A steel rail white layer thickness quantitative inversion method based on parameter constraint simulation and ensemble learning
By constructing a thickness-signal mapping database based on parameter-constrained simulation and ensemble learning, multi-dimensional features are extracted. The Stacking ensemble learning framework and meta-learning mechanism are adopted to solve the problems of low detection accuracy and easy signal confusion in rail white layer detection, and to achieve efficient quantitative inversion of white layer thickness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2026-04-15
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies suffer from low accuracy in detecting white residue on rails, easily confused signals, poor generalization ability, and insufficient interpretability, making efficient online detection impossible.
By using a method based on parameter-constrained simulation and ensemble learning, a thickness-signal mapping database is constructed, multi-dimensional features are extracted, and a Stacking ensemble learning framework and meta-learning mechanism are adopted, combined with a dual-output network to achieve quantitative inversion of white layer thickness.
It significantly improves the accuracy and generalization ability of white layer thickness detection, can quickly adapt to new circuits, reduces the risk of signal confusion and misjudgment, and achieves efficient online detection.
Smart Images
Figure CN122154487A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of non-destructive testing and intelligent assessment technology for transportation, and in particular to a quantitative inversion method for the thickness of the white layer of rails based on parameter-constrained simulation and integrated learning. Background Technology
[0002] Under the rolling contact fatigue of wheel and rail, a martensitic white layer with a thickness of only 50-300 micrometers forms on the surface of the rail. This structure is characterized by high hardness and high brittleness, and is an important source of fatigue cracks in rails. The typical characteristic of the white layer is its extremely thin thickness, usually on the order of 50-300 micrometers, and its existence on the surface of the rail. Currently, the main detection technologies for the white layer include: metallographic analysis: through cutting, sampling, mounting, grinding, polishing, and etching followed by microscopic observation, which has high precision but is highly destructive and cannot be used for online detection; ultrasonic testing: using high-frequency ultrasound to measure changes in surface wave velocity to estimate the thickness of the white layer, but because the thickness of the white layer is much smaller than the wavelength of the ultrasonic wave, there is a significant surface blind zone; eddy current / magnetic flux leakage detection: based on the magnetic field disturbance caused by the difference in magnetic permeability between the white layer and the matrix material, it has relatively high sensitivity, but the signal interpretation is difficult. Summary of the Invention
[0003] Purpose of the invention: The purpose of this invention is to provide a quantitative inversion method for the thickness of the white layer of rails based on parameter-constrained simulation and ensemble learning. Through an integrated technical framework of physical constraint simulation, multi-source feature extraction, ensemble learning regression, meta-learning transfer, and joint discrimination, it solves the problems of low detection accuracy, easy signal confusion, poor generalization ability, and insufficient interpretability in the existing technology.
[0004] Technical solution: The present invention provides a quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning, comprising the following steps:
[0005] Step 1: Based on the inherent physical correlation between the material magnetic property parameters of the white layer of the rail, determine the constraint relationship between the parameters, and sample the magnetic property parameters according to the constraint relationship to generate multiple sets of magnetic property parameter combinations; based on each set of magnetic property parameter combinations, simulate and calculate the leakage magnetic signal response of the white layer at different thicknesses, and construct a thickness-signal mapping database;
[0006] Step 2: Extract multi-dimensional features from the measured magnetic flux leakage signal to characterize the change in white layer thickness. The multi-dimensional features include time-domain morphological features reflecting the signal amplitude and waveform shape, differential features reflecting the signal change rate, and spatial distribution features reflecting the spatial distribution characteristics of magnetic field disturbance.
[0007] Step 3: Construct an ensemble learning regression model containing a first layer and a second layer. The first layer contains multiple heterogeneous base learners, which are used to learn the mapping relationship between the multi-dimensional features and the white layer thickness respectively. The second layer contains a meta-learner, which is used to fuse the output results of multiple base learners to obtain the final white layer thickness prediction value.
[0008] Step 4: Employ a model-independent meta-learning mechanism to pre-train an initial ensemble learning regression model on the thickness-signal mapping database. This enables the initial ensemble learning regression model to quickly adapt to the task of predicting the thickness of the rail white layer under new lines or new working conditions through a limited number of gradient updates using a small number of measured labeled samples.
[0009] Step 5: Construct a dual-output network with a shared feature extraction layer. The dual-output network includes a regression branch for predicting the thickness of the white layer and a classification branch for identifying the type of signal source. The two branches are optimized simultaneously through a joint loss function to achieve simultaneous discrimination and thickness inversion of the white layer signal and the crack signal.
