Ground-based multiple-input multiple-output (GB-MIMO) radar is suitable for vibration monitoring of all kinds of bridges because of its high accuracy, wide detection range and noncontact characteristics. It is necessary to select effective pixels with stable amplitude and regular phase to achieve accurate estimation of bridge vibration. In this paper, a new method for extracting vibration regions of bridges based on GB-MIMO radar is proposed. In the first step, the mask in image processing is combined with the average amplitude to extract the bridge pixels in the radar image and the circle fitting method is used to suppress the static clutter in the bridge pixel sequence. In the second step, the amplitude dispersion index is used to screen out the points with stable pixel amplitude. In the third step, the pixels with stable amplitude are divided into vibrational and non-vibrational regions by vibration similarity. Finally, the Welch method is used to analyze the phase spectrum of pixel sequence in the vibration region to estimate the vibration frequency. In order to verify the effectiveness of the proposed algorithm for bridge vibration detection, the measured data of a bridge in Chongqing is taken as an example to test the algorithm. The results show that the algorithm improves the effective detection rate of vibration region.
Various kinds of bridge structures are affected by dynamic loads such as moving vehicles, crowds
and earthquake during long-term use which will lead to fatigue damage or premature aging of local
bridge structures. If the damaged part of the bridge structure cannot be identified and repaired in time.
Over time, aging will accelerate further. It will lead to the accumulation of systemic damage of the
bridge structure and the attenuation of bridge resistance and even cause serious disasters such as
collapse, which poses a great threat to social property and people. Therefore, the research on bridge
health monitoring technology is of great significance to ensure the normal and safe operation of highway
bridges [
Since the measurement of vibration by GB-MIMO radar needs to process and analyze the differential
interference phase sequence of pixels in time and frequency domain, the pixels of radar image affected
by noise are not suitable for vibration measurement. In order to achieve accurate estimation of bridge
vibration, effective pixels with stable amplitude and continuous phase need to be selected. In 1999,
amplitude dispersion index (ADI) was proposed to effectively screen out points with relatively stable
amplitude in pixel time series [
This paper is divided into five parts. The first part introduces the research background and content of this paper. The second part analyzes the vibration measurement principle of GB-MIMO radar. The third part describes the experimental methods. The fourth part discusses the test results of Chongqing Bridge. The fifth part is the summary of this paper.
The realization of vibration target localization by GB-MIMO radar mainly depends on the
twodimensional high-resolution capability of GB-MIMO radar. A series of two-dimensional high resolution
radar images are generated by imaging the received signals [
I (m, n) = I (m, n) e λ
Where, I (m, n) represents the imaging result after focusing at the position of grid (m, n) . I (m, n) is the amplitude of the imaging result. R is the radial distance between the scatterer of (m, n) and the radar.
According to equation (1), the phase of the imaging result of each pixel contains the distance information between the scatterer and radar in the scene corresponding to the pixel. For the vibration target in the scene, the phase of the imaging result will show a certain periodicity along with the vibration, so the phase curve of the multi-frame imaging result can be used for vibration analysis. After extracting the signal of the same imaging unit from multiple consecutive imaging results, the signal sequence of a vibrating object can be expressed as
j4π Rvib j4π Avib sin(2πfvibkΔt) I(m,n) (k ) = I(m,n) (k ) e λ e λ (1) (2)
Where, I(m,n) (k ) is the signal of imaging unit (m, n) in the k th imaging results. Rvib is the radial distance from the vibration center to the center of radar aperture. Δt is the time for collecting imaging data of an image. Avib and fvib represent the vibration amplitude and frequency of the vibrating object, respectively.
This paper is mainly divided into three parts: preprocessing, bridge vibration pixel extraction and frequency estimation. Firstly, the radar image is preprocessed to extract the target region and suppress the static echo of the vibration signal. Secondly, the vibration pixels of the bridge deck were screened by combining ADI and VSI. Finally, the frequency of the selected pixel sequence is estimated. The flow of the proposed method is shown in Fig. 1.
