Bridge displacement detection method and system based on phase information

Abstract

This invention relates to the field of bridge inspection technology, specifically to a bridge displacement detection method and system based on phase information. The method includes: acquiring acceleration vibration response signals from at least two measuring points on the bridge; filtering out noise and drift using a bandpass filter; performing a Hilbert transform on the filtered signals to obtain an analytical signal and extracting the instantaneous phase sequence; calculating the cross-correlation function of the instantaneous phase sequences of adjacent measuring points and determining the phase difference time sequence through the maximum value; correlating the phase difference time sequence with the distance between measuring points to convert it into a relative displacement time sequence; integrating the relative displacement time sequence twice to obtain a cumulative relative displacement value; using this cumulative value as a benchmark, and combining it with the absolute displacement calculation results of each measuring point to infer the overall bridge displacement; and performing wavelet noise reduction on the overall displacement to obtain the final detection result. This method can improve the accuracy and stability of displacement detection and is suitable for displacement monitoring of bridge structures.

Description

Technical Field

[0001] This invention relates to the field of bridge inspection technology, and in particular to a bridge displacement detection method and system based on phase information. Background Technology

[0002] Bridge displacement detection is a crucial means of ensuring the safe operation of bridge structures. Current technologies for bridge displacement detection primarily employ methods such as direct integration of acceleration signals, laser ranging, and GPS positioning. Specifically, the direct integration of acceleration signals collects acceleration time-history data from bridge measuring points and performs integration calculations to obtain velocity and displacement information. Laser ranging utilizes the propagation characteristics of laser light to directly measure the absolute displacement of the measuring points. GPS positioning uses satellite signals to achieve spatial positioning of the measuring points, thereby acquiring displacement data.

[0003] Existing technologies have shortcomings. The direct integration method of acceleration signals is susceptible to high-frequency noise and low-frequency drift, and even after filtering, it is difficult to completely eliminate errors, resulting in low displacement calculation accuracy. The laser ranging method is greatly affected by factors such as ambient light and airflow, resulting in poor detection stability in complex environments and difficulty in achieving simultaneous detection of multiple measuring points. The GPS positioning method is easily affected by satellite signal blockage, failing to meet the requirements of high-precision displacement detection. Furthermore, existing methods struggle to accurately capture the phase correlation characteristics between adjacent measuring points when processing displacement correlations, leading to deviations in relative displacement calculations. This, in turn, affects the accuracy of back-calculation of the overall bridge displacement. At the same time, environmental interference can cause random jumps in displacement detection results, further reducing detection reliability. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a bridge displacement detection method and system based on phase information.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a bridge displacement detection method based on phase information, comprising: Acquire vibration response signals from at least two measuring points on the bridge structure, wherein the vibration response signals are acceleration time history data; The vibration response signal is bandpass filtered to remove high-frequency noise and low-frequency drift, while retaining the frequency bands corresponding to the main vibration modes of the bridge structure. The filtered vibration response signal is subjected to Hilbert transform to obtain the analytical signal of the vibration response signal, and the instantaneous phase sequence is extracted from the analytical signal; Using the instantaneous phase sequence as input, the cross-correlation function of the instantaneous phase sequences between adjacent measurement points is calculated, and the phase difference time sequence between the two measurement points is determined by the maximum point of the cross-correlation function. The phase difference time series is correlated with the pre-calibrated distance between measuring points and converted into a relative displacement time series between the two measuring points; The relative displacement time series is integrated to obtain the relative velocity time series between the two measuring points. The relative velocity time series is then integrated again to obtain the cumulative relative displacement between the two measuring points. Using the cumulative relative displacement between two measuring points as a benchmark, and combining the absolute displacement calculation results of each measuring point, the overall displacement of the bridge structure in the detection direction is inferred. The overall displacement is subjected to wavelet denoising to remove random jumps caused by environmental interference, resulting in the denoised bridge displacement detection result.

[0006] As a further aspect of the present invention, bandpass filtering is performed on the vibration response signal, including: Based on the design natural frequency of the bridge structure, determine the frequency range corresponding to its principal vibration mode, and use the frequency range as the passband of the bandpass filter; Collect an environmental background vibration signal when there are no vehicles passing by, calculate the power spectral density of the environmental background vibration signal, and remove the frequency bands with power spectral density below a set threshold from the passband to obtain the optimized passband. The vibration response signal is filtered using a Butterworth filter. The filter order is determined based on the attenuation slope requirement at the passband edge to obtain the filtered vibration response signal.

[0007] As a further aspect of the present invention, the step of performing a Hilbert transform on the filtered vibration response signal to obtain an analytical signal of the vibration response signal, and extracting the instantaneous phase sequence from the analytical signal, includes: Perform a Hilbert transform on the filtered vibration response signal to obtain its orthogonal components; The original vibration response signal is used as the real part, and the orthogonal components are used as the imaginary part to construct the analytical signal. Taking the arctangent function of the analytical signal yields the original phase sequence containing the transition points; The original phase sequence is unwound to eliminate the phase jump caused by the periodicity of the arctangent function, resulting in a continuous instantaneous phase sequence.

