A Method and System for Cable Force Analysis Based on Enhanced Frequency Domain Decomposition

Abstract

This invention proposes a method and system for analyzing cable force in stay cables based on enhanced frequency domain decomposition, relating to the field of bridge engineering technology. Addressing the problem of poor cable force monitoring accuracy in existing technologies, this invention acquires vibration videos of stay cables and preprocesses them. The preprocessed vibration videos undergo multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion to extract displacement field data with sub-pixel accuracy. Key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. A displacement time history matrix is ​​constructed based on the displacement data of these key points over time. Trend terms and DC components are removed from the displacement time history matrix to obtain a power spectral density matrix. Singular value decomposition is performed on the power spectral density matrix to construct single-valued spectral curves. Modal confidence criteria are used to screen modes and frequencies in the single-valued spectral curves to determine the natural vibration frequencies of each order of the stay cable. Cable force is calculated based on these natural vibration frequencies. This invention achieves high accuracy in cable force calculation.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and in particular to a method and system for analyzing cable forces in cable stays based on enhanced frequency domain decomposition. Background Technology

[0002] As the core load-bearing component of a cable-stayed bridge, the cable force refers to the tensile force that the cable bears during service. It is a key indicator reflecting the overall stress balance and safety and stability of the bridge. Monitoring the cable force ensures that the cable stays are within the design stress range, providing direct evidence for bridge construction tensioning, operation and maintenance, and safety assessment.

[0003] Currently, traditional cable force measurement methods mainly employ contact-based methods such as pressure sensors and magnetic flux sensors, which suffer from high equipment costs, complex installation, and difficulty in long-term monitoring. While computer vision-based measurement methods can achieve non-contact measurement, their displacement extraction accuracy is limited under interference from environmental noise and changes in lighting. Traditional frequency domain analysis methods lack the ability to identify dense frequency components. Frequency methods, as a commonly used indirect cable force measurement method, require precise measurement of the vibration frequency of the cable to calculate the cable force. The limited displacement extraction accuracy and insufficient frequency identification capability of existing technologies result in low accuracy in cable force monitoring, failing to meet the long-term, high-precision safety monitoring requirements of engineering projects.

[0004] Therefore, developing a cable force analysis method and system based on enhanced frequency domain decomposition is of great significance for improving the accuracy of cable force calculation. Summary of the Invention

[0005] To address the problem of poor accuracy in cable force monitoring in existing technologies, this invention proposes a cable force analysis method based on enhanced frequency domain decomposition, which specifically includes the following steps: S1. Collect vibration videos of the cable stays and preprocess the vibration videos; S2. Perform multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the preprocessed vibration video to extract displacement field data with sub-pixel accuracy. S3. Select key points in the displacement field data based on the mechanical characteristics of the bridge structure, and construct a displacement time history matrix based on the displacement data of the key points in the time series. S4. Remove the trend term and DC component from the displacement time history matrix to obtain the power spectral density matrix; S5. Perform singular value decomposition on the power spectral density matrix to construct a single-valued spectral curve; S6. Combine modal confidence criteria to screen modes and frequencies in single-valued spectrum curves to determine the natural vibration frequencies of each order of the cable-stayed cable; S7. Calculate the cable force of the stay cable based on the natural vibration frequencies of each order.

[0006] Furthermore, in step S2, the phase vector estimation-maximum contribution combination algorithm is used to extract displacement field data with sub-pixel accuracy. Specifically, this includes: performing multi-scale and multi-directional filtering on each frame of the preprocessed vibration video using a Gabor filter bank; calculating the instantaneous phase vector of each pixel in each frame at different scales and directions based on the filtering results; performing time-phase expansion on the instantaneous phase vector at each moment to obtain the phase expansion result; performing quality-weighted fusion on the phase expansion result according to the signal-to-noise ratio of each filtering channel, and converting the fused phase result into displacement data to obtain displacement field data with sub-pixel accuracy.

[0007] Furthermore, in step S3, key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. Based on the displacement data of the key points in the time series, a displacement time history matrix is ​​constructed, including: selecting characteristic positions at the mid-span and support of the cable stays as key points in the displacement field data based on the structural mechanical characteristics of the bridge; extracting the displacement data of each key point in the entire time series of the vibration video; and arranging the time series displacement data of each key point in a matrix manner with the key points as the dimension to form a displacement time history matrix.

[0008] Furthermore, in step S4, the displacement time history matrix is ​​processed by removing the trend term and DC component to obtain the power spectral density matrix. This includes: removing the trend term and DC component from the displacement time history matrix to obtain a preprocessed displacement time history matrix; using the Welch average periodogram method to segment, window, and perform Fourier transform processing on the preprocessed displacement time history matrix; and calculating the power spectral density matrix at each frequency point based on the processing results.

