Low-frequency strain signal high-frequency information reconstruction method and system for traffic facility monitoring

Abstract

The application provides a low-frequency strain signal high-frequency information reconstruction method and system for traffic facility monitoring, belongs to the technical field of information reconstruction, and comprises the following steps: obtaining low-frequency data collected by low-frequency monitoring equipment arranged in a traffic infrastructure and performing pretreatment to obtain denoised low-frequency sparse strain sequences; a double-layer hybrid reconstruction model is constructed: the first layer adopts enhanced Kalman smoothing based on an EM algorithm to estimate a global trend conforming to a physical law from sparse observation; the second layer introduces a LightGBM model to learn and compensate high-frequency nonlinear details in a residual error of the first layer; and the denoised low-frequency sparse strain sequences are input into the double-layer hybrid reconstruction model, and through fusion of a linear trend item and a nonlinear residual error item, a complete high-frequency signal after reconstruction is obtained.

Description

Technical Field

[0001] This invention belongs to the field of information reconstruction technology, and in particular relates to a method and system for high-frequency information reconstruction of low-frequency strain signals for traffic facility monitoring. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In practical engineering applications, due to limitations in monitoring equipment cost, data transmission capabilities, and maintenance conditions, many grassroots highway and railway projects can only deploy low-frequency monitoring equipment with low sampling frequencies, typically below 100 Hz. As a result, high-frequency dynamic response information is irreversibly lost during the acquisition phase. However, high-frequency dynamic strain data is of great value for revealing the transient response characteristics of transportation infrastructure structures, capturing extreme working condition behavior, and conducting dynamic analysis. This practical contradiction makes it difficult for existing monitoring data to fully reflect the true dynamic behavior of structures under complex loads.

[0004] While low-frequency sparse sampling can describe the overall trend of strain response, it lacks the ability to distinguish between high-frequency vibration components, transient impact responses, and subtle changes induced by local damage. This can easily lead to the smoothing or omission of key dynamic features, thus limiting the accuracy of fatigue cumulative effect analysis, dynamic response modeling, and risk warning models. Especially in long-term monitoring scenarios, this lack of high-frequency information continuously amplifies uncertainty and reduces the reliability of structural condition assessment results. Therefore, to address the problem of missing high-frequency dynamic information in low-frequency strain monitoring data, high-frequency reconstruction based on low-frequency sparse sampling data is necessary.

[0005] Existing high-frequency reconstruction methods mostly rely on a single model to interpolate or filter the signal, often making it difficult to balance preserving the global trend with restoring local details. On the one hand, while traditional filtering methods can effectively suppress noise and restore the overall trend, their ability to describe nonlinear local details is limited; on the other hand, purely data-driven models, in the absence of reasonable prior constraints, are prone to producing physically inconsistent reconstruction results. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a method and system for high-frequency information reconstruction of low-frequency strain signals for traffic facility monitoring, which is a high-frequency dynamic reconstruction framework that takes into account both physical constraints and the advantages of data-driven approaches.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] Firstly, a method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring is disclosed, including:

[0009] Low-frequency data collected by low-frequency monitoring equipment deployed in transportation infrastructure is acquired and preprocessed to obtain a denoised low-frequency sparse strain sequence.

[0010] A two-layer hybrid reconstruction model is constructed: the first layer adopts enhanced Kalman smoothing based on the EM algorithm to estimate the global trend that conforms to physical laws from sparse observations; the second layer introduces the LightGBM model to learn and compensate for the high-frequency nonlinear details in the residuals of the previous layer.

[0011] The denoised low-frequency sparse strain sequence is input into a two-layer hybrid reconstruction model. By fusing the linear trend term and the nonlinear residual term, the reconstructed complete high-frequency signal is obtained.

[0012] As a further technical solution, low-frequency data preprocessing is performed, including:

[0013] The acquired analog voltage signal is converted into strain data with actual physical meaning;

[0014] The transformed strain data is separated into transient peak region and steady-state background region in the time domain, and the steady-state background region is subjected to deep denoising.

[0015] Pearson correlation analysis was performed on each variable, and a correlation heatmap of each variable was plotted. The most representative stress-strain variables were selected for signal reconstruction to obtain the denoised low-frequency sparse strain sequence.

[0016] As a further technical solution, the time domain is separated into a transient peak region and a steady-state background region. When performing deep denoising on the steady-state background region, the specific steps include:

[0017] Peak identification and mask construction: First, the transformed strain data is subjected to median filtering to eliminate extreme outliers, and the relative protrusion is used as a criterion to identify peaks;

[0018] A protection window is constructed with the peak value as the center, and the peak value and its neighborhood are marked as the transient peak region, while the rest is marked as the steady-state background region.