[0008] As a further aspect of the present invention, using the instantaneous phase sequence as input, the cross-correlation function of the instantaneous phase sequences between adjacent measurement points is calculated, and the phase difference time sequence between the two measurement points is determined through the maximum point of the cross-correlation function, including: The instantaneous phase sequences of two adjacent measuring points are normalized so that the mean of the two adjacent measuring points is zero and the variance is 1. Perform cross-correlation on the two normalized instantaneous phase sequences to obtain the cross-correlation function curve; Search for the maximum point in the cross-correlation function curve and record the time delay corresponding to the maximum point; Divide the time delay by the signal sampling period to obtain the phase difference between the two measurement points, and arrange them according to the sampling time to form a phase difference time sequence.

[0009] As a further aspect of the present invention, the phase difference time series is correlated with the pre-calibrated measurement point spacing to convert it into a relative displacement time series between the two measurement points, including: Obtain the actual installation distance between the two measuring points as the measuring point distance; Based on the wave number of the bridge structure in the detection direction, the product of the time series of the distance between the measuring points and the phase difference is divided by twice pi to obtain the time series of the relative displacement between the two measuring points. Outlier detection is performed on the relative displacement time series. When the relative displacement value at a certain moment exceeds a set multiple of the average value of the three moments before and after it, the outlier value is replaced with the average value.

[0010] As a further aspect of the present invention, the relative displacement time series is integrated to obtain the relative velocity time series between the two measuring points, and then the relative velocity time series is integrated again to obtain the cumulative relative displacement value between the two measuring points, including: The relative displacement time series is numerically integrated using the trapezoidal rule to obtain the relative velocity time series between the two measuring points. The relative velocity time series is numerically integrated again using the trapezoidal rule to obtain the cumulative value of the relative displacement between the two measuring points. Before each integration, the input time series is detrended to eliminate baseline drift generated during the integration process.

[0011] As a further aspect of the present invention, the cumulative relative displacement between the two measuring points is used as a benchmark, and combined with the absolute displacement calculation results of each measuring point, the overall displacement of the bridge structure in the detection direction is inferred, including: Using the cumulative relative displacement between two measuring points as a constraint, the absolute displacement calculation results of each measuring point are fitted by least squares to obtain the displacement correction of each measuring point relative to the reference measuring point. Add the corresponding displacement correction amount to the absolute displacement calculation results of each measuring point to obtain the corrected absolute displacement of each measuring point; The arithmetic mean of the absolute displacements of all measuring points after correction is taken as the overall displacement of the bridge structure in the detection direction.

[0012] As a further aspect of the present invention, wavelet noise reduction processing is performed on the overall displacement, including: By selecting wavelet basis functions with tight support characteristics, the overall displacement is decomposed into multiple scales to obtain detail coefficients and approximation coefficients at different scales. Based on the energy distribution of detail coefficients at each scale, determine the noise-dominant scale and set the detail coefficients at the noise-dominant scale to zero. Wavelet reconstruction is performed on the retained detail coefficients and approximation coefficients to obtain the denoised bridge displacement detection results.

[0013] As a further aspect of the present invention, before acquiring the vibration response signals at at least two measuring points on the bridge structure, the method further includes: Accelerometers are symmetrically arranged on both sides of the cross section to be tested of the bridge structure, and the sensitive direction of the accelerometers is perpendicular to the bridge axis. Perform static calibration on each accelerometer to obtain its sensitivity coefficient; The installation of the accelerometer was verified by a knocking test to ensure that its output signal was not significantly distorted during bridge vibration.

[0014] As a further aspect of the present invention, the present invention also includes a bridge displacement detection system based on phase information, the system including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, it implements the steps of the bridge displacement detection method based on phase information as described above.

[0015] Compared with the prior art, the advantages and positive effects of the present invention are as follows: The Hilbert transform is performed on the bandpass-filtered acceleration vibration response signal of the bridge measuring points to obtain an analytical signal. The instantaneous phase sequence is then extracted from this analytical signal. Using this instantaneous phase sequence as input, the cross-correlation function of the instantaneous phase sequences between adjacent measuring points is calculated. The maximum value of the cross-correlation function is used to determine the phase difference time sequence between the two measuring points. This technical solution can accurately capture the instantaneous phase characteristics in the vibration response signal of the measuring points, avoiding the problems of inaccurate phase extraction and low correlation between adjacent measuring points in conventional methods. It can effectively eliminate the interference of high-frequency noise and low-frequency drift on phase extraction, making the acquisition of phase difference between adjacent measuring points more targeted and accurate. Compared with conventional phase extraction and phase difference determination methods, it can improve the reliability of the phase difference time sequence, providing a more accurate basis for subsequent displacement conversion.

