A bridge dynamic deflection measurement method based on interferometric radar

Abstract

The present invention discloses a bridge dynamic deflection measurement method based on interferometric radar, belonging to the field of radar measurement technology. The method monitors bridge vibration under excitation, extracts deflection measurement points by improving the vibration point screening method, suppresses clutter at the deflection measurement points, and obtains a bridge dynamic deflection curve based on differential interferometry technology. Using interferometric radar, observations are made along the bridge body direction, and echo data is continuously collected. During the echo data collection period, external excitation is applied to the bridge. The amplitude deviation index of each pixel point is calculated to screen candidate points. Time-frequency analysis is performed on each candidate point to extract the external excitation time period. The complex sequence of each candidate point in the external excitation time period is extracted, and the clutter component is estimated using a circular trace fitting method. The circular trace discreteness and outlier rate of each candidate point are calculated to screen the dynamic deflection measurement points. The dynamic deflection curve of each measurement point is obtained to achieve dynamic deflection measurement of the bridge.

Description

Technical Field

[0001] The invention belongs to the technical field of radar measurement, and in particular relates to a bridge dynamic deflection measurement method based on interferometric radar. Background Art

[0002] Bridge vibration measurement is an important technical means to determine the health status of a bridge. Among the bridge dynamic parameters, dynamic deflection is of great significance for accurately evaluating the safety and stability of the bridge.

[0003] Two typical interferometric radars—real aperture radar and MIMO (multiple input, multiple output) radar—have been gradually applied in the field of bridge vibration measurement. They offer technical advantages such as non-contact, high frame rate, and high precision. Real aperture radar uses a pair of transmitting and receiving antennas to extract measurement points from a one-dimensional range image for analysis, enabling bridge vibration measurement. MIMO radar, on the other hand, employs multiple specially arranged transmitting and receiving antennas to acquire a two-dimensional, high-resolution radar image. This image then extracts measurement points to measure bridge vibration.

[0004] Interferometric radar measures bridge dynamic deflection based on radar differential interferometry. The conventional measurement scheme is as follows: First, pixels with high signal-to-noise ratios are selected from N one-dimensional range profiles or N radar images as vibration measurement points. Next, clutter suppression techniques are used to reduce the impact of strong static clutter on the vibration measurement. Finally, the bridge dynamic deflection curve is obtained based on the principle of phase differential interferometry. However, this conventional scheme suffers from inaccurate selection of deflection measurement points and low clutter suppression accuracy, which seriously limits the accuracy of dynamic deflection measurements.

[0005] Therefore, it is necessary to study new ground-based interferometric radar measurement methods to overcome the defects of conventional technical solutions and achieve accurate measurement of bridge dynamic deflection. Summary of the Invention

[0006] In view of this, the present invention provides a bridge dynamic deflection measurement method based on interferometric radar, which monitors the vibration of the bridge under excitation, extracts the deflection measurement points by improving the vibration point screening method, suppresses the clutter at the deflection measurement points, and obtains the bridge dynamic deflection curve based on differential interferometry technology.

[0007] To achieve the above object, the technical solution of the present invention includes the following steps:

[0008] Step 1: Using an interferometric radar, observation is performed along the bridge body direction to continuously collect echo data; during the echo data collection period, external excitation is applied to the bridge; the echo data of the interferometric radar is processed to obtain a one-dimensional range image or a two-dimensional radar image;

[0009] Step 2: Calculate the amplitude deviation index of each pixel point and screen out candidate points;

[0010] Step 3: Perform time-frequency analysis on each candidate point to extract the external excitation time period;

[0011] Step 4: extract the complex sequence of each candidate point in the external excitation time period and use the circular trace fitting method to estimate the clutter component;

[0012] Step 5: Calculate the circular trace dispersion D and outlier rate η of each candidate point and select the dynamic deflection measurement points;

[0013] Step 6: Suppress the clutter at each dynamic deflection measurement point, obtain the dynamic deflection curve of each measurement point based on the differential interference phase, and realize the dynamic deflection measurement of the bridge.

[0014] Furthermore, the interferometric radar is a real aperture radar or a synthetic aperture radar; it is deployed at the bottom of the bridge or on the side of the bridge body; during the monitoring time, the real aperture radar obtains N one-dimensional range images, and the synthetic aperture radar obtains N radar images.

