Adaptive multi-scale bridge dynamic deflection denoising method and system based on physical constraints

Abstract

The application discloses a kind of based on physical constraint adaptive multi-scale bridge dynamic deflection noise reduction method, including obtaining time series displacement data and pre-processing;Adaptive multi-scale decomposition is carried out based on bridge dynamic prior information;The multi-dimensional statistical characteristics of each subband are calculated and subband classification is executed;Time series adaptive attenuation suppression is carried out to the subband to be estimated;Inverse transform reconstruction is carried out to the subband coefficient, and preliminary noise reduction signal is obtained;The preliminary noise reduction time series displacement sequence is evaluated for structural dynamics physical consistency;Whether each index of the preliminary noise reduction time series displacement sequence meets the preset physical consistency boundary condition is calculated;Feedback correction is carried out based on physical consistency evaluation result, and final noise reduction time series displacement sequence is output.The application improves the accuracy of noise reduction while better preserving the real dynamic displacement response of the bridge, and improves the processing stability under complex noise environment and different working conditions, with high processing efficiency, significantly improving the credibility in engineering application.

Description

Technical Field

[0001] This invention relates to the field of bridge structure monitoring and dynamic deflection noise reduction, and in particular to a method and system for adaptive multi-scale bridge dynamic deflection noise reduction based on physical constraints. Background Technology

[0002] As urban bridges, viaducts, and long-span bridges age, they are prone to stiffness degradation, localized damage accumulation, fatigue cracking, and decreased load-bearing capacity under the combined effects of long-term vehicle loads, wind loads, temperature and humidity changes, and environmental erosion. Bridge dynamic deflection, as a crucial parameter reflecting structural dynamic response, stiffness changes, and service status, has become a key monitoring indicator in bridge health monitoring and safety assessment. Therefore, high-precision, continuous monitoring of bridge dynamic deflection is of great significance. When using GB-SAR to acquire bridge dynamic deflection monitoring data, the original bridge dynamic deflection sequence often contains significant noise components due to various factors such as environmental noise, complex scattering background around the bridge, and instantaneous external interference. This noise is not only random and non-stationary but may also overlap with the bridge's actual dynamic response in the frequency range, resulting in the simultaneous presence of high-frequency noise, low-frequency drift, and localized sudden interference in the bridge dynamic deflection signal, severely affecting the accuracy of bridge dynamic deflection monitoring.

[0003] To improve the accuracy of bridge dynamic deflection monitoring results, existing technologies typically employ methods such as low-pass filtering, wavelet analysis, empirical mode decomposition, variational mode decomposition, and blind source separation to denoise the monitoring signals. However, in actual bridge monitoring scenarios, these methods still have certain limitations: On the one hand, traditional filtering methods usually rely on fixed cutoff frequencies or fixed window parameters, mode decomposition methods are sensitive to parameter selection, and blind source separation methods have certain requirements for data models and statistical characteristics. Therefore, existing methods as a whole are insufficiently adaptable to non-stationary, mixed, and complex noise environments. On the other hand, when the actual dynamic response of the bridge and the noise components overlap in the frequency domain, existing methods struggle to effectively separate the two. This can easily lead to a weakening of the actual structural response while suppressing noise, or a significant amount of residual noise while preserving the effective response, making it difficult to balance noise suppression capability with the ability to maintain the bridge's dynamic characteristics. Furthermore, most existing noise reduction methods focus on reducing noise amplitude in a statistical sense, and usually lack a verification mechanism for the physical rationality of the noise reduction results. This may lead to abnormal fluctuations or pseudo-response components in the processing results that do not conform to the laws of bridge dynamics, thereby affecting the reliability of subsequent bridge condition analysis and safety assessment. Summary of the Invention

[0004] The purpose of this invention is to provide a method for reducing noise in bridge dynamic deflection based on physical constraints and adaptive multi-scale methods.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution: This invention includes the following steps: Step S1: Acquire time-series displacement data and perform preprocessing: acquire the original monitoring sequence output by the ground-based synthetic aperture radar equipment to the bridge target monitoring point, perform sliding window block processing on the original monitoring sequence to obtain multiple overlapping data blocks, and perform endpoint extension on each data block to obtain extended data blocks; Step S2, Adaptive multi-scale decomposition based on prior bridge dynamic information: Obtain prior frequency information of the bridge to be monitored, construct prior frequency vector, calculate adaptive decomposition depth according to the sampling frequency of the ground-based synthetic aperture radar equipment and the lowest order reference frequency in the prior frequency vector, perform multi-scale decomposition on each extended data block using the adaptive decomposition depth, and rearrange the frequency order of the decomposed sub-band coefficients to obtain a normalized sub-band coefficient set arranged monotonically increasing in frequency; Step S3: Calculate the multidimensional statistical features of each sub-band and perform sub-band classification: For each normalized sub-band coefficient sequence, calculate the permutation entropy and sample entropy. Based on the relationship between the permutation entropy and sample entropy of each sub-band and the adaptive classification threshold, divide each sub-band into retained sub-bands, suppressed sub-bands and sub-bands to be estimated. Step S4, perform time-adaptive attenuation suppression on the subband to be estimated: input the coefficient sequence of the subband to be estimated into the deep temporal network model, obtain the time-varying attenuation coefficient, and use the time-varying attenuation coefficient to weight the coefficient sequence of the subband to be estimated to obtain the denoised subband coefficient; Step S5: Perform inverse transformation reconstruction on the subband coefficients to obtain the preliminary denoising signal: Integrate the original coefficients of the retained subband, the zeroed coefficients of the suppressed subband, and the denoising coefficients of the subband to be estimated after processing in step S4, perform inverse multi-scale transformation reconstruction, and perform boundary truncation and overlapping smooth splicing on the reconstructed data blocks to obtain the preliminary denoising time-series displacement sequence. Step S6: Perform a structural dynamic physical consistency evaluation on the preliminary noise reduction time-series displacement sequence: calculate the acceleration index, displacement continuity index, spectrum rationality index, and power spectrum similarity index of the preliminary noise reduction time-series displacement sequence, and determine whether each index meets the preset physical consistency boundary conditions. Step S7: Feedback correction based on physical consistency evaluation results: When any index in step S6 fails to meet the physical consistency boundary conditions, a feedback adjustment control signal is generated. The sub-band classification threshold in step S3 and / or the time-varying attenuation coefficient in step S4 are adjusted according to the feedback adjustment control signal. Steps S3 to S6 are repeated until the preset iterative convergence termination condition is met, and the final denoised time-series displacement sequence is output.

