InSAR-based highway landslide deformation identification method and system

Abstract

Embodiments of the present disclosure provide an InSAR-based highway landslide deformation identification method and system; including obtaining a road structure parameter vector, an InSAR time series deformation signal and a vehicle load time series; inputting the road structure parameter vector and the vehicle load time series into a physical embedding layer, and calculating and generating physical features through a differentiable elastic layered system transfer matrix; inputting the InSAR time series deformation signal into a time series-spectrum feature extractor to generate signal features; taking the physical features as queries, the signal features as keys and values, generating fusion features through a cross-modal physical attention module, and inputting the fusion features into a variational decomposition decoder to obtain a vehicle load component; taking the difference between the InSAR time series deformation signal and the vehicle load component as a net geological deformation signal, and identifying highway landslide deformation. The present application realizes the physical interpretable separation of the vehicle load component and the geological deformation component, and improves the net geological deformation identification performance based on the InSAR time series deformation signal.

Description

Technical Field

[0001] This invention relates to the field of road engineering surveying technology, specifically to a method and system for identifying landslide deformation along highways based on InSAR. Background Technology

[0002] Temporal InSAR technology, with its ability to acquire surface deformation over large areas with millimeter-level accuracy, has become an important tool for highway deformation monitoring. However, highway InSAR temporal deformation signals are a mixture of multiple physical components, including vehicle cyclic loads, geological creep, and temperature effects. Existing highway InSAR deformation models typically use a combination of one or more purely empirical functions to describe temporal deformation, resulting in unclear physical meanings and generally neglecting the contribution of vehicle cyclic loads to settlement. According to the Journal of Radar, in soft soil highway sections, the vehicle cyclic load component is the dominant contributor to deformation in intersection areas, accounting for up to 81%.

[0003] Therefore, the vehicle cyclic load component and the geological deformation component are superimposed in the InSAR time-series signal, making it extremely challenging to separate the pure geological deformation component from the observation signal and reliably identify landslide deformation. How to physically interpretably separate the vehicle load component and obtain the net geological deformation signal from a mechanical mechanism in a highly dynamic highway traffic environment is a core challenge in InSAR highway monitoring. To address these issues, a technical solution is urgently needed that can embed the pavement structure mechanical mechanism into a deep learning framework to achieve interpretable separation of the vehicle load component and the geological deformation component. Summary of the Invention

[0004] This invention takes the fusion of pavement structure mechanics and deep learning as its starting point, and proposes an InSAR-based method and system for identifying landslide deformation along highways. It generates a physically guided deformation sequence with clear mechanical meaning through a differentiable elastic layered system transfer matrix, and combines cross-modal physical attention and variational decomposition decoding to physically interpretably separate vehicle load components and obtain net geological deformation signals, thereby improving the reliability of landslide deformation identification along highways.

[0005] The technical solution adopted in this invention is as follows:

[0006] Methods for identifying landslide deformation along highways based on InSAR include:

[0007] The road structure parameter vector, as well as the spatiotemporally aligned InSAR time-series deformation signal and vehicle load time series, are obtained. The road structure parameter vector includes the elastic modulus, Poisson's ratio, and layer thickness of each structural layer, and also includes the elastic modulus and Poisson's ratio of the subgrade. The structural layers include at least an asphalt layer, a water-stabilized layer, and a graded crushed stone layer.

[0008] The road structure parameter vector and vehicle load time sequence are input into the physical embedding layer, and physical features and physical guided deformation sequences are generated by calculating the transfer matrix of the differentiable elastic layered system.

[0009] The InSAR time-series deformation signal is input into a time-series-spectrum feature extractor to generate signal features;

[0010] Using physical features as queries and signal features as keys and values, a cross-modal physical attention module generates fused features.

[0011] The fused features are input into the variational decomposition decoder to decode several modal components and their corresponding attribution weights. The modal component with the largest attribution weight is determined as the vehicle load component.

[0012] The difference between the InSAR temporal deformation signal and the vehicle load component is used as the net geological deformation signal, and landslide deformation along the highway is identified based on the net geological deformation signal.

[0013] This disclosure also provides a computer-readable storage medium or computer program product having a computer program / instructions stored thereon, characterized in that the computer program / instructions, when executed by a processor, implement the method described in any of the preceding claims.

[0014] This disclosure also provides an InSAR-based system for identifying landslide deformation along highways, characterized in that it includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described in any of the preceding claims.

[0015] This invention establishes a differentiable forward model capable of analytically calculating the Green's function of road surface deflection and generating physically guided deformation sequences with clear mechanical meaning by constructing a differentiable elastic layered system transfer matrix physical embedding layer. By combining this physical embedding layer with a time-series-spectral feature extractor, a cross-modal physical attention module using physical features as queries, and a variational decomposition decoder into an end-to-end training framework, and using reconstruction loss, KL divergence loss, physical consistency loss, modal orthogonality loss, and attribution entropy regularization loss to jointly supervise the joint optimization of the learnable parameters of the physical embedding layer and the neural network parameters, physically interpretable separation of vehicle load components and geological deformation components is achieved, improving the net geological deformation identification performance based on highway InSAR time-series deformation signals. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the method of the present invention.

[0017] Figure 2 This is a schematic diagram of the road structure parameter vector described in this invention.

[0018] Figure 3 This is a schematic diagram illustrating the calculation process of the state vectors of each structural layer in this invention.

[0019] Figure 4 This is a schematic diagram of the process for obtaining the vehicle load component according to the present invention.

[0020] Figure 5 This is a schematic diagram of the system of the present invention. Detailed Implementation

[0021] The method of the present invention will be described in detail below, with detailed implementation methods and specific operation procedures provided. However, the scope of protection of the present invention is not limited to the following implementations.

[0022] Example 1:

[0023] like Figure 1 , Figure 2 , Figure 3 , Figure 4 As shown, the forward reasoning in the InSAR-based method for identifying landslide deformation along highways includes:

[0024] Step S110: Obtain the road structure parameter vector and the spatiotemporally aligned InSAR time-series deformation signal and vehicle load time series. The road structure parameter vector includes the elastic modulus, Poisson's ratio, and layer thickness of each structural layer, as well as the elastic modulus and Poisson's ratio of the subgrade. The structural layers include at least an asphalt layer, a water-stabilized layer, and a graded crushed stone layer.

[0025] Step S110 includes the process of acquiring road structure parameter vectors, the process of acquiring InSAR time-series deformation signals, the process of acquiring vehicle load time series, and the process of aligning the three in time and space.

[0026] To obtain the road structure parameter vector, as-built documents or design documents along the highway to be monitored are collected, and the road structure parameters for each structural section are extracted from them. The structural layers include at least an asphalt layer, a water-stabilized layer, and a graded crushed stone layer. In this embodiment, the asphalt layer is further divided into an asphalt surface layer, an asphalt intermediate layer, and an asphalt bottom layer. The water-stabilized layer is a cement-stabilized crushed stone base course, and the graded crushed stone layer is a graded crushed stone subbase course. The six-layer system, with the subgrade beneath each of the above structural layers, is used as an example for illustration. Other layered system structures can be deduced similarly. For each structural layer, its elastic modulus, Poisson's ratio, and layer thickness are extracted; for the subgrade, its elastic modulus and Poisson's ratio are extracted. The above parameters are arranged in order from the road surface to the roadbed to form a road structure parameter vector. This vector consists of the following components in sequence: the elastic modulus of the top layer, the Poisson's ratio of the top layer, the thickness of the top layer, the elastic modulus of the middle layer, the Poisson's ratio of the middle layer, the thickness of the middle layer, the elastic modulus of the bottom layer, the Poisson's ratio of the bottom layer, the thickness of the bottom layer, the elastic modulus of the water-stabilized layer, the Poisson's ratio of the water-stabilized layer, the thickness of the water-stabilized layer, the elastic modulus of the graded crushed stone layer, the Poisson's ratio of the graded crushed stone layer, the thickness of the graded crushed stone layer, the elastic modulus of the roadbed, and the Poisson's ratio of the roadbed. The unit for each elastic modulus is MPa, each Poisson's ratio is dimensionless, and each layer thickness is mm. The road structure parameter vector is indexed by the cross-section station number. The coherence points between adjacent cross-sections are obtained through linear interpolation or by directly using the parameters of the nearest cross-section. During linear interpolation, the elastic modulus, Poisson's ratio, and layer thickness of each structural layer are linearly interpolated according to the distance ratio between the coherent point station number and the station numbers of two adjacent sections.

[0027] For the acquisition of InSAR time-series deformation signals, multiple synthetic aperture radar images covering the highway area to be monitored are collected. Small baseline set InSAR technology or permanent scatterer InSAR technology is used for processing. The processing flow includes synthetic aperture radar image registration, interferogram generation, terrain phase removal, atmospheric delay correction, phase unwrapping, and deformation inversion based on singular value decomposition to obtain the radar line-of-sight deformation time series of each coherent point along the highway. Each coherent point contains the cumulative deformation value of T time sampling points, in mm.

[0028] For acquiring vehicle load time series data, hourly traffic flow data categorized by vehicle type is collected from ETC gantry systems or traffic survey stations along the highway. The time span must cover the entire period of the InSAR time series deformation signal. For each InSAR image acquisition time, records of all vehicles passing through the corresponding road segment within 24 hours before and after that time are taken. The 24-hour time window is chosen to cover the complete daily traffic volume cycle to eliminate intraday fluctuations, and is sufficiently short compared to the InSAR image acquisition interval (usually 6-12 days) to avoid over-smoothing load characteristics. The traffic volume of different vehicle types can be converted into equivalent standard axle load application times according to the axle load conversion factor specified in the "Specifications for Design of Highway Asphalt Pavement" (JTG D50-2017), and then averaged by the time window length to obtain the vehicle load time series value representing the load level at that time. The vehicle load time series generated in this way has exactly the same time sampling points as the InSAR time series deformation signal at the coherent point, ensuring strict alignment between the two in the time dimension.