[0016] This technical solution correlates the phase difference time series with the pre-calibrated measurement point spacing to convert it into a relative displacement time series. The relative displacement time series is then integrated twice to obtain the cumulative relative displacement value. Using this cumulative relative displacement value as a benchmark, the overall bridge displacement is inferred by combining it with the absolute displacement calculation results of each measurement point. Finally, wavelet denoising is applied to the overall displacement to remove random jumps caused by environmental interference. This solution achieves accurate acquisition of the relative displacement time series through the correlation between phase difference and measurement point spacing. The two integration operations effectively connect the relationship between relative displacement, relative velocity, and cumulative relative displacement, avoiding the error accumulation problem in conventional relative displacement calculations. Inferring the overall displacement by combining the absolute displacement calculation results takes into account the correlation between local relative displacement and overall displacement, improving the rationality of the overall displacement inference. Wavelet denoising specifically removes random jumps caused by environmental interference, avoiding the signal distortion defects easily caused by conventional denoising methods, making the final displacement detection results more stable. Compared with conventional overall displacement inference and denoising methods, this solution effectively optimizes the accuracy and stability of the detection results. Attached Figure Description

[0017] Figure 1 This is a flowchart of the bridge displacement detection method based on phase information described in this invention; Figure 2 Flowchart for calculating phase difference time series; Figure 3 This is a time series analysis diagram of the relative displacement of the bridge; Figure 4 A diagram showing the wavelet noise reduction effect on the overall displacement of the bridge. Figure 5 This is a diagram illustrating the impact of overall bridge displacement on noise. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0020] See Figure 1 The vibration response signals, which are acceleration time history data, are acquired from at least two measuring points on the bridge structure. These signals are then bandpass filtered to remove high-frequency noise and low-frequency drift, retaining the frequency bands corresponding to the main vibration modes of the bridge structure. A Hilbert transform is performed on the filtered vibration response signals to obtain the analytical signals, from which the instantaneous phase sequence is extracted. Using this instantaneous phase sequence as input, the cross-correlation function between the instantaneous phase sequences of adjacent measuring points is calculated. The maximum value of the cross-correlation function determines the phase difference time sequence between the two measuring points. This phase difference time sequence is correlated with a pre-calibrated measuring point spacing to convert it into a relative displacement time sequence between the two measuring points. This relative displacement time sequence is integrated to obtain the relative velocity time sequence between the two measuring points. This relative velocity time sequence is then integrated again to obtain the cumulative relative displacement between the two measuring points. Using the cumulative relative displacement between the two measuring points as a benchmark, combined with the absolute displacement calculation results of each measuring point, the overall displacement of the bridge structure in the detection direction is inferred. Wavelet denoising was performed on the overall displacement to remove random jumps caused by environmental interference, resulting in the denoised bridge displacement detection results.

[0021] In one embodiment of the present invention, before acquiring vibration response signals from at least two measuring points on the bridge structure, accelerometers are symmetrically arranged on both sides of the section to be measured of the bridge structure, with the sensitive direction of the accelerometers perpendicular to the bridge axis. Each accelerometer is statically calibrated to obtain its sensitivity coefficient. The installation firmness of the accelerometers is verified through a knocking test to ensure that their output signal is not significantly distorted during bridge vibration. When performing bandpass filtering on the vibration response signal, the frequency range corresponding to the principal vibration mode is determined based on the design natural frequency of the bridge structure, and this frequency range is used as the passband of the bandpass filter. A segment of environmental background vibration signal without vehicle traffic is acquired, and the power spectral density of this environmental background vibration signal is calculated. Frequency bands with power spectral density below a set threshold are removed from the passband to obtain the optimized passband. A Butterworth filter is used to filter the vibration response signal, with the filter order determined according to the attenuation slope requirement at the passband edge, to obtain the filtered vibration response signal.

[0022] In practice, accelerometers are symmetrically arranged on both sides of the section of the bridge structure to be tested. The sensitive direction of the accelerometers is perpendicular to the bridge axis. Each accelerometer is statically calibrated to obtain its sensitivity coefficient. A hammer test is used to verify the installation firmness of the accelerometers, ensuring that the output signal of the accelerometers is not significantly distorted during bridge vibration. In some embodiments, the accelerometers are installed on the side of the bridge web and fixed with epoxy resin. Optionally, static calibration is performed at a metrology facility, applying a standard sinusoidal acceleration signal, recording the accelerometer output voltage, and calculating the sensitivity coefficient through linear fitting. The hammer test excites a local area of ​​the bridge with a hammer to check whether clipping or resonance peaks appear in the accelerometer output waveform, thus judging the installation quality. Bandpass filtering is based on the dynamic characteristics of the bridge and the analysis of environmental background vibration. According to the design natural frequency of the bridge structure, the frequency range corresponding to its principal vibration mode is determined. This frequency range is used as the passband of the bandpass filter. An environmental background vibration signal with no vehicle traffic is collected, and the power spectral density of the environmental background vibration signal is calculated. Frequency bands with power spectral density below a set threshold are removed from the passband to obtain the optimized passband. A Butterworth filter is then used to filter the vibration response signal. The filter order is determined according to the attenuation slope requirement at the passband edge, resulting in the filtered vibration response signal. In some embodiments, for the aforementioned continuous beam bridge, the design natural frequency is 3.5Hz, and the initial principal vibration mode frequency range is set to 2.0Hz to 5.0Hz. Optionally, the environmental background vibration signal is collected during off-peak traffic hours at night. The power spectral density is estimated using the Welch method, and the set threshold is based on the overall background noise level and calculated using the formula:

[0023] in: Indicates the power spectral density threshold. It is the scaling factor. This represents the average power spectral density of the environmental background vibration signal. , It is the total number of frequency points. It is frequency The power spectral density value at that point, when the power spectral density Below the threshold When the corresponding frequency band is removed from the passband, it can be understood that the Butterworth filter is selected as the 6th order to achieve a 48dB / octave attenuation at the edge of the passband. Data comparison is made by comparing the passband frequency range before and after optimization. The optimized passband removes low-energy noise frequency bands and focuses on the main vibration response of the bridge structure.

[0024] In one embodiment of the present invention, a Hilbert transform is performed on the filtered vibration response signal to obtain an analytic signal of the vibration response signal, and an instantaneous phase sequence is extracted from the analytic signal. A Hilbert transform is then performed on the filtered vibration response signal to obtain its orthogonal components. The analytic signal is constructed using the original vibration response signal as the real part and the orthogonal components as the imaginary part. An arctangent function is taken from the analytic signal to obtain the original phase sequence containing transition points. The original phase sequence is then unwrapped to eliminate phase transitions caused by the periodicity of the arctangent function, resulting in a continuous instantaneous phase sequence.

[0025] In practical implementation, for the mid-span section of the main girder of a long-span cable-stayed bridge, the extraction of the instantaneous phase sequence is achieved through Hilbert transform. A Hilbert transform is performed on the filtered vibration response signal to obtain its orthogonal components. The original vibration response signal is used as the real part, and the orthogonal components as the imaginary part to construct the analytic signal of the original vibration response signal. In some embodiments, the filtered vibration response signal is acceleration time history data, and the Hilbert transform is performed in the frequency domain using a fast Fourier transform algorithm. Optionally, the constructed analytic signal is a complex time series, where the real part is the original acceleration signal and the imaginary part is the orthogonal acceleration signal after the Hilbert transform. It can be understood that the analytic signal contains the amplitude and phase information of the original signal. The extraction of the instantaneous phase sequence from the analytic signal is accomplished through phase calculation and unwinding. The arctangent function is taken from the analytic signal to obtain the original phase sequence containing transition points. The original phase sequence is then unwound to eliminate phase transitions caused by the periodicity of the arctangent function, resulting in a continuous instantaneous phase sequence. In some embodiments, the arctangent function is obtained by using the four-quadrant arctangent function atan2, so as to consider the signs of both the real and imaginary parts simultaneously, thus obtaining a range within... arrive The original phase values ​​between radians, optionally, are unwrapped by detecting and compensating for phase jumps when the absolute value of the phase difference between adjacent sampling points exceeds a set threshold. At that time, add or subtract from the current and all subsequent phase values. multiples of Correction is performed, and the continuous phase value is obtained through the formula. Calculation, where Indicates the first The continuous phase values ​​after unwinding at each sampling point Indicates the first The phase value of the package before unwinding at each sampling point This refers to the cumulative number of phase jump compensations. Data comparison is achieved by plotting phase-time curves before and after unwinding. The unwinding process eliminates the original phase sequence in... and The jump at the arc boundary can be understood as a continuous sequence of instantaneous phases used for subsequent calculations of the phase difference.

[0026] In one embodiment of the present invention, the instantaneous phase sequence is used as input to calculate the cross-correlation function of the instantaneous phase sequences between adjacent measurement points, and the phase difference time sequence between the two measurement points is determined by the maximum value of the cross-correlation function. (See also...) Figure 2 The instantaneous phase sequences of two adjacent measurement points are normalized to ensure that the mean of the two adjacent measurement points is zero and the variance is 1. Cross-correlation is then performed on the two normalized instantaneous phase sequences to obtain the cross-correlation function curve. The maximum value point is searched within the cross-correlation function curve, and the time delay corresponding to the maximum value point is recorded. The time delay is divided by the signal sampling period to obtain the phase difference between the two measurement points, which are then arranged according to the sampling time to form a phase difference time sequence.

[0027] In specific implementations, the continuous instantaneous phase sequences obtained by unwinding two adjacent measuring points are used as input to calculate the cross-correlation function of the instantaneous phase sequences between adjacent measuring points. In some embodiments, the two measuring points are symmetrically arranged on both sides of the arch, and the continuous instantaneous phase sequences are discrete-time sequences of equal length. Optionally, the two continuous instantaneous phase sequences are preprocessed before the cross-correlation calculation to eliminate the influence of dimensional and baseline differences on subsequent peak search. It can be understood that preprocessing makes the cross-correlation function result more reflective of the true delay relationship between signals.