[0015] Furthermore, in step 2, the amplitude deviation index of each pixel point is calculated to screen out candidate points, specifically:

[0016] Filter candidate points using the N radar images or N one-dimensional range images obtained in step 1;

[0017] The amplitude deviation method and the amplitude information combination method are used to screen M pixel points with stable amplitude and phase within the monitoring time, which are the candidate points;

[0018] The amplitude deviation method and amplitude formula are as follows:

[0019]

[0020] Among them, D A is the target point amplitude deviation, σ A is the standard deviation of the target point amplitude time series, m A is the mean of the target point amplitude time series, |S| is the amplitude information of the target point;

[0021] Set the amplitude deviation threshold and amplitude threshold to D T , S T , satisfying D A <D T , |S|≥S T The pixel point is the PS point.

[0022] Furthermore, in step three, time-frequency analysis is performed on each candidate point to extract the external excitation time period, specifically:

[0023] Extract the phase sequence of each candidate point obtained from step 2 i=0,1,…N-1;m=1,2,…M,M is the total number of candidate points. The short-time Fourier transform (STFT) of the sequence is performed as follows:

[0024]

[0025] Where p is the sequence of the current time window, k is the frequency, N is the length of the window, H is the sliding step, and win(n) is the window function;

[0026] Extract the spectrum components under the window function at different times under the candidate point. The continuous time period where the main frequency appears is the excitation time period (n1, n2)

[0027] According to the excitation time period (n1, n2), the complex sequence S of the excitation time period of each candidate point is screened m (n),n=n1,…n2.

[0028] Furthermore, in step 4, the complex sequence of each candidate point in the external excitation time period is extracted, and the clutter component is estimated using the circular trace fitting method, specifically:

[0029] The complex sequence S of the excitation time period of each candidate point is obtained from step 3 m (n), n=n1,…n2;

[0030] The least squares-based circular trajectory fitting method is used to estimate the clutter component and arc radius of the sequence. That is, by modeling the arc and the center position, finding the extreme point of the loss function, and calculating the center coordinates and radius;

[0031] The loss function is the difference between the square of the distance from the point on the arc to the center of the circle and the square of the radius. Its formula is:

[0032]

[0033] Among them, f m Loss function, x m (i),y m (i) are the vibration complex sequence S m The real and imaginary parts of the ith sampling point, (X m ,Y m ) is the clutter component, R m is the arc radius.

[0034] Furthermore, in step five, the circular trace dispersion D and outlier rate η of each candidate point are calculated to select the dynamic deflection measurement points, specifically:

[0035] The complex sequence S of the excitation time period obtained in step 3 m(n), n = n1,…n2, the trajectory distribution in the complex plane is arc-shaped, while the trajectory of the non-vibration sequence in the complex plane is discrete. The discreteness D and outlier rate η of each candidate point are calculated to obtain the influence of the non-vibration segment on the vibration arc fitting effect, and the vibration measurement points are screened out.

[0036] Furthermore, the discreteness D and outlier rate η of each candidate point are calculated, specifically:

[0037] Discreteness D m and outlier rate η m The calculation formula is:

[0038]

[0039] η>η Threshold

[0040] Among them, x m (i),y m (i) are the vibration complex sequence S m The real and imaginary parts of the ith sampling point, (X m ,Y m ) is the clutter component, R m is the arc radius, T is the outlier threshold, N is the length of the candidate point sequence, η Threshold is the outlier rate threshold. m (i) is the discreteness of candidate point m at sampling point i; f m (i) The discreteness mark of candidate point m at sampling point i.

[0041] Furthermore, in step six, clutter suppression is performed on each dynamic deflection measurement point, and the dynamic deflection curve of each measurement point is obtained based on the differential interference phase, specifically:

[0042] Perform differential complex conjugate multiplication on all radar images or one-dimensional range images to obtain the differential interferometric phase sequence. i=0~N-1

[0043] The bridge vibration measurement point is obtained from step 4, and the displacement change curve △s in the line of sight direction of the vibration measurement point is obtained. m (i) Interference phase with point m The calculation formula is as follows:

[0044]

[0045] Where λ is the radar signal wavelength;

[0046] The dynamic deflection curve of a bridge is the displacement change in the vertical direction of the bridge. There is an angle θ between the radar line of sight and the vertical direction. The calculation formula of the dynamic deflection curve of the bridge is:

