Method for determining wave wear damage of steel rail

Abstract

The invention discloses a method for determining wave wear damage of a steel rail. The method comprises the following steps: acquiring rail surface image data and train vibration data which are mutually aligned in time; respectively extracting rail surface image features and vibration features from the rail surface image data and the train vibration data by using a dual-channel deep convolution auto-encoder; inputting the rail surface image features and the vibration features into an efficient multi-scale attention module for dynamic weighted fusion, and generating a continuous health index sequence; inputting the health index sequence into an xLSTM-KAN prediction model, and constructing a steel rail wave wear damage prediction model through a multi-scale gating mechanism and nonlinear mapping based on a B-spline basis function; and the image vibration multi-modal data is predicted through the steel rail wave wear damage prediction model to obtain the steel rail predicted wave wear damage, so that the prediction accuracy of the steel rail wave wear damage prediction model on the steel rail wave wear damage is further improved.

Description

Technical Field

[0001] This invention belongs to the field of track inspection, and in particular relates to a method for determining rail corrugation damage. Background Technology

[0002] At small-radius curves, train wheelsets travel at the same speed on the same axle, but the outer wheel travels longer, and the difference in arc length induces a stick-slip transition between the wheel and rail. When this shearing action couples with the selective frequency resonance of the wheel-rail system, nearly equidistant corrugations gradually form on the rail surface. With the accumulation of total load and increased external disturbances, corrugation evolves rapidly at this interval and in adjacent frequency bands. If a fixed-cycle grinding is still used at this point, it is easy to become mismatched with the actual evolution: prematurely increasing maintenance costs, and prematurely aggravating high-frequency fatigue of fasteners and sleepers, which may lead to train derailment or even derailment in severe cases. Therefore, achieving effective prediction of the evolution trend of corrugation characteristics can provide a basis for on-demand grinding and operation and maintenance decisions, reducing risks and life-cycle costs.

[0003] To predict rail corrugation, a finite element model is typically constructed for analysis and prediction. For example, patent application CN118153364A discloses a method for predicting rail corrugation wear in subway lines. This method involves tracking and investigating rail corrugation phenomena in subway lines. A finite element model of the wheelset-rail system is established based on field survey data, and the vibration characteristics of the wheel-rail system are analyzed to verify the correctness of the finite element model. Based on the measured rail corrugation wear depth from the first field survey, an initial unevenness model of the rail surface is constructed. The tangential stress of the mesh nodes on the rail surface is solved, and the wear amount of the rail surface within the contact patch is calculated based on the friction work theory. Due to the superposition of contact patches, the wear condition of the rail surface is obtained when the wheelset passes through the rail once. Assuming that the wear amount of the rail surface remains constant each time the wheelset passes through, the development of the rail corrugation depth is predicted based on the finite element analysis results over a period of time. A wear correction coefficient is calculated by comparing the results with the field survey data to correct the error between the simulation prediction and the actual measurement, thus achieving the prediction of rail corrugation wear.

[0004] However, the accuracy of its predictions heavily depends on whether the established "wheelset-rail system finite element model" can accurately reflect the complex wheel-rail interactions in the real world. Any model simplification (such as idealization of material properties, boundary conditions, and contact definitions) will introduce errors into the prediction results, leading to inaccurate predictions. Summary of the Invention

[0005] This invention provides a method for determining rail corrugation damage, which improves the accuracy of rail corrugation damage determination.

[0006] According to a first aspect of the present invention, embodiments of the present invention provide a method for determining rail corrugation damage, which may include: Acquire track surface image data and train vibration data that are aligned in time; A dual-channel deep convolutional autoencoder was used to extract track surface image features and vibration features from track surface image data and train vibration data, respectively. The track surface image features and vibration features are input into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence. The health indicator sequence is input into the xLSTM-KAN prediction model, and a rail corrugation damage prediction model is constructed through a multi-scale gating mechanism and a nonlinear mapping based on B-spline basis functions. The rail corrugation damage prediction model is used to predict the multimodal vibration data of the image to obtain the predicted rail corrugation damage.

[0007] Optionally, the dual-channel depth convolutional autoencoder includes: an image encoder and a vibration encoder; Using a dual-channel deep convolutional autoencoder, rail surface image features and vibration features can be extracted from rail surface image data and train vibration data, respectively. This can include: The image encoder extracts track surface image features from track surface image data through a progressive downsampling structure; The vibration encoder uses a pure convolution structure to extract vibration features from train vibration data.

[0008] Optionally, the image encoder extracts track surface image features from the track surface image data through a progressive downsampling structure, including: The image encoder's convolutional layer performs feature compression on the track surface image data by constructing a combination structure of max pooling and leaky linear rectified activation function and two-dimensional convolution. Pooling is removed through the intermediate layer of the image encoder to preserve details; The feature map size is unified by adaptive average pooling, and the orbital surface image features are generated by tensor flattening and fully connected layers.

[0009] Optionally, the vibration encoder employs a pure convolutional structure to extract vibration features from train vibration data, which may include: A three-layer pure convolutional structure is adopted, with each layer using a leaky linear rectified activation function and two-dimensional convolution to extract dynamic response features from train vibration data and generate vibration features.

[0010] Optionally, the track surface image features and vibration features are input into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous sequence of health indicators, which may include: The track surface image features and vibration features are stitched together and reconstructed to obtain a four-dimensional tensor. Multi-scale attention enhancement is applied to the four-dimensional tensor to generate enhanced features; Pooling the enhanced features yields a sequence of health indicators.

[0011] Optionally, the enhanced features include: enhancing long-range dependency features and enhancing local features; Multi-scale attention enhancement is applied to the four-dimensional tensor to generate enhanced features, including: The four-dimensional tensor is grouped to obtain grouped tensors; For each group tensor, perform the following steps 1-2 respectively to obtain the enhanced long-range dependency features and enhanced local features corresponding to each group tensor; Step 1: Perform dual-channel feature extraction to obtain initial long-range dependency features and initial local features; Step 2: The initial long-range dependency features and initial local features are enhanced through a cross-attention mechanism to obtain enhanced long-range dependency features and enhanced local features.

