Dual-constraint second-order blind identification bridge dynamic deflection signal noise reduction method

Abstract

The invention discloses a double-constraint second-order blind identification bridge dynamic deflection signal noise reduction method, which comprises the following steps: acquiring dynamic deflection observation signals of bridge target points, and constructing an observation signal matrix by using the observation signals of at least three adjacent target points; carrying out centralization processing on the observation signal matrix, and carrying out whitening transformation to obtain a whitening signal with a covariance matrix as a unit matrix; selecting a group of non-zero time delay values, calculating a time delay covariance matrix of the whitening signal under each time delay, and performing joint approximate diagonalization on all the time delay covariance matrixes to obtain a separation matrix and an initial separation source signal; optimizing the separation matrix based on sparsity constraint to obtain a hybrid matrix; performing dominant frequency optimization on the initial separation source signal; and reconstructing based on the optimized hybrid matrix and the optimized main frequency source signal to obtain a de-noised bridge dynamic deflection signal. The hybrid matrix optimization based on the sparsity constraint enables the reconstruction result to be closer to the real bridge dynamic deformation.

Description

Technical Field

[0001] This invention relates to the field of signal denoising, and more particularly to a dual-constraint second-order blind identification method for denoising bridge dynamic deflection signals. Background Technology

[0002] Currently, the dynamic deflection monitoring of most urban bridges relies on contact sensors such as accelerometers and strain gauges. While these methods can achieve high-precision measurements, they have inherent drawbacks such as low spatial coverage, high deployment costs, and difficult maintenance. Therefore, non-contact measurement technologies such as Global Navigation Satellite System (GNSS), Terrestrial Laser Scanning (TLS), and Spaceborne Synthetic Aperture Radar (In-SAR) are gradually being applied. However, GNSS sampling rates are typically below 20Hz, making it difficult to capture high-frequency dynamic responses; TLS measurement accuracy is only at the centimeter level, which cannot meet the needs of micro-deformation monitoring; and In-SAR is limited by the satellite revisit period, making real-time monitoring difficult.

[0003] Ground-based synthetic aperture radar (GB-SAR), as an emerging non-contact measurement technology, boasts advantages such as high precision, high sampling rate, all-weather operation, and comprehensive monitoring. It can acquire the dynamic deformation field of bridges in real time, effectively compensating for the shortcomings of traditional technologies in monitoring range, accuracy, and environmental adaptability, providing a new solution for bridge health monitoring. However, when using GB-SAR to monitor bridge dynamic deflection, the dynamic load borne by the bridge is usually unknown, resulting in a lack of prior information in the monitoring signal, making it difficult to directly extract useful components. Simultaneously, in urban environments, traffic flow, pedestrians, ground vibration, and electromagnetic interference introduce complex multi-scale noise. This noise severely overlaps with the nonlinear and non-stationary deflection signal of the bridge in both the time and frequency domains, making the extraction of effective signals extremely difficult.

[0004] Traditional time-domain and frequency-domain denoising methods have significant limitations for denoising nonlinear and non-stationary signals. Time-domain methods rely on the assumption of signal stationarity, which can easily lead to distortion of the useful signal or residual noise under time-varying loads. Frequency-domain methods assume that the signal and noise frequency bands are separated, making it difficult to handle spectral aliasing components and easily damaging transient useful signals or preserving background noise. Conventional time-frequency analysis methods (such as wavelet transform and empirical mode decomposition) can provide time-frequency localization analysis, but they are still generally limited by problems such as mode aliasing, endpoint effects, and sensitivity to parameter selection, resulting in incomplete denoising or signal distortion. Blind source separation (BSS) technology, especially the second-order blind identification (SOBI) algorithm, provides a new approach to these problems by using the time correlation of signals for source separation. However, the traditional SOBI algorithm is based on the assumption of linear independence of source signals. When dealing with highly nonlinear bridge deflection signals, the separation effect is poor, often resulting in residual noise leakage and signal distortion, which is difficult to meet the requirements of high-precision micro-deformation monitoring. Traditional SOBI algorithms often contain weak remnants of other source signals in the separated source signals, leading to cross-interference between signals. Directly retaining the first component for reconstruction may compromise signal quality due to ineffective interference suppression. Therefore, a dual-constraint second-order blind identification method for bridge dynamic deflection signals is needed. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a second-order blind identification bridge dynamic deflection signal denoising method based on the dual constraints of the improved SOBI algorithm with hybrid matrix weight-dominant frequency dual constraints, so as to achieve more accurate and robust denoising processing of GB-SAR bridge monitoring signals.

