Wear evolution prediction method and system based on data-physical dual-driven hierarchical agent framework

Abstract

The application discloses a kind of wear evolution prediction method and system based on data-physical double drive layered agent framework, the method includes the following steps: constructing parameterized finite element model embedded in Archard wear equation, establish the explicit mapping of controllable input and cumulative wear depth output, generate physical environment working condition and low-fidelity sample;Build a layered proxy model, correct the low-fidelity model;Trace the physical parameters to obtain complete high-fidelity samples, train the finite element model;Get the input variable of the object to be detected, calculate the wheel wear depth using the trained finite element model, get the wheel diameter, realize health state prediction.Using this technical solution, a complete high-fidelity sample is formed, making up for the lack of physical interpretability in data-driven prediction methods, solving the problems of unknown input, poor adaptability to variable matrix, unmodeled error and weak physical interpretability in the prior art, significantly improving the precision and robustness of wear prediction.

Description

Technical Field

[0001] This invention belongs to the field of mechanical component wear prediction technology, specifically relating to a wear evolution prediction method and system based on a data-physical dual-driven hierarchical proxy framework. Background Technology

[0002] Technological advancements have driven a continuous increase in the complexity of mechanical systems, a trend that exacerbates the frequency of equipment failures, particularly in safety-critical industries such as subway transportation. In modern subway operations, effective maintenance is crucial for ensuring operational safety, reducing downtime, and improving efficiency. Traditional maintenance strategies have inherent limitations, including fixed-interval preventative maintenance and reactive repair after a failure. These approaches are often accompanied by high costs, inefficient resource utilization, and difficulty in responding to unexpected failures. Therefore, predictive maintenance, as a proactive paradigm, is gaining increasing attention. It uses real-time data and analytical models to predict failures and optimize maintenance plans, thereby achieving a balance between operational efficiency and economic feasibility.

[0003] A prime example of this challenge is the railway wheel-rail system, where wheelsets play a crucial role as core load-bearing components. Wear at the wheel-rail interface not only reduces operational stability but also amplifies safety risks such as derailment and excessive vibration, highlighting the necessity of developing reliable prediction schemes for wear forecasting. Accurate modeling of wheel wear is critical, directly providing a basis for predicting remaining service life and maintenance decisions, potentially reducing unplanned downtime and extending asset life.

[0004] Wheel wear prediction often faces the following challenges: the physical input in engineering is difficult to obtain completely (input unknown); the variability of environmental factors and operational loads in actual scenarios (variable parent); model bias caused by unmodeled factors (unmodeled factors); the prediction result is the numerical optimal solution of the model, but lacks physical interpretability (poor interpretability). Existing wheel wear prediction methods can be roughly divided into three categories: physical base models, data-driven methods, and hybrid frameworks.

[0005] Physical mechanism models integrate key theoretical and simulation components, including vehicle dynamics simulation, Hertzian contact theory, and the Achard wear equation. By simulating contact stress, creep, and material removal processes under controlled conditions, these models can provide mechanistic insights. However, they often require complete inputs (which are often difficult to obtain in engineering) and rely on idealized boundary conditions. They cannot fully account for the variability of environmental factors and operational loads in real-world scenarios, ultimately leading to the accumulation of model errors and difficulty in accurate prediction.

[0006] With the development of machine learning and sensing technologies, data-driven methods have emerged, providing an alternative for related research. Their core is to extract patterns from empirical data. However, their bottleneck lies in the lack of constraints from physical mechanisms; the predicted results are often mathematically optimal solutions, leading to poor interpretability.

[0007] To address these shortcomings, data-physical fusion methods (also known as hybrid models or models with embedded mechanisms) have emerged. These methods combine physical mechanisms with empirical observations to simultaneously improve model interpretability and predictive accuracy. However, this technique lacks the ability to handle variable parent data and trace the source of errors; or it lacks the ability to resolve situations with incomplete data; or it lacks consideration for model errors caused by unmodeled factors.

[0008] Physical mechanism models, data-driven models, and hybrid methods have all made outstanding contributions to addressing the four challenges, but each also has its limitations. These limitations highlight the need for a more adaptive and interpretable framework in the field of wear prediction. Summary of the Invention

[0009] The purpose of this invention is to address the aforementioned problems in existing technologies by proposing a wear evolution prediction method and system based on a data-physical dual-driven hierarchical proxy framework.

[0010] To achieve the above objectives, the basic solution of this invention is: a wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework, comprising the following steps:

[0011] S1, Construct a parameterized finite element model embedded with the Achad wear equation, and establish an explicit mapping between controllable input and cumulative wear depth output;

[0012] S2 generates physical environment conditions through Latin hypercube sampling, resulting in low-fidelity samples.

[0013] S3, Construct a hierarchical proxy model. The offline low-fidelity model is used to capture the physical mapping relationship of the low-fidelity samples. The high-fidelity model considers unmodeled factors, variable parent problem and measurement error, and corrects the low-fidelity model.

[0014] S4. Using incomplete high-fidelity response data, the physical parameters are traced back to obtain complete high-fidelity samples based on the cut-Bayes method and the plug-in method.

[0015] S5. Based on the complete high-fidelity samples, train a high-fidelity model;

[0016] S6: Obtain the input parameters of the object to be detected, calculate the wheel wear depth using the trained high-fidelity model, and combine it with the real-time collected wheel diameter to achieve health status prediction.

[0017] The working principle and beneficial effects of this basic scheme are as follows: This technical scheme ensures the interpretability of the basics through physical modeling, and low-fidelity samples provide a data foundation for model training. The hierarchical proxy model structure utilizes the fast mapping of the low-fidelity model while absorbing the errors caused by unmodeled factors and variable population problems through the high-fidelity model.

[0018] The Cut-Bayes and Plug-in methods are specifically designed to address the common "incomplete data" (unknown input) problem in engineering, enabling the traceability of physical parameters and filling in key data gaps. This technical solution systematically solves the four major challenges mentioned in the background technology: unknown input, variable population, unmodeled factors, and poor interpretability.

[0019] Furthermore, the method for constructing a parameterized finite element model embedding the Archad wear equation is as follows:

[0020] A single-sided wheel-rail model is used, with the wheel and rail meshed using hexahedral elements. The model focuses on wheel diameter wear caused by wheel-rail contact under straight track conditions, yielding the local wear depth. for:

[0021] ,

[0022] in, coordinates Normal contact pressure at the point, Where k is the sliding distance, k is the dimensionless wear coefficient, and H is the material hardness.