[0012] Optionally, pooling the enhanced features to obtain a health indicator sequence may include: Each enhanced feature is then fused to obtain the first fused feature; The first fusion feature is globally averaged and pooled to generate a health indicator sequence.

[0013] Optionally, the health indicator sequence is input into the xLSTM-KAN prediction model, and a rail corrugation damage prediction model is constructed through a multi-scale gating mechanism and a nonlinear mapping based on B-spline basis functions. This model may include: By slicing the health indicator sequence using a sliding window, time-series input-output sample pairs are obtained. By using a dual-branch structure to extract features from temporal input and output samples, global features and temporal features are obtained. The global features and temporal features are concatenated to generate the second fused feature; The second fused feature is modeled in a fine-grained manner to obtain the temporal feature; Based on the temporal characteristics, a multi-path nonlinear mapping is performed to obtain the feature vector of the first layer output in the xLSTM-KAN prediction model. The feature vector is input into the second layer of the xLSTM-KAN prediction model to optimize the initial model parameters of the xLSTM-KAN prediction model and obtain the optimized model parameters. The xLSTM-KAN prediction model corresponding to the optimized model parameters was determined to be the rail corrugation damage prediction model.

[0014] Optionally, feature extraction of temporal input and output samples using a dual-branch structure can yield global and temporal features, which may include: The upper branch of the dual-branch structure extracts global features from temporal input and output samples through linear transformation and GeLU activation function; The lower branch of the dual-branch structure extracts temporal features from temporal input and output samples through linear transformation, causal convolution, and GeLU activation function.

[0015] Optionally, before inputting the track surface image features and vibration features into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence, the method may further include: Cross-modal feature alignment of track surface image features and vibration features is performed using a joint loss function.

[0016] The technical solutions provided by the embodiments of the present invention bring at least the following beneficial effects: This invention provides a method for determining rail corrugation damage. The method involves acquiring time-aligned rail surface image data and train vibration data; using a dual-channel deep convolutional autoencoder to extract rail surface image features and vibration features from the rail surface image data and train vibration data, respectively; inputting the rail surface image features and vibration features into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence; inputting the health indicator sequence into an xLSTM-KAN prediction model, and constructing a rail corrugation damage prediction model through a multi-scale gating mechanism and nonlinear mapping based on B-spline basis functions; and using the rail corrugation damage prediction model to predict multimodal vibration data of the image to obtain the predicted rail corrugation damage. Based on this, the temporal alignment of track surface image data and train vibration data means that the "appearance" (image) and "sensory experience" (vibration) at the same time and place can be correlated. The fusion of these two modalities fundamentally avoids the limitations of a single information source. When vibration features are blurred due to interference, image features can provide reliable evidence, and vice versa. This greatly enhances the robustness and accuracy of state perception. Furthermore, the advanced xLSTM-KAN prediction model solves the problem of inaccurate prediction of complex nonlinear trends, further improving the accuracy of the rail corrugation damage prediction model for rail corrugation damage.

[0017] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention, but do not constitute an undue limitation of the invention.

[0019] Figure 1 This is a flowchart illustrating a method for determining rail corrugation damage according to an exemplary embodiment; Figure 2 This is a general framework diagram illustrating a method for determining rail corrugation damage according to an exemplary embodiment; Figure 3 This is a flowchart illustrating a health index construction process that integrates track surface image features and vibration features, according to an exemplary embodiment. Figure 4 This is a diagram illustrating an xLSTM-KAN combined prediction framework according to an exemplary embodiment; Figure 5 This is a schematic diagram of an image and vibration response as the cumulative load increases, according to an exemplary embodiment. Figure 6 This is a schematic diagram illustrating the prediction results of a model ablation experiment according to an exemplary embodiment; Figure 7 This is a schematic diagram illustrating the prediction results of a model comparison experiment according to an exemplary embodiment. Detailed Implementation

[0020] To better understand the above-mentioned objectives, features, and advantages of this disclosure, the solutions disclosed herein will be further described below. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0021] Numerous specific details are set forth in the following description in order to provide a full understanding of this disclosure, but this disclosure may also be implemented in other ways different from those described herein; obviously, the embodiments in the specification are only some, and not all, of the embodiments of this disclosure.

[0022] As described in the background section: at small-radius curves, train wheelsets travel at the same speed on the same axle, but the outer wheel travels longer, and the difference in arc length induces a stick-slip transition between the wheel and rail. When this shearing action couples with the selective frequency resonance of the wheel-rail system, nearly equidistant corrugations gradually form on the rail surface. With the accumulation of total load and increased external disturbances, corrugation evolves rapidly at this interval and in adjacent frequency bands. If a fixed-cycle grinding of the rail surface is still used at this time, it is easy to become mismatched with the actual evolution: prematurely increasing maintenance costs, and prematurely aggravating high-frequency fatigue of fasteners and sleepers, which may lead to train derailment or derailment in severe cases.

[0023] Based on this, the present invention provides a method for determining rail corrugation damage. The following is a description of a method for determining rail corrugation damage provided by an embodiment of the present invention.

[0024] like Figure 1-2 As shown; Example 1; It may include the following steps: S101, acquire track surface image data and train vibration data that are aligned with each other in time; S102 uses a dual-channel deep convolutional autoencoder to extract track surface image features and vibration features from track surface image data and train vibration data, respectively. S103 inputs track surface image features and vibration features into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence; S104. Input the health indicator sequence into the xLSTM-KAN prediction model, and construct a rail corrugation damage prediction model through multi-scale gating mechanism and nonlinear mapping based on B-spline basis function. S105, the rail corrugation damage prediction model is used to predict the multimodal vibration data of the image to obtain the predicted rail corrugation damage.

[0025] Based on the above embodiments, track surface image data and train vibration data that are aligned in time are acquired; a dual-channel deep convolutional autoencoder is used to extract track surface image features and vibration features from the track surface image data and train vibration data, respectively; the track surface image features and vibration features are input into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence; the health indicator sequence is input into an xLSTM-KAN prediction model, and a rail corrugation damage prediction model is constructed through a multi-scale gating mechanism and a nonlinear mapping based on B-spline basis functions; the rail corrugation damage prediction model is used to predict the multimodal vibration data of the image to obtain the predicted rail corrugation damage. Based on this, the temporal alignment of track surface image data and train vibration data means that the "appearance" (image) and "sensory experience" (vibration) at the same time and place can be correlated. The fusion of these two modalities fundamentally avoids the limitations of a single information source. When vibration features are blurred due to interference, image features can provide reliable evidence, and vice versa. This greatly enhances the robustness and accuracy of state perception. Furthermore, the advanced xLSTM-KAN prediction model solves the problem of inaccurate prediction of complex nonlinear trends, further improving the accuracy of the rail corrugation damage prediction model for rail corrugation damage.