[0047]

[0048] Beneficial effects:

[0049] The present invention discloses a bridge dynamic deflection measurement method based on interferometric radar. First, the amplitude deviation index of pixel points is calculated to screen candidate points. Second, time-frequency analysis is performed on each candidate point to screen out the vibration time period. Then, the clutter component is estimated using the circular trace fitting method. The measurement points are screened based on the discreteness and outlier rate indicators. Finally, the bridge dynamic deflection curve is obtained based on the differential interferometry technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a schematic diagram of bridge monitoring;

[0051] Figure 2 Schematic diagram of clutter influence;

[0052] Figure 3 This is a comparison chart of clutter suppression effects;

[0053] Figure 4 A flow chart of a bridge dynamic deflection measurement method based on interferometric radar provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0054] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0055] The present invention provides a bridge dynamic deflection measurement method based on interferometric radar, the process of which is as follows: Figure 4 As shown, the following steps are included:

[0056] Step 1: Acquisition of radar data

[0057] The radar sight line direction is set along the direction of the bridge body, and the bridge is monitored when external excitation is applied to the bridge. Figure 1 The figure shows a schematic diagram of the radar deployment. During the monitoring period, the radar continuously collects echo data at a high frame rate. Real aperture radars (RARs) produce N one-dimensional range images, while synthetic aperture radars (SARs) acquire N radar images. The frame rate for RARs can reach several hundred hertz, between 100 and 1000 Hz; for SARs, it can reach tens of hertz, between 10 and 100 Hz.

[0058] In the embodiment of the present invention, at least one radar is deployed. The radar can be deployed at the bottom of the bridge or on the side of the bridge body; it can be a real aperture radar or a synthetic aperture radar.

[0059] Step 2: Candidate point screening

[0060] Candidate points are screened from the N radar images or N one-dimensional range images obtained in step 1. Since candidate points have strong temporal stability, target candidate points are screened based on PS (Permanent Scatterer) technology. A combination of amplitude deviation and amplitude information is used, and reasonable thresholds are set to screen M pixels with stable amplitude and phase within the monitoring time. These are the candidate points. The amplitude deviation method and amplitude calculation formula are as follows:

[0061]

[0062] Among them, D A is the target point amplitude deviation, σ A is the standard deviation of the target point amplitude time series, m A is the mean of the target point amplitude time series, |S| is the amplitude information of the target point. Set the amplitude deviation threshold and amplitude threshold to D T , S T , satisfying D A <D T , |S|≥S T The pixel point of is PS point. In the embodiment of the present invention, D T The setting range is 15-25dB, S T Set the interval to 0.1-0.2.

[0063] Step 3: Extract the incentive time period

[0064] The bridge candidate points are obtained from step 2, and the phase sequence of each candidate point is extracted i=0,1,…N-1;m=1,2,…M, M is the total number of candidate points. STFT (Short Time Fourier Transform) is performed on the sequence. The calculation formula is as follows:

[0065]

[0066] Where p is the sequence of the current time window, k is the frequency, N is the length of the window, H is the sliding step, and win(n) is the window function.

[0067] The spectrum components under the window function at different time periods at the candidate point are extracted, and the continuous time period where the main frequency appears is the excitation time period (n1, n2).

[0068] According to the excitation time period (n1, n2), the complex sequence S of the excitation time period of each candidate point is screened m (n),n=n1,…n2.

[0069] Step 4: Vibration measurement point screening

[0070] The complex sequence S of the excitation time period of each candidate point is obtained from step 3 m(n), n = n1,…n2. A least squares-based circular trajectory fitting method is used to estimate the clutter component and arc radius for this sequence. This method models the arc and the center position, finds the extreme point of the loss function, and calculates the coordinates of the center and radius. The loss function is the difference between the square of the distance from a point on the arc to the center and the square of the radius. Its calculation formula is:

[0071]

[0072] Among them, f m Loss function, x m (i),y m (i) are the vibration complex sequence S m The real and imaginary parts of the ith sampling point, (X m ,Y m ) is the clutter component, R m is the arc radius.