[0023] The normal load N and the wear coefficient k appear as a highly coupled product, which is decoupled into parameters γ and κ through a rotational transformation in logarithmic space:

[0024] ,

[0025] ,

[0026] in, It represents a strongly identifiable direction, and the wear response is quite sensitive to its changes; Representing a weakly discernible direction, the original parameters k and N are rotated to the transformed parameter set through the above transformation process. This indicates that k and N are transformed into gamaγ and kappaκ through logarithmic transformation, and the two transformed quantities are written as a set; the original parameter values ​​are obtained through inverse transformation:

[0027] ,

[0028] ,

[0029] After obtaining the parameters γ and κ, N and k were decoupled, which laid the foundation for subsequent tracing work.

[0030] The highly coupled physical parameters (N and k) that jointly affect the wear response are decoupled into strongly identifiable directions (γ) that are "sensitive" to the response and weakly identifiable directions (κ) that are "insensitive". This greatly improves the numerical stability and convergence speed in the subsequent parameter estimation and source tracing process, laying a key foundation for accurate source tracing and avoiding computational failures or multiple solutions caused by parameter coupling.

[0031] Furthermore, the low-fidelity model is as follows:

[0032] ,

[0033] in, ,

[0034] Let represent the undetermined coefficients corresponding to the i-th basis function. It is the input vector. This represents γ after parameter renormalization. This represents the renormalized k; Represents the i-th training sample, Represents the MQ function, the shape parameter in the MQ function. , is the maximum distance between samples, and N is the number of training samples. for Correlation matrix , represents the polynomial quadratic basis function (MQ); Represents the deviation function The associated coefficient vector, τ(), represents a kind of... The mapping to a high-dimensional feature space is expressed in non-homogeneous polynomial form. To balance the computational burden and subsequent adjustments to the weighting coefficients. Scaling factor. Bias term b and deviation function These are all correction terms set based on the hybrid correction method. It is a vector consisting of the undetermined coefficients corresponding to all basis functions.

[0035] Build a fast and stable physical proxy that is easy to use.

[0036] Furthermore, the parameters to be estimated in the low-fidelity model From low-fidelity samples Conduct training;

[0037] Maximization Model With low-fidelity response Pearson correlation coefficient squared :

[0038] ,

[0039] in, The row vector formed by the mean of each column is used for centering. After projection, it is transformed into finding the matrix. Main eigenvectors : This is the output of the low-fidelity model f1. It is the output obtained from finite element simulation;

[0040] ,

[0041] Given a row vector, derived from the matrix The mean of each column constitutes the matrix; P and D are matrices constructed during the process. In solving matrix PYY T The eigenvector corresponding to the largest eigenvalue of P;

[0042] Then, the coefficients are obtained by back substitution. Based on this, Minimize training error while controlling model complexity (regularization):

[0043] ,

[0044] Subsequently, the Lagrange multipliers were introduced. By constructing the Lagrange function and taking its partial derivatives, the KKT conditions can be obtained, which can eliminate... It is then transformed into a system of linear equations:

[0045] ,

[0046] The analytical solution is:

[0047] ,

[0048] In this context, the superscript "-1" represents the inverse of the matrix, the superscript "T" represents the transpose of the matrix, 1 (in bold) represents the identity matrix, and K represents the kinematic unit. ij The matrix formed, Y L It is a vector composed of the outputs of low-fidelity samples, L: Low, and the letter above the letter "^" is the estimated value of the variable; Gaussian kernel, hyperparameters and regularization parameters By minimizing the cross-validation error, an offline mapping model that achieves a fast and stable response can be obtained. At unobserved points The prediction expression at this location is:

[0049] .

[0050] By using CMS (Correlated Mapping Proxy Model) and hybrid correction, the input-output mapping relationship of physical mechanisms can be quickly learned and reproduced based on a small number of finite element simulation samples (generated by S2), thus eliminating the dependence on time-consuming finite element simulations.

[0051] Its training strategy (maximizing correlation + regularization) not only ensures that the model can accurately capture physical trends, but also prevents overfitting by controlling complexity, thus ensuring the model's generalization ability.

[0052] Furthermore, considering unmodeled factors, variable population issues, and measurement errors, the method for constructing a high-fidelity model to correct the low-fidelity model is as follows:

[0053] The high-fidelity model is:

[0054] ,

[0055] ,

[0056] ,

[0057] in, This is the current state. It is the high-fidelity response corresponding to time step t. Used to capture nonlinear model errors caused by factors not modeled in low-fidelity models. This represents measurement error. Radial basis functions (RBF) are used to fit the nonlinear residuals:

[0058] ,

[0059] Where K is the number of basis functions. It is the center (through the current state) K-means clustering is performed to determine the appropriate clustering method to ensure good coverage while avoiding overfitting. These are shape parameters. The kernel function calculates the vector; It is weight;

[0060] Once all model parameters are known and the input values ​​of the high-fidelity samples are traced back, forward propagation can be performed according to the following steps:

[0061] remember For the extracted samples, for each sample m, the frontier propagation of the latent variables and the corresponding... The predicted observation values ​​are:

[0062] ,

[0063] ,

[0064] Point prediction and uncertainty interval are determined by The empirical distribution is obtained,

[0065] ,

[0066] In the above high-fidelity model, These unknown parameters together determine the high-fidelity model.

[0067] The parameter decoupling concept is incorporated into the coefficient matrix A (second row [0,0]) in the state transition equation, tightening the drift in weakly identifiable directions. By introducing RBF to fit the nonlinear model error and Gaussian noise to represent the measurement error, the model can effectively absorb and compensate for the deviation between the low-fidelity model and the real world, thereby significantly improving the accuracy of the final prediction.