[0009] Furthermore, the formula for calculating the power spectral density matrix is ​​as follows: ; in, Let f be the power spectral density matrix at frequency f, and L be the number of segments in the displacement time history matrix. The sampling time interval, For the first The frequency domain data after Fourier transform of the segment data, with the superscript H indicating the conjugate transpose.

[0010] Furthermore, in step S5, singular value decomposition is performed on the power spectral density matrix to construct a single-valued spectral curve, including: performing singular value decomposition on the power spectral density matrix at each frequency point to extract the maximum singular value corresponding to each frequency point; and connecting the maximum singular values ​​of each frequency point in sequence according to the frequency order to construct a single-valued spectral curve.

[0011] Furthermore, the formula for singular value decomposition is: ; For frequency The power spectral density matrix at that location, It is a diagonal matrix whose diagonal elements are singular values, and the superscript H denotes the conjugate transpose. It is a unitary matrix, and its column vectors are... Includes frequency Estimated mode shape information at the location.

[0012] Furthermore, in step S6, the mode and frequency in the single-valued spectrum curve are screened by combining modal confidence criteria to determine the natural vibration frequencies of the cable-stayed cable. This includes: identifying multiple significant peaks on the single-valued spectrum curve using an automatic thresholding method to determine candidate peak frequencies of the cable-stayed cable vibration; selecting a corresponding preset frequency band for each candidate peak frequency, and screening the true mode within the preset frequency band by combining modal confidence criteria, wherein the modal confidence criteria include singular value criteria and modal confidence factor criteria; locating the frequencies corresponding to the screened true modes, and sorting the frequencies of each true mode from low to high order to obtain the natural vibration frequencies of the cable-stayed cable.

[0013] Furthermore, after calculating the cable force of the stay cable based on the natural vibration frequencies of each order, the process also includes: performing stability analysis on the natural vibration frequencies of each order, and making a reasonable judgment on the calculated cable force values ​​of the stay cable; when the vibration frequency analysis results and the cable force value judgment results both meet the preset requirements, the natural vibration frequencies of each order of the stay cable and the corresponding cable force values ​​are output, and a cable force detection report is generated.

[0014] The present invention also provides a cable force analysis system based on enhanced frequency domain decomposition, the system being used to execute the cable force analysis method based on enhanced frequency domain decomposition described in any of the preceding claims, the system comprising: The acquisition module is used to acquire vibration videos of the stay cables and to preprocess the vibration videos; The displacement field extraction module is used to perform multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the pre-processed vibration video to extract displacement field data with sub-pixel accuracy. The displacement time history matrix construction module is used to select key points in the displacement field data based on the mechanical characteristics of the bridge structure, and construct the displacement time history matrix based on the displacement data of the key points in the time series. The power spectral density matrix construction module is used to remove the trend term and DC component from the displacement time history matrix to obtain the power spectral density matrix. The single-valued spectrum curve construction module is used to perform singular value decomposition on the power spectral density matrix and construct single-valued spectrum curves. The vibration frequency determination module is used to filter modes and frequencies in single-valued spectrum curves by combining modal confidence criteria in order to determine the natural vibration frequencies of each order of the cable-stayed bridge. The cable force calculation module is used to calculate the cable force of the stay cables based on their natural vibration frequencies.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention acquires vibration videos of cable-stayed bridges and preprocesses them. The preprocessed videos undergo multi-scale, multi-directional signal processing, phase analysis, and mass-weighted fusion to extract sub-pixel-level displacement field data. Key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. A displacement time-history matrix is ​​constructed based on the displacement data of these key points over time. Trend terms and DC components are removed from the displacement time-history matrix to obtain a power spectral density matrix. Singular value decomposition is performed on the power spectral density matrix to construct single-valued spectral curves. Modal confidence criteria are used to filter modes and frequencies in the single-valued spectral curves to determine the natural vibration frequencies of the cable-stayed bridge. The cable force is calculated based on these natural vibration frequencies. By performing multi-scale, multi-directional signal processing, phase analysis, and mass-weighted fusion on the vibration videos, sub-pixel-level high-precision displacement field data can be extracted from ordinary videos. This effectively suppresses interference from environmental noise and lighting changes, significantly improving the extraction accuracy and robustness of weak vibration signals, and providing high-quality input for subsequent frequency identification.