[0010] Furthermore, in step 1, the magnetic characteristic parameters include coercivity, saturation magnetic induction, remanence, and relative permeability; the constraint relationships include that coercivity is inversely proportional to relative permeability, and remanence is directly proportional to saturation magnetic induction.
[0011] Furthermore, in step 2, the time-domain morphological features include the peak-to-peak value, the ratio of positive to negative peak area, and the signal energy; the differential features include the maximum value of the first derivative of the signal and the slope at the zero crossing point; and the spatial distribution features include the spatial correlation coefficient between signals from the multi-sensor array.
[0012] Furthermore, in step 3, in the ensemble learning regression model, the first layer of multiple heterogeneous base learners includes a gradient boosting decision tree for capturing nonlinear interactions between features, a kernel ridge regression for nonlinear mapping, and a lightweight multilayer perceptron; the second layer of meta-learners is a Bayesian ridge regression, which is used to automatically determine the fusion weights of the outputs of each base learner.
[0013] Furthermore, in step 4, the model-independent meta-learning mechanism obtains initial model parameters that can quickly adapt to new tasks by performing meta-training on meta-tasks constructed from multiple simulation data. For new tasks, only a small number of labeled samples are needed, and the model parameters can be updated through a few steps of gradient descent, thus achieving rapid adaptation to the task of predicting the thickness of the white layer of rails on new lines.
[0014] Furthermore, in step 5, the shared feature extraction layer of the dual-output network is used to extract common features of the leakage magnetic field signal; the regression branch is used to output a thickness prediction value when the classification branch determines that the signal source is a white layer; the classification branch is used to output the probability that the signal source belongs to a white layer, crack, or other type.
[0015] Furthermore, in step 5, the joint loss function is composed of a weighted sum of regression loss, which measures the error in thickness prediction, and classification loss, which measures the error in type discrimination. By optimizing this joint loss function, the network can learn both thickness inversion and type discrimination tasks simultaneously.
[0016] Furthermore, step 5 also includes decision fusion: when the white layer probability output by the classification branch is higher than a preset threshold, the thickness value output by the regression branch is used as the final result; when the crack probability output by the classification branch is higher than a preset threshold, crack quantification assessment is triggered; when the probabilities of all categories are lower than the preset threshold, a label requiring manual review is output.
[0017] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:
[0018] (1) In the simulation stage, this invention establishes physical constraints between coercivity, saturation magnetic induction, remanence, and relative permeability, reducing the original highly free four-dimensional magnetic parameter sampling to two-dimensional principal variable sampling. This makes the generated simulation data more consistent with the real physical properties of white-layer materials and avoids interference from invalid parameter combinations on model training. This invention extracts multi-dimensional features covering temporal morphology, differential characteristics, and spatial distribution from measured magnetic leakage signals, significantly enhancing the sensitivity to sub-millimeter thickness variations. Finally, through the Stacking ensemble learning framework, the advantages of three heterogeneous base learners—gradient boosting decision tree, kernel ridge regression, and lightweight multilayer perceptron—are integrated, and the fusion weights are automatically optimized by Bayesian ridge regression, resulting in a significant advantage in thickness inversion accuracy compared to traditional peak fitting and single-model regression methods (mean absolute). Attached Figure Description
[0019] Figure 1 This is a flowchart of the present invention;
[0020] Figure 2 This is a schematic diagram illustrating the collaborative operation of Stacking ensemble learning and MAML transfer learning in this invention. Detailed Implementation
[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0022] like Figure 1 As shown, an embodiment of the present invention provides a quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning, comprising the following steps:
[0023] Step S1: Jiles-Atherton simulation modeling based on physical parameter constraints: Input: range of white layer magnetic property parameters, range of white layer thickness. This invention uses the AC / DC module in the finite element simulation software MAXWELL to establish a two-dimensional axisymmetric model for detecting magnetic flux leakage in the white layer of the rail. The model geometry is set as follows: the rail substrate area is 20mm × 10mm (length × height), the white layer area is located at the center of the upper surface of the rail substrate, with a width of 5mm and a thickness δ that is variable (50-300μm). Material property settings: the rail substrate uses a nonlinear ferromagnetic material, and its BH curve is obtained through actual measurement; the magnetic property parameters of the white layer area are assigned values according to the range defined in step S1-1. Boundary condition settings: magnetic insulation boundary conditions are applied around the model (…). A lift-off surface is set 1 mm above the white layer on the upper surface to accommodate the sensor. Solver settings: A steady-state solver is used, with a relative tolerance set to... The magnetization source was achieved by applying a background magnetic field, with the magnetic field strength set to 5000 A / m. Mesh generation: a refined mesh with a maximum element size of 2 μm was used in the white layer region, while a free triangular mesh with a maximum element size of 0.2 mm was used in the matrix region to ensure computational accuracy.