[0006] To achieve the above objectives, the present invention is implemented according to the following technical solution: This invention provides a dual-constraint second-order blind identification method for denoising bridge dynamic deflection signals, comprising the following steps: Collect dynamic deflection observation signals of bridge target points and construct an observation signal matrix from the observation signals of at least three adjacent target points; The observed signal matrix is ​​centered and then whitened to obtain a whitened signal with a covariance matrix of identity matrix. Select a set of non-zero time delay values, calculate the time delay covariance matrix of the whitened signal under each time delay, and perform joint approximate diagonalization on all time delay covariance matrices to obtain the separation matrix and the initial separation source signal; The separation matrix is ​​optimized based on sparsity constraints to obtain the mixing matrix; the main frequency of the initial separation source signal is optimized. Based on the optimized hybrid matrix and the optimized main frequency source signal, the denoised bridge dynamic deflection signal is obtained.

[0007] Furthermore, optimizing the separation matrix based on sparsity constraints to obtain the hybrid matrix specifically includes extracting the absolute value vector of each row of the separation matrix, identifying and marking the element that contributes the least to the output signal row by row, setting the element to zero, and obtaining the optimized hybrid matrix.

[0008] Furthermore, the initial separated source signal is subjected to main frequency optimization, specifically including: Power spectral density estimation is performed on the original target signal in the observed signal matrix to determine the dominant frequency of the bridge dynamic deflection signal; The power spectral density of the component with the weakest contribution in the initial separated source signal is estimated, and the signal components containing the main frequency are screened and retained to obtain the optimized source signal.

[0009] Furthermore, the dynamic deflection observation signals of the bridge target points are collected and processed using ground-based synthetic aperture radar, with a sampling frequency of not less than 100Hz.

[0010] Furthermore, the selection range of the non-zero time delay value is 1 to 50 sampling periods, and the joint approximation diagonalization is achieved through orthogonal matrix transformation, so that the transformed time delay covariance matrix approximates the diagonal matrix.

[0011] Furthermore, the element with the weakest contribution is determined by comparing the absolute values ​​of the elements in each row of the separation matrix, and the element with the smallest absolute value in each row is selected as the element to be set to zero.

[0012] Furthermore, when screening signal components containing the dominant frequency, signal components whose peak amplitude corresponding to the dominant frequency in the power spectral density is not less than 5% of the dominant peak value are retained.

[0013] Compared with the prior art, the present invention has the following advantages or beneficial effects: This invention utilizes a sparse constraint-based hybrid matrix optimization method to selectively reset the weights of the weakest cross-interference signals to zero, thereby reducing mutual interference between source signals. This process is performed after signal separation and before signal selection and reconstruction. This ensures that subsequent steps are based on a cleaner set of signals with less interference, thus improving the quality of the final reconstructed signal and achieving high fidelity.

[0014] This invention optimizes the source signal based on the dominant frequency constraint by filtering all separated components containing dominant frequency characteristics and performing collaborative fusion to recover a high-fidelity signal with complete multimodal dynamic characteristics and waveform details, making the reconstruction result closer to the real dynamic deformation of the bridge and having high integrity. Attached Figure Description

[0015] Figure 1 This is a flowchart of a dual-constraint second-order blind identification method for denoising bridge dynamic deflection signals according to the present invention. Figure 2 This is an example of a method for denoising bridge dynamic deflection signals based on a dual-constraint second-order blind identification method of the present invention. The denoising result of a certain bridge is shown in the figure. Detailed Implementation