[0019] Background signal wavelet denoising: The transient peak region signal is removed and interpolated to complete it, resulting in a continuous background signal. The background signal is decomposed into multiple scales using a wavelet basis. The noise level is adaptively estimated using the median absolute deviation of the high-frequency detail coefficients, and the high-frequency coefficients are shrunk to filter out random noise.

[0020] Signal fusion and reconstruction: The processed smooth background signal is fused with the transient peak region signal in the time domain. That is, the original sampled value is forcibly retained in the area covered by the mask, and the denoised value is used in the other areas.

[0021] As a further technical solution, the first layer employs enhanced Kalman smoothing based on the EM algorithm to construct a linear state estimation model, including:

[0022] The structural response is modeled using a discrete linear dynamic system, and the system structure consists of state equations and observation equations;

[0023] State equations describe the evolution of the internal state of a system over time;

[0024] The observation equation describes the mapping relationship between the internal state and the external observations.

[0025] As a further technical solution, it also includes: introducing the expectation-maximization algorithm to adaptively estimate the model parameters of the state equation and observation equation;

[0026] Based on the adaptively optimized model parameters, the Kalman smoothing algorithm is run again. For missing points in the observation sequence, the prior predictions provided by the state transition equation are weighted and fused with the posterior corrections of the effective observations before and after, thereby generating a continuous, smooth, and preliminary reconstructed sequence that conforms to the system dynamics constraints.

[0027] As a further technical solution, the second layer introduces the LightGBM model to construct a nonlinear residual learning model. The reconstruction error of Kalman smoothing is defined as the residual sequence. For each effective sampling point in the observation domain, the deviation between the true observation value and the Kalman smoothing estimate is calculated.

[0028] By using the deviation as the target variable to be learned, a nonlinear mapping relationship between the system state and the residual is established through a machine learning model.

[0029] Construct a high-dimensional feature space that includes state information and temporal dependencies;

[0030] The Kalman-smoothed multi-channel state estimate is used as the basic input, representing the current reference position of the system;

[0031] For time t, construct the feature vector;

[0032] After training, the model is used to extrapolate the feature vectors of the entire time series and generate residual predictions for the entire time domain.

[0033] Secondly, a high-frequency information reconstruction system for low-frequency strain signals for traffic facility monitoring is disclosed, including:

[0034] The low-frequency data acquisition and preprocessing module is configured to: acquire low-frequency data collected by low-frequency monitoring equipment deployed in transportation infrastructure and preprocess it to obtain a denoised low-frequency sparse strain sequence;

[0035] The two-layer hybrid reconstruction model building module is configured to: build a two-layer hybrid reconstruction model: the first layer adopts enhanced Kalman smoothing based on the EM algorithm to estimate the global trend that conforms to physical laws from sparse observations; the second layer introduces the LightGBM model to learn and compensate for the high-frequency nonlinear details in the residuals of the previous layer.

[0036] The reconstruction module is configured to input the denoised low-frequency sparse strain sequence into a two-layer hybrid reconstruction model, and obtain the reconstructed complete high-frequency signal by fusing the linear trend term and the nonlinear residual term.

[0037] The above one or more technical solutions have the following beneficial effects:

[0038] To address the issue of missing high-frequency dynamic information in low-frequency strain monitoring data, this invention employs a two-layer reconstruction strategy integrating enhanced Kalman smoothing and a lightweight gradient booster (LightGBM). The core of this strategy lies in constructing a collaborative reconstruction framework that prioritizes global data over local data: First, an enhanced Kalman smoother based on the expectation-maximization (EM) algorithm estimates a global smoothing trend conforming to physical dynamics from sparse observations. Then, a lightweight gradient booster (LightGBM) is used to accurately learn and compensate for nonlinear residuals that linear smoothing models cannot capture. Through this hybrid EM-AKS-LightGBM framework of global smoothing and local correction, a structurally complete high-frequency dynamic response is effectively recovered from limited low-frequency observations.

[0039] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0040] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0041] Figure 1 This is a diagram of the original data from an embodiment of the present invention;

[0042] Figure 2 This is a comparison image of the smoothing process before and after implementation of an embodiment of the present invention;

[0043] Figure 3 This is a heatmap showing the correlation of the original data in an embodiment of the present invention.

[0044] Figure 4 This is a Kalman smoothing structure diagram according to an embodiment of the present invention;

[0045] Figure 5The following is a diagram showing the signal reconstruction result based on 1250Hz frequency data in an embodiment of the present invention. (a) shows the global interpolation effect of the model, and (b) shows the local interpolation result after amplification at 1250Hz frequency, so as to more intuitively analyze the model interpolation performance.

[0046] Figure 6 The following is a diagram showing the signal reconstruction result based on 715Hz frequency data in an embodiment of the present invention. (a) shows the global interpolation effect of the model, and (b) shows the local interpolation result after amplification at 715Hz frequency, so as to more intuitively analyze the model interpolation performance.