[0016] Furthermore, by removing the trend term and DC component from the displacement time history matrix and estimating the power spectral density matrix, the influence of low-frequency drift and static components can be eliminated, improving the accuracy and stability of frequency domain analysis. Singular value decomposition of the power spectral density matrix and construction of single-valued spectrum curves can highlight the dominant vibration modes of the structure, achieving a clear characterization of modal energy and facilitating the identification of the structure's natural frequencies. Combining modal confidence criteria to screen for true modes and frequencies can effectively eliminate noise peaks and distinguish dense modes, avoiding the problems of misjudgment and low accuracy associated with traditional peak detection, thus achieving accurate and reliable identification of each order of natural vibration frequencies. Calculating the cable force based on the accurately identified natural frequencies can significantly improve the accuracy of cable force measurement results. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1This is a flowchart of the cable force analysis method based on enhanced frequency domain decomposition provided in the embodiments of the present invention; Figure 2 This is a schematic diagram of the structure of the cable force analysis system based on enhanced frequency domain decomposition provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] The specific embodiments of the present invention will be described below.

[0021] To address the issue of poor cable force monitoring accuracy in existing technologies, this invention acquires vibration videos of stay cables and preprocesses them. The preprocessed vibration videos undergo multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion to extract displacement field data with sub-pixel accuracy. Key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. A displacement time history matrix is ​​constructed based on the displacement data of these key points over time. Trend terms and DC components are removed from the displacement time history matrix to obtain a power spectral density matrix. Singular value decomposition is performed on the power spectral density matrix to construct single-valued spectral curves. Modal confidence criteria are used to screen modes and frequencies in the single-valued spectral curves to determine the natural vibration frequencies of each order of the stay cable. Cable force is calculated based on these natural vibration frequencies. This invention achieves high accuracy in cable force calculation.

[0022] Example 1 This invention provides a method for analyzing cable forces in stay cables based on enhanced frequency domain decomposition. Figure 1 This is a flowchart of the cable force analysis method based on enhanced frequency domain decomposition provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the specific steps include the following: S1. Collect vibration videos of the cable stays and preprocess the vibration videos.

[0023] Vibration video refers to a continuous sequence of images that record the dynamic vibration behavior of cable-stayed bridges, captured by a monitoring camera or mobile phone at a sampling frequency of no less than 30Hz.

[0024] High-contrast targets were deployed on the cable-stayed bridge, and the target area was continuously filmed using camera equipment to obtain vibration videos. Each frame of the video was then converted to grayscale and denoised to eliminate interference from lighting and jitter, completing image enhancement and outputting a stable video sequence for subsequent displacement field extraction. This preprocessing of the vibration videos improved signal quality.

[0025] S2. Perform multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the preprocessed vibration video to extract displacement field data with sub-pixel accuracy.

[0026] Multi-scale, multi-directional signal processing refers to filtering, enhancing, and extracting features from vibration videos at different scales and directions. Phase analysis refers to phase calculation, phase tracking, and phase stability determination of image sequences. Quality-weighted fusion refers to weighting and fusing multi-scale, multi-directional results based on signal quality, signal-to-noise ratio, and stability. Subpixel-level precision displacement field data refers to obtaining continuous full-field displacement data smaller than a single image pixel through signal processing and phase analysis. Subpixel-level precision displacement field data can realistically reflect the spatial distribution and temporal history of minute vibrations and deformations of structures, with smooth and continuous displacement changes without step-like jumps, thus reflecting the true physical deformation modes of the structure.

[0027] Specifically, the phase vector estimation-maximum contribution combination algorithm is used to extract displacement field data with sub-pixel accuracy. This includes: performing multi-scale and multi-directional filtering on each frame of the preprocessed vibration video using a Gabor filter bank; calculating the instantaneous phase vector of each pixel in each frame at different scales and directions based on the filtering results; performing time-phase expansion on the instantaneous phase vectors at each time point to obtain the phase expansion results; and performing quality-weighted fusion of the phase expansion results based on the signal-to-noise ratio of each filtering channel, converting the fused phase results into displacement data to obtain displacement field data with sub-pixel accuracy.

[0028] The Phase Vector Estimation-Maximum Contribution Combination (PVE-MCC) algorithm is a non-contact, sub-pixel-level video displacement extraction algorithm for structural vibration monitoring. Through multi-scale, multi-directional filtering, instantaneous phase vector calculation, time-phase unfolding, and quality-weighted fusion, it accurately extracts minute displacements from vibration videos. This algorithm boasts strong anti-interference capabilities and high measurement accuracy, providing high-precision displacement data for flexible structures such as cable-stayed bridges. The Gabor filter is a linear feature extraction filter that combines spatial localization and frequency selectivity, enabling accurate detection of multi-directional, multi-scale edges, textures, and subtle deformations in images. A Gabor filter bank is a set of Gabor filter kernels with different scales and directions, capable of simulating biological visual perception mechanisms to extract features from images at multiple scales and in multiple directions.