[0028] In specific implementation, the instantaneous phase sequences of two adjacent measurement points are normalized to ensure that the mean of the instantaneous phase sequences of the two adjacent measurement points is zero and the variance of the instantaneous phase sequences of the two adjacent measurement points is 1. A cross-correlation operation is then performed on the two normalized instantaneous phase sequences to obtain the cross-correlation function curve. In some embodiments, the normalization process is achieved by subtracting the sequence mean and then dividing by the sequence standard deviation. The cross-correlation operation is performed in the time domain using a variant of discrete convolution to calculate the correlation coefficient under different time delays. Optionally, the cross-correlation function... Calculated using the formula:

[0029] in: Indicates time delay Normalized instantaneous phase sequence of measurement point P at each sampling interval Normalized instantaneous phase sequence with measurement point Q cross-correlation coefficients, It is the sampling point index of the sequence. It is the number of delayed sampling points. Data comparison is accomplished by plotting the waveforms of the two instantaneous phase sequences before and after normalization. The normalization process makes the two sequences have the same zero mean and unit energy.

[0030] In specific implementation, the maximum value point is searched in the cross-correlation function curve, and the time delay corresponding to the maximum value point is recorded. The time delay is divided by the signal sampling period to obtain the phase difference between the two measurement points, and the phase difference time series is formed by arranging them according to the sampling time. In some embodiments, the global maximum value point in the cross-correlation function curve is searched, and the x-coordinate of this point is the desired time delay. Optionally, when there are multiple local peaks in the cross-correlation function curve, the peak point that is closest to zero delay and has the largest amplitude is taken as the effective maximum value point. It can be understood that the phase difference time series is a sequence characterizing the relationship between the vibration phase of two measurement points and the change of time.

[0031] See Figure 3 This is a time series analysis chart of the relative displacement of a bridge, showing the change of the relative displacement between two measuring points over time based on phase difference conversion. The core comparison is between the original and corrected data. The original relative displacement contains a large amount of high-frequency noise and sharp outliers, fluctuating wildly with a maximum amplitude close to ±0.3m, which does not conform to the actual vibration characteristics of the bridge. After smoothing with a moving average, the noise in the corrected relative displacement is significantly suppressed, the curve is smoother, and the amplitude is stabilized within ±0.1m, which is closer to the actual engineering situation. Using a moving window averaging to smooth the original data eliminates instantaneous noise and abnormal peaks, while preserving the low-frequency trend of bridge vibration. The corrected data is more suitable for subsequent integration calculations and overall displacement back-calculation, effectively avoiding the interference of noise on the final detection results, and intuitively demonstrating the crucial role of preprocessing in the accuracy of bridge displacement detection.

[0032] In one embodiment of the present invention, the phase difference time series is correlated with a pre-calibrated measurement point spacing to convert it into a relative displacement time series between the two measurement points. The actual installation spacing between the two measurement points is obtained as the measurement point spacing. Based on the wavenumber of the bridge structure in the detection direction, the product of the measurement point spacing and the phase difference time series is divided by twice pi to obtain the relative displacement time series between the two measurement points. Outlier detection is performed on the relative displacement time series. When the relative displacement value at a certain moment exceeds a set multiple of the average value of the three moments before and after, the outlier value is replaced by the average value. The relative displacement time series is integrated to obtain the relative velocity time series between the two measurement points. The relative velocity time series is then integrated again to obtain the cumulative relative displacement value between the two measurement points. The relative displacement time series is numerically integrated using the trapezoidal rule to obtain the relative velocity time series between the two measurement points. The relative velocity time series is numerically integrated again using the trapezoidal rule to obtain the cumulative relative displacement value between the two measurement points. Before each integration, the input time series is detrended to eliminate baseline drift generated during the integration process.

[0033] In practical implementation, for the stiffening girder of a long-span suspension bridge, the bridge displacement detection method based on phase information converts the phase difference time series into relative displacement, obtains the actual installation distance between two measuring points as the measuring point distance, and, based on the wavenumber of the bridge structure in the detection direction, divides the product of the measuring point distance and the phase difference time series by twice pi to obtain the relative displacement time series between the two measuring points. In some embodiments, the two measuring points are arranged along the longitudinal direction of the bridge at the quarter-span and mid-span positions, and the actual installation distance between the two points is accurately measured using a total station. Optionally, the wavenumber of the bridge structure in the detection direction is obtained through modal analysis or based on design data, and the relative displacement time series... Calculated using the formula:

[0034] in: Indicates at the sampling time The relative displacement between the two measuring points This indicates the actual installation distance between the two measuring points. Indicates at the sampling time Phase difference between two measuring points This indicates the wave number of the bridge structure in the detection direction. Data comparison is achieved by comparing the relative displacement time series calculated under different wave number assumptions.

[0035] In specific implementation, outlier detection is performed on the relative displacement time series. When the relative displacement value at a certain moment exceeds a set multiple of the average of the three moments before and after it, the outlier value is replaced with the average. In some embodiments, the set multiple is 3 times, and the detection window includes the current moment and the three adjacent sampling moments before and after it. Optionally, the replacement operation replaces the marked outlier value with the arithmetic mean of the relative displacement values ​​of the remaining six valid moments within the detection window. It can be understood that the outlier detection and replacement process aims to eliminate data jumps caused by accidental electromagnetic interference or transient signal loss. Referring to Table 1, the outlier detection and replacement process is illustrated, where the relative displacement value at time t3 is marked as an outlier.