Where, Ak is the amplitude value of a pixel in the kth radar image. According to experience, the
threshold can be set to -10dB [
Finally, according to the characteristics that the stationary target echo does not change with time
while the vibration echo phase changes periodically with time, the circular fitting method [
After preprocessing, the approximate range of bridge pixels is filtered out. Because the bridge is an
artificial structure the surface is relatively smooth. The scattering intensity of each structure location is
inconsistent and unpredictable. So, it is necessary to determine the pixels with high SNR when selecting
the effective pixels. ADI is based on the statistical characteristics of pixel amplitude on the time series
to select the point of amplitude stability. For a pixel with a high SNR, the noise level of its phase is
equivalent to the amplitude dispersion index [
The purpose of preprocessing is to extract target region from radar image region and suppress clutter. The first step is to extract the target region by using the mask in image segmentation according to the observed scene image. The second step is based on the strong scattering characteristics of the target echo signal, which is characterized by high energy and large amplitude of the echo signal. The average amplitude threshold method is used to detect the target region. The pixel with high amplitude is selected as the target candidate point by setting an appropriate threshold. The expression is as follows: DA =σmAA (3) (4)
In equation (3), σ A and mA are the amplitude standard deviation and amplitude average value of N
radar images in the temporal dimension. DA is the dispersion index. Empirically, the threshold can be
set to 0.15 [
The bridge amplitude stable pixels selected by ADI can be directly used for deformation monitoring
because the bridge deforms very slowly. In order to realize vibration monitoring of bridge, it is
necessary to select pixels with regular phase. Vibration Similarity Index (VSI) [
Where, Smax and Smean represent the peak amplitude of the spectrum after removing the DC
component and the average amplitude of the whole spectrum, respectively. By setting an appropriate
threshold VSIT , the pixel meeting condition VSI > VSIT is the vibration pixel. When choosing VSIT ,
first determine the number of sampling points and the required detection probability. The detection rate
is the probability that the highest value in the spectrum except the zero-frequency point corresponds to
the vibration frequency. Then the requirement of SNR is obtained according to the required detection
probability. Finally, we find the corresponding VSIT [
Finally, the common pixels of (4) and (5) are obtained. Since the vibration pixels of the structure are not isolated in the image domain, the isolated pixels are removed by the filtering operation in binary morphology.
As shown in Equation (2), the phase of the extracted signal includes the vibration of the vibrating
object. Therefore, Welch method [
P= 1 L N
xi (n)ω (n) exp (− jω n) L i=1 n=1 2
Where xi represents the ith data segment with N elements, L is the segment number, ω (n) is the window function. The position of the spectral peak corresponds to the estimated vibration frequency.
A bridge in Chongqing was monitored by 16 ×16 GB-MIMO radar in the experiment. System parameters are shown in Table 1, and experimental scenes are shown in Fig 2
(a) Monitoring scene diagram Fig. 2 Monitoring scene and MIMO radar imaging results (b) Imaging results
Value 16.2 GHz 0.375 m 0.082 ms 50-500 m (5) (6)
A. Preprocessing: As mentioned in 3.1, Fig. 3 (a) plots the target area extracted by artificial mask in image processing. The entire bridge shape can be clearly seen from the target area. According to (3), the bridge pixels with large amplitude in the target area are screened out, as shown in Fig. 3 (b). Then the candidate pixels are suppressed by circle fitting. Firstly, the trajectory of the bridge pixel sequence is fitted to the complex plane to obtain the center of the circle and the center of the circle is moved back to the origin of coordinates, as shown in Fig. 3 (c). Fig. 3 (d) shows the pixel distribution after clutter suppression.