[0073] Step 5: Calculate the circular trace dispersion D and outlier rate η of each candidate point and select the dynamic deflection measurement points;

[0074] Figure 3 The complex sequence S of the excitation time period shown m The trajectories of (n),n=n1,…n2 in the complex plane are distributed in a circular arc shape, while the trajectories of non-vibration sequences are distributed discretely in the complex plane. The presence of non-vibration sequences affects the fitting of the vibration arc, leading to inaccurate estimation of the clutter component. By calculating the dispersion D and outlier rate η of each candidate point, we can determine the degree of influence of the non-vibration segment on the vibration arc fitting. By setting an appropriate threshold, we can select candidate points that exhibit vibration and are less affected by stationary clutter components, which are then used as vibration measurement points.

[0075] Discreteness D m and outlier rate η m The calculation formula is:

[0076]

[0077] η>η Threshold

[0078] Among them, x m (i),y m (i) are the vibration complex sequence S m The real and imaginary parts of the ith sampling point, (X m ,Y m ) is the clutter component, R m is the arc radius, T is the outlier threshold, N is the length of the candidate point sequence, η Threshold is the outlier rate threshold. m (i) is the discreteness of candidate point m at sampling point i; fm (i) The discreteness mark of candidate point m at sampling point i.

[0079] In this embodiment of the present invention, the outlier threshold T is set by sorting all candidate points in ascending order of dispersion to generate a dispersion curve. Some candidate points have large dispersions, making accurate clutter suppression impossible. Therefore, the dispersion threshold T should be smaller than the inflection point of the dispersion curve. The outlier rate threshold is set to no higher than 50%.

[0080] Step 6: Suppress the clutter at each dynamic deflection measurement point, obtain the dynamic deflection curve of each measurement point based on the differential interference phase, and realize the dynamic deflection measurement of the bridge.

[0081] Figure 2 The figure shows the trajectory distribution characteristics of the target sequence in the complex plane, which effectively distinguishes clutter and vibration components. By moving the center of the target sequence's trajectory in the complex plane coordinate system to the origin, clutter suppression is achieved, resulting in an accurate vibration sequence. Clutter suppression is achieved using the circular trajectory fitting method described in step 4.

[0082] Both real aperture radar and synthetic aperture radar obtain dynamic deflection curves based on the principle of differential interferometry. For two radar images acquired at different times, namely the main image I(1) and the auxiliary image I(2), the differential interferometry phase is obtained by complex conjugate multiplication of the two images. The calculation formula for the differential interference phase of a certain vibration measurement point m is:

[0083]

[0084] Perform differential complex conjugate multiplication on all radar images or one-dimensional range images to obtain the differential interferometric phase sequence. i=0~N-1

[0085] The bridge vibration measurement point is obtained from step 4, and the displacement change curve △s in the line of sight direction of the vibration measurement point is obtained. m (i) Interference phase with point m The calculation formula is as follows:

[0086]

[0087] Where λ is the radar signal wavelength;

[0088] The dynamic deflection curve of a bridge is the displacement change in the vertical direction of the bridge. Figure 1 It can be seen that there is an angle θ between the radar line of sight and the vertical direction. The calculation formula of the dynamic deflection curve of the bridge is:

[0089]

[0090] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A bridge dynamic deflection measurement method based on interferometric radar, characterized in that: include: Step 1: Use interferometric radar to observe along the bridge body and continuously collect echo data; During echo data acquisition, external excitation is applied to the bridge; echo data of the interferometric radar is processed to obtain a one-dimensional range image or a two-dimensional radar image; Step 2: Calculate the amplitude deviation index of each pixel point and screen out candidate points; Step 3: Perform time-frequency analysis on each candidate point to extract the external excitation time period; Step 4: extract the complex sequence of each candidate point in the external excitation time period and use the circular trace fitting method to estimate the clutter component; Step 5: Calculate the circular trace dispersion D and outlier rate η of each candidate point and select the dynamic deflection measurement points; Step 6: Suppress the clutter at each dynamic deflection measurement point, obtain the dynamic deflection curve of each measurement point based on the differential interference phase, and realize the dynamic deflection measurement of the bridge.

2. The bridge dynamic deflection measurement method based on interferometric radar according to claim 1, characterized in that: The interferometric radar is a real aperture radar or a synthetic aperture radar; it is deployed at the bottom of the bridge or on the side of the bridge body; During the monitoring time, the real aperture radar obtains N one-dimensional range images, and the synthetic aperture radar obtains N radar images.