[0029] Each frame of the preprocessed vibration video is input into a Gabor filter bank. The Gabor filter bank performs multi-scale, multi-directional filtering on each frame of the preprocessed vibration video to extract subtle edges, textures, and vibrations from the image. The filtering formula is: ; in, Let (x, y) represent the Gabor filter response with scale s and direction θ, where (x, y) represents the original coordinates of the image pixels. It is the new coordinate system after rotating the original pixel coordinates of the image to the corresponding direction of the filter, where γ represents the aspect ratio. This represents the standard deviation at scale s. φ represents wavelength, φ represents phase offset, and j represents the imaginary unit.

[0030] For each frame of the image, the instantaneous phase of each pixel at each scale and in each direction is calculated. These instantaneous phases are then combined to form an instantaneous phase vector. The formula for calculating the instantaneous phase is: ; in, This represents the instantaneous phase value of the pixel at coordinates (x, y) at time t, scale s, and direction θ. `angle()` represents the complex phase angle calculation. An abbreviation for the Gabor filter response at scale s and direction θ. This represents the pixel grayscale value at coordinates (x, y) at time t, and * represents the convolution operator.

[0031] The instantaneous phase vector at each moment is expanded by time phase to eliminate phase period winding error, and a continuous, non-jump phase expansion result is obtained, which provides basic data for subsequent quality weighted fusion.

[0032] The expanded phase is converted into initial displacement values, and quality weighting is applied based on the signal-to-noise ratio of each channel. The contributions from all scales and directions are then fused to obtain the final sub-pixel precision displacement field data U(x,y,t). The fusion formula is as follows: ; in, This represents the quality weight coefficients of the filter channel corresponding to scale s and direction θ. It is an abbreviation for the instantaneous phase value of a pixel at coordinates (x, y) with time t, scale s, and direction θ.

[0033] By employing multi-scale, multi-directional Gabor filtering, the system can adapt to subtle vibrations of the stay cables in different amplitudes and directions, improving signal adaptability. Instantaneous phase vector extraction based on phase calculation is insensitive to changes in illumination and environmental noise, significantly enhancing anti-interference capabilities. Time-phase expansion eliminates phase period jumps, ensuring continuous, accurate, and distortion-free displacement data. Quality-weighted fusion based on signal-to-noise ratio automatically strengthens high-signal-to-noise-ratio channels and weakens noisy channels, improving the robustness of displacement extraction. Phase-to-displacement conversion achieves sub-pixel-level high-precision extraction, accurately capturing minute vibrations of the stay cables and providing high-quality data for subsequent frequency identification.

[0034] S3. Select key points in the displacement field data based on the structural mechanical characteristics of the bridge, and construct a displacement time history matrix based on the displacement data of the key points in the time series.

[0035] The structural mechanical properties of bridges refer to the mechanical attributes of stay cables as flexible load-bearing components, including vibration mode distribution, displacement-sensitive areas, and stress-deformation patterns. Key points refer to the core vibration monitoring points selected based on the mechanical properties of stay cables, such as the mid-span point and end support points of the stay cable. These points have obvious vibration characteristics and can represent the overall vibration state of the cable.

[0036] Specifically, key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. Based on the displacement data of the key points in the time series, a displacement time history matrix is ​​constructed. This includes: selecting characteristic locations at the mid-span and supports of the cable stays as key points in the displacement field data based on the structural mechanical characteristics of the bridge; extracting the displacement data of each key point in the entire time series of the vibration video; and arranging the time series displacement data of each key point in a matrix format, with the key points as the dimension, to form a displacement time history matrix.

[0037] Based on the structural mechanics characteristics of cable-stayed bridges, key monitoring points were selected from the sub-pixel displacement field data extracted using the PVE-MCC algorithm. These points, such as the mid-span and supports of the cable-stayed bridge, exhibited significant vibration responses and were structurally representative. Temporal displacement data corresponding to each key point was extracted across all time frames within the entire vibration video acquisition period to obtain continuous displacement change information for each key point. Using all selected key points as data dimensions, the time-series displacement data corresponding to each key point were matrix-arranged and combined according to a standardized format, ultimately forming a displacement time-history matrix that can be directly used for subsequent enhanced frequency domain decomposition processing.

[0038] By selecting the mid-span and supports of the stay cables as key points based on their structural mechanics characteristics, the core response region of structural vibration can be accurately focused, redundant and invalid pixel data can be eliminated, and the effective signals that truly reflect the vibration characteristics of the stay cables can be preserved to the greatest extent. Extracting the full-time-series displacement data of the key points and arranging it in a matrix not only significantly reduces the amount of data and computational complexity of subsequent signal processing, improving algorithm efficiency, but also constructs a standard data format that meets the input requirements of the enhanced frequency domain decomposition algorithm. This provides a high-quality, highly targeted data foundation for the accurate identification of subsequent natural frequencies, effectively avoiding interference from invalid data.