[0006] Furthermore, the original monitoring sequence is segmented and truncated using a sliding window with a preset length and sliding step size to obtain multiple overlapping data blocks; symmetric extension, mirror filling, or periodic extension are performed on both ends of each data block to generate extended data blocks with boundary buffers, which are used to suppress the endpoint effect of multi-scale decomposition.

[0007] Furthermore, the reference frequencies of each order of vertical principal vibration of the bridge structure are obtained, and a priori frequency vector is constructed as a frequency band division constraint. Combining the sampling frequency of the ground-based synthetic aperture radar and the lower limit of the prior frequency, the effective separation of the low-frequency principal mode and DC drift is used as a constraint. At the same time, the maximum decomposition depth boundary corresponding to the data block length and the wavelet basis support length is introduced, and the adaptive decomposition depth is obtained by solving the closed analytical expression.

[0008] Furthermore, the multi-scale decomposition adopts wavelet packet full binary tree decomposition. After decomposition, the original subband coefficient sequence is reversed by Gray code to obtain a normalized subband coefficient set arranged monotonically increasing in frequency, so that the frequencies of each core main mode independently fall within the corresponding subband range.

[0009] Furthermore, the step of constructing an adaptive dual-classification threshold and classifying categories based on subband statistical features specifically includes: calculating the mean and standard deviation of the permutation entropy of all subbands and the mean and standard deviation of the sample entropy within the current data block; introducing empirical adjustment coefficients to generate permutation entropy classification thresholds and sample entropy classification thresholds respectively; subbands that simultaneously satisfy both permutation entropy and sample entropy above the corresponding thresholds are determined to be suppressed subbands dominated by high-frequency noise; subbands that simultaneously satisfy both permutation entropy and sample entropy below the corresponding thresholds are determined to be retained subbands of the main response of the bearing structure; the remaining subbands are determined to be subbands to be estimated with mixed components.

[0010] Furthermore, the deep temporal network adopts a bidirectional long short-term memory network, and the feature segments of the sub-band are extracted and input into the network through a time-domain sliding window. After the forward and backward hidden states are concatenated, linearly mapped and activated by Sigmoid, the output is a time-varying decay mask coefficient whose value range is constrained to the interval [0,1].

[0011] Furthermore, the deep temporal network is obtained through two-stage joint optimization training: The first stage is supervised pre-training: based on a semi-physical simulation dataset with real labels, a joint loss function is constructed using the correlation between the time-domain mean square error and the frequency-domain power spectral density for training; The second stage is unsupervised adaptive fine-tuning: based on measured bridge monitoring data, a loss function is constructed using high-frequency suppression constraints of the residual spectrum and KL divergence constraints of the probability distribution before and after noise reduction for fine-tuning, maintaining the topological invariance of the dynamic manifold.

[0012] Furthermore, the steps of inverse multi-scale transformation and global splicing reconstruction specifically include: performing inverse multi-scale transformation on the processed sub-band coefficient set to obtain a time-domain denoising result with boundary extension, and obtaining standard denoised data blocks after symmetrically cutting off the extension segments on both sides; the overlapping regions of adjacent standard denoised data blocks are smoothly spliced ​​using Hanning window gradient weighted fade-in and fade-out fusion rules, and the non-overlapping regions are directly iso-mapped, finally obtaining a long-term preliminary denoised time-series signal with continuous global amplitude and phase.

[0013] Furthermore, the acceleration boundary index is calculated by using a second-order central difference operator to numerically differentiate the preliminary noise reduction sequence to obtain an acceleration sequence, and then determining whether the global maximum instantaneous acceleration is less than or equal to a preset maximum allowable vertical dynamic acceleration threshold. The displacement continuity index is calculated as follows: calculate the maximum displacement increment between adjacent sampling points and determine whether it is less than or equal to the preset maximum displacement step threshold value. The calculation method of the spectrum rationality index is as follows: perform a fast Fourier transform on the preliminary noise reduction sequence, extract the core frequencies corresponding to the first R main peaks of the amplitude spectrum, and determine whether each core frequency falls within the allowable frequency band range determined by the prior frequency vector; The power spectrum similarity index is calculated as follows: the cross-correlation coefficient of the power spectrum between the original monitoring sequence and the preliminary noise reduction sequence and the nonlinear statistical information distribution divergence are calculated, and it is determined whether the cross-correlation coefficient is greater than or equal to a preset lower similarity threshold and whether the distribution divergence is less than or equal to a preset upper divergence threshold.

[0014] Further, in step S7, the iteration convergence termination condition is any one of the following: all four physical consistency indices meet the preset boundary conditions; the number of iterations of the feedback control loop reaches the preset maximum number of iterations; the mean square error between the noise reduction sequences output by two adjacent iterations is less than the preset tolerance.