[0024] Includes the following steps:
[0025] S1-1 (Determination of the domain of four-dimensional magnetic parameters): Based on the physical properties of the white martensite structure, the value ranges of four key magnetic parameters are defined:
[0026]
[0027] S1-2 (Physical Constraint Modeling): Establishing physical constraint relationships between parameters through experimental measurements and theoretical analysis.
[0028]
[0029] in The remanence coefficient is related to the martensite content in the white layer. Based on the above constraints, the original four-dimensional independent parameter sampling is transformed into two-dimensional principal variable sampling, with the principal variable selected as... and , and Automatically generated based on constraint relationships. The value range is based on: coercivity. ∈[8,20]kA / m, saturation magnetic induction intensity ∈[1.8,2.2]T, Remanence ∈[0.8,1.5]T, relative permeability The values of ∈[80,200] are based on the following literature and experimental data:
[0030] Literature[1]: Briffod F, Shiraiwa T, Enoki M.Modeling and CrystalPlasticity Simulations of Lath Martensitic Steel under Fatigue Loading[J].Materials Transactions, 2018, 60(2):199-206.DOI:10.2320 / matertrans.ME201713;
[0031] Reference [2]: Yang Shanjie. Study on contact fatigue properties and microstructure evolution of high-speed wheel steel [D]. Dalian Jiaotong University, 2019;
[0032] The applicant of this invention conducted independent magnetic property tests on rail white layer samples with different service mileages, and used a BH analyzer to measure 20 groups of samples, verifying the rationality of the above-mentioned value range.
[0033] The physical constraint relationship is based on the inverse relationship between coercivity and relative permeability. Based on the Globus model of ferromagnetic materials, this model indicates that the coercivity of polycrystalline ferromagnetic materials is inversely proportional to the square root of the initial permeability. A linear relationship between remanence and saturation magnetic induction is also established. Derived from the theory of remanent magnetization of ferromagnetic materials, the coefficient The range of values was determined by calibration through experimental measurements of white layer samples.
[0034] S1-3 (Construction of Equivalent Thickness-Signal Response Database): Based on the Jiles-Atherton hysteresis model, the equivalent thickness of the white layer is calculated under each parameter combination. The leakage magnetic flux response varies within the range of 50-300 μm, forming a thickness-signal mapping surface. 600 sets of simulation samples are generated through uniform sampling to form a training database. The white layer thickness δ ranges from 50 μm to 300 μm, with the following specific thickness values (26 in total): 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 110 μm, 120 μm, 130 μm, 140 μm, 150 μm, 160 μm, 170 μm, 180 μm, 190 μm, 200 μm, 210 μm, 220 μm, 230 μm, 240 μm, 250 μm, 260 μm, 270 μm, 280 μm, 290 μm, and 300 μm. For each thickness value, different combinations of magnetic characteristic parameters (main variables) are analyzed. Take 13 values, Five values were selected, resulting in 65 groups in total. This generated 65 × 26 = 1690 basic simulation samples. After screening and amplification, 600 training samples were obtained.
[0035] Step S2: Multi-source feature extraction: Three types of features are extracted from simulated and measured magnetic flux leakage signals to comprehensively characterize the signal changes caused by the white layer.
[0036] S2-1 (Time-domain morphological characteristics): Peak-to-peak value : Reflects the amplitude change of the signal; positive and negative peak area ratio Characterizing the symmetry of the signal waveform; signal energy Reflects the overall signal strength
[0037] S2-2 (Differential Characteristic): Maximum Value of the First Derivative Characterizes the rate of change of the signal; zero-crossing slope : Reflects the steepness of the signal near the zero-crossing point
[0038] S2-3 (Spatial Distribution Characteristics): Spatial Correlation Coefficient of Multi-Sensor Array Signals Characterizes the spatial distribution of magnetic field disturbances caused by the white layer.