[0026] In S101 above, the train travels on the track, and the contact between the train wheels and the track generates vibrations, resulting in corrugated wear (corrugation). Rail surface image data can be acquired using sensors installed on the track, and train vibration data can be acquired using sensors on the train. Since corrugation is caused by the train traveling on the track, the causal relationship is consistent in time. Therefore, the acquired rail surface image data... and train vibration data Alignment needs to be performed in time. Here, N is the total number of time windows, C is the number of image channels, and (H, W) and ( , ) represent the spatial dimensions of the image and the reconstructed vibration matrix, respectively.

[0027] Rail surface image data refers to the original visual information of the rail surface directly collected by a dedicated inspection system. This data can be collected synchronously during train operation using a high-speed line scan camera, and can intuitively record geometric changes such as texture, scratches, and periodic ripples on the rail surface.

[0028] Train vibration data refers to the dynamic response signal of the rail-track system as a train passes, recorded by accelerometers. This data is acquired synchronously by triaxial accelerometers, which can capture the vibration acceleration response excited by corrugation.

[0029] In S102 above, the dual-channel deep convolutional autoencoder (DCAE) adopts a parallel dual-channel structure to perform specialized feature extraction for the characteristics of track surface image data and train vibration data, respectively, to obtain track surface image features and vibration features. This design can fully exploit the wave damage features in different modal data, providing high-quality input for subsequent cross-modal fusion.

[0030] The track surface image features refer to the high-level abstract representations extracted from the original track surface image using a dual-channel deep convolutional autoencoder (DCAE). These features focus on the periodic geometric patterns and texture variations of the waviness.

[0031] Vibration characteristics refer to the time-frequency dynamic features extracted from raw vibration data using DCAE. These characteristics capture the vibration response modes and frequency characteristics induced by wave friction.

[0032] A dual-channel deep convolutional autoencoder is an improved autoencoder architecture designed to enhance anomaly detection accuracy by separating and augmenting key region features. It typically comprises two parallel channels, each integrating a deep convolutional network to process global information and local key region information separately. This design helps the model focus on areas prone to anomalous events (such as moving objects in a video) while reducing background interference.

[0033] In S103 above, the efficient multi-scale attention module (EMA) is the core component for constructing rail corrugation health indicators. It is responsible for deeply fusing the rail surface image features and vibration features extracted by the dual-channel deep convolutional autoencoder to generate a sequence of health indicators related to rail corrugation. This module achieves dynamic weighting through a multi-scale attention mechanism to generate a health indicator sequence that can quantify the degree of corrugation evolution, providing robust input for subsequent trend prediction.

[0034] In S104 above, the evolution characteristics and temporal correlation of the health index sequence are first analyzed using the xLSTM model to deepen the understanding of the corrugation changes at each time step. Combined with the nonlinear mapping capability of the KAN model, the extracted features are used for temporal modeling and trend prediction tasks, thereby constructing a rail corrugation damage prediction model.

[0035] The KAN network employs learnable B-spline basis functions to achieve high-order nonlinear mapping, which is the core innovation of the model. B-spline basis functions provide piecewise polynomial representations with local support, exhibiting good numerical stability. Furthermore, the coefficients of the B-spline basis functions are adaptively adjusted through training data, thereby approximating complex functional relationships.

[0036] xLSTM-KAN, as a novel time series prediction model, can effectively capture complex time series dependencies and achieve high-precision prediction of wave erosion evolution trends through flexible nonlinear mapping.

[0037] In S105 above, image vibration multimodal data is collected from the railway system and input into the rail corrugation prediction model for analysis and prediction, thereby obtaining the predicted rail corrugation damage.

[0038] Optionally, in one example, the dual-channel depth convolutional autoencoder includes: an image encoder and a vibration encoder; The above S102 may include: S1021, the image encoder extracts track surface image features from track surface image data through a progressive downsampling structure; The S1022 vibration encoder uses a pure convolution structure to extract vibration features from train vibration data.

[0039] The dual-channel deep convolutional autoencoder (DCAE) is a core component in constructing rail corrugation health indicators. It employs a parallel dual-channel design to extract key features from rail surface image data and train vibration data, respectively. This method utilizes a mode-specific encoder structure to ensure efficient capture of sensitive features related to corrugation damage from heterogeneous data sources.

[0040] In S1021 above, the image encoder is specifically designed to extract periodic geometric features of rail surface corrugation from rail surface image data. It employs a progressive downsampling structure, gradually compressing the feature dimensions while preserving key spatial information, to extract periodic geometric features of rail surface corrugation from the rail surface image data. Extracting track surface image features .

[0041] In S1022 above, the vibration encoder is designed for the time-frequency characteristics of train vibration data, and uses a pure convolution structure to extract the train vibration data. Extract vibration features related to oscillation. .

[0042] Alternatively, in one example, the above S1021 may include: S10211, through the convolutional layer of the image encoder, features are compressed on the track surface image data by constructing a combination structure of max pooling and leaky linear rectified activation function and two-dimensional convolution; S10212, pooling is removed through the intermediate layer of the image encoder to preserve details; S10213 generates orbital image features by unifying the feature map size through adaptive average pooling and then generating them through tensor flattening and a fully connected layer.

[0043] In S10211 above, the image encoder is a key component of the dual-channel deep convolutional autoencoder (DCAE), specifically designed to extract periodic geometric features of corrugation from rail surface image data. This encoder employs a progressive downsampling structure, gradually compressing the feature dimensions through multi-level convolutional operations while preserving key spatial information, ultimately generating high-quality rail surface image features.