[0047] Figure 7 The following is a diagram showing the signal reconstruction result based on 500Hz frequency data in an embodiment of the present invention. (a) shows the global interpolation effect of the model, and (b) shows the local interpolation result after amplification at 500Hz frequency, so as to more intuitively analyze the model interpolation performance.

[0048] Figure 8 The following is a diagram showing the signal reconstruction result based on 250Hz frequency data in an embodiment of the present invention. (a) shows the global interpolation effect of the model, and (b) shows the local interpolation result after amplification at 250Hz frequency, so as to more intuitively analyze the model interpolation performance.

[0049] Figure 9 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0050] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0051] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0052] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0053] Example 1

[0054] See appendix Figure 9 As shown, this embodiment discloses a method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring, which sequentially performs signal preprocessing, linear state estimation, and linear residual compensation, including:

[0055] Step 1: Denoise the original signal using a peak preservation and smoothing strategy to provide high-quality input for subsequent models.

[0056] Step 2: Construct a two-layer hybrid reconstruction model: The first layer uses the enhanced Kalman smoothing AKS technique based on the EM algorithm to estimate the global trend that conforms to physical laws from sparse observations; the second layer introduces the LightGBM model to learn and compensate for the high-frequency nonlinear details in the residuals of the previous layer.

[0057] Step 3: By fusing the linear trend term and the nonlinear residual term, the high-frequency signal is fully reconstructed.

[0058] In step one, regarding data preprocessing methods: High-quality raw data is fundamental to ensuring the accuracy of the model before constructing the strain characteristic repair model. Due to the complex monitoring environment, data is collected from strain sensors in transportation infrastructure. The collected raw data is an electrical signal, which needs to be converted. Furthermore, the collected raw signal is also a low-frequency signal, mixed with a large amount of high-frequency electromagnetic noise. Therefore, physical quantity conversion and refined noise reduction processing are required. The goal is to suppress noise while preserving the transient peak information crucial for structural safety assessment to the greatest extent possible.

[0059] 1-1) Data Conversion and Noise Characteristic Analysis: First, based on the sensor's factory calibration parameters, the analog voltage signal acquired by the data acquisition card is converted into strain data with actual physical meaning. For different sensors, the linear calibration formula y=k1x is used for conversion, where x is the original voltage value (mV), k1 is the independent calibration coefficient for each sensor, and y is the converted strain value. The calibration coefficient k1 for each sensor is shown in Table 1 below:

[0060] Table 1 Calibration coefficients for each sensor

[0061] sensor <![CDATA[Formula parameter (k1)]]> Engineering value unit Strain sensor A 542.6 με Strain sensor B 568.35 με Strain sensor C 577.05 με

[0062] To illustrate the fluctuations in the original data, this study selected a segment of the original data for presentation. The original strain data curve of the fluctuation segment after physical quantity conversion is shown below. Figure 1 As shown, it can be clearly observed from the time-domain waveform that a large amount of dense high-frequency random noise is superimposed on the signal. However, the transient peaks representing the vehicle load also exhibit high-frequency components in the frequency domain due to their extremely short rise and fall edges. Furthermore, although the data in this embodiment are arranged in chronological order, due to the uneven sampling intervals, the sample number is uniformly used as the abscissa in this embodiment.

[0063] The aforementioned overlap between the effective signal peak and the invalid background noise in the frequency domain means that directly using a traditional low-pass filter would inevitably inadvertently damage peaks with similar high-frequency characteristics while filtering out high-frequency noise, leading to peak amplitude attenuation. Traditional denoising methods, while filtering out noise, often treat sharp peaks generated by vehicle loads as high-frequency components and smooth them, resulting in peak amplitude attenuation. Since the core of the technical solution in this embodiment lies in restoring the peak-to-valley difference—a key fatigue indicator—peak fidelity is crucial. Therefore, a dedicated algorithm capable of balancing denoising and peak preservation is needed.

[0064] 1-2) Peak Preservation and Smoothing Strategy Based on Wavelet Transform: To address the above problems, this embodiment proposes a peak preservation and denoising strategy combining signal masking and wavelet transform. The core idea of ​​this method is to separate the signal in the time domain into a transient peak region and a steady-state background region, and apply deep denoising only to the steady-state background region, thereby suppressing noise while completely preserving the structural extreme response. The specific steps are as follows:

[0065] 1-2-1) Peak Identification and Mask Construction: First, the original signal after transformation in step 1-1) is subjected to median filtering to eliminate extreme outliers. Peaks are identified based on the relatively high values ​​among several surrounding peaks. A relative threshold of 20% of the signal range is set to filter out significant vehicle load response points. Subsequently, a protection window is constructed centered on the peak, marking the peak and its neighborhood as the "transient peak region," and the remaining area as the steady-state background region.