[0039] Step S3: Thickness Regression Model Based on Stacking Ensemble Learning: Construct a two-level Stacking ensemble architecture to achieve high-precision regression of white layer thickness.
[0040] S3-1 (First Layer: Construction of Heterogeneous Base Learners): Base Learner 1: Gradient Boosting Decision Tree (GBDT): Used to capture non-linear interactions between features; Base Learner 2: Kernel Ridge Regression (KRR): Employs a Gaussian kernel function. Suitable for nonlinear mappings; Base learner 3: Lightweight Multilayer Perceptron (MLP): Network structure is 32→16→8→1, activation function is ReLU.
[0041] S3-2 (Second Layer: Meta-learner Construction): Bayesian ridge regression is used as the meta-learner, and the outputs of the three base learners are used as new feature inputs; the fusion weights of each base learner are automatically determined by maximizing the marginal likelihood, avoiding manual parameter tuning.
[0042] S3-3 (Training Strategy): Five-fold cross-validation is used to generate the first layer of predicted features to prevent overfitting; higher loss weights are applied to samples with larger thickness to balance the sample distribution.
[0043] Step S4: Fast Transfer Adaptation Based on Few Samples using MAML: To address the issues of limited labeled data and significant differences between simulation and experimental data distributions in practical applications, a model-independent meta-learning framework is employed to achieve fast transfer learning.
[0044] S4-1 (Meta-training phase): Train a general initial model parameter set on 600 sets of samples generated in the simulation. Training objective: To enable the initial parameters to quickly adapt to new tasks through a small number of gradient updates.
[0045] S4-2 (Rapid Adaptation Mechanism): For newly acquired rail samples, only [the following information is required]... One labeled sample ( );pass Step gradient descent ( Update model parameters:
[0046]
[0047] in For learning rate, The loss function is used for the new task; the learning rate is dynamically adjusted based on the distribution characteristics of the new task samples to improve convergence speed and stability; among which,
[0048] Employing a model-independent meta-learning framework, the task construction method for the meta-training phase is as follows: First, randomly sample from the simulation database. Meta-tasks (This invention takes) Each type of meta-task corresponds to a set of magnetic property parameter combinations (i.e., a set of...) and (Value). For each meta-task, randomly select from it. One sample is used as the support set (for rapid adaptation), and another sample is drawn. This invention uses a set of samples as a query set (for calculating the meta-loss). Both the support and query sets contain signal-thickness pairs with varying thicknesses (random sampling from 50-300 μm). The goal of each meta-task is to achieve a low prediction error on the query set after a small number of gradient updates on the support set. Meta-training is performed across all meta-tasks to obtain initial model parameters that can quickly adapt to new tasks. .
[0049] Hyperparameter search process: This invention employs a grid search combined with 5-fold cross-validation to optimize key hyperparameters. The search space is as follows:
[0050] MAML Inner Loop Learning Rate The search range is [0.001, 0.005, 0.01, 0.05, 0.1], with an optimal value of 0.01.
[0051] MAML outer loop learning rate: search range [0.0001, 0.0005, 0.001], optimal value is 0.001;
[0052] Gradient update steps The search range is [1, 3, 5, 10], with an optimal value of 5.
[0053] The number of trees in the GBDT in the Stacking model: search range [50, 100, 150], optimal value is 100;
[0054] Regularization coefficient of kernel ridge regression The search range is [0.001, 0.01, 0.1, 1], with an optimal value of 0.01.
[0055] Hidden layer dimension of MLP: search range [16, 32, 64], optimal value is 32.
[0056] Search process: Divide the simulation data into 5 folds, use 4 folds as the training set and 1 fold as the validation set, traverse all hyperparameter combinations, and select the combination with the smallest average validation error of 5 folds as the final hyperparameters.
[0057] Step S5: Joint discrimination mechanism for white layer and crack: To solve the problem of confusion between white layer signals and crack signals, a joint discrimination mechanism is established:
[0058] S5-1 (Dual Output Network Structure): Constructs a shared feature extraction layer followed by two parallel branches; Regression branch: Outputs thickness prediction value. Classification branch: Outputs the probability of defect type. (White layer / cracks / other)
[0059] S5-2 (Joint Loss Function):
[0060]
[0061] in To balance the weights, a grid search is used to determine them.