[0044] The input orbital plane image data first passes through a convolutional layer to extract primary features; then a max pooling layer halves the feature map size to highlight important feature responses; the LeakyReLU activation function ensures that gradients still flow in negative regions, improving training stability; the second convolutional layer further compresses the feature dimension, forming a compact intermediate representation.

[0045] Max pooling: Spatial downsampling of the input feature map reduces computational complexity while preserving salient features.

[0046] Leaky Rectified Activation Function (LeakyReLU): Introduces a nonlinear transformation to enhance the model's expressive power and prevent gradient vanishing.

[0047] Two-dimensional convolution (Conv2d): Uses convolution kernels to extract local spatial patterns and capture the periodic geometric features of ripples.

[0048] In the above S10212, based on feature compression, the intermediate layer focuses on preserving detailed features to avoid information loss caused by over-downsampling; the intermediate layer adopts a pure convolutional structure to avoid further spatial downsampling, enhances the channel dimension representation capability of the feature map through continuous convolution operations, and expands the receptive field of feature extraction by using larger convolutional kernels or stacking small convolutional kernels.

[0049] The intermediate layer focuses on capturing subtle texture changes and local undulation patterns on the corrugated surface; integrates multi-scale information to form a discriminative high-level feature representation; adjusts the convolution stride and padding method to control the decay rate of the feature map size, maintains spatial resolution while increasing feature depth, avoids loss of detail information, and is particularly optimized for capturing weak signals in the early stage of corrugation, thus enhancing the ability to identify damage in its early stages.

[0050] In S10213 above, the feature map size is unified by average pooling, and the orbital surface image features are generated by tensor flattening and fully connected layers.

[0051] Average pooling unifies the feature map space size, eliminating the influence of input image size differences; specifically, it can generate feature representations of a fixed size to ensure the stability of subsequent processing and provide sufficient feature representation capabilities by preserving rich information in the channel dimension.

[0052] Tensor flattening refers to converting a three-dimensional feature map (channels × height × width) into a one-dimensional feature vector; it provides a suitable input format for fully connected layers, realizes feature space transformation, maintains the spatial correlation of features, and avoids information confusion.

[0053] Fully connected layers are used to map the flattened feature vectors onto a bottleneck space of a specified dimension, generating the final track plane image features. Specifically, the fully connected layer learns the optimal representation of feature combinations through the weight matrix, thereby enhancing feature discriminative power.

[0054] Alternatively, in one example, the above S1022 may include: S10221 employs a 3-layer pure convolutional structure, with each layer using a leaky linear rectified activation function and two-dimensional convolution to extract dynamic response features from train vibration data and generate vibration features.

[0055] In S10221 above, the vibration encoder is an important component of the dual-channel deep convolutional autoencoder (DCAE), specifically designed to extract dynamic response features related to rail corrugation from train vibration data. This encoder employs a simplified three-layer pure convolutional structure and utilizes a specialized time-frequency feature extraction strategy to efficiently capture corrugation-sensitive features in vibration signals.

[0056] Specifically, in the first convolutional layer, the train vibration data undergoes a two-dimensional convolution operation, using a 5×5 convolution kernel to capture the fundamental time-frequency pattern. After convolution, the LeakyReLU activation function is applied, introducing nonlinearity while preserving gradient flow in the negative region. This layer focuses on extracting the overall energy distribution characteristics and fundamental frequency components of the vibration signal.

[0057] The second convolutional layer performs deeper feature extraction based on the primary features. A 3×3 convolutional kernel is used to enhance the extraction capability of local time-frequency features, and the expressive power of the features is improved by increasing the number of output channels. This layer specifically enhances the feature response of the wave-dominant frequency band and captures the resonant frequency patterns generated by wheel-rail coupling.

[0058] The third convolutional layer further abstracts and integrates the features extracted from the first two layers. It uses 1×1 or 3×3 convolutional kernels to perform deep fusion of feature channels, generating a high-level abstract feature representation. This layer focuses on the feature regions most sensitive to wave wear damage, outputting highly discriminative vibration features.

[0059] Example 2: like Figure 3 As shown, optionally, in one example, the above S103 may include: S1031, stitch together and reconstruct the track surface image features and vibration features to obtain a four-dimensional tensor; S1032, multi-scale attention enhancement is applied to the four-dimensional tensor to generate enhanced features; S1033, pooling the enhanced features to obtain the health indicator sequence.

[0060] In S1031 above, the track surface image features Where N is the total number of time windows, Image feature dimension; vibration feature ,in Assuming the vibration feature dimension is the feature dimension, the track surface image features and vibration features are concatenated along this feature dimension to obtain the merged feature matrix. The concatenated feature matrix is ​​two-dimensional, and each row of the feature matrix corresponds to a multimodal fusion representation of a time window, integrating the spatial geometric information of the image and the dynamic response characteristics of vibration.

[0061] Therefore, the two-dimensional matrix is ​​then... Convert to a four-dimensional tensor , where C= + The total number of channels corresponds to the concatenated feature dimension, while h and w are the spatial dimensions. These are adjusted to ensure compatibility of the tensor space dimensions with subsequent modules. This is typically achieved through dimensionality transformation operations, such as reshaping or view operations, integrating the time window dimension N into the batch processing dimension while allocating appropriate spatial dimensions h and w. Essentially, this step reorganizes the features into an image-like structure, facilitating grouped convolutional processing by the EMA (Multi-Scale Attention) module.

[0062] In step S1032 above, the spliced ​​and reconstructed four-dimensional tensor is subjected to multi-scale attention enhancement to obtain enhanced features, which is a key step in constructing rail corrugation health indicators. This process is achieved through an efficient multi-scale attention module (EMA), which aims to dynamically extract the information most relevant to corrugation evolution from the fused multi-modal features and generate enhanced features sensitive to the degree of damage.

[0063] In S1033 above, for each enhancement feature Perform global average pooling to generate a continuous health indicator (HI) sequence.

[0064]

[0065] in, Let be the health indicator value corresponding to the t-th time window. This HI sequence integrates image surface state and vibration dynamic response information, providing a robust and sensitive input to degradation status for subsequent trend prediction.