[0066] 1-2-2) Background Signal Wavelet Denoising: Transient peak data is removed and interpolated to obtain a continuous background signal. After constructing the background signal, the Daubechies8 wavelet basis, which has good compact support, is used for multi-scale decomposition, representing the signal as a low-frequency approximation component and multiple layers of high-frequency detail components. Since random noise is mainly concentrated in the high-frequency detail components, the highest-level high-frequency detail coefficients are selected, and the noise standard deviation is adaptively estimated using their median absolute deviation (MAD). Based on this, a threshold is constructed according to the VisuShrink universal threshold criterion, and soft thresholding is applied to the high-frequency detail coefficients at each scale to effectively suppress random noise. Finally, the smoothed background signal is obtained through wavelet reconstruction.

[0067] 1-2-3) Signal fusion and reconstruction: The processed smooth background signal is fused with the original transient peak region signal in the time domain. That is, the original sampled values ​​are forcibly retained in the area covered by the mask, while the denoised values ​​are used in the remaining areas.

[0068] To verify the actual processing effect of the above peak preservation and smoothing strategy, this example also selects a segment of fluctuating data for application testing. The comparison results of the original noisy data and the data after peak preservation and smoothing processing in this fluctuating segment are as follows: Figure 2 As shown.

[0069] Depend on Figure 2 As can be seen, the red curve of the data processed by the algorithm of the sub-implementation technical solution in this embodiment exhibits significant optimization characteristics: on the one hand, in the steady-state background region where no vehicles pass, the algorithm effectively filters out dense, spiky high-frequency random noise, making the baseline smooth and stable, and significantly improving the signal-to-noise ratio; on the other hand, and most importantly, at the transient peak caused by vehicle load, the red curve maintains a high degree of overlap with the original blue signal, without the peak reduction or phase lag phenomenon commonly seen in traditional low-pass filtering. This result strongly demonstrates that this strategy can completely preserve the extreme value characteristics that determine the accuracy of structural fatigue assessment while performing deep denoising, providing a reliable and clean input data foundation for subsequent high-frequency reconstruction tasks.

[0070] 1-3) Correlation Analysis: Subsequently, in order to select the most representative stress-strain variables for signal reconstruction research, this example performed Pearson correlation analysis on strain 1, strain 2, strain 3, and stress, and plotted the correlation heatmap for each variable, as shown below. Figure 3 As shown, the variables with the strongest correlations are selected through this correlation heatmap to facilitate interpolation of the correlations between variables in the subsequent model. The analysis results show that among the four stress-strain data, strain 2 and strain 3 have the highest average Pearson correlation coefficients with other variables. This indicates that strain 2 and strain 3 data contain the richest information and better reflect the overall trend of change compared to other variables. Therefore, strain 3 is selected as the target variable for signal reconstruction to facilitate the study.

[0071] In one implementation example, specifically in step two, the hybrid interpolation method fusing enhanced Kalman smoothing and gradient boosting trees, after preprocessing, yields the denoised low-frequency sparse strain sequence of the signal fusion reconstruction output from steps 1-2-3). The next challenge is how to extract the lost high-frequency dynamic components from these sparse observation points. Relying solely on physical models or single data-driven models often fails to simultaneously achieve both the physical smoothness of the global trend and the accurate richness of local details. Therefore, this step proposes a two-layer hybrid reconstruction strategy of EM-AKS-LightGBM, combining linear state estimation and nonlinear residual compensation. The innovation of this method lies in decoupling the reconstruction task: first, the enhanced Kalman smoothing (AKS) technique based on physical dynamics captures the global linear trend of the signal; then, the LightGBM machine learning model learns from the filtered residuals and compensates for nonlinear high-frequency details, achieving high-fidelity reconstruction through two-level collaboration.

[0072] 2-1) State-space modeling based on enhanced Kalman filter: As the first layer of the hybrid model, the goal of this step is to construct an adaptive, optimal linear state estimator. Its core task is to establish a smooth, continuous baseline or trend term for the signal that conforms to physical and dynamic constraints, providing a stable reference frame for subsequent detailed compensation.

[0073] Kalman smoothing (KS) is an optimal recursive estimation algorithm based on the minimum mean square error criterion, widely used in state monitoring and signal smoothing of dynamic systems. However, standard Kalman smoothing is often difficult to apply directly to structural monitoring due to the large amount of missing data and unknown noise statistics. Therefore, this example constructs an enhanced Kalman smoothing (AKS) algorithm combined with the expectation-maximization (EM) algorithm to adaptively recover the true dynamic evolution trajectory of the system from sparse and noisy observation data.