[0068] Furthermore, by using incomplete high-fidelity response data and employing the cut-Bayes and plug-in methods to trace the physical parameters and obtain complete high-fidelity samples, the following method is employed:

[0069] Using low-fidelity samples By obtaining the estimated parameters of the low-fidelity model Through the cut-Bayes framework, plug-in Marginal likelihood of the post-high-fidelity model for:

[0070] ,

[0071] ,

[0072] ,

[0073] Log-likelihood Expanded to:

[0074] The high-fidelity sample data is incomplete and lacks input states. At the same time, it is necessary to meet the needs of the prediction model, which is achieved through the following two estimation objectives:

[0075] (a) Obtain the physical parameters after rotational transformation by using the prediction distribution of the low-fidelity model and the posterior distribution of the likelihood inference from the high-fidelity model. and The optimal estimated mean, i.e.:

[0076] ,

[0077] in, , It is the likelihood of the high-fidelity function. It is a low-fidelity sample The low-fidelity model trained for source value The predicted distribution and the mean of the posterior distribution will be used as the source input value for the missing high-fidelity samples;

[0078] for Assume prior Then first In Set to zero, other parameters from Initialization in the prior (assuming the low-fidelity model has no error, to obtain the prior...) The approximate posterior distribution simplified using Gibbs sampling is expanded in detail as follows:

[0079] ,

[0080] Wherein, the normalization constant ;

[0081] (b) Estimated parameters using a low-fidelity model And based on the plug-in, it is fixed and inserted, the model's unestimated target via plug-in Maximizing the posterior yields:

[0082] ,

[0083] in, For the edge likelihood (to (integral), if prior Flat, simplified to edge MLE: ;

[0084] Model parameters Only the two key parameters that were previously set to zero remain. The estimated parameters , , , Plug-in, and because of the low-fidelity model's parameter estimates The low-fidelity response has been obtained and can be computed. To minimize residuals (Continue assuming the target is estimated) Measurement error With the objective of zero, the sampling weight vector First, assume The prior is The posterior and likelihood functions are:

[0085] ,

[0086] ,

[0087] Perform MAP estimation on it:

[0088] ,

[0089] in Design matrix ,

[0090]

[0091] Ultimately, all the estimates obtained from the plug-in were... Calculate the final measurement error. Assuming a priori (Conjugate), then its posterior distribution is:

[0092] ,

[0093] Its posterior mean estimate can be solved analytically directly:

[0094] ,

[0095] At this point, all targets to be estimated have been obtained.

[0096] The Cut-Bayes framework protects the stable physical mapping capability of low-fidelity models by cutting off the path through which high-fidelity data affects the parameters of low-fidelity models, and prevents error attribution mismatch from contaminating the core model.

[0097] The plug-in method decouples the coupled model parameters from the unknown inputs and estimates them step by step, enabling model construction and parameter calibration under conditions of incomplete information. This is the key to ensuring that the model can be applied in real industrial scenarios.

[0098] Furthermore, the Gibbs sampling steps are as follows:

[0099] Set the iteration count from t=1 to T, and initialize... Using the prior mean as an assumption, invalid samples outside the physical boundary are rejected:

[0100] S71, for each i, the sampling condition posterior Due to the independence assumption, it simplifies to Conditional density expansion:

[0101] ,

[0102] This is a non-standard Gaussian, which can be sampled using Metropolis-Hastings inline sampling;

[0103] S72, the source value for missing high-fidelity samples can be obtained using the following formula:

[0104] ,

[0105] in This is the combustion period; thus, objective (a) has been determined.

[0106] S73, using k-means clustering Obtain the central value and variance .

[0107] .

[0108] Using Gibbs sampling and Cut-Bayes posterior, the missing physical inputs (γ, κ) are inferred from the high-fidelity response under the "guidance" of the low-fidelity model.

[0109] Furthermore, the method for predicting health status is as follows:

[0110] Based on the design diameter and wear condition of each individual wheel, determine its actual diameter. If the actual diameter is not lower than the threshold (770 mm), it is considered a safe condition.

[0111] For coaxial wheels i and j, the diameter difference is calculated as follows: ,in, and These represent the predicted diameters of wheel i and j at time t, respectively.

[0112] The diameter of a healthy state is When this value approaches 1, it represents A value close to 0 indicates that the diameters of the two wheels on the same axle are not significantly different, which is a safe condition.

[0113] By directly linking the model's predicted output (wheel diameter) with the actual standards of subway operation and maintenance (such as axle diameter difference), the Healthy State Diameter (SOH) is defined. This transforms the abstract predicted value into a safety indicator that operation and maintenance personnel can directly understand and use, making the predicted result no longer just a numerical value, but a health indicator with clear physical and engineering significance, which greatly enhances the practical value of the invention.

[0114] Furthermore, it also includes remaining useful life prediction, the specific method of which is as follows:

[0115] By combining the results of health status prediction with probabilistic wear prediction from a state-space model, the remaining operational mileage is estimated based on the currently predicted wear rate. Through forward propagation of recursive equations, this framework identifies two failure mileages: Mileage corresponding to a 1mm difference in wheel diameter on the same axle; (Among coaxial wheels, at the current wear rate, the mileage corresponding to when any wheel diameter drops to the lowest threshold (e.g., 770mm)), the remaining service life (RUL) is the minimum of the two: .

[0116] By simultaneously considering two failure modes, "excessive coaxial diameter difference" and "lower limit of single wheel diameter", and taking the minimum of the two as the final RUL, a more comprehensive and safer basis for maintenance decision-making is provided.

[0117] The present invention also provides a wear evolution prediction system based on the method described in the present invention, including a signal acquisition unit, a control unit and a display unit;

[0118] The control unit constructs a parameterized finite element model embedded with the Achad wear equation, establishing an explicit mapping between controllable input and cumulative wear depth output. Physical environment conditions are generated through Latin hypercube sampling, producing low-fidelity samples. A hierarchical proxy model is constructed; the offline low-fidelity model captures the physical mapping relationship of the low-fidelity samples, while the high-fidelity model considers unmodeled factors, variable parent body issues, and measurement errors to correct the low-fidelity model. Using incomplete high-fidelity response data, the physical parameters are traced back to their source based on the cut-Bayes and plug-in methods to obtain complete high-fidelity samples. Based on these complete high-fidelity samples, the finite element model is trained.

[0119] The control unit also acquires the input parameters of the object to be detected collected by the signal acquisition unit, and uses the trained finite element model to calculate the wheel wear depth to achieve health status prediction.

[0120] This system, through a signal acquisition unit, a control unit, and a display unit, realizes a closed loop from data acquisition and intelligent processing to result display, making it easy to deploy and apply in actual engineering projects. Attached Figure Description

[0121] Figure 1 This is a flowchart illustrating the wear evolution prediction method based on the data-physical dual-driven hierarchical agent framework of the present invention.

[0122] Figure 2 This is a schematic diagram of the process of constructing a parameterized finite element model that embeds the Achad wear equation in the wear evolution prediction method based on the data-physical dual-driven hierarchical agent framework of the present invention.

[0123] Figure 3 This is a graph showing the processing results of the original wheel diameter data for the wear evolution prediction method based on the data-physical dual-drive hierarchical proxy framework of this invention. Detailed Implementation

[0124] Embodiments of the present invention are described in detail below. Examples of these embodiments 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.