[0029] For spatiotemporal alignment, the InSAR temporal deformation signal, vehicle load time series, and road structure parameter vector of the aforementioned coherent point are associated according to the spatial location of the coherent point. In this embodiment, the road structure section where the coherent point is located is determined based on the latitude, longitude, or station number of the coherent point, thereby assigning the corresponding road structure parameter vector. Simultaneously, based on the road segment interval to which the coherent point belongs, the vehicle load time series recorded by the adjacent ETC gantry, which has undergone time alignment processing, is extracted. In summary, each coherent point yields a data set containing the InSAR temporal deformation signal of that coherent point, the vehicle load time series of that coherent point, and the road structure parameter vector of that coherent point. In the subsequent steps S120 to S160 of this embodiment, the corresponding data in this data set is used as input.

[0030] Step S120: Input the road structure parameter vector and vehicle load time sequence into the physical embedding layer, and generate physical features and physical guided deformation sequences through the transfer matrix of the differentiable elastic layered system.

[0031] The physical embedding layer receives the road structure parameter vector and vehicle load time series of the coherent point obtained in step S110 as input, realizes the analytical solution of the elastic layered system theory as a differentiable computation graph, and outputs physical features and a physical guided deformation sequence. Among them, the physical features are used for query calculation of the subsequent cross-modal physical attention module, and the physical guided deformation sequence is used for constructing the physical consistency loss in the variational decomposition decoder.

[0032] Step S121: In the Hankel transform domain, according to the preset transform parameters (including the integral order of the Hankel transform, the range of discrete wavenumbers, and the number of integration points), calculate the transfer matrix based on the elastic modulus, Poisson's ratio, and layer thickness of each structural layer, and obtain the state vector of the graded crushed stone layer by using the elastic half-space boundary conditions of the roadbed's elastic modulus and Poisson's ratio.

[0033] In cylindrical coordinates, the transfer relationship of the i-th layer of an elastic layered system in the Hankel transform domain is expressed as the product of the transfer matrix of the i-th layer and the state vector of the (i-1)-th layer. The state vector contains four components: radial displacement, vertical displacement, vertical normal stress, and radial shear stress. The transfer matrix is ​​a 4×4 matrix, and its analytical form adopts the known expression in the mechanics of layered elastic systems, namely:

[0034]

[0035] in The coefficient matrix is ​​a 4×4 matrix consisting of the elastic modulus and Poisson's ratio of the layer. Each element of the transfer matrix is ​​a known function of the elastic modulus, Poisson's ratio, layer thickness, and Hankel transformation parameters of the layer.

[0036] For each structural layer, the elastic modulus, Poisson's ratio, and layer thickness corresponding to that layer are extracted from the road structural parameter vector at that coherence point, and then substituted into the analytical expression of the transfer matrix for calculation. Taking the asphalt surface layer as an example, the elastic modulus, Poisson's ratio, and layer thickness of the surface layer are read from the road structural parameter vector, and combined with the preset Hankel transformation parameters, the transfer matrix of the asphalt surface layer is calculated. Similarly, the transfer matrices of the asphalt intermediate layer, asphalt lower layer, water-stabilized layer, and graded crushed stone layer are calculated sequentially.

[0037] The subgrade is considered as an elastic half-space, and its elastic modulus and Poisson's ratio are derived from the road structure parameter vector at the coherent point. Based on the elastic half-space boundary condition, i.e., displacement and stress tend to zero at infinite depth, the state vector at the bottom of the graded crushed stone layer is directly determined. Each component in this state vector is analytically expressed using the subgrade's elastic modulus, Poisson's ratio, and Hankel transform parameters. Here, the elastic half-space boundary condition is expressed as follows: at infinite depth, radial displacement, vertical displacement, vertical normal stress, and radial shear stress are all zero. Therefore, the proportional relationships and amplitudes of each component in the state vector at the bottom of the graded crushed stone layer can be uniquely determined.

[0038] Step S122: Starting from the graded crushed stone layer, the state vector of the current layer is obtained by multiplying the state vector of the previous layer with the transfer matrix of the current layer. This state vector is then transferred upwards through the water-stabilized layer and the asphalt layer to the road surface, thereby obtaining the vertical displacement of the road surface in the Hankel transform domain. The state vector includes radial displacement, vertical displacement, vertical normal stress, and radial shear stress.

[0039] Starting with the state vector of the bottom surface of the graded crushed stone layer determined by the elastic half-space boundary conditions in step S121, the state vector of the bottom surface of the graded crushed stone layer is multiplied by the transfer matrix of the graded crushed stone layer to obtain the state vector of the top surface of the graded crushed stone layer (i.e., the bottom surface of the water-stabilized layer). Then, the state vector of the bottom surface of the water-stabilized layer is multiplied by the transfer matrix of the water-stabilized layer to obtain the state vector of the top surface of the water-stabilized layer (i.e., the bottom surface of the asphalt lower layer). This process is repeated layer by layer upwards, passing through the asphalt lower layer, the asphalt intermediate layer, and the asphalt upper layer, finally obtaining the state vector at the road surface. The vertical displacement component is extracted from the state vector at the road surface, which is the vertical displacement of the road surface in the Hankel transform domain.

[0040] In summary, the transfer relationship between the state vector of each layer and its bottom and top surfaces is uniquely determined by the transfer matrix of that layer. The transfer matrix contains all the mechanical information regarding the layer's elastic modulus, Poisson's ratio, and layer thickness. Since each element of the transfer matrix is ​​a differentiable analytic function, the entire layer-by-layer transfer process from the roadbed to the road surface constitutes a complete differentiable computational path. During the backpropagation process of subsequent end-to-end training, the gradient generated by the total loss of the variational decomposition decoder can be backpropagated layer by layer to the learnable parameters of the physical embedding layer via the cross-modal physical attention module, thereby achieving optimized updates of the physical parameters.

[0041] Step S123: Transform the vertical displacement of the road surface back into physical space using the inverse Hankel transform based on numerical integration, and obtain the Green's function of road surface deflection under unit vertical load.

[0042] The vertical displacement of the road surface in the Hankel transform domain obtained in step S122 is a function of the Hankel transform parameters. It needs to be transformed back to physical space using the inverse Hankel transform to obtain the vertical displacement of the road surface in physical space. The inverse Hankel transform is that the vertical displacement of the road surface in physical space is equal to the integral of the product of the vertical displacement of the road surface in the Hankel transform domain, the first-order zero-order Bessel function, and the Hankel transform parameters over zero to infinity. This integral is achieved through numerical integration. In this embodiment, the Gauss-Legendre integral is used, with 64 integration points and an upper limit of 50 / R, where R is the radius of the aforementioned circular uniformly distributed load region. This ensures that the Bessel function completes a sufficient oscillation period within the integration interval while maintaining numerical accuracy.

[0043] In this embodiment, to suppress the numerical instability caused by the Bessel function during high-frequency oscillations, an exponentially decaying window function with a decay factor of 0.1 is introduced into the integrator kernel. After numerical integration, the vertical displacement of the road surface when a unit vertical load is applied to the center of a circular uniformly distributed load area of ​​radius R is obtained, where R is typically 150 mm (i.e., the single-wheel ground contact radius of a standard axle load BZZ-100). This displacement value is the road surface deflection Green's function. The road surface deflection Green's function depends only on the road structure parameter vector at this coherent point, reflecting the mechanical response characteristics of the road structure itself, and is independent of the load magnitude. The entire numerical integration process is implemented using a differentiable calculation method to ensure that the gradient can be propagated back to the structural layer parameters in the transfer matrix through the inverse Hankel transform.

[0044] Step S124: For each coherent point in the InSAR time-series deformation signal, multiply and superimpose the vehicle load time series with the road surface deflection Green's function to obtain the physical characteristics.

[0045] For the coherent point, the vehicle load time series value of each time sampling point in the vehicle load time series obtained in step S110 is multiplied by the road surface deflection Green's function obtained in step S123 to obtain the road surface deflection value of each time sampling point. According to the linear superposition principle of elastic layered system theory, when multiple loads act simultaneously, the total deflection is equal to the sum of the deflections when each load acts alone. Since the loads at each time sampling point in the vehicle load time series are independent of each other, the road surface deflection value of each time sampling point is the vertical displacement of the road surface caused by the vehicle load acting alone at that moment.

[0046] Arrange the road surface deflection values ​​of all time sampling points along the time dimension to form a T-dimensional vector. This vector represents the physical feature of the coherent point, with a shape of T×1, indicating the time series of theoretical vertical displacements of the road surface caused by vehicle loads at T time sampling points. The physical feature represents the theoretically calculated value of the vertical deformation of the road surface caused by the vehicle load time series under the current road structure parameter vector, serving as the source of the query vector in the subsequent cross-modal physical attention module.

[0047] Step S125: Map the physical features into a one-dimensional physical guided deformation sequence via linear projection.