1 0.5 0 -0.5 -1 -1.5 -2 (a) Target area
(b) Distribution of candidate pixels Beforeclut ersuppression
After clut er suppression
B. Select bridge deck pixels: The local graph of ADI value according to (4) is shown in Fig. 4 (a) after preprocessing. Some of the stronger amplitude pixels on the bridge have poorer ADI values due to dihedral Angle scattering and dwell. Fig.4 (b) shows the distribution of bridge deck pixels after screening by setting ADI threshold.
(d) Distribution after clutter suppression (a) Local graph of ADI value Fig. 4 The rule of ADI (b) Pixel distribution of bridge deck
C. Select vibrating pixels: According to equation (5), the preprocessed pixel sequence is taken as
the input to calculate the VSI then setting an appropriate threshold according to experience [
(a) Distribution of vibration pixel Fig. 5 VSI selection result (b) Deformation curve
Finally, the pixels common to the bridge deck pixels and vibration pixels are defined as effective pixels, a total of 12587 pixels. Then, the isolated pixels are removed through binary morphology filtering operation, and a total of 12132 pixels are selected, as shown in Fig. 6 (a). Fig. 6 (b) shows the deformation curve of the effective pixel. The deformation changes of selected pixels are basically the same. Therefore, this method can effectively screen the vibrating pixels of the bridge deck. (a) Effective pixel distribution Fig. 6 Results of the proposed method selection (b)
D. Frequency estimation: Fig. 7(a) depicts the phase curve of a vibrating pixel in the vibration area
of the bridge. According to Section 3.4, the vibration frequency of the vibrating pixel is estimated to be
0.34Hz, as shown in Fig. 7(b). According to the data, the natural frequency of the first order vibration
of long-span cable-stayed bridge is about 0.2~0.5Hz [
(a) Vibration phase curve of vibrating pixels
Finally, the vibration frequencies of the bridge vibration regions selected by the double threshold method and the bridge vibration regions selected by the VSI method are estimated respectively. Fig 8 (a) is the first-order frequency distribution of the proposed method and Fig 8 (b) is the first-order frequency distribution of the VSI method.
1 2 frequency/3Hz 4 5 (b) Spectrum diagram of vibration phase curve (a) First order vibration frequency distribution diagram (The proposed method) (b) First order vibration frequency distribution diagram (VSI method)
In order to further compare the vibration region recognition effects of the two methods, the vibration frequencies in Fig. 8(a) and Fig. 8(b) were statistically analyzed. The results are shown in Table 2. The frequencies of pixels selected by the two methods are all concentrated at 0.34Hz. The pixels with a frequency of 0.34Hz selected by the proposed method accounted for 75.3% of the total selected structure pixels, which was larger than that of the VSI method. Therefore, the detection rate of bridge vibration region is higher with the proposed method.
Vibration frequency
In the bridge vibration measurement technology, in order to ensure the accuracy and reliability of the bridge vibration estimation, the bridge vibration region with stable amplitude and regular phase is selected. This article uses the stability characteristics of deck amplitude in time series and the energy distribution characteristics of vibration phase sequence spectrum. A method combining amplitude dispersion index and vibration similarity index is proposed, which can effectively improve the detection rate of bridge vibration region based on GB-MIMO radar. In the experiment, GB-MIMO radar is used to observe a bridge in Chongqing and obtain multiple radar image data continuously. The vibration region of radar image is selected by using the vibration similarity index method and the improved method. Finally, the frequency of selected vibration region is estimated by spectrum analysis principle. The experimental results show that the proposed method can effectively improve the detection rate of bridge vibration region.
This work was supported by the National Natural Science Foundation of China (619701037); Youth project of science and technology research program of Chongqing Education Commission of China. (Grant No. KJQN202101226). [1] T. Pa, A. Ja, D. Ga, et al. "Remote Structural Health Monitoring System for Bridges", 2020 IEEE International Students' Conference on Electrical, Electronics and Computer Science (SCEECS), 2020, pp. 1-4.