[0125] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0126] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0127] This invention discloses a wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework. It constructs a hierarchical proxy model that integrates physical mechanisms, considers unmodeled factors and measurement errors, and adapts to varying parent body working conditions. In view of the incomplete input information often found in engineering, it proposes a decoupling-source tracing approach to form complete high-fidelity samples, thereby making up for the lack of physical interpretability in data-driven prediction methods.

[0128] This is a hybrid approach that combines the advantages of purely data-driven and purely physical methods, compensating for each other's shortcomings. The model employs a hierarchical structure, with a low-fidelity layer capturing the mapping relationships from finite element simulations and a high-fidelity layer correcting model errors.

[0129] like Figure 1 As shown, the wear evolution prediction method based on the data-physical dual-driven hierarchical agent framework includes the following steps:

[0130] S1, construct a parameterized finite element model embedded in the Achad wear equation, such as Figure 2 As shown, an explicit mapping is established between controllable inputs (all of which can be set in the finite element simulation software, such as the normal pressure estimated by adding the train's own weight to the number of passengers (assuming an average of 50KG per person), the wear coefficient obtained through actual measurement calculations, the movement distance which can be set arbitrarily, and the material hardness obtained from the supplier) and the cumulative wear depth output; this model will establish a controllable input (such as normal load) With wear coefficient ) is explicitly mapped to the cumulative wear output.

[0131] Specifically, the Archard wear equation can be used as the wear model: Compared with complex energy dissipation models or purely empirical formulas, the Archard model establishes an explicit and intuitive physical mapping relationship between wear amount, contact pressure and wear coefficient in a concise way. This provides the most interpretable and computationally feasible framework for the inverse solution of the two parameters that need to be estimated in reverse.

[0132] Latin hypercube sampling (LHS) can be used to generate physical environment conditions, thereby constructing a diverse and computationally efficient low-fidelity dataset for training surrogate models. LHS is chosen because of its excellent space-filling properties; it requires far fewer samples than traditional methods to cover the space of parameter uncertainty, making it suitable for computationally expensive finite element simulations.

[0133] S2 generates physical environment conditions through Latin hypercube sampling, resulting in low-fidelity samples.

[0134] S3, Construct a hierarchical proxy model. The offline low-fidelity model is used to capture the physical mapping relationship of the low-fidelity samples. The high-fidelity model considers unmodeled factors, variable parent problem and measurement error, and corrects the low-fidelity model.

[0135] S4. Using incomplete high-fidelity response data, the physical parameters are traced back to obtain complete high-fidelity samples based on the cut-Bayes method and the plug-in method.

[0136] S5. Based on the complete high-fidelity samples, train a high-fidelity model;

[0137] S6. Obtain the input parameters of the object to be detected (the diameter of the wheel, measured approximately every 90km using a laser-industrial camera (real output). Substitute the real output into the high-fidelity model for training and extrapolation prediction). Calculate the wheel wear depth using the trained high-fidelity model and combine it with the real-time collected wheel diameter to achieve health status prediction.

[0138] In a preferred embodiment of the present invention, the method for constructing a parametric finite element model embedded with the Archard wear equation (calculated using ANSYS software, with the wear amount calculated by embedding the Archard model) is as follows:

[0139] To accurately solve the complex wheel-rail contact mechanics problem required by the Achad wear equation, this invention employs a finite element analysis (FEA) model. Analytical solutions cannot fully capture the nonlinear Hertzian pressure distribution and creep under the actual geometry. The finite element analysis is implemented in ANSYS, a software proven to handle iterative profile updates and contact nonlinearities in tribological simulations.

[0140] This model simulates wheel-rail contact under straight track conditions, focusing on wheel diameter wear. Considering the structural and load symmetry of subway wheelsets during straight-line operation, a single-sided wheel-rail model is adopted to reduce computational costs. Accuracy losses due to model simplification and unmodeled factors will be compensated for through subsequent model construction.

[0141] Based on established modeling methods, the wheel (LM tread shape, initial diameter 840 mm) and rail (CHN60 cross-section) are meshed using hexahedral elements, with the mesh in the contact area refined to 1 mm to ensure convergence. Boundary conditions are fixed at the rail ends, and rotational / translational constraints are applied to the wheel. An elastoplastic model is used for the materials; relevant parameters are shown in Table 1.

[0142] Table 1 Material parameters of the finite element model

[0143]

[0144] A single-sided wheel-rail model was used, with the wheel and rail meshed using hexahedral elements. Wheel diameter wear caused by wheel-rail contact under straight track conditions was modeled (calculated internally by the finite element simulation software based on set constraints and loads), yielding the local wear depth. (That is, the output of the low-fidelity sample, together with the corresponding input physical quantity, constitutes the low-fidelity sample) is:

[0145] ,

[0146] in, coordinates Normal contact pressure (MPa) at a point (unit: m), i.e., stress. Where is the sliding distance (in meters), k is the dimensionless wear coefficient, and H is the material hardness (in MPa). The contact is modeled using a surface-to-surface contact formula combined with penalty function friction (friction coefficient 0.3) to capture time-varying pressure and creep. The Archard wear model is used to calculate the local wear depth. .

[0147] To balance the computational cost and accuracy requirements of long-term simulations, a scaling factor is introduced. (For example, =1000km, L=200m). In addition, the wheel diameter is parametrically modeled, which enables precise iterative updates of the wheel diameter based on the scaling wear.

[0148] In the Achad wear equation, the normal load N (the stress distribution of each mesh is calculated in finite element simulation using the load (pressure N)) and the wear coefficient k appear as a highly coupled product, which can cause identifiability problems in parameter estimation and extrapolation. Therefore, this invention decouples them into parameters γ and κ through a rotational transformation in logarithmic space:

[0149] ,

[0150] ,

[0151] in, It represents a strongly identifiable direction, and the wear response is quite sensitive to its changes; Representing a weakly discernible direction, the original parameters k and N are rotated to the transformed parameter set through the above transformation process. k and N are transformed into gamaγ and kappaκ through a logarithmic transformation. These two transformed quantities are then written as a set. This transformation decouples the parameters by aligning them with the principal axes of the parameter space, thereby improving the numerical stability and convergence of the optimization or inference process. The original parameter values ​​are obtained through an inverse transformation:

[0152] ,

[0153] ,

[0154] After obtaining the parameters γ and κ, N and k were decoupled, which laid the foundation for subsequent tracing work.