[0048] At the end of the physical embedding layer, a physical feature aggregation head is set. This aggregation head consists of a linear projection layer, which maps the T×1 dimensional physical features generated in step S124 into a physical guided deformation sequence through trainable linear projection parameters. The physical guided deformation sequence also has a dimension of T×1, and the value of each time sampling point represents the deformation value at the corresponding moment in the theoretical deformation time series of vehicle load simulated by the physical embedding layer under the current learnable road structure parameters and the vehicle load time series at that coherent point.

[0049] The projection parameters of this linear projection, as part of the trainable parameters of the physics-guided neural decomposition network, participate in gradient optimization during subsequent end-to-end training. The physics-guided deformation sequence will be directly used to construct the physical consistency loss in the variational decomposition decoder, including calculating the alignment and orthogonality terms between each modal component and the physics-guided deformation sequence.

[0050] In the pure forward inference of Example 1 (i.e., the deployment phase after the training of Example 2 has been completed), physical features are used as query Q of the cross-modal physical attention module to participate in the fusion calculation of S140-S144. The physical guidance deformation sequence is reserved as a supervision signal for the physical consistency loss in the training phase and does not participate in the deformation decomposition calculation of forward inference.

[0051] Some parameters in the physical embedding layer are used as learnable parameters, initialized with design values, and participate in gradient-based update training. In this embodiment, based on sensitivity analysis, the elastic modulus of the subgrade and the equivalent elastic modulus of the surface layer in the road structure parameter vector are set as learnable parameters. The equivalent elastic modulus of the surface layer is the equivalent modulus after the asphalt surface layer, asphalt intermediate layer, and asphalt bottom layer are equivalent to a homogeneous layer. The remaining parameters, including the Poisson's ratio of each structural layer, the layer thickness of each structural layer, and the elastic modulus of the intermediate structural layers other than the surface layer and subgrade, are fixed at design values. Before training begins, the learnable parameters are initialized with the design values ​​obtained from the as-built documents or design documents in step S110. During training, the gradient of the learnable parameters comes from the total loss of the variational decomposition decoder. This gradient is backpropagated to the physical embedding layer via the cross-modal physical attention module, driving the learnable parameters to adjust from the design values ​​to the optimal values. For specific training methods, see Embodiment 2.

[0052] Step S130: Input the InSAR time-series deformation signal into the time-series-spectrum feature extractor to generate signal features.

[0053] The time-series-spectrum feature extractor receives the InSAR time-series deformation signal of the coherent point obtained in step S110 as input, extracts signal features that combine temporal multi-scale patterns and frequency-domain local structures from the InSAR time-series deformation signal, and outputs them to the subsequent cross-modal physical attention module as the source of keys and values. Components from different physical sources in the InSAR deformation signal have different time-frequency characteristics: vehicle load deformation is related to traffic flow and has a daily and weekly cycle; geological deformation is mainly characterized by long-term linear trends and seasonal cycles; temperature effect deformation is mainly characterized by daily and annual cycles. The time-series-spectrum feature extractor captures the above-mentioned temporal patterns and frequency-domain structures through parallel temporal convolution branches and spectral attention branches, respectively, and then fuses the features of the two branches and captures long-range dependencies through a bidirectional long short-term memory network to generate signal features.

[0054] Step S131: Input the InSAR temporal deformation signal into the temporal convolution branch and the spectral attention branch respectively.

[0055] The time-series-spectrum feature extractor comprises two parallel branches: a time-series convolution branch and a spectral attention branch. The InSAR time-series deformation signal at the coherence point is simultaneously input into both branches. The time-series convolution branch is responsible for extracting temporal patterns at different scales in the time domain, while the spectral attention branch is responsible for extracting local structural features of the spectrum in the frequency domain. The outputs of the two branches are fused in step S134.

[0056] Step S132: The temporal convolution branch extracts the multi-scale temporal pattern of the InSAR temporal deformation signal through multiple layers of one-dimensional convolution, and each convolution is followed by batch normalization and activation function.

[0057] The temporal convolution branch consists of multiple stacked one-dimensional convolutional layers. In this embodiment, three one-dimensional convolutional layers are used, with kernel sizes of 7, 5, and 3 respectively, a stride of 1 for each, and equal-length padding for all layers. The decreasing kernel size design allows each layer to focus on different temporal patterns: the first layer captures patterns with longer periods, the second layer captures patterns with intermediate periods, and the third layer captures patterns with shorter periods. Each one-dimensional convolutional layer is followed by batch normalization and the GELU activation function. Batch normalization is used to accelerate training and stabilize the feature distribution, while the GELU activation function is a smooth non-linear activation function that alleviates the gradient vanishing problem while maintaining non-linear expressive power.

[0058] The number of channels in the three one-dimensional convolutional layers are set to 32, 64, and 64 respectively. The InSAR temporal deformation signal of the input coherent point, with a shape of T×1, is processed through the first convolutional layer (kernel size 7, number of channels 32) to obtain a feature map of shape T×32. The second convolutional layer (kernel size 5, number of channels 64) yields a feature map of shape T×64, and the third convolutional layer (kernel size 3, number of channels 64) produces a feature map of shape T×64. This T×64 feature map represents the multi-scale temporal pattern extracted by the temporal convolutional branch.

[0059] Step S133: The spectral attention branch performs a short-time Fourier transform on the InSAR time-series deformed signal to obtain a time-spectral map. The local spectral pattern is extracted by performing two-dimensional convolution on the time-spectral map, and then the spectral features are obtained by global average pooling in the frequency dimension.

[0060] The spectral attention branch first performs a short-time Fourier transform (SFT) on the InSAR temporal deformation signal at the coherent point to obtain a time-spectrum graph. In this embodiment, the window length of the SFT is set to 16 time sampling points, the window overlap is set to 8 time sampling points, and the Hanning window is selected as the window function. The SFT converts the one-dimensional InSAR temporal deformation signal into a two-dimensional time-spectrum graph, with the horizontal axis representing the time dimension and the vertical axis representing the frequency dimension. Each pixel value represents the complex spectral amplitude at the corresponding time and frequency.

[0061] Two-dimensional convolutional layers are applied to the time-spectrum graph, both with a kernel size of 3×3, a stride of 1, and equal-length padding. The number of channels is 16 and 32 respectively. Each 2D convolutional layer is followed by batch normalization and a GELU activation function. The 2D convolution extracts local patterns in the spectral space by sliding the convolution kernel along the time and frequency dimensions of the time-spectrum graph, such as the energy variation of a specific frequency band over time and the energy transfer between adjacent frequency bands.

[0062] After two layers of 2D convolution, a feature map of shape T×F×32 is obtained, where F is the frequency dimension length. In this embodiment, the number of FFT points is 16 (equal to the window length), and a single-sided spectrum is used, so F=16 / 2+1=9. Global average pooling is then performed along the frequency dimension of this feature map, compressing the frequency dimension to 1, resulting in a spectral feature of shape T×32. The spectral feature retains the variation information in the time dimension, and simultaneously integrates the spectral structure information of all frequency bands through global pooling in the frequency dimension.

[0063] Step S134: The multi-scale time pattern and spectral features are concatenated along the feature dimension, mapped to a unified feature space by linear projection, and then long-range dependencies are captured through a bidirectional long short-term memory network to generate signal features.

[0064] The multi-scale temporal pattern with shape T×64 obtained in step S132 is concatenated with the spectral feature with shape T×32 obtained in step S133 along the feature dimension to obtain a concatenated feature with shape T×96. This concatenated feature is then mapped to a unified feature space through a linear projection layer. The linear projection layer has an input dimension of 96 and an output dimension of d, where d is the unified feature dimension; in this embodiment, d is set to 128. The function of the linear projection layer is to map features from different branches with different numerical distribution ranges to a feature space of the same scale, facilitating subsequent processing.

[0065] After linear projection, the feature sequence of shape T×d is input into a single layer of bidirectional long short-term memory (BiLSTM) network. Each unidirectional hidden dimension of the BiLSTM is set to d / 2, or 64; the hidden states in the forward and backward directions are concatenated along the feature dimensions, resulting in a total output dimension of d, or 128. By establishing recursive connections in both the forward and backward directions of the time dimension, the BiLSTM ensures that the output at each time sampling point depends not only on the signal before that moment but also on the signal after that moment, thus capturing the long-range dependencies in InSAR time-series deformed signals. The output shape of the BiLSTM is T×d, which represents the signal features generated by the time-series-spectral feature extractor.

[0066] The signal features simultaneously include the multi-scale time patterns, local spectral structure, and long-range temporal dependencies of the InSAR time-deformed signal, which will serve as the source of keys and values ​​in the subsequent cross-modal physical attention module.

[0067] Step S140: Using physical features as queries and signal features as keys and values, generate fused features through the cross-modal physical attention module.

[0068] The cross-modal physical attention module receives the physical features generated in step S125 and the signal features generated in step S134 as input. Using the physical features as queries and the signal features as keys and values, it employs a multi-head cross-attention mechanism to structurally guide the physical modality towards the data modality, outputting fused features. The core design of the cross-modal physical attention module lies in the asymmetric allocation of queries, keys, and values; that is, physical features generate queries, and signal features generate keys and values. This allows physical features to guide the selective aggregation of components in the signal features consistent with physical predictions, rather than undifferentiatedly fusing the two types of features on an equal footing. The fused features will serve as input to the subsequent variational decomposition decoder.

[0069] Step S141: Obtain the query by linear projection of the physical features, and obtain the key and value by linear projection of the signal features.

[0070] The cross-modal physical attention module employs a multi-head attention mechanism. In this embodiment, the number of attention heads is set to 8, the uniform feature dimension d is set to 128, and the dimension of each attention head is d divided by the number of attention heads, which is 16.