[0039] S4. Remove the trend term and DC component from the displacement time history matrix to obtain the power spectral density matrix.

[0040] The displacement time history matrix is ​​a two-dimensional matrix composed of time-series displacement data from key points such as the mid-span and supports of the cable-stayed bridge. It records the sub-pixel-level vibration displacement of multiple key points at various times. The trend term refers to the linear, low-frequency, slow drift component in the displacement time history matrix, which is usually generated by non-vibration factors such as equipment vibration and environmental interference, and does not belong to the actual vibration signal of the structure. The DC component refers to the static constant offset in the displacement time history matrix, which does not reflect dynamic vibration characteristics and can interfere with the frequency domain analysis results. The power spectral density matrix is ​​a second-order statistical matrix obtained by performing a frequency domain transformation on the displacement time histories of multiple key points. It is used to quantitatively describe the distribution of structural vibration energy at different frequencies and the correlation between the vibrations of each key point.

[0041] Specifically, the displacement time history matrix is ​​processed by removing the trend term and DC component to obtain the power spectral density matrix. This includes: removing the trend term and DC component from the displacement time history matrix to obtain a preprocessed displacement time history matrix; using the Welch average periodogram method to segment, window, and perform Fourier transform on the preprocessed displacement time history matrix; and calculating the power spectral density matrix at each frequency point based on the processing results.

[0042] By employing signal processing methods to remove trend terms and DC components, and eliminating invalid interference caused by equipment drift and static offset, only the true dynamic vibration signal is retained, ensuring the accuracy of subsequent frequency domain analysis. The Welch average periodogram method is used to process the clean displacement time-history data. First, the long time-history data is segmented, with overlap between adjacent segments to improve statistical smoothness. Then, a Hanning window is applied to each segment to suppress spectral leakage. A Fast Fourier Transform is performed on each windowed segment to convert the time-domain vibration signal into a frequency-domain signal. Statistical averaging and conjugate transpose calculations are performed on the frequency domain results for each segment, ultimately generating an n×n order self-power spectral density matrix at each frequency point.

[0043] The formula for calculating the power spectral density matrix is ​​as follows: ; in, Let be the power spectral density matrix at frequency f, L be the number of segments in the displacement time history matrix, and M be the length of each segment. The sampling time interval, For the first The frequency domain data after Fourier transform of the segment data, with the superscript H indicating the conjugate transpose.

[0044] By removing trend terms and DC components, interference from non-structural vibrations such as equipment drift, static offset, and slow environmental changes can be eliminated, allowing the signal to retain only the true dynamic vibration of the cable-stayed bridge and preventing noise from masking the true frequency. Segmentation and windowing effectively reduce spectral distortion caused by data truncation, making energy peaks more concentrated and significantly improving the positioning accuracy of the cable-stayed bridge's natural frequency. Multi-segment averaging using the Welch method weakens random interference such as environmental noise and image jitter, resulting in a smoother power spectrum curve and more prominent modal peaks, facilitating subsequent peak detection and modal selection.

[0045] S5. Perform singular value decomposition on the power spectral density matrix to construct a single-valued spectral curve.

[0046] Specifically, this includes: performing singular value decomposition on the power spectral density matrix at each frequency point to extract the maximum singular value corresponding to each frequency point; and connecting the maximum singular values ​​of each frequency point in sequence according to the frequency order to construct a single-valued spectral curve.

[0047] Singular value decomposition (SVD) is a matrix decomposition operation that decomposes the power spectral density matrix into a unitary matrix, a singular value diagonal matrix, and a conjugate transpose matrix, used to extract the dominant vibrational components. A single-valued spectrum curve is formed by connecting the largest singular values ​​at each frequency point, reflecting the frequency domain distribution of vibrational energy. The peak values ​​of the single-valued spectrum curve correspond to the natural frequencies of the cable-stayed bridge.

[0048] The formula for singular value decomposition is: ; For frequency The power spectral density matrix at that location, It is a diagonal matrix whose diagonal elements are singular values, and the superscript H denotes the conjugate transpose. It is a unitary matrix, and its column vectors are... Includes frequency Estimated mode shape information at the location.

[0049] By performing singular value decomposition on the power spectral density matrix at each frequency point and extracting the maximum singular value, and constructing single-valued spectrum curves in frequency order, it is possible to effectively highlight the dominant vibration mode of the cable-stayed bridge, suppress noise and interference components, clearly present the distribution characteristics of vibration energy in the frequency domain, and make the peak values ​​corresponding to the natural frequencies more obvious and easier to identify.

[0050] S6. Combine modal confidence criteria to screen the modes and frequencies in the single-valued spectrum curves to determine the natural vibration frequencies of each order of the cable-stayed cable.