[0066] Optionally, in one example, the enhanced features include: enhancing long-range dependency features and enhancing local features; The above S1032 may include: S10321, The four-dimensional tensor is grouped to obtain grouped tensors; S10322, For each of the group tensors, perform the following steps 1-2 respectively to obtain the enhanced long-range dependency features and enhanced local features corresponding to each of the group tensors; Step 1: Perform dual-channel feature extraction to obtain initial long-range dependency features and initial local features; Step 2: The initial long-range dependency features and the initial local features are enhanced through a cross-attention mechanism to obtain enhanced long-range dependency features and enhanced local features.

[0067] In S10321 above, the multi-scale attention module will use the four-dimensional tensor Divide the data into g groups according to the channel dimension to obtain the grouped tensor.

[0068] In S10322 above, for each group tensor, the following steps 1-2 are performed respectively to obtain the enhanced long-range dependency features and enhanced local features corresponding to each group tensor.

[0069] Specifically, in step 1, the four-dimensional tensor of the i-th input group... A 1×1 branch is first subjected to average pooling along both the vertical and horizontal directions, resulting in... and Then, the two are concatenated in the spatial dimension, and attention weights are generated by 1×1 convolution Convlx1 and Sigmoid activation. After element-wise multiplication with the original features, GroupNorm is normalized to obtain the initial long-range dependency features. Another 3×3 branch extracts local patterns through standard Conv3×3 convolution, and obtains initial local features through batch normalization (BatchNorm) and ReLU activation. .

[0070] In step 2, to achieve information complementarity, a cross-attention mechanism is employed, using global information from one branch to modulate local features of another branch:

[0071]

[0072]

[0073]

[0074] in, and For global context features; Softmax(·) is the soft maximum value function; and Spatial attention weight map; Scaling factor to prevent gradient vanishing; This indicates that global feature broadcasting is extended to the (h, w) spatial dimension; , These are the features enhanced by cross-attention, namely, enhanced long-distance dependency features and enhanced local features.

[0075] Optionally, S1033 above may include: S10331, fuse each enhanced feature to obtain the first fused feature; S10332, the first fusion feature is globally averaged and pooled to generate a health indicator sequence.

[0076] In S10331 above, the enhanced long-range dependency features within the same enhanced feature are... and enhance local features Integration, to obtain And aggregate across all grouping dimensions to obtain ,right Global average pooling with Sigmoid weighting is performed to obtain the final first fused feature.

[0077] In S10332 above, for each time window Perform global average pooling to generate a continuous sequence of health indicators:

[0078] in, The HI sequence, which integrates image surface condition and vibration dynamic response information, represents the health indicator values ​​corresponding to t time windows. It provides a robust and sensitive input to the degradation state for subsequent trend prediction.

[0079] In the above embodiment 2, each method described in any one of embodiments 1-2 is included, and each process in any one of embodiments 1-2 can be implemented, achieving the same technical effect. To avoid repetition, it will not be described again here.

[0080] Example 3: like Figure 4 As shown, in one example, the above S104 may include: S1041, the health indicator sequence is sliced ​​by a sliding window to obtain time-series input-output sample pairs; S1042 uses a dual-branch structure to extract features from temporal input and output samples, obtaining global features and temporal features. S1043, concatenate the global features and temporal features to generate the second fused feature; S1044, The second fused feature is modeled in a fine-grained manner to obtain the temporal feature; S1045, perform multi-path nonlinear mapping based on temporal characteristics to obtain the feature vector of the first layer output in the xLSTM-KAN prediction model; S1046, Input the feature vector into the second layer of the xLSTM-KAN prediction model to optimize and train the initial model parameters of the xLSTM-KAN prediction model, and obtain the optimized model parameters; S1047, the xLSTM-KAN prediction model corresponding to the optimized model parameters is determined to be the rail corrugation damage prediction model.

[0081] In S1041 above, a sliding window of length n is used to process the constructed HI sequence. Slice the data to form time-series input-output sample pairs:

[0082] in, Let n be the historical state window at time step t; n is the length of the sliding window. This is the target prediction value for the next time step.

[0083] In S1042 above, the captured timing input-output sample pairs After normalization, the model enters a two-branch structure. The parallel two-branch structure aims to capture global features from the health indicator sequence from two different scales: global and local. and time series characteristics .

[0084] In S1043 above, global features are... and time series characteristics The concatenated features are activated by Sigmoid and then fed into a KAN algorithm to learn adaptive nonlinear transformations. Finally, they are passed through a linear layer and causal convolution to generate a second fused feature. .

[0085] In S1044 above, to supplement the matrix-level representation capability of mLSTM, LSTM (sLSTM) is introduced for fine-grained modeling:

[0086]

[0087]

[0088] in, , , These are the input gate, forget gate, output gate, and candidate state weight matrix of the sLSTM, respectively. , , It is a scalar gate value; , These are scalar cell state and hidden state, respectively; (·) is the hyperbolic tangent activation function.

[0089] The second fusion feature After performing fine-grained modeling using the above formula, the temporal features are obtained. ,in:

[0090] In S1045 above, in order to further improve the expressive power of the model, the temporal features obtained by fine-grained modeling are obtained through the xLSTM-KAN prediction model. Perform a high-order nonlinear transformation to extract the feature vector from the first layer of the xLSTM-KAN prediction model. .

[0091] Time series features Simultaneously output two different KAN networks （ and ） Perform multi-path nonlinear mapping to obtain and These two features and After splicing and activation, input the fourth KNA network ( Finally, the first layer output feature vector is generated. .

[0092] Specifically, it can be calculated using the following formula:

[0093]

[0094]

[0095] In S1046 above, the xLSTM-KAN prediction model is composed of two stacked layers. Therefore, the output feature vector of the first layer... This will be used as the input to the second-layer xLSTM-KAN model, and after a processing flow similar to the first layer but with independent parameters, the final predicted value is obtained. .

[0096] Then based on the predicted value Determine the joint loss to use during training:

[0097] Where N is the number of training samples; , These are the predicted value and the actual value of the i-th sample, respectively; Let be the learnable parameters of the j-th KAN module; 1 is the L1 norm; is the L1 regularization coefficient.