[0071] For each attention head, the physical feature of shape T×1 generated in step S125 is mapped to a query through a linear projection layer. The input dimension of the linear projection layer is 1 and the output dimension is 16. That is, the physical feature of shape T×1 is linearly projected step by step over time to obtain a query of shape T×16. The signal feature of shape T×d generated in step S134 is mapped to a key and a value through two independent linear projection layers. The input dimension of each linear projection layer is d (128) and the output dimension is 16. That is, the signal feature of shape T×d is linearly projected step by step over time to obtain a key and a value of shape T×16. Taking the h-th attention head as an example, its query, key, and value are calculated as follows: the query of the h-th attention head is equal to the product of the physical feature and the query projection matrix of the h-th attention head; the key of the h-th attention head is equal to the product of the signal feature and the key projection matrix of the h-th attention head; and the value of the h-th attention head is equal to the product of the signal feature and the value projection matrix of the h-th attention head. The query projection matrix, key projection matrix, and value projection matrix of the h-th attention head are all trainable linear projection parameters. The query projection matrix, key projection matrix, and value projection matrix of each of the eight attention heads are independent and do not share parameters, allowing different attention heads to focus on different aspects of the physical-data association patterns in the signal features.

[0072] After the query, key, and value calculations are completed, layer normalization is applied to the query, key, and value of each attention head to ensure that the features of the physical modality and the data modality are at similar numerical scales before entering the attention calculation, thus avoiding excessive differences in feature scales between different modalities that could cause the attention weights to be biased towards a certain modality.

[0073] Step S142: Divide the similarity between the query and the key by the scaling factor to obtain the scaled attention score matrix, superimpose the learnable physical prior bias matrix for bias correction, obtain the attention weights through the Softmax function, and multiply the attention weights by the values ​​to obtain the single-head attention output.

[0074] For each attention head, the query obtained in step S141 is multiplied by the key of that attention head to calculate a similarity matrix between the query and the key. The similarity matrix has a shape of T×T, where the element in the i-th row and j-th column represents the similarity between the physical feature query at the i-th time sampling point and the signal feature key at the j-th time sampling point. Each element of the similarity matrix is ​​divided by a scaling factor, which is the square root of the dimension of each attention head, i.e., √16 equals 4, to alleviate the problem of the gradient of the Softmax function tending to zero due to excessively large dot product values.

[0075] A learnable physical prior bias matrix is ​​superimposed on the similarity matrix after scaling. All its elements are trainable parameters, automatically updated during training via gradient descent. The physical prior bias matrix is ​​initialized as a local prior at the beginning of training, denoted as:

[0076]

[0077] Wherein, σ is the attenuation scale parameter, which is set to 5 in this embodiment. The physical meaning of this initialization is: the closer two sampling points are in time, the stronger the correlation between their physical characteristics and signal characteristics should be; the deformation of the vehicle load at a certain moment is most correlated with the signal characteristics near that moment. As training progresses, the value of the physical prior bias matrix starts from this local prior and is automatically adjusted according to the total loss of the variational decomposition decoder, learning a bias pattern suitable for the current data distribution.

[0078] The similarity matrix, superimposed with the physical prior bias matrix, is input into the Softmax function and normalized along the key dimension to obtain the attention weight matrix. The attention weight matrix has a shape of T×T, with the sum of elements in each row being 1, representing the distribution of attention to the keys at each time sampling point for each query. Multiplying the attention weight matrix by the value of the attention head yields the attention output of the attention head, which has a shape of T×16. This attention output signifies that, guided by physical features, components consistent with physical predictions are selectively aggregated from signal features.

[0079] Step S143: Concatenate all attention outputs along the feature dimension and obtain the output of the cross-modal physical attention module through linear projection.

[0080] The attention outputs of the eight attention heads obtained in step S142 are concatenated along the feature dimensions. The attention output shape of each attention head is T×16, resulting in a multi-head attention concatenated feature with a shape of T×128. This multi-head attention concatenated feature is then integrated through a linear projection layer. The input dimension of this linear projection layer is d(128), and its output dimension is also d(128). Its projection matrix is ​​a trainable parameter. The output shape after linear projection is T×d, which is the output of the cross-modal physical attention module.

[0081] Step S144: The output of the cross-modal physical attention module and the signal features are residually fused using learnable gating parameters to obtain fused features.

[0082] A learnable gating parameter is set, which is initialized to 0 during training and automatically adjusted during training via gradient descent. When calculating the fused features, the gating parameter is mapped to the (0,1) interval using the Sigmoid function, resulting in the actual gating weight α = Sigmoid(gating parameter), α ∈ (0,1). The fused features are calculated as follows: the fused feature equals α multiplied by the output of the cross-modal physical attention module plus (1-α) multiplied by the signal feature.

[0083] This gated residual fusion mechanism enables the network to adaptively determine the degree of physical guidance during training: when α approaches 1, the fused features are primarily guided by physical features, with signal features playing a secondary role; when α approaches 0, the fused features are primarily guided by the signal features themselves, with physical guidance playing a secondary role. The actual value of α is optimized by the total loss of the variational decomposition decoder, and the network automatically finds the optimal balance between physical guidance and data-driven approaches. The shape of the fused features is T×d, which will serve as the input to the subsequent variational decomposition decoder.

[0084] Step S150: Input the fused features into the variational decomposition decoder to decode several modal components and their corresponding attribution weights, and determine the modal component with the largest attribution weight as the vehicle load component.

[0085] It should be noted that the physical-guided neural decomposition network constructed in steps S120 to S154 needs to obtain optimal parameters in advance through end-to-end joint training in Example 2; the forward inference described in Example 1 refers to the process of inferring new coherent point data sets using a fully trained network.

[0086] The variational decomposition decoder receives the fused features generated in step S144 as input, compresses the fused features to a low-dimensional latent space, decodes K independent modal components from it, and outputs an attribution weight for each modal component, indicating the probability that the modal component belongs to the vehicle load component. The number of modes K is preset according to physical priors; in this embodiment, K is 4, corresponding to the vehicle load component, long-term geological deformation trend component, seasonal geological response component, and thermal expansion and contraction and noise residual component, respectively. The modal component corresponding to the attribution weight with the largest value among the K attribution weights is determined to be the vehicle load component. The variational decomposition decoder adopts a variational autoencoder framework, utilizes the natural decoupling capability of the latent space to achieve meaningful decomposition of the signal, and performs physical attribution in the latent space through a built-in physical attribution head, avoiding misclassification that may be caused by post-hoc correlation analysis.

[0087] In this embodiment, the reconstruction objective of the variational decomposition decoder is: the K modal components satisfy a linear superposition relationship in the time domain, and the sum of the K modal components approximates the InSAR time-series deformation signal of the coherent point obtained in step S110, satisfying the following formula:

[0088]

[0089] in, To reconstruct the signal vector (dimension T×1). Let K be the vector of the k-th modal component (dimension T×1), k=1,2,…,K. The reconstruction loss is the mean square error between the sum of the K modal components and the InSAR time-series deformed signal, and the KL divergence loss is the Kullback-Leibler divergence between the latent variable distribution and the standard normal distribution. Simultaneously, the attribution weights output by the physical attribution head and the modal decomposition results are co-optimized through the total loss of the variational decomposition decoder: the total loss includes reconstruction loss, KL divergence loss, physical consistency loss, modal orthogonality loss, and attribution entropy regularization loss (see Example 2 for the specific mathematical forms and weight coefficients of each item). Driven by this total loss, the modal decomposition results and attribution weights are synergistically consistent; that is, the modal component with the largest attribution weight has the strongest physical consistency with the vehicle load time series (the vehicle load time series obtained in step S110) in the time domain waveform.

[0090] Step S151: The fused features are input into the encoder after global pooling, and the output of the latent variable distribution containing the mean and log-variance is obtained through the fully connected layer.

[0091] The fused features of shape T×d generated in step S144 are subjected to global average pooling along the time dimension, compressing the time dimension to 1, resulting in a pooling vector of shape d. The pooling vector integrates the fused information from all time sampling points and serves as the input to the encoder.

[0092] The encoder consists of fully connected layers with an input dimension of d (128) and an output dimension twice the latent space dimension, i.e., 2 times the latent space dimension. In this embodiment, the latent space dimension is set to 32. The fully connected layers of the encoder map the pooling vector to a vector with twice the latent space dimension. The first latent space dimension of the vector is used as the mean, and the second latent space dimension of the vector is used as the log-variance, thereby obtaining the latent variable distribution. This latent variable distribution is a diagonal Gaussian distribution, and the dimensions of the mean vector and the log-variance vector are both the latent space dimension (32).

[0093] Step S152: Obtain latent variables from the latent variable distribution through reparameterized sampling.

[0094] Sample a random noise vector with a dimension equal to the latent space dimension from the standard normal distribution; that is, sample independent standard normal random numbers with a latent space dimension. Use the mean obtained in step S151... Sum of logarithmic variance The latent variable z is calculated using the reparameterization technique, i.e.:

[0095]

[0096] in, , A random noise vector sampled from a standard normal distribution. , ϵ and ϵ are both vectors with dimensions equal to the latent space dimension. The addition and multiplication operations in the formula are operations on the corresponding vector components. The result of reparameterized sampling is a latent variable with a dimension equal to the latent space dimension. This latent variable carries the encoded information of the fused features while maintaining randomness, enabling the subsequent decoder to generate diverse modal components.

[0097] Step S153: Input the latent variable into several independent decoder heads respectively, and each decoder head maps the latent variable to a modal component.