[0036] Table 1: Detection and Replacement of Outliers in Relative Displacement Time Series

[0037] In specific implementation, the relative displacement time series is integrated to obtain the relative velocity time series between the two measuring points. Then, the relative velocity time series is integrated again to obtain the cumulative relative displacement between the two measuring points. The trapezoidal rule is then applied to numerically integrate the relative displacement time series to obtain the relative velocity time series between the two measuring points. Finally, the trapezoidal rule is applied again to numerically integrate the relative velocity time series to obtain the cumulative relative displacement between the two measuring points. In some embodiments, the numerical integration is performed in the discrete time domain, and the trapezoidal rule approximates the curve between adjacent sampling points as a trapezoid for calculation. Optionally, the value of the k-th point in the relative velocity time series... By analyzing the relative displacement time series The value at the k-th point is obtained by integration. By analyzing the relative velocity time series The integration yields the following result: it can be understood that two numerical integrations elevate the relative kinematic quantities measured by the accelerometer, after conversion, from the acceleration order to the displacement order.

[0038] In practice, before each integration, the input time series is detrended to eliminate baseline drift generated during integration. In some embodiments, detrending is performed by applying a linear least-squares fit to the input time series to obtain an optimal fitting line. This fitted line is then subtracted from the original sequence. The fitted line is represented as:

[0039] in: It's the slope. It is the intercept. It's time, the detrended sequence. The data comparison was accomplished by plotting the integral results of the sequences before and after detrending. Detrending effectively suppressed the spurious trend term that grows linearly over time in the integral results.

[0040] See Figure 4 This is an analysis chart of the overall bridge displacement using wavelet denoising, visually demonstrating the changes in the overall bridge displacement before and after denoising. The original overall displacement contained subtle high-frequency noise and random jumps, resulting in a jagged curve reflecting environmental interference. After wavelet denoising, the noise in the overall displacement was effectively filtered out, and the curve became smooth and completely preserved the low-frequency trend of the original displacement, highly consistent with the original curve trend. A multi-scale decomposition of the overall displacement was performed using wavelet basis functions with tight support characteristics. Noise-dominant detail coefficients were identified and zeroed, and then reconstructed to obtain the denoised signal. The core trend of bridge vibration was preserved, high-frequency random jumps were eliminated, making the displacement curve more consistent with engineering reality. The denoised signal was undistorted and did not change the amplitude and phase characteristics of the displacement, visually verifying the effectiveness of wavelet denoising in bridge displacement detection.

[0041] In one embodiment of the present invention, the cumulative relative displacement between two measuring points is used as a benchmark, and combined with the absolute displacement calculation results of each measuring point, the overall displacement of the bridge structure in the detection direction is inferred. Using the cumulative relative displacement between the two measuring points as a constraint, least-squares fitting is performed on the absolute displacement calculation results of each measuring point to obtain the displacement correction amount of each measuring point relative to the benchmark measuring point. The absolute displacement calculation results of each measuring point are added to the corresponding displacement correction amount to obtain the corrected absolute displacement of each measuring point. The arithmetic mean of the corrected absolute displacements of all measuring points is taken as the overall displacement of the bridge structure in the detection direction. Wavelet denoising processing is performed on the overall displacement. A wavelet basis function with tight support characteristics is selected, and the overall displacement is decomposed into multiple scales to obtain detail coefficients and approximation coefficients at different scales. Based on the energy distribution of the detail coefficients at each scale, the noise-dominant scale is determined, and the detail coefficients at the noise-dominant scale are set to zero. Wavelet reconstruction is performed on the retained detail coefficients and approximation coefficients to obtain the denoised bridge displacement detection result.

[0042] In practical implementation, for multiple monitoring sections of a prestressed concrete continuous rigid frame bridge, the overall displacement in the bridge displacement detection method based on phase information is back-calculated based on the cumulative relative displacement value and the absolute displacement of each measuring point. Using the cumulative relative displacement value between two measuring points as a constraint, the absolute displacement calculation results of each measuring point are subjected to least-squares fitting to obtain the displacement correction amount of each measuring point relative to the reference measuring point. In some embodiments, five measuring points are arranged along the longitudinal direction of the bridge. The absolute displacement calculation results are obtained from a satellite positioning module integrated in the accelerometer or a total station automatic measurement system. Specifically, least-squares fitting constructs an overdetermined system of equations with the correction amount of each measuring point as the unknown. The objective function is to minimize the sum of squares of the differences between the corrected displacement differences between each measuring point and the corresponding cumulative relative displacement values. The fitting formula is:

[0043] in: and These represent the absolute displacement calculation results for measuring point i and measuring point j, respectively. and Let i and j represent the displacement corrections of the measurement points i and j relative to the reference measurement point, respectively. This represents the cumulative relative displacement between measuring point i and measuring point j obtained by the phase method. It can be understood that by solving this least squares problem, a set of displacement corrections that best matches the relative constraints and the absolute measurement results can be obtained.