3. A bridge dynamic deflection measurement method based on interferometric radar according to claim 1 or 2, characterized in that: The second step is to calculate the amplitude deviation index of each pixel point and screen out candidate points, specifically: Filter candidate points using the N radar images or N one-dimensional range images obtained in step 1; The amplitude deviation method and the amplitude information combination method are used to screen M pixel points with stable amplitude and phase within the monitoring time, which are the candidate points; The amplitude deviation method and amplitude formula are as follows: Among them, D A is the target point amplitude deviation, σ A is the standard deviation of the target point amplitude time series, m A is the mean of the target point amplitude time series, |S| is the amplitude information of the target point; Set the amplitude deviation threshold and amplitude threshold to D T , S T , satisfying D A <D T , |S|≥S T The pixel point is the PS point.

4. The bridge dynamic deflection measurement method based on interferometric radar according to claim 3, characterized in that: The third step is to perform time-frequency analysis on each candidate point to extract the external excitation time period, specifically: Extract the phase sequence of each candidate point obtained from step 2 i=0,1,…N-1;m=1,2,…M,M is the total number of candidate points. The short-time Fourier transform (STFT) of the sequence is performed as follows: Where p is the sequence of the current time window, k is the frequency, N is the length of the window, H is the sliding step, and win(n) is the window function; Extract the spectrum components under the window function at different times under the candidate point. The continuous time period where the main frequency appears is the excitation time period (n1, n2) According to the excitation time period (n1, n2), the complex sequence S of the excitation time period of each candidate point is screened m (n),n=n1,…n2.

5. The bridge dynamic deflection measurement method based on interferometric radar according to claim 3, characterized in that: The fourth step is to extract the complex sequence of each candidate point in the external excitation time period and estimate the clutter component using the circular trace fitting method, specifically: The complex sequence S of the excitation time period of each candidate point is obtained from step 3 m (n), n=n1,…n2; The least squares-based circular trajectory fitting method is used to estimate the clutter component and arc radius of the sequence. That is, by modeling the arc and the center position, finding the extreme point of the loss function, and calculating the center coordinates and radius; The loss function is the difference between the square of the distance from the point on the arc to the center of the circle and the square of the radius. Its formula is: Among them, f m Loss function, x m (i),y m (i) are the vibration complex sequence S m The real and imaginary parts of the ith sampling point, (X m ,Y m ) is the clutter component, R m is the arc radius.

6. The bridge dynamic deflection measurement method based on interferometric radar according to claim 5, characterized in that: The fifth step is to calculate the circular trace dispersion D and the outlier rate η of each candidate point and select the dynamic deflection measurement points, specifically: The complex sequence S of the excitation time period obtained in step 3 m (n), n = n1,…n2, the trajectory distribution in the complex plane is arc-shaped, while the trajectory of the non-vibration sequence in the complex plane is discrete. The discreteness D and outlier rate η of each candidate point are calculated to obtain the influence of the non-vibration segment on the vibration arc fitting effect, and the vibration measurement points are screened out.

7. The bridge dynamic deflection measurement method based on interferometric radar according to claim 6, characterized in that: The calculation of the discreteness D and outlier rate η of each candidate point is specifically as follows: Discreteness D m and outlier rate η m The calculation formula is: the>the Threshold Among them, x m (i),y m (i) are the vibration complex sequence S m The real and imaginary parts of the ith sampling point, (X m ,Y m ) is the clutter component, R m is the arc radius, T is the outlier threshold, N is the length of the candidate point sequence, η Threshold is the outlier rate threshold, U m (i) is the discreteness of candidate point m at sampling point i; f m (i) The discreteness mark of candidate point m at sampling point i.

8. The bridge dynamic deflection measurement method based on interferometric radar according to claim 7, characterized in that: The sixth step is to suppress clutter at each dynamic deflection measurement point and obtain the dynamic deflection curve of each measurement point based on the differential interference phase, specifically: Perform differential complex conjugate multiplication on all radar images or one-dimensional range images to obtain the differential interferometric phase sequence. The bridge vibration measurement point is obtained from step 4, and the displacement change curve △s in the line of sight direction of the vibration measurement point is obtained. m (i) Interference phase with point m The calculation formula is as follows: Where λ is the radar signal wavelength; The dynamic deflection curve of a bridge is the displacement change in the vertical direction of the bridge. There is an angle θ between the radar line of sight and the vertical direction. The calculation formula of the dynamic deflection curve of the bridge is:

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