[0098] The variational decomposition decoder comprises K structurally identical but parameter-independent decoder heads, each corresponding to a modal component. Each decoder head consists of fully connected layers that map latent variables of dimension T (the dimension of the latent space) to modal components of dimension T. In this embodiment, the structure of each decoder head is as follows: the latent variables are first mapped to intermediate features of twice the latent space dimension (64 dimensions) through a first fully connected layer, then activated by the GELU function, and finally mapped to dimension T through a second fully connected layer, outputting the modal component corresponding to that decoder head. The output of the k-th decoder head is denoted as the k-th modal component, k = 1, 2, ..., K.

[0099] All K decoder heads share the same latent variable input, but because their network parameters are independent, they can learn different decoding mapping relationships, thus decoding the same latent variable into K modal components with different time-domain waveforms, each corresponding to a different physical source. The K modal components satisfy a linear superposition relationship in the time domain, that is, the sum of all modal components is the reconstructed signal. This reconstructed signal gradually approximates the InSAR time-series deformation signal of the coherent point obtained in step S110 during the training process.

[0100] Step S154: Input the latent variables into the physical attribution head, and output the attribution weights corresponding to each modal component through the fully connected layer and the Softmax function.

[0101] The physical attribution head is an independent classification sub-network whose input is the latent variables obtained in step S152, rather than the fused features or the original signal. The physical attribution head consists of multiple fully connected layers, mapping the latent variables to an attribution weight vector of dimension K. In this embodiment, the structure of the physical attribution head is as follows: the first fully connected layer maps the latent space dimension to 16 dimensions and then connects it to the ReLU activation function; the second fully connected layer maps the 16 dimensions to K dimensions to obtain the original attribution score vector; finally, the original attribution score vector is normalized using the Softmax function to output the attribution weight vector. The attribution weight vector has a dimension of K, and the sum of its components is 1. Each component represents the probability that the corresponding modal component belongs to the vehicle load component. The modal component corresponding to the component with the largest attribution weight is determined to be the vehicle load component.

[0102] Since the latent variables have already condensed all the information of the fused features through the encoder-decoder structure of the variational autoencoder, and the dimension of the latent space is much lower than that of the original signal, performing physical attribution in the latent space can effectively avoid misclassification caused by the correlation between modal components in post-hoc correlation analysis. The physical attribution head shares latent variables with the encoder and decoder heads, and performs end-to-end optimization by variationally decomposing the total loss of the decoder during training, so that the attribution weights are consistent with the modal decomposition results.

[0103] Step S160: Use the difference between the InSAR temporal deformation signal and the vehicle load component as the net geological deformation signal, and identify landslide deformation along the highway based on the net geological deformation signal.

[0104] In step S150, among the K modal components output, the modal component with the largest attribution weight is determined to be the vehicle load component. In this embodiment, the InSAR temporal deformation signal of the coherent point is subtracted from the vehicle load component's time-series sampling points to obtain the net geological deformation signal of the coherent point.

[0105] The net geological deformation signal eliminates the periodic deformation component caused by vehicle loads, retaining two main types of deformation components: the first type is geological deformation, characterized by low-frequency deformation that combines long-term linear trends with seasonal cycles, representing the core characteristic of landslide activity; the second type is thermal expansion and contraction and residual noise, where the high-frequency thermal expansion and contraction deformation, dominated by a daily cycle, shows a significant frequency difference in time scale compared to the long-term creep of landslides (annual scale). Since both the linear fitting in step S161 and the quadratic polynomial fitting in step S162 use a long sliding window covering approximately two years of deformation evolution to extract the low-frequency trend component from the net geological deformation signal, the high-frequency daily oscillations are naturally suppressed during the long-window fitting process, and will not substantially affect the extraction results of the annual average deformation rate and creep acceleration. Given that landslide deformation typically manifests as a continuous downward displacement along a slope, and its annual average deformation rate exhibits significant magnitude and spatial clustering characteristics, this embodiment, based on net geological deformation signals, sequentially completes the extraction of annual average deformation rate, creep acceleration extraction, accelerated creep point identification, landslide candidate region clustering, and deformation activity assessment through steps S161 to S165, ultimately achieving the identification and monitoring of landslide deformation along highways.

[0106] Step S161: Perform linear fitting on the net geological deformation signal to obtain the annual average deformation rate.

[0107] For each coherent point, the change of its net geological deformation signal over time is linearly fitted, and the resulting fitting slope is the annual average deformation rate of that coherent point, in millimeters per year.

[0108] In this embodiment, the least squares method is used for linear fitting, with the time unit being years. A negative annual average deformation rate indicates deformation along the radar line of sight away from the sensor (typically corresponding to the slope's downward displacement component); a positive value indicates deformation along the radar line of sight towards the sensor. The annual average deformation rate will serve as one of the fundamental indicators for subsequent landslide deformation activity assessment.

[0109] Step S162: Perform quadratic polynomial fitting on the net geological deformation signal within a preset sliding window, and extract the quadratic coefficients as creep acceleration.

[0110] To capture the nonlinear acceleration trend in the net geological deformation signal, this embodiment employs a sliding window to perform quadratic polynomial fitting on the signal. In this embodiment, the preset sliding window length is set to 60 time sampling points. Based on a typical revisit cycle for InSAR satellites (e.g., a 12-day revisit for a single satellite), 60 time sampling points cover approximately 720 days (about 2 years), encompassing at least two complete annual seasonal cycles. This provides sufficient sample size for quadratic polynomial fitting to distinguish between linear and accelerating trends. Simultaneously, this window length matches the typical timescale (annual scale) of landslide creep evolution, avoiding instability due to an excessively short window or smoothing of acceleration features due to an excessively long window. The sliding step size is set to 30 time sampling points (i.e., adjacent windows overlap by 50%) to ensure the continuity of the creep acceleration time series.

[0111] For each subset of net geological deformation signals within a sliding window, a quadratic polynomial fitting is performed, and the coefficients of the resulting quadratic term are extracted as creep acceleration. The physical meaning of creep acceleration is: the quadratic rate of change of the net geological deformation signal within that time window. A creep acceleration greater than 0 indicates that the deformation rate increases with time (accelerated creep), less than 0 indicates that the deformation rate decreases with time (decelerated creep), and close to 0 indicates approximately linear creep.

[0112] The quadratic polynomial fitting simultaneously outputs the estimated values ​​and standard errors of each fitted coefficient, including the estimated values ​​and standard errors of the quadratic term coefficients. The goodness of fit of this quadratic polynomial fitting is also calculated; creep acceleration extracted by this window is considered valid only if the goodness of fit is greater than a preset goodness of fit threshold of 0.6. The creep accelerations and their standard errors extracted by all valid sliding windows are arranged in chronological order to form the creep acceleration time series and creep acceleration standard error time series for that coherence point.

[0113] Step S163: If the creep acceleration is greater than 0 and meets the preset confidence threshold, then the corresponding coherence point is marked as an accelerated creep point.

[0114] Based on the creep acceleration time series obtained in step S162, it is determined whether accelerated creep has occurred at the coherent point. When the creep acceleration extracted from a coherent point within at least one effective sliding window is greater than 0, and the goodness of fit corresponding to the positive creep acceleration meets the goodness of fit threshold requirement, and the estimated value of the positive creep acceleration is significantly different from 0 in the 95% confidence interval, the coherent point is marked as an accelerated creep point.

[0115] The physical meaning of an accelerated creep point is that the net geological deformation signal at this coherence point exhibits statistically significant accelerated creep characteristics, which is an important indicator of landslide activity. In this embodiment, for coherence points marked as accelerated creep points, the maximum value of their creep acceleration and their corresponding time location are further recorded as feature quantities for subsequent spatial clustering and activity assessment.

[0116] Coherent points that do not meet the above accelerated creep determination criteria are temporarily not marked as accelerated creep points, but are recorded as non-accelerated creep points.

[0117] Step S164: Perform density-based spatial clustering on the accelerated creep points to form candidate landslide areas.

[0118] All accelerated creep points identified in step S163 are subjected to density-based spatial clustering (DBSCAN algorithm) based on their geographical coordinates (longitude, latitude, or station number + lateral offset) to divide spatially clustered accelerated creep points into the same landslide candidate area.

[0119] In this embodiment, the two core parameters of the DBSCAN algorithm are set as follows: the neighborhood radius is set to 50 meters, meaning that accelerated creep points with a spatial distance of less than 50 meters are considered as neighborhood relationships; the minimum number of samples is set to 5, meaning that a cluster contains at least 5 accelerated creep points. These parameters are set for the data characteristics of approximately 2800 coherent points (average coherent point spacing of approximately 21 meters) across a 60-kilometer road segment in this embodiment: the 50-meter neighborhood radius is approximately 2 to 3 times the average coherent point spacing, which can ensure spatial connectivity while avoiding the erroneous merging of distant, unrelated coherent points; the minimum number of samples of 5 can filter out isolated noise points or single anomalous coherent points, ensuring that the clustering results correspond to landslides with actual geological significance.

[0120] The DBSCAN algorithm starts from any unvisited accelerated creep point and recursively searches for all accelerated creep points in its neighborhood. When the number of accelerated creep points in the neighborhood is not less than the minimum sample size, a core point is formed and the cluster is expanded. This process is iterated until all accelerated creep points have been visited. Each cluster in the final output is a candidate landslide area.