[0015] The beneficial effects of this invention are: This invention is an adaptive multi-scale bridge dynamic deflection noise reduction method based on physical constraints. Compared with the prior art, this invention has the following technical advantages: This invention first performs adaptive multi-scale decomposition of the displacement time series based on prior bridge dynamic information and sampling frequency. Then, it characterizes the complexity and randomness of sub-bands using permutation entropy and sample entropy, distinguishing sub-bands into retained sub-bands, suppressed sub-bands, and sub-bands to be estimated. Further refined temporal suppression is applied only to mixed sub-bands. Therefore, it can more effectively distinguish and process effective responses and noise components based on different data characteristics, improving noise reduction accuracy while better preserving the true dynamic displacement response of the bridge, and enhancing processing stability in complex noise environments and under different working conditions. After obtaining the initial noise reduction results, this invention further verifies the results from the perspective of bridge dynamics, determining whether they meet the acceleration boundary constraints, displacement continuity constraints, and spectrum rationality constraints. If the conditions are not met, the sub-band classification results or suppression parameters are adjusted through a feedback mechanism and reprocessed to make the final output results more consistent with the actual dynamic response law of the bridge. This invention preprocesses and segments the original displacement time series, dividing the long-term series into multiple local data blocks for separate processing. It maintains the continuity of the results by fusing overlapping areas. At the sub-band level, it introduces a time-adaptive estimation model to process only the sub-bands that truly require fine-grained discrimination. Sub-bands that are clearly valid responses are directly retained, while sub-bands that are clearly noise are directly suppressed. Therefore, while ensuring the noise reduction effect, it reduces unnecessary computation and improves the overall processing efficiency, making it more suitable for long-term monitoring and engineering deployment applications of actual bridges. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the working steps of an adaptive multi-scale bridge dynamic deflection noise reduction method based on physical constraints proposed in this invention. Detailed Implementation

[0017] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0018] The present invention discloses an adaptive multi-scale bridge dynamic deflection noise reduction method based on physical constraints, comprising the following steps: like Figure 1 As shown, this embodiment includes the following steps: Step S1: Acquire time-series displacement data and perform preprocessing. 1.1 Acquisition of raw time-series data and parameter initialization Acquire the time-series displacement data output by the GB-SAR device for the bridge target monitoring points, and denote the original monitoring sequence as... ,in, For the first Displacement observation values ​​corresponding to each sampling time. Let be the total number of sampling points, and let be the sampling frequency of the GB-SAR device. The time interval between adjacent sampling points ( The original monitoring sequence The data simultaneously includes the bridge's actual dynamic response components, random noise, local sudden disturbances, and low-frequency background disturbances.

[0019] 1.2 Data Block Segmentation Based on Sliding Window To eliminate the boundary discontinuity defects caused by fixed-length short sequence processing methods when processing large-scale, long-term continuous monitoring data, this invention modifies the original monitoring sequence... Perform sliding window segmentation processing.

[0020] Let the window length be The window sliding step size is And the window parameters satisfy the constraints. This creates overlapping areas between adjacent data blocks. The original monitoring sequence is then analyzed based on the sliding window. Extract the total. The overlapping data blocks, of which the first The data blocks are denoted as Its mathematical expression is: (1-2) In the formula, the data block index The range of values ​​is Total number of blocks Determined by the following formula: (1-3) in, This represents the floor operator.

[0021] 1.3 Data Block Boundary Endpoint Extension To reduce the endpoint effect (or boundary effect) that occurs when performing multi-scale decomposition (such as wavelet packet decomposition or empirical mode decomposition) on each data block, this invention, after completing the sliding window block division, performs the following on each independent data block: Signal extension is performed at both ends.

[0022] Specifically, the single-sided extension length is set to... (in Using symmetrical extension, mirror filling, or periodic extension methods, the length is... raw data blocks Expand to a length of Extended data blocks Its expression is: (1-4) This provides a boundary buffer for the filter bank in subsequent multi-scale algorithms, ensuring the core monitoring segment... The signal within does not become distorted during decomposition.

[0023] Step S2 performs adaptive multi-scale decomposition based on prior bridge dynamic information. 2.1 Construction of the Prior Frequency Matrix for Bridge Dynamics First, the initial prior reference frequency information of the bridge to be monitored is obtained, and a prior frequency vector is constructed. : (2-2) in, The first part of the bridge structure represents the first part. Vertical principal vibration reference frequency The prior reference frequency information is derived from one or more combinations of the bridge design document, finite element modal analysis results, historical health monitoring reports, or environmental random vibration test results under no-load conditions.

[0024] The prior frequency vector It is used only as a boundary constraint for determining the adaptive frequency band division and decomposition depth, and is used to reduce the risk of frequency band aliasing between the main response of the bridge structure and the low-frequency trend term (DC drift) or high-frequency random noise at the source, rather than as the sole criterion for the correctness of the final noise reduction output.

[0025] 2.2 Adaptive Decomposition Depth Closed-form solution For each independent extended data block obtained in step 1 To ensure effective separation between the bridge's first-order dominant mode (i.e., the lower frequency limit of the full-bridge vibration) and the DC-variable drift, this invention combines the sampling frequency of the GB-SAR device. With the lower bound of prior frequency Adaptive calculation of optimal multi-scale decomposition depth .

[0026] The adaptive decomposition depth The following frequency band isolation inequality constraint must be satisfied: (2-3) To prevent boundary distortion caused by insufficient data block length, a maximum allowable decomposition depth boundary constraint is introduced. The The calculation formula is defined as follows: (2-4) In the formula, The length of the sliding window. The compact support length (number of filter taps) of the selected wavelet basis function. Combining the aforementioned inequality constraints and boundary limitations, this invention provides the final adaptive decomposition depth. Standard explicit analytical expression: (2-5) in, This represents the floor operator.

[0027] 2.3 Adaptive Wavelet Packet Decomposition Based on Frequency Order Rearrangement Using the adaptive decomposition depth Using orthogonal or bioorthogonal wavelet bases with compact support properties (preferably Daubechies wavelet base or Symlets wavelet base in this embodiment), the extended data blocks are... implement Layered full binary tree wavelet packet decomposition (WPD).

[0028] After decomposition, the total obtained at the bottom layer is... The original sub-band coefficient sequence. To eliminate the frequency band interleaving phenomenon caused by wavelet packet downsampling, this invention... The original subband coefficient sequences are subjected to Gray code inversion permutation and topological rearrangement to obtain a normalized set of subband coefficients arranged monotonically in increasing order of frequency. : (2-6) in, Indicates the first The data block is in the frequency sequence. The coefficient sequence of each sub-band After the Gray code rearrangement, each normalized subband Corresponding physical frequency range Strictly satisfying the following linear partitioning rule: (2-7) Through the above steps, adaptive frequency band self-fine division based on bridge dynamic physics priors is realized, ensuring that the frequencies of each core main mode of the bridge fall into the normalized sub-band range that can be processed individually with priority and isolation, laying a deterministic feature input boundary for the accurate targeted noise reduction of subsequent deep learning models.