[0074] 2-2) Construction of the Kalman smoothing model: The Kalman smoothing model used is for multi-channel strain monitoring data. Here, the multi-channel strain monitoring data is the strain with the strongest correlation selected after the data preprocessing step 1-2-3) signal fusion and reconstruction. It is assumed that the true state of the system at time t is... x t The description is different from the actual observations acquired by the sensor. z t Because strain data changes continuously over time and has a certain inertial characteristic, a discrete linear dynamic system is used to model the structural response. This system structure consists of state equations and observation equations, and the Kalman smoothed structure diagram is shown below. Figure 4 As shown.

[0075] The system state equation describes the evolution of the system's internal state over time. Let the state vector be... x t This includes the current strain amplitude and its first-order difference, i.e., the rate of change / generalized velocity, for each monitoring channel. The state transition process of the system at time t is defined as follows:

[0076] (1)

[0077] Where A is the state transition matrix, which determines how the state at the next moment is derived from the current state; The state vector at time t-1 serves as the basic input for predicting the state at the current time. The system noise represents system disturbances not included in the model, and is assumed to follow a Gaussian distribution with zero mean. , Let A be the process noise covariance matrix. In this embodiment, based on the constant velocity model assumption, the transition matrix A is designed to include the identity matrix and the time step. The block matrix form is used to capture the temporal continuity of the strain signal.

[0078] It should be noted that in this embodiment, the correlation between strain 3 and strain 1 is established, the correlation between strain 3 and strain 2 is established, and the correlation between strain 3 and stress is established. Based on the above correlations, a model is established for interpolating strain 3.

[0079] The observation equation describes the mapping relationship between the internal state and external observations. Considering the missing data at some time points, the observation equation is expressed as:

[0080] (2)

[0081] Among them, z t Let v be the sparse observation vector at time t; H is the observation matrix, used to map the high-dimensional state space to the observation space; v t To observe noise, reflecting sensor measurement errors and environmental interference, it obeys... , To observe the noise covariance matrix, x t This is the state vector.

[0082] 2-3) Parameter Adaptive Enhancement Based on EM Algorithm: In practical engineering applications, the state transition matrix A, observation matrix H, and noise covariance matrices Q and R are often unknown and fluctuate with changes in the working environment. Relying on experience to set fixed parameters is not only highly subjective but also easily leads to filter divergence or over-smoothing. Therefore, this example introduces the Expectation-Maximization (EM) algorithm to adaptively estimate the above model parameters, thereby achieving enhanced filtering.

[0083] The EM algorithm maximizes the log-likelihood function of the observed data through an iterative process. ,in Let A be the set of parameters to be estimated, where A is the state transition matrix and H is the observation matrix. To observe the noise covariance matrix, The process noise covariance matrix is... The initial state mean represents the prior mean estimate of the system state at the initial moment. Let be the initial state covariance, used to characterize the uncertainty of the initial state. The specific iterative process is as follows:

[0084] E-step: Parameter estimates based on the k-th iteration The Kalman smoother is used to perform bidirectional extrapolation on the entire time series to calculate the state variable x. t The posterior expectation and its second-order statistics, such as the covariance matrix. and cross-covariance matrix ;

[0085] M-step: Based on the state statistics calculated in the E-step, the expected value of the log-likelihood function is maximized by taking its derivative, thereby updating the parameter set. For example, the new state transition matrix can be derived by minimizing the sum of squared prediction errors. .

[0086] By setting the number of iterations, in this example n=5, the algorithm can automatically learn the dynamic parameters that best match the current structural response characteristics from sparse observation data.

[0087] 2-4) Global Smoothing Reconstruction of Sparse Data: Based on the adaptively optimized model parameters, the Kalman smoothing algorithm is run again. Unlike standard Kalman smoothing, which only utilizes past information, the smoothing algorithm can use all observation information before and after time t to make the optimal estimate of the current state. For missing points in the observation sequence, the algorithm uses the prior predictions provided by the state transition equation and the posterior corrections of the effective observations before and after time t to perform weighted fusion, thereby generating a continuous, smooth, and preliminary reconstruction sequence that conforms to the system dynamics constraints. This process effectively fills data gaps and filters out high-frequency observation noise, providing a high-quality baseline trend line for subsequent nonlinear residual correction.

[0088] 2-5) Nonlinear Residual Learning Mechanism Based on LightGBM: Although enhanced Kalman smoothing can effectively recover the global evolution trend and linear dynamic characteristics of sparse monitoring data, due to its assumption of a linear Gaussian system, the inherent nonlinear oscillations, abrupt changes, and complex environmental coupling effects in the structural response are often treated as noise and smoothed out. This leads to the initial reconstruction results... Information loss occurs in the high-frequency details of the signal. To compensate for this deficiency, a lightweight gradient booster (LightGBM) is introduced to construct a nonlinear residual learning mechanism, which aims to mine the structured information contained in the residuals of the linear model and perform fine-grained compensation on the reconstruction results.