[0121] In this embodiment, the spatial extent (minimum bounding rectangle or convex hull) of each landslide candidate region is further calculated, and the number of accelerated creep points, the range of annual average deformation rate, and the maximum value of creep acceleration within the region are recorded as inputs for the activity assessment in step S165. The DBSCAN algorithm can effectively cluster coherent points with similar deformation characteristics to accurately identify landslide deformation zones, and does not require pre-specifying the number of clusters, making it very suitable for landslide identification scenarios along highways where the landslide boundaries are unknown.

[0122] The combination of a neighborhood radius of 50 meters and a minimum sample size of 5 is suitable for highway InSAR monitoring scenarios where the average spacing between coherent points is in the range of 15 to 30 meters. When the average spacing between coherent points exceeds this range, the neighborhood radius can be adjusted proportionally to 2 to 3 times the average spacing between coherent points, and the minimum sample size can be adjusted to the range of 3 to 8.

[0123] Step S165: Based on the annual average deformation rate, creep acceleration, and spatial distribution characteristics of landslide candidate areas, assess the deformation activity of the landslide and output the deformation monitoring results.

[0124] For each landslide candidate region formed in step S164, its deformation activity is evaluated by combining the following three types of characteristics.

[0125] The first type of feature is the annual average deformation rate feature. The mean and maximum annual average deformation rates of all coherent points (including accelerated creep points and non-accelerated creep points) within the candidate area of ​​the landslide body are calculated. The mean reflects the average creep rate level of the area, and the maximum reflects the peak deformation rate within the area.

[0126] The second type of feature is the creep acceleration feature, which calculates the average value of the maximum creep acceleration of all accelerated creep points within the candidate area of ​​the landslide body. This average value reflects the overall acceleration degree of the area.

[0127] The third type of feature is the spatial distribution feature, which calculates the number of accelerated creep points, the area of ​​the region (calculated by the minimum bounding rectangle or convex hull), and the spatial density of accelerated creep points (the number of accelerated creep points divided by the area of ​​the region) within the candidate area of ​​the landslide body.

[0128] Based on the above three types of characteristics, a landslide deformation activity index is constructed. In this embodiment, the four characteristics—average annual deformation rate, maximum annual deformation rate, average maximum creep acceleration, and spatial density of accelerated creep points—are normalized to the interval between 0 and 1, and then weighted and summed according to preset weight coefficients to obtain the deformation activity index. The preset weight coefficients for the four characteristics are 0.3, 0.3, 0.2, and 0.2, respectively.

[0129] Based on the deformation activity index, landslide candidate areas are divided into three levels: those with a deformation activity index of not less than 0.7 are judged as highly active landslides and a red alert is issued; those with a deformation activity index between 0.4 and 0.7 are judged as moderately active landslides and an orange alert is issued; and those with a deformation activity index below 0.4 are judged as low-activity landslides and a yellow alert is issued.

[0130] The final deformation monitoring results include: the boundary range of each landslide candidate area, statistical characteristics of the annual average deformation rate (mean and maximum), statistical characteristics of creep acceleration (mean), number and spatial density of accelerated creep points, deformation activity index, and corresponding warning level. These deformation monitoring results can be directly used by highway maintenance departments for landslide disaster early warning and prevention decisions.

[0131] Example 2:

[0132] In the InSAR-based method for identifying landslide deformation along highways, the end-to-end joint training process of the time-series-spectral feature extractor, cross-modal physical attention module, variational decomposition decoder, and physical embedding layer includes:

[0133] S210: Before training begins, the learnable parameters in the physical embedding layer, determined based on sensitivity analysis, are initialized to pre-acquired design values. The time-spectrum feature extractor, cross-modal physical attention module, and variational decomposition decoder are randomly initialized.

[0134] In this embodiment, the learnable parameters of the physical embedding layer are the subgrade elastic modulus and the surface layer equivalent elastic modulus (that is, the equivalent modulus after the asphalt surface layer, asphalt intermediate layer, and asphalt bottom layer are equivalent to a homogeneous layer), both of which are initialized with the design values ​​obtained from the as-built documents or design documents in step S110.

[0135] All parameters of the temporal-spectral feature extractor (including all weights and biases of one-dimensional convolutional layers, two-dimensional convolutional layers, and BiLSTM layers), the cross-modal physical attention module (including query projection matrices, key projection matrices, value projection matrices, output linear projection matrices, physical prior bias matrix B, and the underlying learnable scalars in gated residual fusion), and the variational decomposition decoder (including weights and biases of the encoder fully connected layer, weights and biases of each of the K decoder heads, and weights and biases of each fully connected layer of the physical attribution head) are randomly initialized using Xavier uniform distribution initialization. Specifically, the underlying learnable scalars of gated residual fusion in the cross-modal physical attention module (see step S144) are randomly initialized to 0, and after mapping with the Sigmoid function, the initial value of the gate weight α is approximately 0.5.

[0136] S220: During training, the learnable parameters of the temporal-spectral feature extractor, cross-modal physical attention module, variational decomposition decoder, and physical embedding layer all participate in end-to-end joint optimization with the total loss of variational decomposition decoder as the objective. The learning rate of the learnable parameters of the physical embedding layer is higher than that of the other modules. The learning rate of all modules is set using a scheduling strategy based on learning rate warm-up and cosine annealing.

[0137] In this embodiment, the learning rate of the physically meaningful learnable parameters (i.e., the subgrade elastic modulus and the surface layer equivalent elastic modulus) in the physical embedding layer is set to 5 times the learning rate of the other modules. Preliminary experiments show that the model converges within a learning rate range of 3 to 8 times. Setting it to 5 times ensures sufficient optimization of the physical parameters without affecting the stable convergence of the other neural network modules. The linear projection parameters of the physical feature aggregation head in the physical embedding layer (see step S125) are network parameters and do not benefit from the aforementioned learning rate multiplier; instead, they use the same base learning rate as the other neural network modules. The reason for setting the learning rate of the physically learnable parameters to 5 times is that the subgrade elastic modulus and the surface layer equivalent elastic modulus have clear physical meanings and engineering prior value ranges. Based on sensitivity analysis, they are confirmed as the two parameters most sensitive to road surface deflection response. Giving them a higher learning rate allows them to quickly adjust to the optimal value from the design value during training, without affecting the normal convergence of the other neural network modules.

[0138] All modules employ a learning rate preheating and cosine annealing scheduling strategy. Specifically, in the first few training steps (set as 5% of the total training steps in this embodiment, i.e., preheating steps), the learning rate starts from a minimum value (in this embodiment, 5%). The learning rate is linearly increased to a preset base learning rate (in this embodiment, the base learning rate of the time-series-spectral feature extractor, the cross-modal physical attention module, and the variational decomposition decoder is set to...). The base learning rate of the learnable parameters of the physical embedding layer is set to After the warm-up phase, the learning rate smoothly decays from the base learning rate to the minimum learning rate (set to a cosine function in this embodiment). This scheduling strategy avoids oscillations caused by random parameter initialization and large gradient variance in the early stages of training, and achieves refined convergence through smooth decay in the later stages of training.

[0139] S230: The gradient of the learnable parameters of the physical embedding layer is derived from the total loss of the variational decomposition decoder. This gradient is backpropagated to the physical embedding layer via the cross-modal physical attention module to update the learnable parameters.

[0140] Since the physical embedding layer (steps S120 to S125) realizes the analytical solution of the elastic layered system theory as a differentiable computational graph (see steps S121 to S123, where the analytical expression of the transfer matrix and the numerical integration of the Hankel inverse transform are both implemented using differentiable computational methods), the entire layer-by-layer transfer process from the roadbed to the road surface constitutes a complete differentiable computational path. Therefore, the gradient generated by the total loss of the variational decomposition decoder can be backpropagated layer by layer to the learnable parameters (roadbed elastic modulus and surface equivalent elastic modulus) of the physical embedding layer via the cross-modal physical attention module, driving the learnable parameters to adjust from the design value to the optimal value. This process enables the physical characteristics output by the physical embedding layer (i.e., the time series of theoretical vertical displacement of the road surface caused by vehicle load) to gradually align with the vehicle load component in the real InSAR time-series deformation signal.

[0141] S240: Define the total loss of the variational decomposition decoder, including reconstruction loss, KL divergence loss, physical consistency loss, modal orthogonality loss, and attribution entropy regularization loss.

[0142] The total loss of the variational decomposition decoder consists of five terms, expressed as follows:

[0143]

[0144] in, To reconstruct the loss, For KL divergence loss, For physical consistency loss, For modal orthogonality loss, This is the attribution entropy regularization loss; , , , These are the weighting coefficients for each item.

[0145] In this embodiment, Set it to 10.0. Set it to 0.1. Set it to 0.01; A scheduling strategy that gradually increases in weight is adopted (see step S242). For the specific values ​​of each weight coefficient and the scheduling strategy, please refer to steps S241 to S246. The reason for choosing 10.0 is that the physically guided deformation sequence, as a strong physical prior, needs to be given a high weight to ensure that the modal decomposition results are consistent with the mechanical response of the elastic layered system; through ablation experiments, The model converges in the range of 5.0 to 15.0, and the vehicle load component separation accuracy is optimal when the value is 10.0.

[0146] S241: The reconstruction loss is used to ensure that the sum of all modal components can reconstruct the original InSAR time-series deformed signal.

[0147] The reconstruction loss is the mean square error between the sum of the K modal components defined in step S150 and the InSAR temporal deformation signal obtained in step S110. Specifically, for the InSAR temporal deformation signal (dimension T×1) and the sum of the K modal components (dimension T×1) at the coherent point, the average of the sum of squared differences between the two at each time sampling point is calculated as the reconstruction loss. The role of the reconstruction loss is to constrain the variational decomposition decoder to learn meaningful signal decomposition, so that the sum of the K modal components can approximate the original InSAR temporal deformation signal as closely as possible.