[0155] In a preferred embodiment of the present invention, due to the time-consuming nature of finite element simulation of the finite element model, a large number of computational samples cannot be obtained. The CMS model, however, is suitable for small sample sizes and can respond quickly. Therefore, the Correlation Mapping Proxy Model (CMS)[] is used to quickly implement the input-output (low-fidelity sample) mapping process of the finite element model in Section 2.

[0156] The low-fidelity model is:

[0157] Low-fidelity models achieve fast and stable input-output mapping through finite element models. That is, low-fidelity input-output samples are obtained through finite element simulation, and the low-fidelity model is trained through the samples (solving the undetermined coefficients in the model). With the model coefficients, the output can be directly calculated by formula for a new input x.

[0158] In this study, multiple quadratic basis functions (MQ) were chosen to initially construct a low-fidelity model, capturing the trend of low-fidelity sample responses. The advantages of MQ basis functions lie in their fewer parameter requirements and excellent overall performance. The preliminary model can be written in matrix form as follows: ,

[0159] Let represent the undetermined coefficients corresponding to the i-th basis function. It is the input vector. This represents γ after parameter renormalization. Let k be the parameter renormalized form, and X be a vector containing two variables. Represents the i-th training sample, Represents the MQ function, the shape parameter in the MQ function. , is the maximum distance between samples, and N is the number of training samples. for Correlation matrix , represents the polynomial quadratic basis function (MQ); Represents the deviation function The associated coefficient vector, τ(), represents a kind of... The mapping to a high-dimensional feature space is expressed in non-homogeneous polynomial form. To balance the computational burden and subsequent adjustments to the weighting coefficients. Scaling factor. Bias term b and deviation function These are all correction terms set based on the hybrid correction method. It is a vector consisting of the undetermined coefficients corresponding to all basis functions.

[0160] In a preferred embodiment of the present invention, the parameters to be estimated in the low-fidelity model From low-fidelity samples Conduct training;

[0161] Maximization Model (For hierarchical models, training should be done separately, and the undetermined parameters of each model should be calculated. Here, we first calculate the low-fidelity f1 and low-fidelity response.) Pearson correlation coefficient squared :

[0162] ,

[0163] in, The row vector formed by the mean of each column is used for centering. After projection, it is transformed into finding the matrix. Main eigenvectors : This is the output of the low-fidelity model f1. It is the output obtained from finite element simulation;

[0164] ,

[0165] Given a row vector, derived from the matrix The mean of each column constitutes the matrix; P and D are matrices constructed during the process. In solving matrix PYY T The eigenvector corresponding to the largest eigenvalue of P;

[0166] Then, the coefficients are obtained by back substitution. Based on this, Minimize training error while controlling model complexity (regularization):

[0167] ,

[0168] Subsequently, the Lagrange multipliers were introduced. By constructing the Lagrange function and taking its partial derivative, we obtain the Karush-Kuhn-Tucker conditions (the first-order necessary conditions in nonlinear programming for a local optimal solution to a constrained optimization problem satisfying certain constraints. It generalizes the Lagrange multiplier method and can handle optimization problems containing both equality and inequality constraints), which can eliminate... It is then transformed into a system of linear equations:

[0169] ,

[0170] The analytical solution is:

[0171] ,

[0172] In this context, the superscript "-1" represents the inverse of the matrix, the superscript "T" represents the transpose of the matrix, 1 (in bold) represents the identity matrix, and K represents the kinematic unit. ij The matrix formed, Y L It is a vector composed of the outputs of low-fidelity samples, L: Low, and the letter above the letter "^" is the estimated value of the variable; Gaussian kernel, hyperparameters and regularization parameters By minimizing the cross-validation error, an offline mapping model that achieves a fast and stable response can be obtained. At unobserved points The prediction expression at this location is:

[0173] .

[0174] By using CMS (Correlated Mapping Proxy Model) and hybrid correction, the input-output mapping relationship of physical mechanisms can be quickly learned and reproduced based on a small number of finite element simulation samples (generated by S2), thus eliminating the dependence on time-consuming finite element simulations.

[0175] In a preferred embodiment of the present invention, unmodeled factors, variable population problems, and measurement errors (in high-fidelity models) are considered. The term describes the model error in a high-fidelity model. The method for constructing a high-fidelity model to correct a low-fidelity model (describing measurement errors) is as follows:

[0176] Low-fidelity models address the time-consuming nature of finite element models and can capture the mapping relationships of physical mechanisms. However, they still suffer from measurement errors and model errors caused by unmodeled factors, and they do not consider the variable parent body problem.

[0177] To address the aforementioned issues, an adaptive state-space model considering full information (a high-fidelity model) was constructed. The high-fidelity model is as follows:

[0178] ,

[0179] ,

[0180] ,

[0181] in, This is the current state. It is the high-fidelity response corresponding to time step t. Used to capture nonlinear model errors caused by factors not modeled in low-fidelity models. This represents measurement error. Radial basis functions (RBF) are used to fit the nonlinear residuals:

[0182] ,

[0183] Where K is the number of basis functions. It is the center (through the current state) K-means clustering is performed to determine the appropriate clustering method to ensure good coverage while avoiding overfitting. These are shape parameters. The kernel function calculates the vector; It is weight;

[0184] The second row of the inner coefficient matrix A is [0,0] instead of [0,1]. This is due to the rotation transformation. For weakly discernible quantities, prevent them from changing over time and tighten their drift space, while for strongly discernible directions... Then it can be passed Iterative changes are performed, which facilitates parameter decoupling. Once all model parameters are known and the input values ​​of the high-fidelity samples are traced back, forward propagation can be performed according to the following steps:

[0185] remember For the extracted samples, for each sample m, the frontier propagation of the latent variables and the corresponding... The predicted observation values ​​are:

[0186] ,

[0187] ,

[0188] Point prediction and uncertainty interval are determined by The empirical distribution is obtained,

[0189] ,

[0190] In the above high-fidelity model, These unknown parameters together determine the high-fidelity model.