[0029] Step S3: Calculate the multidimensional statistical characteristics of each subband and perform subband classification. 3.1 Subband Multidimensional Dynamic Entropy Feature Extraction The first step is to adaptively decompose and rearrange the frequencies in step 2 to obtain the second... The normalized subband coefficient sequences of each data block (in This invention provides quantitative characterization from two dimensions: temporal structure randomness and amplitude self-similarity complexity. (1) Calculation of Permutation Entropy (PE): This is used to characterize the temporal randomness of the sub-band coefficient sequence. Its normalization calculation formula satisfies: (3-2) In the formula, For the defined phase space embedding dimension, This represents the spatial arrangement pattern of the reconstructed vectors. The total number of permutation patterns ( ), For a specific permutation pattern The probability of occurrence in the current subband coefficient sequence. The value range is [0,1]. The closer the value is to 1, the stronger the randomness of the sub-band signal, and the more it tends to be white noise or high-frequency irregular random interference.

[0030] (2) Calculation of Sample Entropy (SE): This is used to characterize the complexity and dynamic self-similarity of the subband coefficient sequence. Its calculation formula satisfies: (3-3) In the formula, For embedded dimensions, The similarity tolerance threshold is typically set to 0.1 to 0.25 times the standard deviation of the current subband sequence. Indicates tolerance Under constraints, the subband sequence in The total number of matching pairs of similar vectors reconstructed in the phase space; Indicates the same tolerance Below, the dimension increases to The number of similar vector pairs matched in dimension 1.

[0031] 3.2 Sub-band classification decision based on dual-index dynamic statistical boundary To achieve targeted and precise processing of various components, this invention is based on the current... All data blocks The statistical manifold of each subband is used to dynamically construct an adaptive classification threshold.

[0032] First, calculate the mean of the permutation entropy of the current data block's full subbands and the sample entropy. , ) and standard deviation ( , Its mathematical expression is as follows: (3-4) (3-5) Based on this, we define the permutation entropy adaptive classification threshold. and sample entropy adaptive classification threshold They are respectively: (3-6) (3-7) In the formula, and This is a preset empirical adjustment coefficient.

[0033] Based on the aforementioned adaptive classification threshold, a dual-index diversion determination rule is constructed to determine the total. Subband adaptive classification is divided into the following three categories: (1) Rule 1: Suppress subband set

[0034] If a sub-band simultaneously satisfies and This indicates that the subband exhibits extremely high dynamic randomness and high-frequency chaotic complexity, and is determined to be dominated by high-frequency random noise or sudden pulse interference, thus belonging to the suppression subband set.

[0035] (2) Rule 2: Preserve the set of sub-bands

[0036] If a sub-band simultaneously satisfies and If the sub-band has strong self-similarity and low randomness, it is determined that it carries the main global macroscopic dynamic structural response information of the bridge (such as low-order main modes) and is included in the reserved sub-band set.

[0037] (3) Rule 3: Set of subbands to be estimated

[0038] The remaining cross-bands that do not satisfy Rules 1 and 2 are determined to be mixed information subbands that simultaneously contain some weak structure response and broadband modulation noise, and are uniformly included in the set of subbands to be estimated.

[0039] 3.3 Sub-band Differentiation Fine-grained Drive Processing Based on the above classification decision results, completely independent differential spatial mapping processing is performed on the three types of sub-band sets: (1) For the retained subband ( ): Without any attenuation, directly copy and retain its original subband coefficient sequence to lock the lossless characteristics of the bridge core dynamics.

[0040] (2) For the suppression subband ( ): Perform hard suppression and zeroing process, forcibly clear the corresponding subband coefficient sequence to zero, and achieve complete blocking of strong random interference.

[0041] (3) For the subband to be estimated ( ): The corresponding hybrid subband coefficient sequence is used as the key feature input and fed into the deep neural network time-adaptive decay estimation module shown in step 4 for refined targeted stripping.

[0042] Step S4: Perform time-adaptive decay suppression and global physical manifold constraint training on the subband to be estimated. 4.1 Adaptive Suppression of Execution Timing for the Estimated Subband For each subband coefficient sequence to be estimated obtained by determination and splitting in step 3 To meet the dynamic input requirements of deep temporal networks, temporal feature samples are first constructed according to a preset length. Let the original coefficient sequence of any subband to be estimated be: (4-2) In the formula, This represents the length of a single wavelet packet subband sequence. A length of [length value] is used. The time-domain sliding window for the Segment truncation is performed to reconstruct the temporal feature input fragment. : (4-3) In the formula, This is the index of the starting time position of the current time-domain sliding window.

[0043] 4.2 Time-varying decay coefficient mapping based on bidirectional long short-term memory network Input the time-series features into the segment The input is fed into a pre-trained deep temporal network model, which utilizes long-term contextual correlation characteristics to adaptively solve for the nonlinear time-varying decay coefficient sequence that strictly corresponds to each time position. In this embodiment, the deep temporal network model preferably employs a bidirectional long short-term memory network (BiLSTM). For time... Subband input coefficients Its forward hidden state and backward hidden state They are represented as follows: (4-4) (4-5) The forward hidden state With backward hidden state After tensor concatenation, the final time-varying decay mask is obtained by sequentially mapping through a linear mapping layer and a nonlinear activation constraint function. : (4-6) In the formula, This is the weight matrix. For bias vectors, The Sigmoid activation function is used to force the magnitude of the attenuation mask coefficients to be within a certain range. Within the closed interval. Utilizing the aforementioned time-varying decay coefficient. The original coefficients of the subband to be estimated Perform higher-order element-wise multiplication and weighting to obtain the refined subband coefficients after noise reduction. : (4-7) The time-varying decay coefficient It has strict physical mapping boundaries: then Time (of which) (As a preset small positive number), it indicates that the characteristics of this time node highly match the bridge dynamic response manifold, and the coefficients are fully preserved; when Time (of which) (If the value is a preset small positive number), it indicates that the time point is dominated by sudden strong random noise, and the coefficient is strongly suppressed and set to zero; when At that time, the network performs continuous spectrum nonlinear soft suppression on it.