[0016] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0017] Reference Figure 1 As shown, this invention provides a dual-constraint second-order blind identification method for denoising bridge dynamic deflection signals, comprising: This invention provides a dual-constraint second-order blind identification method for denoising bridge dynamic deflection signals, comprising the following steps: Collect dynamic deflection observation signals of bridge target points and construct an observation signal matrix from the observation signals of at least three adjacent target points; The observed signal matrix is ​​centered and then whitened to obtain a whitened signal with a covariance matrix of identity matrix. Select a set of non-zero time delay values, calculate the time delay covariance matrix of the whitened signal under each time delay, and perform joint approximate diagonalization on all time delay covariance matrices to obtain the separation matrix and the initial separation source signal; The separation matrix is ​​optimized based on sparsity constraints to obtain the mixing matrix; the main frequency of the initial separation source signal is optimized. Based on the optimized hybrid matrix and the optimized main frequency source signal, the denoised bridge dynamic deflection signal is obtained.

[0018] This method proposes sparsity-constrained optimization of the mixing matrix. By selectively resetting the weights of the weakest cross-interference to zero, it weakens the mutual interference between source signals and improves the purity of the separated signal. The specific steps are as follows: Dynamic deflection observation signals from bridge target points were collected using ground-based synthetic aperture radar (SAR) sampling and processing at a sampling frequency of no less than 100Hz. Centering and whitening processing were performed on the observed signals. Subtract the mean to achieve data centralization Then, the centered signal is whitened to transform its covariance matrix into an identity matrix. ; Calculate the time delay covariance matrix: To extract the second-order statistical characteristics of the signal under different time delays, select a set of non-zero delay values. Calculate the time delay covariance matrix of the whitened signal. ; Joint approximate diagonalization estimation of the separation matrix and source signal: using orthogonal matrices Jointly diagonalize all delay covariance matrices so that the transformed matrix As close as possible to the diagonal matrix ; and then the separation matrix is ​​obtained. The source signal is estimated. ; Optimization of the mixture matrix under sparse constraints: obtaining the separation matrix Find the absolute value of each row and iterate through them one by one. For a given row... Identify its smallest element This element represents the first The separated signal in the first The weights in each output. Since this value is usually very small and close to zero, it is set to zero, i.e. Applying this operation to each row yields the optimized transformation matrix. This helps to suppress cross-interference components.

[0019] Sparsity-constrained hybrid matrix optimization reduces mutual interference between source signals by selectively zeroing the weights of the weakest cross-interference. This is performed after signal separation and before signal selection and reconstruction. It ensures that subsequent steps are based on a cleaner set of signals with less interference, thereby improving the quality of the final reconstructed signal and achieving high fidelity.

[0020] Bridge dynamic response signals typically exhibit multimodal characteristics, and during actual separation, they may be dispersed across multiple output components due to modal coupling or noise. Traditional SOBI methods, which only retain the first component, discard modal information distributed across different components, leading to signal distortion in the reconstructed signal. This method proposes a source signal reconstruction strategy based on dominant frequency constraints. By filtering all separated components containing dominant frequency characteristics and performing collaborative fusion, a high-fidelity signal with complete multimodal dynamic characteristics and waveform details is recovered. The specific steps are as follows: Spectrum analysis and dominant frequency identification: Power spectral density estimation is performed on the original target signal to identify the dominant frequencies of the bridge's dynamic response. ; Optimization of the source signal constrained by the dominant frequency: Estimate the power spectrum of the separation signal with the weakest contribution, based on the dominant frequency in step ①. The dominant frequency information in the separated signal is retained to obtain the optimized source signal. ; Signal reconstruction: using the mixing matrix from Part 1 Optimized source signal with main frequency constraint Perform signal reconstruction, i.e. ,in It is a scaling factor or gain adjustment coefficient used to maintain amplitude consistency.

[0021] Source signal optimization based on dominant frequency constraints recovers a high-fidelity signal with complete multimodal dynamic characteristics and waveform details by screening all separated components containing dominant frequency features and performing collaborative fusion. This makes the reconstruction result closer to the real dynamic deformation of the bridge and has high integrity.