[0098] The xLSTM-KAN model is trained end-to-end using the Adam optimizer, and the complete set of trainable parameters is as follows:

[0099] in, For the entire set of trainable parameters; These are the parameters of all linear layers in the xLSTM-KAN model; These are the parameters of the convolutional layers in the xLSTM-KAN model; These are the weight parameters of mLSTM in the xLSTM-KAN model; These are the weight parameters of sLSTM in the xLSTM-KAN model. This is a set of parameters for the trivial and complex KAN module.

[0100] right The initial model parameters are optimized to obtain the final optimized model parameters.

[0101] Optionally, in S1047 above, after optimizing the initial model parameters in the xLSTM-KAN model, the xLSTM-KAN model with optimized model parameters can be confirmed as the rail corrugation damage prediction model.

[0102] Alternatively, in one example, before S03 above, the method may further include: S106 uses a joint loss function to align track surface image features and vibration features across modes.

[0103] In S106 above, the main challenge in multimodal learning, directly fusing data from different sources (such as track surface image data and train vibration data), lies in the semantic inconsistency between modes. Track surface image data records the static geometry of corrugations (such as corrugation spacing and depth), while train vibration data reflects the dynamic response excited by corrugations when a train passes. Simply concatenating these two features makes it difficult for the model to directly establish an accurate correlation between them due to their different original numerical distributions and semantic scales.

[0104] Therefore, it is necessary to have feature vectors (track surface image features and vibration features) from the same time point but different modes in a unified feature space so that they can point to the same degree of wave wear. This process is called cross-modal feature alignment.

[0105] To ensure the characteristics of the track surface image and vibration characteristics To achieve cross-modal semantic consistency and information completeness, vibration energy is used as a weak supervision signal to guide the alignment of images and vibration features in the semantic space. Information fidelity is ensured by constraining the reconstruction task, and a joint reconstruction loss function is designed.

[0106] in, =mean( ,1) represents the average value of the bottleneck feature of the m-th mode along the time dimension; Weakly supervised labels are constructed based on vibrational energy. This is the m-th modal data reconstructed by the DCAE decoder through transposed convolution ConvTrans2d and upsampling; These are the error weighting coefficients for reconstruction.

[0107] The alignment term aims to align features between them, allowing the features of the track surface image to be aligned. and vibration characteristics Align with the same standard on the feature encoder.

[0108] This step involves identifying the bottleneck features for the m-th mode (image or vibration). The average value is calculated over the time dimension. This means condensing the feature information over a period of time into a representative vector, aiming to capture the overall characteristics of the erosion state within that period.

[0109] This is a weakly supervised label, constructed from the L1 norm of the vibration data (which can be approximated as vibration energy). Vibration energy was chosen as the label because the more severe the wave wear, the greater the vibration energy it usually generates, making vibration energy a continuous quantitative indicator that is highly correlated with the severity of wave wear.

[0110] Minimize distance: The loss function requires the average value of image features. and the average value of vibration characteristics Both must be as close as possible to this common vibration energy label y. This forces the image encoder and vibration encoder to cooperate: they must adjust their parameters so that the features they extract, after global averaging, express a degree of erosion consistent with the degree indicated by the vibration energy.

[0111] To reconstruct the project, this is to ensure information integrity and prevent the loss of important information unique to the view modality during alignment. This term is the standard loss of the autoencoder. It requires the entire network (encoder + decoder) to be able to extract bottleneck features. The original input data is reconstructed from the data. .

[0112] If only the alignment item is retained, the encoder might learn to output a very simple value in order to "please" the alignment target. It must contain enough original information; otherwise, the original data cannot be reconstructed.

[0113] These are the weighting coefficients for the reconstruction error, used to balance the importance of the alignment and reconstruction terms.

[0114] In the above embodiment 3, each method described in any one of embodiments 1-3 is included, and each process in any one of embodiments 1-3 can be implemented, achieving the same technical effect. To avoid repetition, it will not be described again here.

[0115] Example 4: Experimental verification and result analysis: Measured data acquisition and preprocessing: To evaluate the applicability of the proposed method in practical engineering scenarios, the Guoneng Baoshen Heavy-Haul Railway, characterized by complex terrain and prominent corrugation issues, was selected as the test line. An integrated image-vibration detection system was employed for synchronous data acquisition. This system integrates a high-speed linear array camera, a three-axis accelerometer, and a high-precision GNSS / odometer positioning module, enabling simultaneous acquisition of track surface images and vibration responses beneath the rails during train operation. Through a unified timestamp and spatial location alignment mechanism, precise synchronization of heterogeneous modal data was achieved, providing high-resolution spatiotemporal information support for corrugation condition observation.

[0116] To obtain a continuous wave-erosion evolution sequence, 10 typical sampling points were set up in the high-incidence area of ​​wave-erosion. Data was continuously collected for 14 cycles at each point to ensure that the samples formed a longitudinal evolution chain at equal time intervals. In terms of preprocessing, the original track surface image was first cropped and grayscale normalized to enhance the structural contrast and texture clarity of the surface morphology. Then, the vertical component related to the wave depth height was extracted from the triaxial acceleration, and the triaxial information was weighted and fused according to the peak response to obtain a single-channel vibration sequence for modeling.

[0117] The changes in rail corrugation images and vibration response at sampling points during the cumulative load increase process are as follows: Figure 5 As shown, with increasing load, the accumulated stress on the rail surface gradually intensifies corrugation, and the surface morphology evolves from shallow scratches to obvious periodic ripples; the vibration acceleration increases synchronously and exhibits stronger disturbance amplitude. The consistency between the two modes in the evolution process provides reliable data support and physical basis for multimodal modeling based on image-vibration fusion.

[0118] Analysis of experimental results: Experimental setup: To verify the engineering applicability of the proposed method, experiments were conducted based on image-vibration multimodal measured data collected from the Guoneng Baoshen Heavy-Haul Railway. Ten typical corrugation samples were selected from the dataset, each containing 14 observation points increasing with cumulative load, forming a time series with continuous evolution characteristics. The samples were divided in a 9:1 ratio: the first nine groups were used for model training, and the remaining group served as an independent test set to evaluate the model's predictive ability in scenarios without observed damage evolution. The main parameter configurations of the model are shown in Table 1.