[0044] Deep temporal networks (BiLSTM) are not applied uniformly to all subbands, but only to the subbands to be estimated selected by both permutation entropy and sample entropy. This avoids the over-computation of pure noise subbands by deep learning models and prevents the erroneous attenuation of pure response subbands, thus reducing the computational load of network inference while ensuring the accuracy of noise reduction.

[0045] 4.3 Optimization Training Using a Joint Loss Function Incorporating Physical Consistency and Residual Spectrum Constraints The parameters of the deep temporal network model are obtained through two-stage joint optimization training to eliminate the distribution differences between the source domain (simulation data domain) and the target domain (measured data domain).

[0046] Phase 1: Supervised Semi-Physical Simulation Pre-training to Optimize Objectives Training is performed using a semi-physical simulation dataset containing real bridge environmental noise. A global total loss function is defined, which includes joint constraints on the correlation between time-domain mean square error and frequency-domain power spectral density (PSD). : (4-8) In the formula, The mean square error in the time domain between the reconstructed subband coefficients and the pure prior label is: (4-9) This represents the power spectral density correlation loss between the denoised sequence and the clean labeled sequence, used to force the network to ensure the consistency of the physical energy spectrum. (4-10) In the formula, The power spectral density operator represents a time series. and These are the covariance and variance operators, respectively. This is the frequency domain weighting balance coefficient.

[0047] Phase 2: Unsupervised adaptive fine-tuning of the objective in the measured domain In practical continuous monitoring applications of the target bridge, explicit pseudo-labels are not relied upon; instead, physical manifold consistency and residual spectrum constraints are used as the training basis. A target domain fine-tuning loss function is defined. : (4-11) In the formula, Constraints for suppressing high-frequency noise in the residual spectrum: (4-12) The Körbek-Leibler (KL) divergence constraint on the probability distribution before and after denoising is used to prevent dynamic nonlinear distortion caused by excessive denoising and to maintain the topological invariance of the physical manifold. (4-13) In the formula, This represents the probability density manifold mapping of the wavelet packet coefficient sequence. Through collaborative iterative training using the aforementioned dual loss functions, the network is ensured to track and adapt to slowly varying noise environments in real time.

[0048] Step S5 performs an inverse transform on the subband coefficients to reconstruct the signal, obtaining the initial denoised signal. 5.1 Integration of Noise Reduction Standardized Subband Sets For the current number The processing results of all sub-bands in each data block are integrated along the matrix dimension to construct a set of reconstructed sub-band coefficients. : (4-14) In the formula, the coefficients of each sub-band are filled with differentiated values ​​based on their classification and diversion paths in step 3, and the specific rules are as follows: For retaining subbands ( ), and its corresponding fill factor The original subband coefficients obtained from step 2 decomposition; for the suppressed subband ( ), and its corresponding fill factor To perform strong suppression and zeroing on the all-zero sparse sequence; for the subband to be estimated ( ), and its corresponding fill factor The time-varying decay coefficient output by the deep temporal network model described in step 4 The denoising coefficient sequence after soft suppression weighting.

[0049] 5.2 Inverse Multi-Scale Reconstruction of Temporally Extended Data Blocks For the reconstructed subband coefficient set Execute the inverse multiscale transformation reconstruction operator corresponding to step 2 to obtain the first... The preliminary temporal denoising results of each data block, including boundary extensions, are denoted as follows: In this embodiment, the inverse multi-scale transformation reconstruction operator is preferably the inverse wavelet packet transform (IWPT), whose mathematical mapping expression is: (4-15) because The one-sided length introduced in step 1 of the preprocessing stage is To ensure strict alignment in the time domain, this invention provides auxiliary extension boundaries. The time-domain sequence is subjected to symmetric inverse truncation, forcibly removing the lengths on both sides. The transition segment is used to restore the value corresponding to the standard sliding window length. Standard noise reduction data block : (4-16) 5.3 Global Signal Recovery Based on Smooth Splicing of Overlapping Time-Domain Window Functions All totals One standard noise reduction data block Global temporal stitching is performed according to the overlapping topology positions of the sliding window as described in step 1. The number of overlapping points between adjacent standard denoising data blocks is known to be... To completely eliminate the amplitude steps and phase discontinuities caused by block-based independent noise reduction at the block boundaries, this invention applies the following to any adjacent... Data blocks With the Data blocks The overlapping areas are smoothly stitched together using a window function algorithm. Let the local time point index within the overlapping area be... (in Define a superimposed weighted smoothing function that monotonically and smoothly varies with the time series. The present invention preferably employs a Hanning window fade-in / fade-out structure, wherein the overlapping weighted smoothing function... The mathematical formula for calculation satisfies: (4-17) Therefore, the reconstructed continuous noise-reduced displacement output value within the overlapping region The following time-domain nonlinear fusion rules must be met: (4-18) Iterate through and concatenate all of them in sequence. For overlapping areas between blocks, data points in non-overlapping areas are directly assigned weights through equivalent mapping at their corresponding locations, and finally, the data is stitched together to reconstruct the original monitoring sequence. Long-term continuous bridge dynamic noise reduction time-series displacement sequence with strict length alignment and global amplitude and phase continuity. : } (4-19) The long-term continuous bridge dynamic noise reduction time-series displacement sequence This serves as the initial noise reduction signal and as the standard input source for subsequent bridge structure physical consistency evaluation, damage identification, and feedback correction modules.

[0050] 6. Structural dynamics and physical consistency evaluation of the preliminary noise reduction signals The long-term continuous preliminary denoised temporal displacement sequence obtained by reconstructing and smoothly stitching in step 5 Based on the prior boundary of bridge structural dynamics, a multi-dimensional physical consistency manifold verification is performed. The evaluation index includes at least the following four manifold joint determinations: 6.1 Kinematic boundary index verification (1) Acceleration boundary index verification: The initial denoising sequence was processed using the second-order central difference operator. Numerical differential derivation is performed, and the instantaneous temporal velocity value of each sampling node is adaptively solved. With the instantaneous value of time-series acceleration : (5-2) (5-3) In the formula, The sampling time interval is denoted as . Calculate the global maximum instantaneous acceleration and determine whether it satisfies the following structural safety dynamic boundary constraints: (5-4) In the formula, The maximum permissible vertical dynamic acceleration threshold is preset for the bridge monitoring point process.