[0089] In this implementation example, the actual observed value Kalman smoothing estimate The deviation between them is R t For R t For larger areas, the corresponding Kalman smoothing estimates are needed. The data is then input into the LightGBM model for retraining and correction.

[0090] 2-5-1) Extraction and characteristic analysis of residual sequences.

[0091] First, the reconstruction error of Kalman smoothing is defined as a residual sequence. For the observation domain... For each valid sampling point t within the range, calculate the true observed value. Kalman smoothing estimate Deviation between:

[0092] (3)

[0093] In actual structural monitoring, the residual sequence often contains nonlinear components with specific patterns, such as small oscillations caused by local nonlinear stiffness changes in the structure. Therefore, this example will use R... t As the target variable to be learned, we attempt to establish a nonlinear mapping relationship between the system state and the residual through a machine learning model.

[0094] 2-5-2) Construction of multi-order temporal feature engineering.

[0095] To enable the LightGBM model to infer future residual changes based on the current system state, this example constructs a high-dimensional feature space that includes state information and temporal dependencies.

[0096] Regarding the basic state characteristics, the multi-channel state estimates after Kalman smoothing are directly used. As a basic input, it represents the current reference position of the system.

[0097] Regarding the temporal lag characteristics, considering the significant memory property of the structural dynamic response—that is, the residual at the current moment is often related to the state at past moments—this example introduces a multi-order lag feature. For time t, a feature vector f is constructed. t :

[0098] (4)

[0099] in, This represents the state estimate after k-step lag. The subsequent constructed eigenvector f... t Input the data into the LightGBM regression model for training and prediction.

[0100] This feature construction method transforms the time series prediction problem into a supervised learning regression problem, enabling the model to capture the dynamic patterns of residual evolution as the system state changes. Furthermore, to handle data boundaries, a backfilling strategy is employed to fill in missing values ​​caused by lags.

[0101] 2-5-3) Training and prediction of the LightGBM regression model.

[0102] Based on the constructed feature set f tThe LightGBM algorithm is used for nonlinear regression training. LightGBM is a distributed gradient boosting framework based on decision tree algorithm. Unlike traditional GBDT or XGBoost, it introduces two methods: gradient-based one-sided sampling (GOSS) and mutually exclusive feature binding (EFB).

[0103] The GOSS algorithm reduces the amount of data while retaining samples with larger gradients, thus significantly improving training speed without sacrificing accuracy; while the EFB algorithm reduces feature dimensionality by bundling mutually exclusive features.

[0104] In this embodiment, the mean absolute error (MAE) is selected as the loss function to enhance the model's robustness to outliers; the number of iterations is set to 100, and the learning rate is 0.05. After training, the model is used to extrapolate the feature vectors of the full-time series containing both observed and missing points, generating full-time domain residual predictions. This prediction result is essentially a nonlinear correction to the enhanced Kalman smoothing linear assumption, which can effectively recover the high-frequency details that have been smoothed out in the signal.

[0105] Fusion of linear and nonlinear components of time series signals: Based on the linear state estimation model and nonlinear residual learning model constructed above, specifically formula (5), the final reconstruction of sparse monitoring signals is achieved through additive coupling mechanism.

[0106] From the perspective of signal composition, the complex structural dynamic response X t It can be viewed as a superposition of a low-frequency global trend term (linear component) and a high-frequency local detail term (nonlinear component). In the preceding steps, enhanced Kalman smoothing utilizes a state-space model and extracts the global evolution trend of the signal, i.e., the linear component estimate, through a full-time-domain smoothing algorithm. The LightGBM model, on the other hand, captures high-frequency fluctuations in the signal by mining the mapping relationship between state features and prediction bias, i.e., nonlinear residual estimates. .

[0107] Therefore, the final time series reconstruction process is completed by linearly superimposing the two estimated values:

[0108] (5)

[0109] In the formula, This is the result of a linear state estimation model. It is the result of a nonlinear residual learning model.

[0110] Accuracy Evaluation and Result Analysis of High-Frequency Signal Reconstruction: Based on measured high-frequency strain data, the signal reconstruction capability of the proposed EM-AKS-LightGBM hybrid model under different low-frequency sampling conditions was systematically evaluated. Five sparsity gradients were set up, with one data point retained for every 3, 6, 9, and 19 data points, corresponding to sampling frequencies of 1250Hz, 715Hz, 500Hz, and 250Hz. This aimed to simulate the data recovery scenario where the above four low-frequency signals are reconstructed into the original 5000Hz high-frequency signal.

[0111] Analysis of reconstruction effects at different frequencies: Figures 5-8 The waveforms of the reconstructed signal (green curve) and the original high-frequency ground truth (red curve) are compared under four different sparsity conditions. Figure 5 (a) in Figure 8 (a) in the figure shows the global repair effect of the model, while Figure 5 (b) in Figure 8 (b) shows the magnified local repair results at the corresponding frequency, so as to analyze the model repair performance more intuitively.