[0119] Table 1: Main Parameter Settings of the Model

[0120] Ablation experiment: To evaluate the contribution of each substructure of xLSTM–KAN to performance improvement and to verify the effectiveness of the HI sequence constructed by DCAE–EMA in representing wave-erosion states, four ablation models were designed for comparison. Using LSTM–MLP as the baseline, three variants were constructed sequentially: LSTM–KAN, which introduces KAN into the baseline to enhance nonlinear fitting; xLSTM–MLP, which replaces the standard LSTM with a multi-gated xLSTM to strengthen temporal dependency modeling while maintaining the output structure; and the complete model xLSTM–KAN, which integrates multi-scale memory and higher-order nonlinear mapping mechanisms. All models were trained and tested on the same dataset using a unified HI sequence generated by DCAE–EMA as input.

[0121] Ablation test results as follows Figure 6 As shown, the real HI sequence (solid black line) exhibits a phased evolution: initially, growth is slow, with indices distributed in the range of [0.015, 0.032], corresponding to the nascent stage of wave erosion; in the middle stage, it enters a rapid evolution phase, with some samples showing an increase of up to 0.678, reflecting accelerated degradation under the influence of wheel-rail coupling; in the final stage, growth slows down, with changes concentrated in the range of [0.030, 0.080], and the system evolution gradually approaches saturation. The overall trend shows a "stable-rapid-convergent" evolution pattern, consistent with existing understandings of wave erosion formation mechanisms, verifying that the constructed HI sequence characterization has good physical interpretability.

[0122] Model comparisons show that xLSTM-MLP (orange dashed line) fits well on the training set (samples 1-9), but exhibits overshoot and fluctuations on the test set, with predictions deviating from the true values ​​(black solid line). This indicates that enhancing time-series modeling alone easily overfits to local structures and is difficult to generalize to unknown nonlinear evolution. Both LSTM-KAN (green dotted line) and LSTM-MLP (blue dashed line) show significant fluctuations and deviations from the true curves in both the training and testing phases, indicating that traditional structures have limited ability to represent complex wave erosion evolution. While LSTM-KAN improves curve smoothness due to the introduction of KAN, it still exhibits trend lag and local errors, making it difficult to capture cross-period dependencies.

[0123] In contrast, the proposed xLSTM-KAN outputs prediction results (red solid line) that are highly consistent with the true HI curve (black solid line) on all samples. The results show that introducing memory structures or nonlinear mappings alone is insufficient to fully characterize the multi-scale temporal and complex nonlinear evolution in wave erosion. The proposed xLSTM-KAN, by fusing gated memory with higher-order KAN mappings, achieves synergistic modeling of short-term perturbations, long-term dependencies, and nonlinear trends, thereby improving prediction accuracy and generalization ability.

[0124] Comparative experiment: To verify the superiority and generalization ability of the proposed xLSTM-KAN model, a unified HI sequence generated by DCAE-EMA was used as input, and it was compared with three typical temporal networks (GRU, BiLSTM, and TCN) and two recent fusion structures (TCN-GRU-Att and SA-TCN-LSTM). All models were trained on Damage1-9 and tested on independent samples on Damage10 to evaluate their stability under unknown wave-patterning.

[0125] Figure 7 In the diagram, the gray area represents the training phase, the orange area represents the testing phase, and the black solid line represents the real HI sequence. The proposed xLSTM-KAN (red solid line) closely follows the real curve (black solid line) during the training phase and can still accurately reproduce the nonlinear evolution trend on the test sample (Damage10), with no significant lag or oscillation during prediction, demonstrating good cross-sample generalization ability. In contrast, GRU (blue dashed line) performs poorly overall in the testing phase and has response delay; BiLSTM (orange dashed line) can capture the main trend, but overshoots at inflection points; TCN (purple dotted line) exhibits local oscillations and insufficient prediction continuity.

[0126] in conclusion: In the fusion structure, TCN-GRU-Att (yellow long and short dashed lines) and SA-TCN-LSTM (green dotted lines) have better overall fitting than a single network, but there is still a lag in the wave-moistening accelerated evolution section, and the fitting accuracy at key turning points is insufficient.

[0127] The above phenomena indicate that traditional gating or convolutional structures have limitations in capturing long-range dependencies and strong nonlinear jumps; while simple network stacking can alleviate some bottlenecks, it still lacks a unified and high-order nonlinear representation. The proposed xLSTM-KAN achieves collaborative modeling through a multi-scale memory mechanism and a high-order mapping based on B-splines, which improves training accuracy while enhancing the consistency and robustness of the representation of unseen ripple patterns.

[0128] To further quantify the predictive power of each model, the training and testing phases were evaluated using mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²), respectively. The results are shown in Table 2.

[0129] Table 2: Prediction Errors of Different Models

[0130] In Table 2, the proposed xLSTM-KAN achieved the lowest error (MSE=0.001, MAE=0.027) and the highest coefficient of determination (R2=0.987) during the testing phase. Compared with traditional GRU, BiLSTM, and TCN, the MSE was reduced by 83.3%, 93.8%, and 85.7%, respectively, while the R2 was improved by 9.9%, 37.1%, and 10.6%, respectively. Compared with the fusion structures TCN-GRU-Att and SA-TCN-LSTM, the R2 was still improved by 3.1% and 16.2%, respectively, while the MSE decreased by 50.0% and 87.5%, respectively. In addition, the proposed model also maintained low error during the training phase (MSE=0.001, R2=0.989), indicating that it achieved a good trade-off between fitting accuracy and generalization ability, and has the ability to operate stably in complex evolutionary scenarios.

[0131] in conclusion: This application proposes a method for predicting the evolution trend of rail corrugation features by fusing image and vibration information. The method extracts and aligns rail surface images and vibration features using a dual-channel DCAE, constructs an EMA to adaptively fuse the aligned features, and generates a continuous HI sequence to quantify the corrugation evolution process. The HI sequence is then input into an xLSTM-KAN predictor, which uses alternating-gated long / short-term memory to model multi-timescale dependencies and learnable B-splines to achieve high-order nonlinear mapping, thereby completing end-to-end modeling and prediction of the corrugation feature evolution trend.