[0191] In a preferred embodiment of the present invention, physical parameters are traced using incomplete high-fidelity response data based on the cut-Bayes method and the plug-in method to obtain complete high-fidelity samples. The method for using high-fidelity input and knowing output—namely, wheel diameters measured from subway trains and wear measurements obtained from the differences, with the input and output combined to form a complete sample—is as follows:

[0192] Using low-fidelity samples By obtaining the estimated parameters of the low-fidelity model Through the cut-Bayes framework, plug-in Marginal likelihood of the post-high-fidelity model for:

[0193] ,

[0194] ,

[0195] ,

[0196] Log-likelihood Expanded to:

[0197] The high-fidelity sample data is incomplete and lacks input states. At the same time, it is necessary to meet the needs of the prediction model, which is achieved through the following two estimation objectives:

[0198] (a) Obtain the physical parameters after rotational transformation by using the prediction distribution of the low-fidelity model and the posterior distribution of the likelihood inference from the high-fidelity model. and The optimal estimated mean, i.e.:

[0199] ,

[0200] in, , It is the likelihood of the high-fidelity function. It is a low-fidelity sample The low-fidelity model trained for source value The predicted distribution and the mean of the posterior distribution will be used as the source input value for the missing high-fidelity samples;

[0201] for Assume prior Then first In Set to zero, other parameters from Initialization in the prior (assuming the low-fidelity model has no error, to obtain the prior...) The approximate posterior distribution simplified using Gibbs sampling is expanded in detail as follows:

[0202] ,

[0203] Wherein, the normalization constant ;

[0204] (b) Estimated parameters using a low-fidelity model And based on the plug-in, it is fixed and inserted, the model's unestimated target via plug-in Maximizing the posterior yields:

[0205] ,

[0206] in, For the edge likelihood (to (integral), if prior Flat, simplified to edge MLE: ;

[0207] Model parameters Only the two key parameters that were previously set to zero remain. The estimated parameters , , , Plug-in, and because of the low-fidelity model's parameter estimates The low-fidelity response has been obtained and can be computed. To minimize residuals (Continue assuming the target is estimated) Measurement error With the objective of zero, the sampling weight vector First, assume The prior is The posterior and likelihood functions are:

[0208] ,

[0209] ,

[0210] Perform MAP estimation on it:

[0211] ,

[0212] in Design matrix ,

[0213]

[0214] Ultimately, all the estimates obtained from the plug-in were... Calculate the final measurement error. Assuming a priori (Conjugate), then its posterior distribution is:

[0215] ,

[0216] Its posterior mean estimate can be solved analytically directly:

[0217] ,

[0218] At this point, all targets to be estimated have been obtained.

[0219] The Cut-Bayes framework protects the stable physical mapping capability of low-fidelity models by cutting off the path through which high-fidelity data affects the parameters of low-fidelity models, and prevents error attribution mismatch from contaminating the core model.

[0220] In a preferred embodiment of the present invention, the Gibbs sampling step is as follows:

[0221] Set the iteration count from t=1 to T, and initialize... Using the prior mean as an assumption, invalid samples outside the physical boundary are rejected:

[0222] S71, for each i, the sampling condition posterior Due to the independence assumption, it simplifies to Conditional density expansion:

[0223] ,

[0224] This is a non-standard Gaussian, which can be sampled using Metropolis-Hastings inline sampling;

[0225] S72, the source value for missing high-fidelity samples can be obtained using the following formula:

[0226] ,

[0227] in This is the combustion period; thus, objective (a) has been determined.

[0228] S73, using k-means clustering Obtain the central value and variance .

[0229] .

[0230] In a preferred embodiment of the present invention, the method for predicting health status is as follows:

[0231] Based on the design diameter and wear condition of each individual wheel, determine its actual diameter. If the actual diameter is not lower than a threshold (e.g., 770 mm), it is considered a safe condition.

[0232] For coaxial wheels i and j, the diameter difference is calculated as follows: ,in, and These represent the predicted diameters of wheel i and j at time t, respectively.

[0233] The diameter of a healthy state is When this value approaches 1, it represents A value close to 0 indicates that the diameters of the two wheels on the same axle are not significantly different, which is a safe condition.

[0234] In a preferred embodiment of the present invention, the wear evolution prediction method further includes remaining service life prediction, the specific method being:

[0235] By combining the results of health status prediction with probabilistic wear predictions from a state-space model (where all parameters to be estimated have been calculated after model training and the sample is complete, and predictions are made recursively using a forward propagation method), the remaining operational mileage is estimated based on the currently predicted wear rate. Through forward propagation of recursive equations, this framework determines two failure mileages: Mileage corresponding to a 1mm difference in wheel diameter on the same axle; (Among coaxial wheels, at the current wear rate, the mileage corresponding to when any wheel diameter drops to the lowest threshold (e.g., 770mm)), the remaining service life (RUL) is the minimum of the two: .

[0236] This invention is used to assess the State of Health (SOH) of metro train wheels and predict their Remaining Useful Life (RUL). The assessment strictly adheres to metro operation and maintenance standards, which specify two key thresholds: the diameter difference between coaxial wheels must not exceed 1 mm to avoid severe vibration, uneven wear, and derailment risks; and the diameter of a single wheel must not be less than 770 mm to ensure structural integrity and operational safety.

[0237] The present invention also provides a wear evolution prediction system based on the method described in the present invention, including a signal acquisition unit, a control unit and a display unit.

[0238] The control unit constructs a parameterized finite element model embedded with the Achad wear equation, establishing an explicit mapping between controllable input and cumulative wear depth output. Physical environment conditions are generated through Latin hypercube sampling, producing low-fidelity samples. A hierarchical proxy model is constructed; the offline low-fidelity model is used to capture the physical mapping relationship of the low-fidelity samples, while the high-fidelity model considers unmodeled factors, variable parent body issues, and measurement errors to correct the low-fidelity model. Using incomplete high-fidelity response data, the physical parameters are traced back to their source based on the cut-Bayes and plug-in methods to obtain complete high-fidelity samples. The finite element model is trained based on these complete high-fidelity samples.

[0239] The control unit also acquires the input parameters of the object to be detected collected by the signal acquisition unit, and uses the trained finite element model to calculate the wheel wear depth to achieve health status prediction.

[0240] To validate the proposed model, a dynamic wheel wear monitoring system was built in collaboration with a rail transit operating company. This system, based on non-contact laser measurement principles, primarily comprises the following core modules: a wheel tread size detection subsystem, a tread image scratch detection subsystem, a vehicle number image recognition module, a field control room, and a client terminal. The system collects laser contour data and high-resolution images of the wheel tread. After image recognition, contour extraction, and parameter calculation, it not only outputs the wheel diameter measurement but also generates other wear indicators through this process.

[0241] The validation dataset consisted of operational records from a subway train system acquired using optical digital acquisition technology over an 8-month observation period, with data points spaced approximately 90 km apart (corresponding to a single round trip). The study systematically measured the diameters of all 48 wheels across multiple train cars. To reduce data redundancy while preserving the visibility of wear trends, diameter variation data from four randomly selected wheels on a bogie were downsampled, resulting in a final data point interval of [missing information]. km.