[0112] From each figure Figures 5 to 8 From a global perspective (a) in the diagram, the green reconstruction curve and the red ground truth curve maintain a very high degree of overlap across different frequency data. Even with 250Hz frequency data, which is 19 times sparser in terms of data points, see... Figure 8 In (a), the model is still able to accurately capture the overall evolution trend and large-amplitude fluctuation period of the strain signal, without obvious phase shift or trend divergence, which verifies the robustness of the hybrid model in global state estimation.

[0113] Further observation of each figure Figures 5 to 8 The magnified view in (b) shows subtle differences in reconstruction quality as the sampling frequency decreases. At high-frequency data, such as... Figure 5 (b) Figure 6 In (b), the model's reconstruction of the data closely resembles the original data curve; as the frequency of data reconstruction decreases, such as Figure 7 (b) Figure 8 In (b), the model's reconstruction performance also decreases, but the overall waveform remains highly faithful. This indicates that although the extremely low sampling rate causes some irreversible loss of high-frequency information, thanks to LightGBM's effective compensation for nonlinear residuals, the model can still deduce most of the lost dynamic details from a limited number of sparse points, achieving an excellent balance between data compression ratio and reconstruction accuracy.

[0114] Reconstruction accuracy evaluation at different frequencies: To further quantify the reconstruction accuracy of the model, Table 2 summarizes the evaluation indicators of root mean square error (RMSE), mean absolute error (MAE), and weighted average absolute percentage error (Wmape) at different sparsities.

[0115] Table 2 Evaluation table of model reconstruction effect at different frequencies

[0116] Evaluation indicators 1250Hz 715Hz 500Hz 250Hz MAE(με) 0.016822 0.031782 0.046658 0.130513 Wmape 0.000828% 0.001564% 0.002297% 0.006424% RMSE(με) 0.453501 0.659402 0.723902 0.934335

[0117] The results show that the model proposed in this embodiment exhibits extremely high reconstruction accuracy across all frequencies. Even at the lowest sampling frequency (250Hz), Wmape remains at an extremely low level of 0.006%, and RMSE does not exceed 1.0. This excellent performance is attributed to the hybrid model effectively fusing multivariate collaborative information through enhanced Kalman smoothing to lock in the global physical trend of the signal, and combining it with the LightGBM model to accurately compensate for smoothed nonlinear high-frequency details, thus achieving highly accurate signal reconstruction even at extremely low sampling rates. Furthermore, as the sampling frequency increases from 250Hz to 1250Hz, various error indicators show a significant decreasing trend, such as RMSE decreasing from 0.934 to 0.453, verifying that increasing the sampling point density can effectively improve the model's ability to capture local details.

[0118] Example 2

[0119] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method.

[0120] Example 3

[0121] The purpose of this embodiment is to provide a computer-readable storage medium.

[0122] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above method.

[0123] Example 4

[0124] The purpose of this embodiment is to provide a high-frequency information reconstruction system for low-frequency strain signals for traffic facility monitoring, including:

[0125] The low-frequency data acquisition and preprocessing module is configured to: acquire low-frequency data collected by low-frequency monitoring equipment deployed in transportation infrastructure and preprocess it to obtain a denoised low-frequency sparse strain sequence;

[0126] The two-layer hybrid reconstruction model building module is configured to: build a two-layer hybrid reconstruction model: the first layer adopts enhanced Kalman smoothing based on the EM algorithm to estimate the global trend that conforms to physical laws from sparse observations; the second layer introduces the LightGBM model to learn and compensate for the high-frequency nonlinear details in the residuals of the previous layer.

[0127] The reconstruction module is configured to input the denoised low-frequency sparse strain sequence into a two-layer hybrid reconstruction model, and obtain the reconstructed complete high-frequency signal by fusing the linear trend term and the nonlinear residual term.

[0128] Example 5

[0129] The purpose of this embodiment is to provide a computer program product containing instructions that, when run on a computer, cause the computer to perform the methods and functions involved in any of the above embodiments.

