6.3 with the crosslinking degree prediction values ​​output by S5, and perform ± error range annotation on the crosslinking degree prediction values ​​to form the core content of the evaluation report; The dynamic causal path visualization primitives generated in step S6.3 are integrated with the spatial data of the crosslinking degree prediction values ​​output in step S5 by using a coordinate overlay and fusion algorithm (parameters: three-dimensional coordinate frame, path identifier sequence, measured fractal value, error propagation interval). Furthermore, by using the error range labeling method (parameters: predicted value, upper and lower limits of error propagation interval), the predicted crosslinking degree is presented in a range-based manner in the 3D visualization scene, and predicted value primitives with numerical boundary information are obtained. Furthermore, by utilizing a data synchronization rendering algorithm (parameters: path primitive attribute set, predicted value primitive attribute set), the color mapping consistency between predicted value primitives and dynamic causal path primitives is achieved, and core visualization content with unified visual encoding is generated. Furthermore, numerical association annotation processing (parameters: predicted value, corresponding path contribution, fractal feature sensitivity ranking) is adopted to realize the quantitative association display between the crosslinking degree prediction value and the main causal path, and generate a data linkage annotation matrix; By using a primitive combination algorithm based on spatial layout optimization, the primitive fusion result of the previous step is transformed into core visualization information containing cross-linking degree prediction value and error range, thereby achieving the core display effect of an interpretable evaluation report. For example, in the online evaluation scenario of a continuous vulcanization production line for ultra-high voltage cables, the input crosslinking degree prediction value is 78.3, with an error propagation range of ±1.2. A coordinate overlay fusion algorithm is used to map the X-axis to the three-level causal hierarchy of process-structure-chemistry, the Y-axis to the fractal feature sensitivity ranking value (range 0.15 to 0.87), and the Z-axis to the path confidence value (range 0.65 to 0.94), overlaying dynamic primitive information containing three high-confidence causal paths. Using an error range annotation method, the upper limit of the prediction value (78.3 + 1.2) and the lower limit of the prediction value (78.3 - 1.2) are calculated respectively, and the numerical range is presented as a semi-transparent color band in the 3D visualization scene. A data synchronization rendering algorithm is used to ensure that the color coding of the crosslinking degree prediction value primitive is consistent with the color coding of the high-confidence causal path primitive to enhance visual relevance. Through a data linkage annotation matrix, the crosslinking degree prediction value, path contribution (range 0.23 to 0.41), and corresponding fractal feature sensitivity ranking are quantitatively correlated and displayed. In this embodiment, the core content of the report, after being visualized, has been verified to significantly improve the intuitive understanding of the prediction formation mechanism among operations and maintenance personnel, making it easier to make process optimization decisions based on the report during production line operation; S6.5: The core content of the evaluation report formed in S6.4 is documented and encapsulated to generate an interpretable evaluation report containing crosslinking degree prediction values ​​and a three-dimensional visualized causal path diagram, so as to output the final decision support document.

[0027] Step S7: When the evaluation error of the new production line sample exceeds a preset threshold of 1.5%, the causal graph incremental update module based on the contribution threshold in step S5 is triggered. Only causal edge association nodes with a contribution greater than 0.15 are fine-tuned with small samples, while the remaining graph parameters are frozen to maintain knowledge stability. Specifically, this includes: S7.1: Analyze and process the causal path contribution vector and preset contribution threshold output in step S5, determine the set of high-impact nodes based on the contribution screening algorithm, and design a small sample learning fine-tuning mechanism to construct the causal graph incremental update module. S7.2: Obtain the real-time evaluation error of the new production line sample, and perform a threshold comparison operation on the evaluation error to determine whether it exceeds the preset evaluation error threshold of 1.5%; S7.3: When the threshold comparison operation output trigger signal is true, the causal graph incremental update module is called to perform contribution threshold filtering based on the causal path contribution calculated in step S5, so as to filter out the set of causal edge associated nodes with contribution greater than the preset contribution threshold of 0.15. S7.4: For each node in the set of causal edge-related nodes, apply a few-sample fine-tuning algorithm to optimize the parameters in order to update the weight parameters of the causal edges associated with the node. S7.5: Freeze all node parameters in the causal knowledge graph except for the set of nodes associated with causal edges, and output the updated causal knowledge graph to maintain knowledge stability.

[0028] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0029] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and rules of the present invention should be included within the scope of protection of the present invention.

Claims

1. An online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables, characterized in that, Includes the following steps: S1: Collect online ultrasonic reflection signals and synchronous process parameters of ultra-high voltage cable insulation material on the continuous vulcanization production line to obtain raw signal inputs with different operating conditions. S2: Perform variational mode decomposition preprocessing on the online ultrasonic reflection signal to separate the intrinsic mode functions, and calculate the rescaled range analysis Hurst exponent, box dimension and generalized fractal dimension spectral width of each intrinsic mode function to generate a fractal feature set; S3: Based on the causal entities of cable insulation materials, a cross-scale causal knowledge graph is constructed, in which the degree of cross-linking is the top-level target node and three layers of causal relationships are extended downwards. Each causal edge is labeled with the source type of experimental data, molecular dynamics simulation or expert experience and the confidence weight. S4: Input the fractal feature set into the causal-aware fractal embedding module of the cross-scale causal knowledge graph design, and output the attribution distribution vector of each fractal feature in the causal graph; S5: Based on the attribution distribution vector and the cross-scale causal knowledge graph, and combining the causal path confidence backpropagation algorithm with the constructed improved SHAP value calculation module, calculate the contribution of each causal path to the crosslinking degree prediction value. S6: Map the contribution to the cross-scale causal knowledge graph, construct a three-dimensional visualization coordinate framework, label the measured fractal values ​​and error propagation intervals based on the three-dimensional visualization coordinate framework, and integrate them with the predicted cross-linking degree to generate an interpretable evaluation report.

2. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 1, characterized in that, Following step S6, the following is also included: S7: When the evaluation error of the new production line sample is greater than the preset threshold of 1.5%, the incremental update module of the causal graph based on the contribution threshold in step S5 is triggered. Only the causal edge association nodes with a contribution greater than 0.15 are fine-tuned with small samples, and the remaining graph parameters are frozen to maintain knowledge stability.

3. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 1, characterized in that, In the online ultrasonic reflection signal acquisition, the ultrasonic signal sampling rate is not less than 20MHz and covers the 0.5–15MHz frequency band. The process parameters include temperature gradient, traction speed and irradiation dose.

4. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 1, characterized in that, The variational mode decomposition preprocessing includes using an adaptive center frequency optimized variational mode decomposition algorithm to separate the online ultrasonic reflection signal into 6 intrinsic mode functions for each 10ms sliding window. The initial distribution of the adaptive center frequency covers 0.5–15MHz, the iteration step size is 0.1MHz, and the mode bandwidth converges to less than 0.2MHz.

5. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 1, characterized in that, Step S3 specifically includes: Based on the causal entity data of cable insulation materials, the bottom node set of the knowledge graph is defined, and the cross-linking degree is used as the top target node to initialize the knowledge graph structure, forming the basic node layer of the cross-scale causal knowledge graph. Based on experimental data of macroscopic process parameters, a first-level causal relationship is constructed, which associates macroscopic process parameters with molecular chain mobility, generates a first-level causal edge set, and labels the source type as experimental data and initial confidence weight. Based on experimental data of mesoscopic structural parameters, a second-layer causal relationship is constructed, which associates mesoscopic structural parameters with the topological parameters of the cross-linked network to generate a set of second-layer causal edges, and labels the source type as experimental data and confidence weight. Based on experimental data of microscopic chemical parameters, a third-level causal relationship is constructed, which associates microscopic chemical parameters with the chemical type of crosslinking points and the spatial heterogeneity of crosslinking points, generating a set of third-level causal edges, and labeling the source type as experimental data and confidence weight. Based on the set of all causal edges in the cross-scale causal knowledge graph, source type labeling and confidence weight calculation are performed to generate a complete cross-scale causal knowledge graph.

6. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 5, characterized in that, The causal entity data includes molecular chain entanglement density, spatial distribution of crosslinking points, ratio of crystalline to amorphous regions, and interface states of the filler matrix.

7. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 1, characterized in that, Step S4 specifically includes: Based on the cross-scale causal knowledge graph constructed in step S3, a causal perception fractal embedding module is designed. The fractal feature set generated in step S2 is input into the causal-aware fractal embedding module to generate a feature embedding representation. The feature embedding representation is subjected to node initialization processing, which maps the fractal features to the initial state vectors of the corresponding nodes in the cross-scale causal knowledge graph; Based on the causal edge weights of the cross-scale causal knowledge graph, a graph neural network aggregation operation is performed on the initial state vector to calculate the weighted sum of neighbor information and obtain the updated node feature vector. Based on the updated node feature vectors and the topological structure data of the cross-scale causal knowledge graph, an attribution distribution vector is generated through multi-layer information propagation, and the attribution distribution of each fractal feature in the cross-scale causal knowledge graph is output.

8. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 7, characterized in that, The causal perception fractal embedding module adopts a graph neural network architecture with 3 layers, 64 hidden units per layer, and ReLU activation function. Its aggregation operation is constrained by the causal edge weights in the cross-scale causal knowledge graph.

9. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 1, characterized in that, Step S5 specifically includes: Based on the structural topology data of the cross-scale causal knowledge graph constructed in step S3, a backpropagation algorithm for causal path confidence is constructed. The set of causal edge confidence weights and the hierarchical relationship matrix of the cross-scale causal knowledge graph are input. By aggregating the experimental data, molecular dynamics simulation or expert experience source type weights labeled with causal edge source type, a path confidence threshold filtering function is generated. Based on the transitive closure constraint of the cross-scale causal knowledge graph, an improved SHAP value calculation module is constructed. The transitive closure constraint equations of the causal graph and the standard SHAP value basic framework are input. The standard SHAP value is modified using the graph topology consistency constraint to generate a contribution calculation kernel function that satisfies the transitive closure constraint. For the attribution distribution vector output in step S4, the causal path confidence backpropagation algorithm is applied to perform path selection processing, and the top 3 causal paths with the highest confidence are selected. Based on the node activation intensity sequence of the attribution distribution vector, a confidence threshold filtering operation is performed to generate a set of high-confidence causal paths. A reverse tracing operation is performed along the hierarchical relationship of the knowledge graph to backtrack to the original fractal feature nodes, and a causal path identification sequence and a feature attribution mapping relationship table are generated. Based on the causal path identification sequence and the improved SHAP value calculation module, the causal path contribution calculation process is performed. The causal path identification sequence, the feature attribution mapping relationship table, and the crosslinking degree prediction value benchmark data are input. The constrained contribution calculation kernel function of the improved SHAP value calculation module is applied to perform path sensitivity analysis and generate a set of contribution values ​​of each causal path to the crosslinking degree prediction value. The set of contribution values ​​is formatted to generate structured contribution output data. Based on the path contribution quantification index and error propagation interval parameter of the set of contribution values, data standardization is performed to generate a standardized causal path contribution dataset.

10. The online ultrasonic evaluation method for the crosslinking degree of insulation material in ultra-high voltage cables according to claim 9, characterized in that, The standardized causal path contribution dataset includes path identifiers, contribution values, error propagation intervals, and descriptions of the physical mechanisms.

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