[0044] In specific implementation, the absolute displacement calculation results of each measuring point are added to the corresponding displacement correction amount to obtain the corrected absolute displacement of each measuring point. The arithmetic mean of the corrected absolute displacements of all measuring points is taken as the overall displacement of the bridge structure in the detection direction. In some embodiments, the reference measuring point is selected as a measuring point located near the fixed support of the bridge, and its displacement correction amount is set to zero. The corrected absolute displacement of other measuring points is calculated by adding the displacement correction amount obtained by least squares fitting to their original absolute displacement calculation results. Optionally, the overall displacement is:

[0045] in: This represents the overall displacement of the bridge structure at time t. Indicates the total number of measuring points. This represents the result of the absolute displacement calculation at measuring point i at time t. This represents the displacement correction amount for measuring point i. The data comparison is displayed in a list showing the absolute displacement values ​​of each measuring point before and after correction. The correction process eliminates the system deviation or inconsistency of reference that may exist between different absolute displacement measurement systems, making the relative relationship of the displacement values ​​of each measuring point more consistent.

[0046] In practical implementation, wavelet denoising is performed on the overall displacement. A wavelet basis function with compact support characteristics is selected, and the overall displacement is decomposed into multiple scales to obtain detail coefficients and approximation coefficients at different scales. In some embodiments, the wavelet basis function is selected as 'db4', and the number of decomposition levels is selected as 5. Optionally, the multi-scale decomposition is implemented using the Mallat algorithm to decompose the overall displacement time series into detail coefficients of different frequency sub-bands. Approximation coefficient of the lowest frequency ,in Indicates the decomposition scale. The term "maximum decomposition scale" indicates that the detail coefficients primarily contain the high-frequency components and noise of the signal, while the approximation coefficients retain the low-frequency trend components. In specific implementations, based on the energy distribution of the detail coefficients at each scale, the noise-dominant scale is determined. The detail coefficients at the noise-dominant scale are set to zero, and wavelet reconstruction is performed on the retained detail coefficients and approximation coefficients to obtain the denoised bridge displacement detection results. In some embodiments, the energy of the detail coefficients at each scale is evaluated by calculating the variance or norm. Optionally, scales with energy below a set threshold are identified as noise-dominant scales, and the detail coefficients at these scales are set to zero. The inverse Mallat algorithm is then used to reconstruct the detail coefficients and approximation coefficients that are not set to zero. It can be understood that wavelet denoising effectively filters out spikes introduced by high-frequency environmental random vibrations or measurement electrical noise in the overall displacement time series, making the displacement time history curve smoother.

[0047] See Figure 5This is a diagram analyzing the impact of noise on the overall displacement of a bridge. It compares the actual overall displacement with the noise-infused overall displacement, visually demonstrating the influence of environmental interference on bridge displacement detection data. This serves as a prerequisite for subsequent wavelet denoising processing. The smooth multi-frequency vibration curve of the actual overall displacement reflects the true vibration modes of the bridge structure, with amplitudes stable within ±7mm and no additional spikes. The noise-infused overall displacement, on the other hand, has high-frequency Gaussian noise superimposed on the actual displacement, resulting in obvious spikes and random jumps in the curve. While highly consistent with the actual displacement trend, it distorts details. The noise is a high-frequency, low-amplitude signal that does not alter the overall trend and periodic characteristics of the displacement, but it interferes with the extraction of key feature points such as peaks and troughs. Noisy data can lead to errors in subsequent integration calculations and modal analysis; therefore, wavelet denoising and other methods must be used to remove noise and restore the true displacement signal.

[0048] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A bridge displacement detection method based on phase information, characterized in that, include: Acquire vibration response signals from at least two measuring points on the bridge structure, wherein the vibration response signals are acceleration time history data; The vibration response signal is bandpass filtered to remove high-frequency noise and low-frequency drift, while retaining the frequency bands corresponding to the main vibration modes of the bridge structure. The filtered vibration response signal is subjected to Hilbert transform to obtain the analytical signal of the vibration response signal, and the instantaneous phase sequence is extracted from the analytical signal; Using the instantaneous phase sequence as input, the cross-correlation function of the instantaneous phase sequences between adjacent measurement points is calculated, and the phase difference time sequence between the two measurement points is determined by the maximum value of the cross-correlation function. The phase difference time series is correlated with the pre-calibrated distance between measuring points and converted into a relative displacement time series between the two measuring points; The relative displacement time series is integrated to obtain the relative velocity time series between the two measuring points. The relative velocity time series is then integrated again to obtain the cumulative relative displacement between the two measuring points. Using the cumulative relative displacement between two measuring points as a benchmark, and combining the absolute displacement calculation results of each measuring point, the overall displacement of the bridge structure in the detection direction is inferred. The overall displacement is subjected to wavelet denoising to remove random jumps caused by environmental interference, resulting in the denoised bridge displacement detection result.

