=Paper=
{{Paper
|id=Vol-3304/paper01
|storemode=property
|title=Vibration Region Extraction Method of Bridge Based on Ground-Based MIMO Radar
|pdfUrl=https://ceur-ws.org/Vol-3304/paper01.pdf
|volume=Vol-3304
|authors=Xiang Cao,Xiangfei Nie,Yunkai Deng,Zhengquan Hu,Fei Xiang
}}
==Vibration Region Extraction Method of Bridge Based on Ground-Based MIMO Radar==
https://ceur-ws.org/Vol-3304/paper01.pdf
Vibration Region Extraction Method of Bridge Based on Ground-
Based MIMO Radar 1
Xiang Cao 1,2; Xiangfei Nie 1; Yunkai Deng 3; Zhengquan Hu 1; Fei Xiang 1,2;
1
School of Electronic and Information Engineering, Chongqing Three Gorges University, Chongqing, 404000，
China
2
Beijing Institute of Technology Chongqing Innovation Centre, Chongqing, 401120, China
3
School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081, China
Abstract
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 non-
contact 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.
Keywords
GB-MIMO radar; vibration area; static echo suppression; Frequency estimation
1. Introduction
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 [1-2]. Vibration monitoring is an important method to evaluate the stability of bridge structure.
As an advanced non-contact sensor, real aperture radar has been widely used in structural health
monitoring. Its data acquisition speed is in the sub-millisecond level [3], but it has no azimuth resolution
ability. GB-MIMO radar has the ability of two-dimensional high-resolution imaging which can resolve
the vibration target in different directions on the same range gate and provides an effective technical
means for vibration measurement.
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
ICBASE2022@3rd International Conference on Big Data & Artificial Intelligence & Software Engineering, October 21-
23, 2022, Guangzhou, China
Cycnus.cao@qq.com (Xiang Cao)
© 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
1
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 [6]. In 2007, the double threshold method of amplitude intensity and
amplitude deviation index was proposed to solve the problem of ignoring the strong scattering of the
target by the amplitude deviation method alone [7]. In 2019, Tian et al. [8] proposed the vibration
similarity index (VSI) according to the frequency angle of the vibration phase sequence to represent the
similarity between the phase sequence signal of the detected pixel and the ideal sinusoidal signal. The
pixels with continuous phase sequence are effectively screened but the stability of scattering
characteristics isn’t considered and the pixels with unstable amplitude are easily selected. This article
combines the characteristics of vibration pixels and phase sequences. The combination of ADI and VSI
is used to screen the effective pixels of bridge vibration.
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.
2. Vibration measurement principle of GB-MIMO radar
The realization of vibration target localization by GB-MIMO radar mainly depends on the two-
dimensional high-resolution capability of GB-MIMO radar. A series of two-dimensional high resolution
radar images are generated by imaging the received signals [9-10]. The imaging results in an imaging
unit can be expressed as
j
4π
R (1)
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
j
4π
Rvib j
4π
Avib sin ( 2πf vib k Δt ) (2)
I ( m,n) ( k ) = I (m,n ) ( k ) e λ e λ
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.
3. The proposed method
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.
2
Fig. 1 Flow chart of bridge vibration region extraction
3.1. Preprocessing
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:
1 K (3)
A=20*log10 Ak , k = 1, 2,, K
K k =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 [13].
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 [11] is used
to suppress the stationary clutter of the target candidate pixel sequence.
3.2. Select bridge deck pixels
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 [6]. Therefore, the ADI method can effectively screen out
the pixels with stable bridge amplitude by setting an appropriate threshold. The expression is as follows:
σA
DA = (4)
mA
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 [12].
3.3. Select vibrating pixels
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) [8-11] can represent the
3
Similarity between phase sequence signal and ideal sinusoidal signal. When the VSI is larger, the
Vibration amplitude is larger. The expression is as follows:
Smax
VSI= (5)
Smean
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 [8].
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.
3.4. Frequency estimation
As shown in Equation (2), the phase of the extracted signal includes the vibration of the vibrating
object. Therefore, Welch method [16] can be used to estimate the vibration frequency according to the
phase of the signal sequence. The expression is as follows:
2
1 L N
P= xi ( n ) ω ( n ) exp ( − jω n )
L i =1 n =1
(6)
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.
4. Bridge vibration experiment
4.1. Experimental information
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 (b) Imaging results
Fig. 2 Monitoring scene and MIMO radar imaging results
Table 1. GB-MIMO radar system parameters
Parameter Value Parameter Value
Bandwidth 656 MHz Central Frequency 16.2 GHz
Acquisition Frequency 47.84 Hz Range Resolution 0.375 m
Azimuth Resolution 7.4 mrad PRT 0.082 ms
Wavelength 0.0185 m Measurement Range 50-500 m
4
4.2. Experimental results
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.
(a) Target area (b) Distribution of candidate pixels
Before clutter suppression
1
After clutter suppression
0.5
0
-0.5
-1
-1.5
-2
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
imag
(c) Bridge pixel sequence trajectory (d) Distribution after clutter suppression
Fig. 3 Data preprocess results
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.
(a) Local graph of ADI value (b) Pixel distribution of bridge deck
Fig. 4 The rule of ADI
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 [8] to select
the vibration pixels. Fig. 5 (a) shows the distribution of the vibration pixels. A total of 52302 vibrating
pixels were selected. As the bridge body is a whole, its deformation in the same period should be regular
[14]. The phase sequence of the selected pixels is used for deformation estimation [15]. Fig. 4 (b) shows
the deformation curve of the selected pixels. The deformation of the bridge body is disorderly. This is
because the selected vibration pixels of the bridge body include the vibration pixels outside the bridge
5
body. Therefore, it is necessary to screen the bridge structure pixels (pixels with stable amplitude)
before screening the vibration pixels.
(a) Distribution of vibration pixel (b) Deformation curve
Fig. 5 VSI selection result
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 (b) Deformation curve
Fig. 6 Results of the proposed method selection
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 [17]. So, it is considered that the result is reliable.
0.5
0.45
0.4
0.35
phase /rad
0.3
0.25
0.2
X 0.3444
0.15
Y 0.1129
0.1
0.05
0
0 1 2 3 4 5
frequency/Hz
(a) Vibration phase curve of vibrating pixels (b) Spectrum diagram of vibration phase curve
Fig. 7 The frequency spectrum
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.
6
(a) First order vibration frequency distribution (b) First order vibration frequency distribution
diagram (The proposed method) diagram (VSI method)
Fig.8 Vibration frequency distribution
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.
Table 2 Estimation of vibration frequency
Total points Measured Vibration
Method proportion
selected pixels frequency
The proposed method 12132 9136 0.34 Hz 75.3%
VSI method 25512 18363 0.34 Hz 71.9%
5. Conclusion
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.
6.Acknowledgments
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).
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