[0051] Modal confidence criterion is a quantitative evaluation index used to determine whether a vibration signal is a true structural mode. Its core function is to verify whether the mode shape vectors near the candidate frequency point are stable and consistent, thereby distinguishing between true modes and noise peaks.

[0052] Specifically, the modal confidence criteria are used to screen modes and frequencies in the single-valued spectrum curve to determine the natural vibration frequencies of the cable-stayed bridge. This includes: identifying multiple significant peaks on the single-valued spectrum curve using an automatic thresholding method to determine candidate peak frequencies of the cable-stayed bridge vibration; selecting a corresponding preset frequency band for each candidate peak frequency, and screening the true modes within the preset frequency band using modal confidence criteria, which include singular value criteria and modal confidence factor criteria; locating the frequencies corresponding to the screened true modes, and sorting the frequencies of each true mode from low to high order to obtain the natural vibration frequencies of the cable-stayed bridge.

[0053] The automatic thresholding method is a method for automatically identifying significant peaks based on the statistical characteristics of curves, used for preliminary location of candidate peak frequencies. A significant peak is a peak point on a single-valued spectrum curve with energy significantly higher than the background, representing a potential vibration frequency. The singular value criterion is the basis for determining whether a certain frequency is the dominant vibration mode of a structure. The modal confidence factor criterion is an evaluation index for testing the stability and consistency of mode shapes near candidate frequencies, used to measure the similarity of mode shape vectors at different frequency points within the same frequency band.

[0054] Significant peaks are identified on the single-valued spectrum curve using an automatic thresholding method to obtain candidate peak frequencies. Then, for each candidate frequency, a combination of singular value criterion and modal confidence factor criterion is used within its preset frequency band to confirm whether it represents a true mode. The singular value criterion process involves comparing the magnitude of the first singular value at the same frequency point with other singular values ​​to determine if the frequency component dominates the vibration response. When the first singular value is significantly larger than the others, it indicates that the frequency corresponds to a true, concentrated modal energy, rather than noise or interference. The modal confidence factor criterion process involves calculating the modal confidence factor between the mode shape vectors at each frequency point and the mode shape vector at the center frequency point within the frequency band. When the factor value is close to 1, the mode shapes are considered consistent, confirming it as a true mode. Lower factor values ​​indicate disordered mode shapes, belonging to noise or spurious peaks.

[0055] For true modes that meet the screening criteria, the first singular value curve within the corresponding frequency range is treated as the spectral density curve of a single-degree-of-freedom system. An inverse Fourier transform is first performed on this curve to obtain the correlation function. Then, the logarithmic decay method or the zero-crossing method is used to accurately calculate the undamped natural frequency of this mode. By converting the singular value curve into a correlation function and then calculating the frequency using the logarithmic decay method or the zero-crossing method, local errors caused by spectral peaks can be avoided. The overall signal characteristics within the complete frequency band are used for fitting calculations, fully utilizing the continuous distribution information of the mode in the frequency domain. This effectively reduces the offset effects caused by local noise and spectral distortion, thereby obtaining an undamped natural frequency that more closely approximates the vibration characteristics of the actual structure, significantly improving the accuracy and stability of frequency identification.

[0056] S7. Calculate the cable force of the stay cable based on the natural vibration frequencies of each order.

[0057] Based on the identified natural vibration frequencies, the cable force is calculated using the cable's physical parameters and correction factors. The formula for calculating the cable force is as follows: ; Where T is the cable force, m is the mass per unit length, B is the length of the stay cable, and f is the mass per unit length. k Let ξ be the k-th natural vibration frequency, where k is the order and ξ is the correction factor considering sag and bending stiffness.

[0058] Based on the identified natural vibration frequencies, the cable force is calculated by combining the cable's own physical parameters and correction coefficients. This allows for full utilization of the accurately identified frequency results, and the correction coefficients compensate for errors caused by sag and bending stiffness, making the calculation results more consistent with engineering practice.

[0059] After calculating the cable force of the stay cable based on the natural vibration frequencies of each order, the process also includes: performing stability analysis on the natural vibration frequencies of each order and judging the rationality of the calculated cable force values; when the vibration frequency analysis results and the cable force value judgment results both meet the preset requirements, the natural vibration frequencies of each order of the stay cable and the corresponding cable force values ​​are output, and a cable force detection report is generated.

[0060] By conducting frequency stability analysis and judging the rationality of cable forces, the reliability of the identification and calculation results can be effectively verified, avoiding abnormal data and erroneous results, and ensuring the accuracy of cable force measurement results. Outputting the final results and generating a report after all indicators meet the standards enhances the rigor and engineering practicality of the entire measurement method, providing a reliable basis for bridge structural health monitoring.