2. The bridge displacement detection method based on phase information according to claim 1, characterized in that, Bandpass filtering of the vibration response signal includes: Based on the design natural frequency of the bridge structure, determine the frequency range corresponding to its principal vibration mode, and use the frequency range as the passband of the bandpass filter; Collect an environmental background vibration signal when there are no vehicles passing by, calculate the power spectral density of the environmental background vibration signal, and remove the frequency bands with power spectral density below a set threshold from the passband to obtain the optimized passband. The vibration response signal is filtered using a Butterworth filter. The filter order is determined based on the attenuation slope requirement at the passband edge to obtain the filtered vibration response signal.

3. The bridge displacement detection method based on phase information according to claim 2, characterized in that, The step of performing a Hilbert transform on the filtered vibration response signal to obtain the analytic signal of the vibration response signal, and extracting the instantaneous phase sequence from the analytic signal, includes: Perform a Hilbert transform on the filtered vibration response signal to obtain its orthogonal components; The original vibration response signal is used as the real part, and the orthogonal components are used as the imaginary part to construct the analytical signal. Taking the arctangent function of the analytical signal yields the original phase sequence containing the transition points; The original phase sequence is unwound to eliminate the phase jump caused by the periodicity of the arctangent function, resulting in a continuous instantaneous phase sequence.

4. The bridge displacement detection method based on phase information according to claim 3, characterized in that, Using the instantaneous phase sequence as input, the cross-correlation function of the instantaneous phase sequences between adjacent measurement points is calculated. The phase difference time sequence between the two measurement points is determined by the maximum value of the cross-correlation function, including: The instantaneous phase sequences of two adjacent measuring points are normalized so that the mean of the two adjacent measuring points is zero and the variance is 1. Perform cross-correlation on the two normalized instantaneous phase sequences to obtain the cross-correlation function curve; Search for the maximum point in the cross-correlation function curve and record the time delay corresponding to the maximum point; Divide the time delay by the signal sampling period to obtain the phase difference between the two measurement points, and arrange them according to the sampling time to form a phase difference time sequence.

5. The bridge displacement detection method based on phase information according to claim 4, characterized in that, The phase difference time series is correlated with the pre-calibrated distance between measuring points to convert it into a relative displacement time series between the two measuring points, including: Obtain the actual installation distance between the two measuring points as the measuring point distance; Based on the wave number of the bridge structure in the detection direction, the product of the time series of the distance between the measuring points and the phase difference is divided by twice pi to obtain the time series of the relative displacement between the two measuring points. Outlier detection is performed on the relative displacement time series. When the relative displacement value at a certain moment exceeds a set multiple of the average value of the three moments before and after it, the outlier value is replaced with the average value.

6. The bridge displacement detection method based on phase information according to claim 5, characterized in that, Integrating the relative displacement time series yields the relative velocity time series between the two measuring points. Then, integrating the relative velocity time series again yields the cumulative relative displacement between the two measuring points, including: The relative displacement time series is numerically integrated using the trapezoidal rule to obtain the relative velocity time series between the two measuring points. The relative velocity time series is numerically integrated again using the trapezoidal rule to obtain the cumulative value of the relative displacement between the two measuring points. Before each integration, the input time series is detrended to eliminate baseline drift generated during the integration process.

7. The bridge displacement detection method based on phase information according to claim 6, characterized in that, Using the cumulative relative displacement between two measuring points as a benchmark, and combining it with the absolute displacement calculation results of each measuring point, the overall displacement of the bridge structure in the detection direction is inferred, including: Using the cumulative relative displacement between two measuring points as a constraint, the absolute displacement calculation results of each measuring point are fitted by least squares to obtain the displacement correction of each measuring point relative to the reference measuring point. Add the corresponding displacement correction amount to the absolute displacement calculation results of each measuring point to obtain the corrected absolute displacement of each measuring point; The arithmetic mean of the absolute displacements of all measuring points after correction is taken as the overall displacement of the bridge structure in the detection direction.

8. The bridge displacement detection method based on phase information according to claim 7, characterized in that, Wavelet noise reduction processing is performed on the overall displacement, including: By selecting wavelet basis functions with tight support characteristics, the overall displacement is decomposed into multiple scales to obtain detail coefficients and approximation coefficients at different scales. Based on the energy distribution of detail coefficients at each scale, determine the noise-dominant scale and set the detail coefficients at the noise-dominant scale to zero. Wavelet reconstruction is performed on the retained detail coefficients and approximation coefficients to obtain the denoised bridge displacement detection results.

9. The bridge displacement detection method based on phase information according to claim 8, characterized in that, Before acquiring vibration response signals from at least two measuring points on the bridge structure, the following steps are also included: Accelerometers are symmetrically arranged on both sides of the cross section to be tested of the bridge structure, and the sensitive direction of the acceleration sensors is perpendicular to the bridge axis. Perform static calibration on each accelerometer to obtain its sensitivity coefficient; The installation of the accelerometer was verified by a knocking test to ensure that its output signal was not significantly distorted during bridge vibration.

10. A bridge displacement detection system based on phase information, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the bridge displacement detection method based on phase information as described in any one of claims 1 to 9.

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