[0148] S242: KL divergence loss is used to constrain the distribution of latent variables to be close to the standard normal distribution. The weight coefficients of KL divergence loss gradually increase from small to large during training.

[0149] The KL divergence loss uses the latent variable distribution (diagonal Gaussian distribution, mean vector μ, logarithmic variance vector) output by the encoder in step S151. The KL divergence loss is calculated as the KL divergence between the latent variable distribution and the standard normal distribution. This divergence measures the difference between the two probability distributions and is used to normalize the latent variable distribution to approximate the standard normal distribution, thereby ensuring the continuity and normalization of the latent space.

[0150] In this embodiment, the weighting coefficients of the KL divergence loss are... An annealing scheduling strategy that gradually increases from small to large is adopted during the training process: in the early stage of training (the first few steps). Set to a smaller value (in this embodiment, initially is 1). As the number of training steps increases, The value is gradually increased to the target value (0.1 in this example). This scheduling strategy of gradually increasing the value from small to large can avoid the latent space being overly constrained due to the excessively strong KL divergence loss in the early stage of training, which would limit the diversity of mode decomposition. As training progresses, the gradually increasing KL divergence constraint helps to normalize the latent space and improve the generalization ability of the model.

[0151] S243: The physical consistency loss includes an alignment term, weighted by the attribution weights, between each modal component and the physically guided deformation sequence scaled by the scaling factor, and an orthogonality term, weighted by the difference between the attribution weights and 1, between the modal components other than the vehicle load component and the physically guided deformation sequence scaled by the scaling factor.

[0152] In this embodiment, the scaling factor is calculated first. The scaling factor is analytically obtained by dividing the inner product of each modal component and the physically guided deformation sequence by the square of the modulus of the physically guided deformation sequence. Furthermore, the scaling factor is truncated during the forward computation and does not participate in gradient backpropagation. The physical meaning of the scaling factor is to align the amplitude of the physically guided deformation sequence to the amplitude scale of each modal component, eliminating alignment deviations caused by amplitude differences between different modal components. The scaling factor is truncated during the forward computation and does not participate in gradient backpropagation. In this embodiment, gradient truncation is achieved through a gradient-stopping operation: after calculating the scaling factor, a gradient-stopping process is applied, causing the computation graph of the scaling factor to be truncated during backpropagation, and its gradient is not backpropagated to the physically guided deformation sequence and the physical embedding layer. The reason is that the scaling factor is only used as an auxiliary variable for magnitude alignment. If its gradient is backpropagated to the physical embedding layer, it will interfere with the normal optimization of the learnable parameters (subgrade elastic modulus, surface equivalent elastic modulus) of the physical embedding layer. By truncating the gradient, the gradient of the physical consistency loss is backpropagated only through the difference between the alignment term and the orthogonality term, ensuring that the learnable parameters of the physical embedding layer are updated according to the reasonable path of the total loss of the variational decomposition decoder.

[0153] Physical consistency loss is the core loss term in this embodiment. Its design idea is to use the physical guided deformation sequence (i.e., the vehicle load theoretical deformation time sequence simulated by the physical embedding layer) output in step S125 as a physical supervision signal, so that the mode decomposition result of the constraint variational decomposition decoder is consistent with the physical prior.

[0154] Physical consistency loss includes two items:

[0155] The first term is the alignment term, weighted by attribution weights. Let the physically guided deformation sequence be... (Dimension T×1), the k-th modal component is (Dimension T×1), scaling factor is (Calculated by step S244), the attribution weight of the k-th modal component is The alignment term is calculated as follows: for k=1 to K, calculate... Multiply and The sum of squares of the differences (averaged after squaring at each time sampling point). The purpose of the alignment term is to encourage modal components with higher attribution weights to be as consistent as possible with the physically guided deformation sequence in the time domain waveform, that is, to encourage modal components identified as vehicle load components to align with the theoretical deformation of vehicle load.

[0156] The second term is the orthogonal term, weighted by the difference between the attribution weights and 1. The orthogonal term is calculated as follows: for k=1 to K, calculate... Multiply and The square of the absolute value of the inner product. The role of the orthogonal term is to encourage modal components with lower attribution weights (i.e., non-vehicle load components) to be as orthogonal as possible to the physically guided deformation sequence, i.e., those that do not include the physical characteristics of vehicle loads.

[0157] Physical consistency loss That is, the sum of the alignment terms and the orthogonal terms (the coefficient of the sum of the alignment terms and the orthogonal terms has been changed by...). (Unified control in total loss). Through physical consistency loss, the mode decomposition results of the variational decomposition decoder and the physical priors output by the physical embedding layer form a closed-loop supervision, which significantly improves the accuracy of vehicle load component separation.

[0158] S244: The scaling factor is analytically obtained by dividing the inner product of each modal component and the physical guided deformation sequence by the square of the modulus of the physical guided deformation sequence. The scaling factor is truncated by the gradient in the forward calculation and does not participate in the gradient backpropagation. The calculation method of the scaling factor and the gradient truncation mechanism are explained in step S243, and will not be repeated here.

[0159] S245: Modal orthogonality loss is used to encourage uncorrelatedness between different modal components.

[0160] Modal orthogonality loss is calculated as the sum of the squares of the absolute values ​​of the inner products of each pair of K modal components (calculated pairwise and then summed). The purpose of modal orthogonality loss is to constrain the K decoder heads to learn modal components that are uncorrelated in the time domain waveform, avoiding redundant overlap of different modal components in the time domain, thereby improving the physical interpretability of signal decomposition. Each modal component corresponds to an independent physical source (vehicle load, long-term geological trends, seasonal response, thermal expansion and contraction, and residual noise).

[0161] In this embodiment, the weighting coefficients of the modal orthogonality loss are... Set to 0.1 to moderately constrain the orthogonality between modes, while avoiding excessive constraints that would prevent the model from fitting complex real signals.

[0162] S246: Attribution entropy regularization loss is used to encourage attribution weights to tend towards a sparse unimodal distribution.

[0163] The attribution entropy regularization loss is calculated as the Shannon entropy of the attribution weight vector output by the physical attribution head, i.e.:

[0164]

[0165] in, Let η be the attribution weight of the k-th modal component, and η be a preset minimum positive number (taken as η in this embodiment). This is to prevent negative infinity from occurring in logarithmic operations. By minimizing this entropy value, the attribution weights are encouraged to tend towards a sparse unimodal distribution, that is, the attribution weight of a certain modal component is significantly higher than that of the other components, thereby making the determination result of the vehicle load component clear and unique.

[0166] In this embodiment, the weighting coefficients of the attribution entropy regularization loss Set to 0.01 to lightly constrain the sparsity of attribution weights, avoiding excessive constraints that could lead to optimization difficulties in the early stages of model training due to insufficient differentiation of attribution weights.

[0167] S250: Iteratively train the network using training samples until the total loss converges.

[0168] In this embodiment, the training samples are a set of data groups of multiple coherent points obtained in step S110 (each data group contains the InSAR temporal deformation signal, vehicle load time series, and road structure parameter vector of that coherent point). During training, each training step randomly selects a batch of data groups of coherent points from the training sample set, and sequentially performs forward computation in steps S110 (spatiotemporal alignment), S120-S125 (physical embedding layer), S130-S134 (temporal-spectral feature extractor), S140-S144 (cross-modal physical attention module), and S150-S154 (variational decomposition decoder) to obtain the total loss. Then, the gradient of the learnable parameters of each module is calculated by backpropagation algorithm, and the parameters are updated according to the learning rate scheduling strategy set in step S220.

[0169] In this embodiment, the training termination condition is the total loss. The decrease within a consecutive number of steps (set to 500 steps in this embodiment) is less than a preset threshold (set to a threshold in this embodiment). The training continues until the maximum number of training steps is reached (100,000 steps in this embodiment). When the termination condition is met, training stops, the parameters of each module are saved, and end-to-end joint training is completed. After training, the learnable parameters of the physical embedding layer (subgrade elastic modulus, surface layer equivalent elastic modulus) have been adjusted from the design value to the optimal value, and the time-series-spectrum feature extractor, cross-modal physical attention module, and variational decomposition decoder have all reached their optimal state, and can be deployed for landslide deformation recognition tasks along actual highways (i.e., the process of step S160).

[0170] Example 3: Computer-readable storage medium or computer program product.

[0171] This embodiment provides a computer-readable storage medium or computer program product storing a computer program / instruction thereon, which, when executed by a processor, implements the steps of the InSAR-based method for identifying landslide deformation along highways in any of the above embodiments.

[0172] Specifically, computer-readable storage media may include: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other computer-readable storage media; computer program products may take the form of APP installation packages, firmware images, container images, SaaS service interfaces, etc., and when they are loaded and run on a computing device, they cause the computing device to execute the method steps in any of the above embodiments.

[0173] Example 4: InSAR-based landslide deformation identification system along highways.