[0130] The steps and methods involved in the apparatus of the above embodiments correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0131] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0132] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring, characterized by: include: Low-frequency data collected by low-frequency monitoring equipment deployed in transportation infrastructure is acquired and preprocessed to obtain a denoised low-frequency sparse strain sequence. A two-layer hybrid reconstruction model is constructed: the first layer adopts enhanced Kalman smoothing based on the EM algorithm to estimate the global trend that conforms to physical laws from sparse observations; The second layer introduces the LightGBM model to learn and compensate for the high-frequency nonlinear details in the residuals of the previous layer. The second layer introduces the LightGBM model to construct a nonlinear residual learning model. The reconstruction error of Kalman smoothing is defined as the residual sequence. For each effective sampling point in the observation domain, the deviation between the true observation value and the Kalman smoothing estimate is calculated. By using the deviation as the target variable to be learned, a nonlinear mapping relationship between the system state and the residual is established through a machine learning model. Construct a high-dimensional feature space that includes state information and temporal dependencies; The Kalman-smoothed multi-channel state estimate is used as the basic input, representing the current reference position of the system; For time t, construct the feature vector; After training, the model is used to extrapolate the feature vectors of the entire time series to generate residual predictions for the entire time domain. The denoised low-frequency sparse strain sequence is input into a two-layer hybrid reconstruction model. By fusing the linear trend term and the nonlinear residual term, the reconstructed complete high-frequency signal is obtained.

2. The method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring as described in claim 1, characterized in that, Data preprocessing for low-frequency data includes: The acquired analog voltage signal is converted into strain data with actual physical meaning; The transformed strain data is separated into transient peak region and steady-state background region in the time domain, and the steady-state background region is subjected to deep denoising. Pearson correlation analysis was performed on each variable, and a correlation heatmap of each variable was plotted. The most representative stress-strain variables were selected for signal reconstruction to obtain the denoised low-frequency sparse strain sequence.

3. The method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring as described in claim 2, characterized in that, Separating the time domain into transient peak regions and steady-state background regions, the deep denoising of the steady-state background region specifically includes: Peak identification and mask construction: First, the transformed strain data is subjected to median filtering to eliminate extreme outliers, and the relative protrusion is used as a criterion to identify peaks; A protection window is constructed with the peak value as the center, and the peak value and its neighborhood are marked as the transient peak region, while the rest is marked as the steady-state background region. Background signal wavelet denoising: The transient peak region signal is removed and interpolated to complete it, resulting in a continuous background signal. The background signal is decomposed into multiple scales using a wavelet basis. The noise level is adaptively estimated using the median absolute deviation of the high-frequency detail coefficients, and the high-frequency coefficients are shrunk to filter out random noise. Signal fusion and reconstruction: The processed smooth background signal is fused with the transient peak region signal in the time domain. That is, the original sampled value is forcibly retained in the area covered by the mask, and the denoised value is used in the other areas.

4. The method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring as described in claim 1, characterized in that, The first layer employs enhanced Kalman smoothing based on the EM algorithm to construct a linear state estimation model, including: The structural response is modeled using a discrete linear dynamic system, and the system structure consists of state equations and observation equations; State equations describe the evolution of the internal state of a system over time; The observation equation describes the mapping relationship between the internal state and the external observations.

5. The method for reconstructing high-frequency information from low-frequency strain signals for traffic facility monitoring as described in claim 4, characterized in that it further... include: An expectation-maximization algorithm is introduced to adaptively estimate the parameters of the state equation and observation equation models. Based on the adaptively optimized model parameters, the Kalman smoothing algorithm is run again. For missing points in the observation sequence, the prior predictions provided by the state transition equation are weighted and fused with the posterior corrections of the previous and subsequent valid observations to generate a continuous, smooth, and preliminary reconstructed sequence that conforms to the system dynamics constraints.

6. A low-frequency strain signal high-frequency information reconstruction system for traffic facility monitoring, characterized in that, include: The low-frequency data acquisition and preprocessing module is configured to: acquire low-frequency data collected by low-frequency monitoring equipment deployed in transportation infrastructure and preprocess it to obtain a denoised low-frequency sparse strain sequence; The two-layer hybrid reconstruction model building module is configured to: build a two-layer hybrid reconstruction model: the first layer adopts enhanced Kalman smoothing based on the EM algorithm to estimate the global trend that conforms to physical laws from sparse observations; The second layer introduces the LightGBM model to learn and compensate for the high-frequency nonlinear details in the residuals of the previous layer. The second layer introduces the LightGBM model to construct a nonlinear residual learning model. The reconstruction error of Kalman smoothing is defined as the residual sequence. For each effective sampling point in the observation domain, the deviation between the true observation value and the Kalman smoothing estimate is calculated. By using the deviation as the target variable to be learned, a nonlinear mapping relationship between the system state and the residual is established through a machine learning model. Construct a high-dimensional feature space that includes state information and temporal dependencies; The Kalman-smoothed multi-channel state estimate is used as the basic input, representing the current reference position of the system; For time t, construct the feature vector; After training, the model is used to extrapolate the feature vectors of the entire time series to generate residual predictions for the entire time domain. The reconstruction module is configured to input the denoised low-frequency sparse strain sequence into a two-layer hybrid reconstruction model, and obtain the reconstructed complete high-frequency signal by fusing the linear trend term and the nonlinear residual term.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 5.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method described in any one of claims 1-5.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it performs the steps of the method described in any one of claims 1-5 above.

Images