[0062] S5-3 (Decision Fusion): When the classification branch outputs "white layer", the thickness value output by the regression branch is used; when the classification branch outputs "crack", the crack quantification assessment module is triggered (optional); when the classification confidence is lower than the threshold (e.g., 0.7), a "manual review required" label is output; the input of the joint discriminant network is the feature vector output by the shared feature extraction layer, which shares the same input features (temporal morphological features, differential features, and spatial distribution features) with the Stacking ensemble learning model. During network training, the input is the multi-dimensional feature vector extracted from the measured magnetic leakage signal and its corresponding label; during network inference, the input is the multi-dimensional feature vector of the sample to be tested.
[0063] Classification label definition: The output of the classification branch is the probability distribution of the three signal sources, as defined below:
[0064] Label 0 (White Layer): The signal originates from the martensitic white layer structure on the surface of the rail, and the corresponding regression branch outputs the thickness prediction value.
[0065] Tag 1 (Crack): The signal originates from cracks on the rail surface (including transverse cracks, longitudinal cracks, etc.). In this case, the thickness output of the regression branch is invalid, triggering the crack quantification assessment module.
[0066] Label 2 (Other / Interference): The signal originates from structural interference or noise such as welds, bolt holes, etc. In this case, the "Manual Verification Required" flag is triggered. During training, the classification labels are determined through metallographic analysis or manual expert annotation to ensure the accuracy of the annotations.
[0067] Example 1:
[0068] Constructing the simulation dataset: Based on the parameter range and constraint relationships defined in steps S1-1 and S1-2, uniform sampling is performed on the main variables Hc and Bs. : 8-20 kA / m, sampling step size 1 kA / m, a total of 13 values; : 1.8-2.2T, sampling step size 0.1T, a total of 5 values; a total of 13×5=65 parameter combinations, in each combination and It is automatically generated from constraints.
[0069] Calculate thickness-signal response: For each combination of parameters, calculate the equivalent thickness of the white layer. exist Response of leakage magnetic field signal when varying within a certain range: Thickness step size: There are 26 thickness values in total; a total of 65 × 26 = 1690 sets of simulation samples;
[0070] Sample selection and amplification: To improve the robustness of the model, the 1690 generated samples were processed as follows: samples with a signal-to-noise ratio below 20dB (about 5%) were removed; Gaussian noise of different intensities (SNR=20-40dB) was added, and each original sample was amplified 3 times; finally, about 4800 valid samples were obtained, 600 of which were randomly selected as the training set, and the rest were used for validation.
[0071] Model Training and Parameter Settings: Feature Extraction Parameters: Temporal Feature Extraction Interval: Centered on the signal peak point, extending 50 sampling points before and after it; Differential Features: Calculating the first derivative using a Savitzky-Golay filter, with a window length of 11 and a polynomial order of 3; Spatial Correlation: Calculating the correlation coefficient matrix using signals from three adjacent channels.
[0072] Stacking model parameters: GBDT: 100 trees, maximum depth 6, learning rate 0.1; KRR: Gaussian kernel, kernel parameters... Regularization coefficient MLP: Network structure 32-16-8-1, learning rate 0.001, training epochs 200; Bayesian Ridge Regressor Meta-Learner: Using default parameters, automatically optimized by maximizing marginal likelihood.
[0073] MAML parameters: Number of meta-training tasks: 20, each task contains 10 samples; Inner loop learning rate. Gradient update steps The outer loop learning rate is 0.001, and the number of meta-training rounds is 1000.
[0074] Joint discriminant network parameters: Shared feature layer: 3 fully connected layers, dimension 64→32→16; Classification branch: 16→8→3 (white layer / crack / other); Regression branch: 16→8→1; Loss weights ,
[0075] Test Results and Analysis: Thickness Inversion Accuracy Test: The test was conducted on a test set containing 200 measured samples, and the results are shown in Table 1.
[0076] Table 1 shows the evaluation performed on a test set of 200 actual samples. ;
[0077] Migration adaptability test: Migration tests were conducted on 50 samples collected from the new line, and the results are shown in Table 2.
[0078] Table 2 shows the migration tests performed on 50 samples. ;
[0079] The test results for the ability to distinguish between white layers and cracks are shown in Table 3.
[0080] Table 3 shows the testing results for a test set containing 150 samples (80 white layers and 70 cracks): ;
[0081] Field Verification: This system was deployed on an actual rail flaw detection vehicle of a railway bureau's engineering section to inspect a damaged section containing a white layer. The system detected 15 areas of white layer, outputting predicted thickness values and confidence intervals. Subsequently, metallographic verification was performed on samples from 8 of these areas. The results showed that the average deviation between the system's output thickness values and the metallographic measurements was [missing information]. The predicted interval with a confidence interval of 90% actually covered 87.5% of the true values. The system marked the 5 samples as "high confidence" (>0.85), with an average deviation of only... .