[0051] (2) Verification of displacement transient continuity index: To eliminate non-physical abrupt changes caused by numerical singularities during the noise reduction process, the maximum displacement increment between adjacent sampling points is calculated to determine whether it satisfies the continuity constraint: (5-5) In the formula, This is the maximum displacement step threshold value determined based on the maximum allowable structural displacement velocity and the sampling rate.

[0052] Step S6.2 Verification of Spectral Topology Rationality and Power Spectrum Similarity Indicators (1) Verification of the rationality index of spectrum prior: For the preliminary noise reduction sequence Perform Fast Fourier Transform (FFT) to extract the amplitude spectrum before For each main peak value, a core frequency corresponding to that peak value is used to construct a reconstructed set of main peak frequencies. It is then verified whether this set strictly falls within the physically feasible region of the bridge's dynamic response.

[0053] (6-2) In the formula, The bridge prior reference frequency vector in step 2 Locked primary mode frequency band boundaries, This represents the allowable modal drift tolerance.

[0054] (2) Power spectrum similarity and information manifold distribution verification: Calculate the original monitoring sequence With the initial noise reduction sequence The power spectral density (denoted as respectively) and ), and derive its power spectrum cross-correlation coefficient. : (6-3) Simultaneously, the nonlinear statistical information distribution divergence before and after noise reduction is constructed. : (6-4) Determine whether the preset joint energy distribution limit is met simultaneously: and (in This is the lower limit threshold for similarity. (This refers to the upper limit threshold for divergence). When any one or more of the above physical consistency evaluation indicators fail to meet the preset boundary conditions, the system adaptively triggers the global feedback adjustment control signal. Then feed it into step 7 for parameter iterative correction.

[0055] Step S7: A refined noise reduction method based on feedback-corrected decision-making 7.1 Closed-loop feedback regulation and control strategy Adjust the control signal based on the feedback generated in step 6. To address the failure type, this invention performs the following dynamic gain matrix adjustment on the control flow parameters of the pre-core algorithm and re-drives steps 3 to 6 to form a closed-loop control flow: Scenario 1: If unreasonable high-frequency spurious peaks or acceleration exceeding limits are found during spectrum verification ( ): The system determines that the high-frequency random interference suppression is insufficient or that there are missed detections in wavelet packet classification. The system automatically triggers a strong suppression operator, step-decreasing the permutation entropy threshold adjustment coefficient in step 3. Simultaneously, a global contraction multiplier is applied to the time-varying decay mask coefficients output by the deep temporal network in step 4. (in ): (6-2) This is used to forcibly reduce the non-stationary spike components in the subband to be estimated.

[0056] During the feedback correction iteration process, the mean and standard deviation of the permutation entropy and sample entropy in step S3 are updated and calculated in real time based on the current iteration classification results to adaptively track the changes in signal statistical characteristics with noise reduction processing; each iteration reconstructs the classification threshold based on the actual sub-band coefficient distribution of the current data block, so that the classification boundary matches the current signal state.

[0057] Scenario 2: If the energy spectrum similarity or amplitude is low ( ): The system determined that excessive denoising in the deep learning model was causing false negatives to capture the bridge's true weak principal modal dynamic responses. The system automatically triggered the manifold repair operator, incrementally broadening the sample entropy threshold adjustment coefficient from step 3. And increase the soft retention compensation coefficient for the network output in step 4: This is to protect the integrity of the structural fundamental frequency.

[0058] 7.2 Determination of Iterative Convergence Termination Criteria The closed-loop feedback correction circuit automatically terminates when any of the following convergence conditions are met: All four structural dynamic physical consistency indicators described in step 6 have passed the preset boundary verification. The number of iterations in the feedback control loop reaches the set maximum iteration limit. ; The mean square convergence magnitude between consecutive denoised sequences generated in two adjacent iterations is lower than the set tolerance. (6-2) 7.3 Final Refined Noise Reduction Data Matrix Output When the above termination condition is triggered, the algorithm stops iterating and outputs the standard continuous denoised displacement sequence in the current convergence state as the final technical result of this invention, denoted as the global final pure dynamic response sequence. .

[0059] In this implementation example, the test data is simulated GB-SAR monitoring data of a long-span bridge, with a sampling frequency of 100Hz, a continuous acquisition time of 60 minutes, and a total of 360,000 sampling points. Based on the pure bridge dynamic deflection simulation signal, three types of noise components are superimposed: the first type is high-frequency random noise, using Gaussian white noise with a mean of 0 and a standard deviation of 10% of the monitoring signal amplitude; the second type is low-frequency drift noise, with a frequency range of 0.01Hz to 0.1Hz; and the third type is localized sudden interference, simulating the instantaneous impact disturbance generated when a vehicle passes, occurring randomly, lasting from 0.1 seconds to 0.5 seconds, and with an amplitude 3 to 8 times that of the normal signal.

[0060] The comparison method is a bridge dynamic deflection denoising method based on empirical mode decomposition and wavelet threshold denoising. The two methods are run on 60 minutes of monitoring data containing the above three types of mixed noise. The signal-to-noise ratio, root mean square error and mode retention rate of the denoised signal are calculated based on the pure simulated signal.

[0061] On 60 minutes of mixed noise monitoring data, the signal-to-noise ratio (SNR) after denoising using the comparative method was 18.6 dB, while the SNR after denoising using our method was 26.3 dB, an improvement of 7.7 dB over the comparative method. The root mean square error (RMS) of the comparative method was 0.42 mm, while the RMS of our method was 0.18 mm, a reduction of 57.1%. Regarding modal frequency retention, the retention rates of the first, second, and third modal frequencies using the comparative method were 89.2%, 76.5%, and 61.3%, respectively; while the retention rates of the first, second, and third modal frequencies using our method were 98.7%, 95.1%, and 90.4%, respectively, all significantly higher than the comparative method.