[0022] like Figure 2 As shown, three target points are selected: the mid-span and adjacent points of a bridge. Data is collected using microwave radar at a sampling frequency of 100Hz. The signals from the three adjacent points are constructed into an N*3 matrix and input into an improved I-SOBI algorithm module. Through an improved joint diagonalization strategy or source signal number estimation method, the ability to separate weak useful signals from noise is enhanced. Furthermore, the denoised signal corresponding to the true dynamic displacement of the target point is identified and extracted from the separated multiple source signal components, while effectively suppressing irrelevant components such as environmental interference and instrument noise. According to the denoising results output, as shown in Table 1, compared with traditional SOBI, the RMSE of the signal processed by I-SOBI is reduced (from 1.6625 to 1.5852), the PSNR is improved (from 6.4397 to 6.8530), the signal waveform is smoother, the main vibration characteristics are preserved more completely, and the reliability is significantly improved.

[0023] Table 1 Comparison of RMSE noise reduction results between traditional SOBI and I-SOBI processed signals ; This method performs detailed analysis of the mixing matrix, prioritizing the retention of the main signal components while selectively preserving important elements from secondary signals. Secondly, it extracts and retains the dominant frequency features from the target removed signal. Through a phased, dual-constraint processing mechanism, it effectively overcomes the residual noise leakage and signal distortion problems of traditional methods. While strongly suppressing complex environmental noise, it maximizes the preservation of the nonlinearity and integrity of the bridge's dynamic response, significantly improving the fidelity of signal reconstruction and providing a reliable data foundation for the accurate assessment of bridge structural conditions.

[0024] The above description is merely an example and illustration of the structure of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the structure of the invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

Claims

1. A method for denoising bridge dynamic deflection signals using a second-order blind identification method with dual constraints, characterized in that, Includes the following steps: Collect dynamic deflection observation signals of bridge target points and construct an observation signal matrix from the observation signals of at least three adjacent target points; The observed signal matrix is ​​centered and then whitened to obtain a whitened signal with a covariance matrix of identity matrix. Select a set of non-zero time delay values, calculate the time delay covariance matrix of the whitened signal under each time delay, and perform joint approximate diagonalization on all time delay covariance matrices to obtain the separation matrix and the initial separation source signal; The separation matrix is ​​optimized based on the sparsity constraint to obtain the mixture matrix; The initial separated source signal is then optimized for its main frequency. Based on the optimized hybrid matrix and the optimized main frequency source signal, the denoised bridge dynamic deflection signal is obtained.

2. The method for denoising bridge dynamic deflection signals under dual constraints in a second-order blind identification system according to claim 1, characterized in that: The optimization of the separation matrix based on sparsity constraints to obtain the hybrid matrix specifically includes: extracting the absolute value vector of each row of the separation matrix, identifying and marking the element that contributes the least to the output signal row by row, setting the element to zero, and obtaining the optimized hybrid matrix.

3. The method for denoising bridge dynamic deflection signals under dual constraints in a second-order blind identification system according to claim 1, characterized in that: The initial separated source signal is subjected to main frequency optimization, specifically including: Power spectral density estimation is performed on the original target signal in the observed signal matrix to determine the dominant frequency of the bridge dynamic deflection signal; The power spectral density of the component with the weakest contribution in the initial separated source signal is estimated, and the signal components containing the main frequency are screened and retained to obtain the optimized source signal.

4. The method for denoising bridge dynamic deflection signals under dual constraints in a second-order blind identification system according to claim 1, characterized in that, The dynamic deflection observation signals of the bridge target points are collected using ground-based synthetic aperture radar for sampling and processing, with a sampling frequency of not less than 100Hz.

5. The method for denoising bridge dynamic deflection signals under dual constraints in a second-order blind identification system according to claim 1, characterized in that: The non-zero time delay value is selected from 1 to 50 sampling periods. The joint approximation diagonalization is achieved through orthogonal matrix transformation, so that the transformed time delay covariance matrix approximates the diagonal matrix.

6. The method for denoising bridge dynamic deflection signals under dual constraints in a second-order blind identification system according to claim 2, characterized in that: The element with the weakest contribution is determined by comparing the absolute values ​​of the elements in each row of the separation matrix, and the element with the smallest absolute value in each row is selected as the element to be set to zero.

7. The method for denoising bridge dynamic deflection signals under dual constraints in a second-order blind identification system according to claim 3, characterized in that: When screening signal components containing the dominant frequency, retain signal components whose peak amplitude corresponding to the dominant frequency in the power spectral density is not less than 5% of the dominant peak value.

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