[0061] This embodiment acquires vibration videos of the stay cables and preprocesses them. Multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion are then performed on the preprocessed vibration videos to extract sub-pixel-level displacement field data. Key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. A displacement time history matrix is ​​constructed based on the displacement data of these key points over time. Trend terms and DC components are removed from the displacement time history matrix to obtain a power spectral density matrix. Singular value decomposition is performed on the power spectral density matrix to construct single-valued spectral curves. Modal confidence criteria are used to filter modes and frequencies in the single-valued spectral curves to determine the natural vibration frequencies of the stay cables. The cable force is calculated based on these natural vibration frequencies. By performing multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the vibration videos, sub-pixel-level high-precision displacement field data can be extracted from ordinary videos. This effectively suppresses interference from environmental noise and lighting changes, significantly improving the extraction accuracy and robustness of weak vibration signals, and providing high-quality input for subsequent frequency identification.

[0062] Furthermore, by removing the trend term and DC component from the displacement time history matrix and estimating the power spectral density matrix, the influence of low-frequency drift and static components can be eliminated, improving the accuracy and stability of frequency domain analysis. Singular value decomposition of the power spectral density matrix and construction of single-valued spectrum curves can highlight the dominant vibration modes of the structure, achieving a clear characterization of modal energy and facilitating the identification of the structure's natural frequencies. Combining modal confidence criteria to screen for true modes and frequencies can effectively eliminate noise peaks and distinguish dense modes, avoiding the problems of misjudgment and low accuracy associated with traditional peak detection, thus achieving accurate and reliable identification of each order of natural vibration frequencies. Calculating the cable force based on the accurately identified natural frequencies can significantly improve the accuracy of cable force measurement results.

[0063] Example 2 This invention also provides a cable force analysis system based on enhanced frequency domain decomposition. Figure 2 This is a schematic diagram of the structure of the cable-stayed bridge force analysis system based on enhanced frequency domain decomposition provided in an embodiment of the present invention, as shown below. Figure 2 As shown, the system includes: The acquisition module is used to acquire vibration videos of the stay cables and to preprocess the vibration videos; The displacement field extraction module is used to perform multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the pre-processed vibration video to extract displacement field data with sub-pixel accuracy. The displacement time history matrix construction module is used to select key points in the displacement field data based on the mechanical characteristics of the bridge structure, and construct the displacement time history matrix based on the displacement data of the key points in the time series. The power spectral density matrix construction module is used to remove the trend term and DC component from the displacement time history matrix to obtain the power spectral density matrix. The single-valued spectrum curve construction module is used to perform singular value decomposition on the power spectral density matrix and construct single-valued spectrum curves. The vibration frequency determination module is used to filter modes and frequencies in single-valued spectrum curves by combining modal confidence criteria in order to determine the natural vibration frequencies of each order of the cable-stayed bridge. The cable force calculation module is used to calculate the cable force of the stay cables based on their natural vibration frequencies.

[0064] The cable-stayed bridge force analysis system based on enhanced frequency domain decomposition provided in this embodiment is used to execute the cable-stayed bridge force analysis method based on enhanced frequency domain decomposition in any of the above embodiments, and has the beneficial effects of any of the above embodiments, which will not be repeated here.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing cable-stayed bridge forces based on enhanced frequency domain decomposition, characterized in that, include: S1. Collect vibration videos of the cable stays and preprocess the vibration videos; S2. Perform multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the preprocessed vibration video to extract displacement field data with sub-pixel accuracy. S3. Select key points in the displacement field data based on the mechanical characteristics of the bridge structure, and construct a displacement time history matrix based on the displacement data of the key points in the time series. S4. Remove the trend term and DC component from the displacement time history matrix to obtain the power spectral density matrix; S5. Perform singular value decomposition on the power spectral density matrix to construct a single-valued spectral curve; S6. Combine modal confidence criteria to screen modes and frequencies in single-valued spectrum curves to determine the natural vibration frequencies of each order of the cable-stayed cable; S7. Calculate the cable force of the stay cable based on the natural vibration frequencies of each order.

2. The cable force analysis method based on enhanced frequency domain decomposition according to claim 1, characterized in that, In step S2, the phase vector estimation-maximum contribution combined algorithm is used to extract displacement field data with sub-pixel accuracy, specifically including: The preprocessed vibration video is subjected to multi-scale, multi-directional filtering of each frame using a Gabor filter bank. The instantaneous phase vector of each pixel in each frame of the image is calculated at different scales and directions based on the filtering results. Perform time-phase expansion on the instantaneous phase vector at each moment to obtain the phase expansion result; The phase expansion results are quality-weighted and fused based on the signal-to-noise ratio of each filter channel. The fused phase results are then converted into displacement data to obtain displacement field data with sub-pixel accuracy.