[0132] Comparative experiments based on measured data from the Guoneng Baoshen Line show that, compared to the two fusion structure models (TCN-GRU-Att and SA-TCN-LSTM), the constructed model achieves superior performance on the test set, with R² improvements of 3.1% and 16.2% respectively, and MSE reductions of 50.0% and 87.5%. Meanwhile, it maintains low error during the training phase (MSE=0.001, R²=0.989), demonstrating strong modeling accuracy and stability.

[0133] While this method performs well in multimodal feature fusion and prediction of complex evolutionary trends, it has not yet demonstrated its ability to model distribution differences across sections and operating conditions, or sensor anomalies (such as missing or drifting). There is still room for improvement in its robustness to large-scale domain migration and data loss. Future work will introduce domain adaptation and incremental update mechanisms, combine uncertainty estimation with threshold-linked decision-making, and explore weak labeling and semi-supervised strategies to further reduce labeling dependence and enhance the sustainability of engineering deployment.

[0134] In the above embodiment 4, each method described in any one of embodiments 1-4 is included, and each process in any one of embodiments 1-4 can be implemented, achieving the same technical effect. To avoid repetition, it will not be described again here.

[0135] The above description is merely a specific embodiment of the present invention. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the protection scope of the present invention.

Claims

1. A method for determining rail corrugation damage, characterized in that, The steps of the method are as follows: Acquire track surface image data and train vibration data that are aligned in time; A dual-channel deep convolutional autoencoder was used to extract track surface image features and vibration features from the track surface image data and the train vibration data, respectively. The track surface image features and the vibration features are input into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence. The health indicator sequence is input into the xLSTM-KAN prediction model, and a rail corrugation damage prediction model is constructed through a multi-scale gating mechanism and a nonlinear mapping based on B-spline basis functions. The rail corrugation damage prediction model is used to predict the multimodal vibration data of the image to obtain the predicted rail corrugation damage.

2. The method for determining rail corrugation damage as described in claim 1, characterized in that, The dual-channel depth convolutional autoencoder includes: an image encoder and a vibration encoder; The method of extracting track surface image features and vibration features from the track surface image data and the train vibration data using a dual-channel deep convolutional autoencoder includes: The image encoder extracts track surface image features from the track surface image data through a progressive downsampling structure; The vibration encoder uses a pure convolutional structure to extract vibration features from the train vibration data.

3. The method for determining rail corrugation damage as described in claim 2, characterized in that, The image encoder extracts track surface image features from the track surface image data through a progressive downsampling structure, including: The image encoder's convolutional layer performs feature compression on the track surface image data by constructing a combination structure of max pooling and leaky linear rectified activation function and two-dimensional convolution. Pooling is removed through the intermediate layer of the image encoder to preserve details; The feature map size is unified by adaptive average pooling, and the orbital surface image features are generated by tensor flattening and fully connected layers.

4. The method for determining rail corrugation damage as described in claim 2, characterized in that, The vibration encoder employs a pure convolutional structure to extract vibration features from the train vibration data, including: A three-layer pure convolutional structure is adopted, with each layer using a leaky linear rectified activation function and two-dimensional convolution to extract dynamic response features from the train vibration data and generate vibration features.

5. The method for determining rail corrugation damage as described in claim 1, characterized in that, The step of inputting the track surface image features and the vibration features into a high-efficiency multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence includes: The track surface image features and the vibration features are stitched together and reconstructed to obtain a four-dimensional tensor. The four-dimensional tensor is subjected to multi-scale attention enhancement to generate enhanced features; The enhanced features are pooled to obtain the health indicator sequence.

6. The method for determining rail corrugation damage as described in claim 5, characterized in that, The enhanced features include: enhanced long-range dependency features and enhanced local features; The step of performing multi-scale attention enhancement on the four-dimensional tensor to generate enhanced features includes: The four-dimensional tensor is grouped to obtain grouped tensors; For each of the group tensors, perform the following steps 1-2 respectively to obtain the enhanced long-range dependency features and enhanced local features corresponding to each of the group tensors; Step 1: Perform dual-channel feature extraction to obtain initial long-range dependency features and initial local features; Step 2: The initial long-range dependency features and the initial local features are enhanced through a cross-attention mechanism to obtain enhanced long-range dependency features and enhanced local features.

7. The method for determining rail corrugation damage as described in claim 5, characterized in that, The process of pooling the enhanced features to obtain the health indicator sequence includes: Each of the enhanced features is fused to obtain a first fused feature; The first fused feature is then subjected to global average pooling to generate a health indicator sequence.

8. The method for determining rail corrugation damage as described in claim 1, characterized in that, The process involves inputting health indicator sequences into the xLSTM-KAN prediction model, and constructing a rail corrugation damage prediction model through a multi-scale gating mechanism and nonlinear mapping based on B-spline basis functions, including: The health indicator sequence is sliced ​​using a sliding window to obtain time-series input-output sample pairs. The time-series input and output samples are used to extract features through a dual-branch structure to obtain global features and time-series features. The global features and the temporal features are concatenated to generate a second fused feature; The second fused feature is then modeled in a fine-grained manner to obtain the temporal feature; Based on the aforementioned temporal characteristics, a multi-path nonlinear mapping is performed to obtain the feature vector of the first layer output in the xLSTM-KAN prediction model. The feature vector is input into the second layer of the xLSTM-KAN prediction model to optimize the initial model parameters of the xLSTM-KAN prediction model and obtain the optimized model parameters. The xLSTM-KAN prediction model corresponding to the optimized model parameters is determined to be a rail corrugation damage prediction model.

9. The method for determining rail corrugation damage as described in claim 8, characterized in that, The step of extracting features from the temporal input and output samples using a dual-branch structure to obtain global features and temporal features includes: The upper branch of the dual-branch structure extracts global features from the temporal input and output samples through linear transformation and GeLU activation function. The lower branch of the dual-branch structure extracts temporal features from the temporal input and output samples by sequentially applying linear transformation, causal convolution, and GeLU activation function.

10. A method for determining rail corrugation damage as described in any one of claims 1-9, characterized in that, Before inputting the track surface image features and the vibration features into an efficient multi-scale attention module for dynamic weighted fusion to generate a continuous health indicator sequence, the method further includes: The track surface image features and the vibration features are aligned across modes using a joint loss function.

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