[0242] The time series of high-fidelity sample responses was decomposed using a seasonal-trend decomposition with Loess (STL) method based on locally weighted regression. The results showed that a monotonic wear trend was superimposed with continuous periodic fluctuations. The extracted trend component (orange curve) exhibited a stable downward trajectory, providing a basis for quantitative wear analysis. Under the same operating conditions, the wheel diameter changes of different axles showed significant consistency. Figure 3 The trend components of wheel 1 obtained by STL decomposition at different number of cycles (20~80) are shown.

[0243] The physical parameters were determined based on experience from subway operation regulations: the normal load F follows a Gaussian distribution (μ = 58,900 N, σ = 5,000 N) to cover load variations under standard passenger load (242 people) and overloaded (336 people) conditions in a Type B car; the wear coefficient was also modeled as a normal distribution based on historical data experience (μ = 2.5 × 10⁻⁻⁶). 4 σ = 1×10⁻ 4 Thirty sets of parameter combinations were generated through Latin hypercube sampling, and the corresponding wear response was obtained through simulation using the finite element method.

[0244] The model performance is shown in Table 2:

[0245] Table 2 Single-step prediction performance

[0246]

[0247] The low-fidelity layer roughly captures the changing trends of the samples, while the high-fidelity layer serves to correct the model.

[0248] In multi-step prediction, the wear rate of the four wheels is extrapolated based on the training results (including inferred physical parameters) of the first 40% of time steps. This study compares three prediction methods: a Bayesian hierarchical surrogate model (Method 1); a deep latent variable state-space model (Method 2); and the data-physical dual-driven hierarchical surrogate model proposed in this invention. Although Method 1 also uses sampling hierarchical modeling, it does not cut off the feedback information in parameter inference through cut-Baysa, which may lead to attribution mismatch and contaminate the model parameters. Although Method 2 introduces a dependent variable, it cannot explicitly trace the underlying physical parameters, resulting in poor physical interpretability. Method 3 reduces the root mean square error (RMSE) by 33.9% and 36.8%, respectively, and the mean absolute error (MAE) by 36.9% and 35.9%, respectively. After overcoming the limitations of the compared models, the proposed method outperforms the first two methods in prediction.

[0249] This invention effectively overcomes the limitations of purely physics-based and purely data-driven methods, taking into account errors caused by unmodeled factors and measurement errors, thus exhibiting strong physical interpretability. Validation results based on measured subway vehicle data show that the proposed method demonstrates higher prediction accuracy and robustness, outperforming existing methods. Therefore, this research provides a robust, interpretable, and adaptive solution for predictive maintenance under conditions of incomplete data and changing populations in engineering projects.

[0250] The specific embodiments described herein are merely illustrative examples of the present invention. Those skilled in the art can make various modifications or additions to the described embodiments or use similar methods to substitute them, without departing from the technology of the present invention or exceeding the scope defined by the appended claims.

Claims

1. A wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework, characterized in that, Includes the following steps: S1, Construct a parameterized finite element model embedded with the Achad wear equation, and establish an explicit mapping between controllable input and cumulative wear depth output; S2 generates physical environment conditions through Latin hypercube sampling, resulting in low-fidelity samples. S3, Construct a hierarchical proxy model. The offline low-fidelity model is used to capture the physical mapping relationship of the low-fidelity samples. The high-fidelity model considers unmodeled factors, variable parent problem and measurement error, and corrects the low-fidelity model. S4. Using incomplete high-fidelity response data, the physical parameters are traced back to obtain complete high-fidelity samples based on the cut-Bayes method and the plug-in method. S5. Based on the complete high-fidelity samples, train a high-fidelity model; S6: Obtain the input parameters of the object to be detected, calculate the wheel wear depth using the trained high-fidelity model, and combine it with the real-time collected wheel diameter to achieve health status prediction.

2. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 1, characterized in that, The method for constructing a parametric finite element model embedding the Archad wear equation is as follows: A single-sided wheel-rail model is used, with the wheel and rail meshed using hexahedral elements. The model focuses on wheel diameter wear caused by wheel-rail contact under straight track conditions, yielding the local wear depth. for: ， in, coordinates Normal contact pressure at the point, Where k is the sliding distance, k is the dimensionless wear coefficient, and H is the material hardness. The normal load N and the wear coefficient k appear as a highly coupled product, which is decoupled into parameters γ and κ through a rotational transformation in logarithmic space: ， ， in, It represents a strongly identifiable direction, and the wear response is quite sensitive to its changes; Representing a weakly discernible direction, the original parameters k and N are rotated to the transformed parameter set through the above transformation process. This indicates that k and N are transformed into gamaγ and kappaκ through logarithmic transformation, and the two transformed quantities are written as a set; the original parameter values ​​are obtained through inverse transformation: ， ， After obtaining the parameters γ and κ, N and k are decoupled.

3. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 1, characterized in that, The low-fidelity model is: ， in, , Let represent the undetermined coefficients corresponding to the i-th basis function. It is the input vector. This represents γ after parameter renormalization. This represents the renormalized k; Represents the i-th training sample, Represents the MQ function, the shape parameter in the MQ function. , is the maximum distance between samples, and N is the number of training samples. for Correlation matrix , represents the polynomial quadratic basis function (MQ); Represents the deviation function The associated coefficient vector, τ(), represents a kind of... The mapping to a high-dimensional feature space is expressed in non-homogeneous polynomial form. To balance the computational burden and subsequent adjustments to the weighting coefficients. Scaling factor. Bias term b and deviation function These are all correction terms set based on the hybrid correction method. It is a vector consisting of the undetermined coefficients corresponding to all basis functions.

4. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 3, characterized in that, Parameters to be estimated in low-fidelity models From low-fidelity samples Conduct training; Maximization Model With low-fidelity response Pearson correlation coefficient squared : ， in, The row vector formed by the mean of each column is used for centering. After projection, it is transformed into finding the matrix. Main eigenvectors : This is the output of the low-fidelity model f1. It is the output obtained from finite element simulation; ， Given a row vector, derived from the matrix The mean of each column constitutes the matrix; P and D are matrices constructed during the process. In solving matrix PYY T The eigenvector corresponding to the largest eigenvalue of P; Back substitution yields coefficients Based on this, Minimize training error while controlling model complexity (regularization): ， Introducing Lagrange multipliers By constructing the Lagrange function and taking its partial derivatives, the KKT conditions can be obtained, which can eliminate... It is then transformed into a system of linear equations: ， The analytical solution is: ， In this context, the superscript "-1" represents the inverse of the matrix, the superscript "T" represents the transpose of the matrix, 1 (in bold) represents the identity matrix, and K represents the kinematic unit. ij The matrix formed, Y L It is a vector composed of the outputs of low-fidelity samples, L: Low, and the letter above the letter "^" is the estimated value of the variable; Gaussian kernel, hyperparameters and regularization parameters By minimizing the cross-validation error, an offline mapping model that achieves a fast and stable response can be obtained. At unobserved points The prediction expression at this location is: 。 5. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 4, characterized in that, Considering unmodeled factors, variable population issues, and measurement errors, the method for constructing a high-fidelity model to correct the low-fidelity model is as follows: The high-fidelity model is: ， ， ， in, This is the current state. It is the high-fidelity response corresponding to time step t. Used to capture nonlinear model errors caused by factors not modeled in low-fidelity models. This represents measurement error. Radial basis functions (RBF) are used to fit the nonlinear residuals: ， Where K is the number of basis functions. It is the center; These are shape parameters. The kernel function calculates the vector; It is weight; Once all model parameters are known and the input values ​​of the high-fidelity samples are traced back, forward propagation can be performed according to the following steps: remember For the extracted samples, for each sample m, the frontier propagation of the latent variables and the corresponding... The predicted observation values ​​are: ， ， Point prediction and uncertainty interval are determined by The empirical distribution is obtained, ， In the high-fidelity model, These unknown parameters together determine the high-fidelity model.

6. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 5, characterized in that, The method for obtaining complete high-fidelity samples by tracing the physical parameters using incomplete high-fidelity response data based on the cut-Bayes and plug-in methods is as follows: Using low-fidelity samples Obtain the estimated parameters of the low-fidelity model. Through the cut-Bayes framework, plug-in Marginal likelihood of the post-high-fidelity model for: ， ， ， Log-likelihood Expanded to: The high-fidelity sample data is incomplete and lacks input states. At the same time, it is necessary to meet the needs of the prediction model, which is achieved through the following two estimation objectives: (a) Obtain the physical parameters after rotational transformation by using the prediction distribution of the low-fidelity model and the posterior distribution of the likelihood inference from the high-fidelity model. and The optimal estimated mean, i.e.: ， in, , It is the likelihood of the high-fidelity function. It is a low-fidelity sample The low-fidelity model trained for source value The predicted distribution and the mean of the posterior distribution will be used as the source input value for the missing high-fidelity samples; for Assume prior ,Will In Set to zero, other parameters from Initialization in the prior (assuming the low-fidelity model has no error, to obtain the prior...) The approximate posterior distribution simplified using Gibbs sampling is expanded in detail as follows: ， Wherein, the normalization constant ; (b) Estimated parameters using a low-fidelity model And based on the plug-in, it is fixed and inserted, the model's unestimated target via plug-in Maximizing the posterior yields: ， in, For the edge likelihood (to (integral), if prior Flat, simplified to edge MLE: ; Model parameters Only the two key parameters that were previously set to zero remain. The estimated parameters , , , Plug-in, and because of the low-fidelity model's parameter estimates The low-fidelity response has been obtained and can be computed. To minimize residuals (Continue assuming the target is estimated) Measurement error With the objective of zero, the sampling weight vector First, assume The prior is The posterior and likelihood functions are: ， ， Perform MAP estimation on it: ， in Design matrix , ， Ultimately, all the estimates obtained from the plug-in were... Calculate the final measurement error. Assuming a priori (Conjugate), then its posterior distribution is: ， Its posterior mean estimate can be solved analytically directly: ， At this point, all targets to be estimated have been obtained.

7. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 6, characterized in that, The Gibbs sampling steps are as follows: Set the iteration count from t=1 to T, and initialize... Using the prior mean as an assumption, invalid samples outside the physical boundary are rejected: S71, for each i, the sampling condition posterior Due to the independence assumption, it simplifies to Conditional density expansion: ， This is a non-standard Gaussian, which can be sampled using Metropolis-Hastings inline sampling; S72, the input source value for high-fidelity sample missing values, is: ， in, The combustion period; S73, using k-means clustering Obtain the central value and variance : 。 8. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 1, characterized in that, The methods for predicting health status are as follows: Based on the design diameter and wear condition of each individual wheel, determine its actual diameter. If the actual diameter is not lower than a threshold, it is considered a safe condition. For coaxial wheels i and j, the diameter difference is calculated as follows: ,in, and These represent the predicted diameters of wheel i and j at time t, respectively. The diameter of a healthy state is When this value approaches 1, it represents A value close to 0 indicates that the diameters of the two wheels on the same axle are not significantly different, which is a safe condition.

9. The wear evolution prediction method based on a data-physical dual-driven hierarchical proxy framework according to claim 1 or 8, characterized in that, It also includes remaining useful life prediction, the specific method of which is as follows: By combining the results of health status prediction with probabilistic wear prediction from a state-space model, the remaining operational mileage is estimated based on the currently predicted wear rate. Through forward propagation of recursive equations, this framework identifies two failure mileages: Mileage corresponding to a 1mm difference in wheel diameter on the same axle; For wheels on the same axle, at the current wear rate, the remaining service life (RUL) is the minimum of the following two values, corresponding to the mileage at which any wheel diameter drops to the minimum threshold: .

10. A wear evolution prediction system based on the method of any one of claims 1-9, characterized in that, It includes a signal acquisition unit, a control unit, and a display unit; The control unit constructs a parameterized finite element model embedded with the Achad wear equation, establishes an explicit mapping between controllable input and cumulative wear depth output; and generates physical environment conditions through Latin hypercube sampling to generate low-fidelity samples. A hierarchical proxy model is constructed. An offline low-fidelity model is used to capture the physical mapping relationships of the low-fidelity samples, while a high-fidelity model considers unmodeled factors, variable parent problems, and measurement errors to correct the low-fidelity model. Using incomplete high-fidelity response data, the physical parameters are traced back to their source using the cut-Bayes and plug-in methods to obtain complete high-fidelity samples. Based on these complete high-fidelity samples, a finite element model is trained. The control unit also acquires the input parameters of the object to be detected collected by the signal acquisition unit, and uses the trained finite element model to calculate the wheel wear depth to achieve health status prediction.

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