3. The cable force analysis method based on enhanced frequency domain decomposition according to claim 1, characterized in that, In step S3, key points in the displacement field data are selected based on the structural mechanical characteristics of the bridge. A displacement time history matrix is ​​constructed based on the displacement data of these key points over time, including: Based on the structural mechanical properties of the bridge, key points were selected at the mid-span and support locations of the stay cables in the displacement field data. Extract displacement data of each key point over the entire time series of the vibration video; Using key points as the dimension, the time series displacement data of each key point are arranged in a matrix to form a displacement time history matrix.

4. The cable force analysis method based on enhanced frequency domain decomposition according to claim 1, characterized in that, In step S4, the displacement time history matrix is ​​processed by removing the trend term and DC component to obtain the power spectral density matrix, including: The displacement time history matrix is ​​processed by removing the trend term and DC component to obtain the preprocessed displacement time history matrix; The Welch average periodogram method was used to segment, window, and perform Fourier transform on the preprocessed displacement time history matrix, and the power spectral density matrix at each frequency point was calculated based on the processing results.

5. The cable force analysis method based on enhanced frequency domain decomposition according to claim 4, characterized in that, The formula for calculating the power spectral density matrix is: ； in, Let f be the power spectral density matrix at frequency f, and L be the number of segments in the displacement time history matrix. The sampling time interval, For the first The frequency domain data after Fourier transform of the segment data, with the superscript H indicating the conjugate transpose.

6. The cable force analysis method based on enhanced frequency domain decomposition according to claim 1, characterized in that, In step S5, singular value decomposition is performed on the power spectral density matrix to construct a single-valued spectral curve, including: Singular value decomposition is performed on the power spectral density matrix at each frequency point to extract the maximum singular value corresponding to each frequency point. By connecting the maximum singular values ​​at each frequency point in chronological order, a single-valued spectrum curve is constructed.

7. The cable force analysis method based on enhanced frequency domain decomposition according to claim 6, characterized in that, The formula for singular value decomposition is: ； For frequency The power spectral density matrix at that location, It is a diagonal matrix whose diagonal elements are singular values, and the superscript H denotes the conjugate transpose. It is a unitary matrix, and its column vectors are... Includes frequency Estimated mode shape information at the location.

8. The cable force analysis method based on enhanced frequency domain decomposition according to claim 1, characterized in that, In step S6, the modes and frequencies in the single-valued spectrum curves are screened using modal confidence criteria to determine the natural vibration frequencies of the cable-stayed bridge, including: Multiple significant peaks were identified on the single-value spectrum curve using an automatic thresholding method to determine the candidate peak frequencies of cable vibration. For each candidate peak frequency, a corresponding preset frequency band is selected, and the true mode is screened within the preset frequency band by combining modal confidence criteria. The modal confidence criteria include singular value criteria and modal confidence factor criteria. The frequencies corresponding to the selected true modes are located, and the frequencies of each true mode are sorted from low to high order to obtain the natural vibration frequencies of each order of the cable-stayed bridge.

9. The cable force analysis method based on enhanced frequency domain decomposition according to claim 1, characterized in that, After calculating the cable force of the stay cables based on the natural vibration frequencies of each order, the following is also included: Stability analysis was performed on the natural vibration frequencies of each order, and the rationality of the calculated cable force values ​​was judged. When the vibration frequency analysis results and cable force value judgment results both meet the preset requirements, the natural vibration frequencies of each order of the stay cable and the corresponding cable force values ​​are output, and a cable force detection report is generated.

10. A cable-stayed bridge force analysis system based on enhanced frequency domain decomposition, characterized in that, The system is used to execute the cable force analysis method based on enhanced frequency domain decomposition as described in any one of claims 1-9, and the system comprises: The acquisition module is used to acquire vibration videos of the stay cables and to preprocess the vibration videos; The displacement field extraction module is used to perform multi-scale, multi-directional signal processing, phase analysis, and quality-weighted fusion on the pre-processed vibration video to extract displacement field data with sub-pixel accuracy. The displacement time history matrix construction module is used to select key points in the displacement field data based on the mechanical characteristics of the bridge structure, and construct the displacement time history matrix based on the displacement data of the key points in the time series. The power spectral density matrix construction module is used to remove the trend term and DC component from the displacement time history matrix to obtain the power spectral density matrix. The single-valued spectrum curve construction module is used to perform singular value decomposition on the power spectral density matrix and construct single-valued spectrum curves. The vibration frequency determination module is used to filter modes and frequencies in single-valued spectrum curves by combining modal confidence criteria in order to determine the natural vibration frequencies of each order of the cable-stayed bridge. The cable force calculation module is used to calculate the cable force of the stay cables based on their natural vibration frequencies.

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