[0082] The above embodiments fully demonstrate that the quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and integrated learning proposed in this invention is significantly superior to existing technologies in terms of detection accuracy, generalization ability, anti-interference ability, and engineering practicality.
Claims
1. A quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning, characterized in that, Includes the following steps: Step 1: Based on the inherent physical correlation between the material magnetic property parameters of the white layer of the rail, determine the constraint relationship between the parameters, and sample the magnetic property parameters according to the constraint relationship to generate multiple sets of magnetic property parameter combinations; based on each set of magnetic property parameter combinations, simulate and calculate the leakage magnetic signal response of the white layer at different thicknesses, and construct a thickness-signal mapping database; Step 2: Extract multi-dimensional features from the measured magnetic flux leakage signal to characterize the change in white layer thickness. The multi-dimensional features include time-domain morphological features reflecting the signal amplitude and waveform shape, differential features reflecting the signal change rate, and spatial distribution features reflecting the spatial distribution characteristics of magnetic field disturbance. Step 3: Construct an ensemble learning regression model containing a first layer and a second layer. The first layer contains multiple heterogeneous base learners, which are used to learn the mapping relationship between the multi-dimensional features and the white layer thickness respectively. The second layer contains a meta-learner, which is used to fuse the output results of multiple base learners to obtain the final white layer thickness prediction value. Step 4: Employ a model-independent meta-learning mechanism to pre-train an initial ensemble learning regression model on the thickness-signal mapping database. This enables the initial ensemble learning regression model to quickly adapt to the task of predicting the thickness of the rail white layer under new lines or new working conditions through a limited number of gradient updates using a small number of measured labeled samples. Step 5: Construct a dual-output network with a shared feature extraction layer. The dual-output network includes a regression branch for predicting the thickness of the white layer and a classification branch for identifying the type of signal source. The two branches are optimized simultaneously through a joint loss function to achieve simultaneous discrimination and thickness inversion of the white layer signal and the crack signal.
2. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, In step 1, the magnetic property parameters include coercivity, saturation magnetic induction, remanence, and relative permeability; the constraint relationships include that coercivity is inversely proportional to relative permeability, and remanence is directly proportional to saturation magnetic induction.
3. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, In step 2, the temporal morphological features include the peak-to-peak value, the ratio of positive to negative peak area, and the signal energy; the differential features include the maximum value of the first derivative of the signal and the slope at the zero crossing point; and the spatial distribution features include the spatial correlation coefficient between the signals of the multi-sensor array.
4. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, In step 3, the ensemble learning regression model includes multiple heterogeneous base learners in the first layer, such as gradient boosting decision trees for capturing nonlinear interactions between features, kernel ridge regression for nonlinear mapping, and lightweight multilayer perceptron; the meta-learner in the second layer is Bayesian ridge regression, which is used to automatically determine the fusion weights of the outputs of each base learner.
5. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, In step 4, the model-independent meta-learning mechanism obtains initial model parameters that can quickly adapt to new tasks by performing meta-training on meta-tasks constructed from multiple simulation data. For new tasks, only a small number of labeled samples are needed, and the model parameters can be updated through a few steps of gradient descent, thus achieving rapid adaptation to the task of predicting the thickness of the white layer of rails on new lines.
6. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, In step 5, the shared feature extraction layer of the dual-output network is used to extract common features of the leakage magnetic field signal; the regression branch is used to output the thickness prediction value when the classification branch determines that the signal source is a white layer; the classification branch is used to output the probability that the signal source belongs to a white layer, crack or other type.
7. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, In step 5, the joint loss function is composed of a weighted sum of regression loss, which measures the error in thickness prediction, and classification loss, which measures the error in type discrimination. By optimizing this joint loss function, the network can learn both thickness inversion and type discrimination tasks simultaneously.
8. The quantitative inversion method for rail white layer thickness based on parameter-constrained simulation and ensemble learning according to claim 1, characterized in that, Step 5 also includes decision fusion: when the probability of white layer output by the classification branch is higher than the preset threshold, the thickness value output by the regression branch is used as the final result; when the probability of crack output by the classification branch is higher than the preset threshold, crack quantification assessment is triggered; when the probabilities of all categories are lower than the preset threshold, a label requiring manual review is output.