[0062] The above results show that the proposed method, through adaptive frequency band division guided by bridge dynamic priors, ensures that each main mode falls preferentially into the normalized sub-band range that can be processed independently. Then, it performs accurate classification using both permutation entropy and sample entropy as indicators. The method does not attenuate the retained sub-bands that carry the main mode information. Therefore, it can effectively preserve the true dynamic response characteristics of the bridge and is superior to the comparative methods in terms of noise reduction accuracy and mode preservation capability.

[0063] After the noise reduction process is completed, the physical consistency of the output results of the two methods is checked, and the failure rate of each physical index is calculated.

[0064] Regarding acceleration boundary exceedances, the exceedance rate of the comparative method was 12.4%, while that of our method was 0.3%. Regarding displacement continuity exceedances, the exceedance rate of the comparative method was 8.7%, while that of our method was 0.1%. Regarding spectral frequency drift, the drift rate of the comparative method was 15.6%, while that of our method was 1.2%. Regarding power spectrum similarity below the threshold, the rate of the comparative method was 18.3%, while that of our method was 2.5%. The failure rate of all physical indicators using our method was controlled within 3%.

[0065] The above results show that after obtaining the initial noise reduction results, this method performs multi-dimensional physical consistency evaluation through kinematic boundary verification, displacement continuity verification, spectrum rationality verification, and power spectrum similarity verification. When any index is not satisfied, the sub-band classification threshold or attenuation coefficient is adaptively adjusted through a feedback correction loop and then reprocessed, thereby ensuring that the final output results strictly conform to the dynamic laws of bridge structures. This method is significantly better than the comparative methods that lack physical consistency constraint mechanisms.

[0066] III. Comparison of Processing Efficiency In practical bridge monitoring applications, the aforementioned 60-minute continuous monitoring data was processed using two different methods, and the total processing time was recorded and the processing time for each session was calculated.

[0067] The total processing time of the comparative method was 286.4 seconds, with a single processing latency of 4.77 seconds; the total processing time of this method was 195.7 seconds, with a single processing latency of 3.26 seconds. The total processing time of this method is reduced by 31.7% compared to the comparative method, and the processing speed is increased to 1.46 times that of the comparative method.

[0068] The above results show that the proposed method divides long-term sequences into multiple local data blocks through sliding window block processing, avoiding the waste of computational resources caused by processing the entire sequence at once. At the same time, it adopts a differentiated processing strategy at the sub-band level, directly copying the sub-bands that carry the main modality information, directly setting the sub-bands with strong noise suppression to zero, and introducing a deep temporal network for fine processing only for the sub-bands with mixed information to be estimated, which greatly reduces the computational amount of neural network inference and the processing efficiency is significantly better than the comparative methods.

[0069] IV. Robustness Testing under Different Noise Intensities The noise intensity of various types of noise was increased stepwise by 0.5, 1.0, 1.5 and 2.0 times the baseline value to test the noise reduction performance stability of the two methods under different noise intensities.

[0070] When the noise intensity factor is 0.5, the signal-to-noise ratio (SNR) after noise reduction using the comparative method is 22.1 dB, while that using this method is 28.5 dB, a difference of 6.4 dB. When the noise intensity factor is 1.0, the SNR after noise reduction using the comparative method is 18.6 dB, while that using this method is 26.3 dB, a difference of 7.7 dB. When the noise intensity factor is 1.5, the SNR after noise reduction using the comparative method is 15.2 dB, while that using this method is 24.1 dB, a difference of 8.9 dB. When the noise intensity factor is 2.0, the SNR after noise reduction using the comparative method is 12.0 dB, while that using this method is 21.8 dB, a difference of 9.8 dB. As the noise intensity factor increases from 0.5 to 2.0, the signal-to-noise ratio (SNR) of the comparative method decreases from 22.1 dB to 12.0 dB, showing a significant performance degradation. In contrast, the SNR of our method decreases from 28.5 dB to 21.8 dB, a significantly smaller reduction than the comparative method. Furthermore, the performance difference between our method and the comparative method gradually increases to 9.8 dB as the noise intensity increases.

[0071] The above results demonstrate that the adaptive classification thresholds for permutation entropy and sample entropy in this method are dynamically constructed based on the statistical manifold of all subbands in the current data block, and can adaptively adjust the classification boundary according to the noise level. When the noise intensity increases, more high-frequency subbands are automatically assigned to the suppressed subbands or attenuated by the deep network, while the retained subbands always lock the core modal information of the bridge. Therefore, it has strong noise intensity adaptability and processing stability, and has significant engineering application advantages in complex and ever-changing actual monitoring environments.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for denoising bridge dynamic deflection based on physical constraints and adaptive multi-scale methods, characterized in that, Includes the following steps: Step S1: Acquire time-series displacement data and perform preprocessing: acquire the original monitoring sequence output by the ground-based synthetic aperture radar equipment to the bridge target monitoring point, perform sliding window block processing on the original monitoring sequence to obtain multiple overlapping data blocks, and perform endpoint extension on each data block to obtain extended data blocks; Step S2, Adaptive multi-scale decomposition based on prior bridge dynamic information: Obtain prior frequency information of the bridge to be monitored, construct prior frequency vector, calculate adaptive decomposition depth according to the sampling frequency of the ground-based synthetic aperture radar equipment and the lowest order reference frequency in the prior frequency vector, perform multi-scale decomposition on each extended data block using the adaptive decomposition depth, and rearrange the frequency order of the decomposed sub-band coefficients to obtain a normalized sub-band coefficient set arranged monotonically increasing in frequency; Step S3: Calculate the multidimensional statistical features of each sub-band and perform sub-band classification: For each normalized sub-band coefficient sequence, calculate the permutation entropy and sample entropy. Based on the relationship between the permutation entropy and sample entropy of each sub-band and the adaptive classification threshold, divide each sub-band into retained sub-bands, suppressed sub-bands and sub-bands to be estimated. Step S4, perform time-adaptive attenuation suppression on the subband to be estimated: input the coefficient sequence of the subband to be estimated into the deep temporal network model, obtain the time-varying attenuation coefficient, and use the time-varying attenuation coefficient to weight the coefficient sequence of the subband to be estimated to obtain the denoised subband coefficient; Step S5: Perform inverse transformation reconstruction on the subband coefficients to obtain the preliminary denoising signal: Integrate the original coefficients of the retained subband, the zeroed coefficients of the suppressed subband, and the denoising coefficients of the subband to be estimated after processing in step S4, perform inverse multi-scale transformation reconstruction, and perform boundary truncation and overlapping smooth splicing on the reconstructed data blocks to obtain the preliminary denoising time-series displacement sequence. Step S6: Perform a structural dynamic physical consistency evaluation on the preliminary noise reduction time-series displacement sequence: calculate the acceleration index, displacement continuity index, spectrum rationality index, and power spectrum similarity index of the preliminary noise reduction time-series displacement sequence, and determine whether each index meets the preset physical consistency boundary conditions. Step S7: Feedback correction based on physical consistency evaluation results: When any index in step S6 fails to meet the physical consistency boundary conditions, a feedback adjustment control signal is generated. The sub-band classification threshold in step S3 and / or the time-varying attenuation coefficient in step S4 are adjusted according to the feedback adjustment control signal. Steps S3 to S6 are repeated until the preset iterative convergence termination condition is met, and the final denoised time-series displacement sequence is output.

2. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, The original monitoring sequence is segmented and truncated using a sliding window with a preset length and sliding step size to obtain multiple overlapping data blocks. Symmetrical extension, mirror filling, or periodic extension are performed on both ends of each data block to generate extended data blocks with boundary buffers, which are used to suppress the endpoint effect of multi-scale decomposition.

3. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, The reference frequencies of vertical principal vibrations of the bridge structure are obtained, and a priori frequency vectors are constructed as frequency band division constraints. Combining the sampling frequency of the ground-based synthetic aperture radar and the lower limit of the prior frequency, the effective separation of low-frequency principal modes and DC drift is used as a constraint. At the same time, the maximum decomposition depth boundary corresponding to the data block length and the wavelet basis support length is introduced. The adaptive decomposition depth is obtained by solving the closed analytical expression.

4. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 3, characterized in that, The multi-scale decomposition adopts wavelet packet full binary tree decomposition. After decomposition, the original sub-band coefficient sequence is reversed by Gray code to obtain a normalized sub-band coefficient set arranged monotonically increasing in frequency, so that the frequencies of each core main mode independently fall within the corresponding sub-band range.

5. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, The steps of constructing an adaptive dual-classification threshold and classifying categories based on subband statistical features specifically include: calculating the mean and standard deviation of the permutation entropy of all subbands and the mean and standard deviation of the sample entropy within the current data block; introducing empirical adjustment coefficients to generate permutation entropy classification thresholds and sample entropy classification thresholds respectively; subbands that simultaneously satisfy both permutation entropy and sample entropy being higher than the corresponding thresholds are determined to be suppressed subbands dominated by high-frequency noise; subbands that simultaneously satisfy both permutation entropy and sample entropy being lower than the corresponding thresholds are determined to be retained subbands of the main response of the bearing structure; the remaining subbands are determined to be subbands to be estimated with mixed components.

6. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, The deep temporal network adopts a bidirectional long short-term memory network. It extracts sub-band feature segments through a time-domain sliding window and inputs them into the network. After concatenation of forward and backward hidden states, linear mapping and Sigmoid activation, the output is a time-varying decay mask coefficient whose value range is constrained to the interval [0,1].

7. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 6, characterized in that, The deep temporal network is obtained through two-stage joint optimization training: The first stage is supervised pre-training: based on a semi-physical simulation dataset with real labels, a joint loss function is constructed using the correlation between the time-domain mean square error and the frequency-domain power spectral density for training; The second stage is unsupervised adaptive fine-tuning: based on measured bridge monitoring data, a loss function is constructed using high-frequency suppression constraints of the residual spectrum and KL divergence constraints of the probability distribution before and after noise reduction to maintain the topological invariance of the dynamic manifold.

8. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, The steps of inverse multi-scale transformation and global splicing reconstruction specifically include: performing inverse multi-scale transformation on the processed sub-band coefficient set to obtain a time-domain denoising result with boundary extension; symmetrically cutting off the extension segments on both sides to obtain standard denoised data blocks; smoothing the overlapping regions of adjacent standard denoised data blocks using Hanning window weighted fade-in / fade-out fusion rules, and directly iso-mapping non-overlapping regions to finally obtain a long-term preliminary denoised time-series signal with continuous global amplitude and phase.

9. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, The acceleration boundary index is calculated by using a second-order central difference operator to numerically differentiate the preliminary noise reduction sequence to obtain the acceleration sequence, and then determining whether the global maximum instantaneous acceleration is less than or equal to the preset maximum allowable vertical dynamic acceleration threshold. The displacement continuity index is calculated as follows: calculate the maximum displacement increment between adjacent sampling points and determine whether it is less than or equal to the preset maximum displacement step threshold value. The calculation method of the spectrum rationality index is as follows: perform a fast Fourier transform on the preliminary noise reduction sequence, extract the core frequencies corresponding to the first R main peaks of the amplitude spectrum, and determine whether each core frequency falls within the allowable frequency range determined by the prior frequency vector, where R is a preset positive integer; The power spectrum similarity index is calculated as follows: the cross-correlation coefficient of the power spectrum between the original monitoring sequence and the preliminary noise reduction sequence and the nonlinear statistical information distribution divergence are calculated, and it is determined whether the cross-correlation coefficient is greater than or equal to a preset lower similarity threshold and whether the distribution divergence is less than or equal to a preset upper divergence threshold.

10. The method for reducing bridge dynamic deflection noise based on physical constraints and adaptive multi-scale as described in claim 1, characterized in that, In step S7, the iteration convergence termination condition is met if any of the following conditions are satisfied: All four physical consistency indicators meet the preset boundary conditions. The number of iterations in the feedback control loop reaches the preset maximum number of iterations; Alternatively, the mean square error between the denoised sequences output from two adjacent iterations is less than the preset tolerance.

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