[0174] like Figure 5 As shown, the InSAR-based roadside landslide deformation identification system 500 may include a processor 510, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 520 or a program loaded from a storage device 580 into a random access memory (RAM) 530. The RAM 530 also stores various programs and data required for the operation of the system 500, including a computer program for executing the InSAR-based roadside landslide deformation identification method of this application. The processor 510, ROM 520, and RAM 530 are interconnected via a bus 540. An input / output (I / O) interface 550 is also connected to the bus 540. Typically, the following devices can be connected to I / O interface 550: input device 560 for acquiring InSAR time-series deformation signals, road structure parameter vectors, and vehicle load time series; output device 570 for outputting landslide deformation identification results along the highway; storage device 880 for storing computer programs and various types of data; and communication device 590 for allowing system 500 to communicate wirelessly or wiredly with other devices to exchange data.

[0175] It is important to note that Figure 5 The system 500 shown is merely an example and does not impose any limitations on the functionality and scope of use of the embodiments of this application. Although Figure 5 A system 500 with various devices is shown, but it should be understood that it is not required to implement or have all of the devices shown, and the system 500 may alternatively implement or have more or fewer devices.

[0176] For example, the computer program may be divided into one or more modules / units, which are stored in RAM 530 (or storage device 580) and executed by processor 510 to complete this application. Specifically, the computer program may be divided into a physical embedding layer, a time-series-spectral feature extractor, a cross-modal physical attention module, a variational decomposition decoder, a net geological deformation extraction module, and a landslide deformation identification module, each module corresponding to the function of the corresponding step in the method of claim 1.

Claims

1. A method for identifying landslide deformation along highways based on InSAR, characterized in that, Includes the following steps: The road structure parameter vector, as well as the spatiotemporally aligned InSAR time-series deformation signal and vehicle load time series, are obtained. The road structure parameter vector includes the elastic modulus, Poisson's ratio, and layer thickness of each structural layer, and also includes the elastic modulus and Poisson's ratio of the subgrade. The structural layers include at least an asphalt layer, a water-stabilized layer, and a graded crushed stone layer. The road structure parameter vector and vehicle load time sequence are input into the physical embedding layer, and physical features and physical guided deformation sequences are generated by calculating the transfer matrix of the differentiable elastic layered system. The InSAR time-series deformation signal is input into a time-series-spectrum feature extractor to generate signal features; Using physical features as queries and signal features as keys and values, a cross-modal physical attention module generates fused features. The fused features are input into the variational decomposition decoder to decode several modal components and their corresponding attribution weights. The modal component with the largest attribution weight is determined as the vehicle load component. The difference between the InSAR temporal deformation signal and the vehicle load component is used as the net geological deformation signal, and landslide deformation along the highway is identified based on the net geological deformation signal.

2. The method for identifying landslide deformation along highways based on InSAR according to claim 1, characterized in that, The road structure parameter vector and vehicle load time sequence are input into the physical embedding layer. Physical features and physically guided deformation sequences are generated through the calculation of a differentiable elastic layered system transfer matrix, including: In the Hankel transform domain, the transfer matrix is ​​calculated based on the elastic modulus, Poisson's ratio and layer thickness of each structural layer according to the preset transformation parameters, and the state vector of the graded crushed stone layer is obtained by using the elastic half-space boundary conditions of the roadbed elastic modulus and Poisson's ratio. Starting from the graded crushed stone layer, the state vector of the current layer is obtained by multiplying the state vector of the previous layer with the transfer matrix of the current layer. This process is then passed up layer by layer through the water-stabilized layer and the asphalt layer to the road surface, thus obtaining the vertical displacement of the road surface in the Hankel transform domain. The state vector includes radial displacement, vertical displacement, vertical normal stress, and radial shear stress. The vertical displacement of the road surface is transformed back to the physical space by the inverse Hankel transform based on numerical integration, and the Green's function of road surface deflection under unit vertical load is obtained. For each coherent point in the InSAR time-series deformation signal, the vehicle load time series is multiplied by the road surface deflection Green's function and then superimposed to obtain the physical characteristics. The physical features are mapped into a one-dimensional physical guided deformation sequence via linear projection; Among them, some parameters in the road structure parameter vector are used as learnable parameters of the physical embedding layer, initialized with design values ​​and participating in gradient-based update training.

3. The method for identifying landslide deformation along highways based on InSAR according to claim 1, characterized in that, The InSAR time-series deformed signal is input into a time-series-spectrum feature extractor to generate signal features, including: The InSAR temporal deformation signal is input into the temporal convolution branch and the spectral attention branch, respectively; The temporal convolutional branch extracts the multi-scale temporal patterns of InSAR temporal deformation signals through multiple layers of one-dimensional convolution, with batch normalization and activation functions following each convolutional layer. The spectral attention branch performs a short-time Fourier transform on the InSAR time-series deformed signal to obtain a time-spectral map. It then extracts local spectral patterns by performing two-dimensional convolution on the time-spectral map and obtains spectral features by global average pooling in the frequency dimension. Multi-scale time patterns and spectral features are concatenated along the feature dimension, linearly projected onto a unified feature space, and then long-range dependencies are captured through a bidirectional long short-term memory network to generate signal features.

4. The method for identifying landslide deformation along highways based on InSAR according to claim 1, characterized in that, Using physical features as queries and signal features as keys and values, a cross-modal physical attention module generates fused features, including: The query is obtained by linearly projecting physical features, and the key and value are obtained by linearly projecting signal features. The similarity between the query and the key is divided by the scaling factor, then the learnable physical prior bias matrix is ​​superimposed, and the attention weights are obtained through the Softmax function. The attention weights are multiplied by the values ​​to obtain the single-head attention output. All attention outputs are concatenated along the feature dimension and linearly projected to obtain the output of the cross-modal physical attention module; By using learnable gating parameters, the output of the cross-modal physical attention module is residually fused with signal features to obtain fused features.

5. The method for identifying landslide deformation along highways based on InSAR according to claim 1, characterized in that, The fused features are input into the variational decomposition decoder, which decodes to obtain several modal components and their corresponding attribution weights, including: The fused features are input into the encoder after global pooling, and the output, which includes the latent variable distribution containing the mean and log-variance, is passed through a fully connected layer. Latent variables are obtained from the latent variable distribution through reparameterized sampling; The latent variables are input into several independent decoder heads, and each decoder head maps the latent variable to a modal component; The latent variables are input into the physical attribution head, and the attribution weights corresponding to each modal component are output through a fully connected layer and the Softmax function.

6. The method for identifying landslide deformation along highways based on InSAR according to claim 1, characterized in that, The difference between the InSAR temporal deformation signal and the vehicle load component is used as the net geological deformation signal. Based on the net geological deformation signal, landslide deformation along the highway is identified, including: Linear fitting was performed on the net geological deformation signal to obtain the annual average deformation rate; The net geological deformation signal is fitted with a quadratic polynomial within a preset sliding window, and the coefficients of the quadratic term are extracted as creep acceleration. If the creep acceleration is greater than 0 and meets the preset confidence threshold, then the corresponding coherence point is marked as an accelerated creep point. Density-based spatial clustering of accelerated creep points is used to form candidate landslide regions; Based on the annual average deformation rate, creep acceleration, and spatial distribution characteristics of landslide candidate areas, the deformation activity of landslides is assessed, and deformation monitoring results are output.

7. The method for identifying landslide deformation along highways based on InSAR according to claim 2, characterized in that, Some parameters in the road structure parameter vector are used as learnable parameters of the physical embedding layer, initialized with design values ​​and participating in gradient-based update training, including: Before training begins, the learnable parameters in the physical embedding layer, determined based on sensitivity analysis, are initialized to pre-acquired design values. The time-spectrum feature extractor, cross-modal physical attention module, and variational decomposition decoder are randomly initialized. During training, the learnable parameters of the temporal-spectral feature extractor, cross-modal physical attention module, variational decomposition decoder, and physical embedding layer all participate in end-to-end joint optimization with the total loss of variational decomposition decoder as the objective. The learning rate of the learnable parameters of the physical embedding layer is higher than that of the other modules. The learning rate of all modules is set using a scheduling strategy based on learning rate warm-up and cosine annealing. The gradient of the learnable parameters of the physical embedding layer is derived from the total loss of the variational decomposition decoder. This gradient is backpropagated to the physical embedding layer via the cross-modal physical attention module to update the learnable parameters.

8. The method for identifying landslide deformation along highways based on InSAR according to claim 7, characterized in that, The total loss of the variational decomposition decoder includes reconstruction loss, KL divergence loss, physical consistency loss, modal orthogonality loss, and attribution entropy regularization loss: The reconstruction loss is used to ensure that the sum of all modal components can reconstruct the original InSAR temporal deformation signal; The KL divergence loss is used to constrain the distribution of latent variables to approximate a standard normal distribution, and the weight coefficients of the KL divergence loss gradually increase from small to large during the training process; The physical consistency loss includes an alignment term, weighted by attribution weights, between each modal component and the physically guided deformation sequence scaled by the scaling factor, and an orthogonal term, weighted by the difference between the attribution weights and 1, between the modal components other than the vehicle load component and the physically guided deformation sequence scaled by the scaling factor. The scaling factor is analytically obtained by dividing the inner product of each modal component and the physical guided deformation sequence by the square of the modulus of the physical guided deformation sequence, and the scaling factor is truncated by the gradient in the forward calculation and does not participate in the gradient backpropagation. The modal orthogonality loss is used to encourage uncorrelatedness between different modal components; The attribution entropy regularization loss is used to encourage attribution weights to tend towards a sparse unimodal distribution.

9. A computer-readable storage medium or computer program product having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the InSAR-based method for identifying landslide deformation along highways as described in any one of claims 1 to 8.

10. A landslide deformation identification system along highways based on InSAR, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the InSAR-based method for identifying landslide deformation along highways as described in any one of claims 1 to 8.

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