Vibration Measurement of High-Speed Railway Bridges Based on GB-MIMO Interferometric Radar

As a novel type of ground-based interferometric radar, ground-based multiple-input multiple-output (GB-MIMO) interferometric radar utilizes multiple transmitting and receiving antennas to compose a specific structure and acquire a large synthetic aperture. Using electronic beam scanning instead of common mechanical scanning, GB-MIMO interferometric radar can achieve two-dimensional high-resolution imaging with image acquisition frequency at tens of Hertz, and has the ability to perform bridge health monitoring through vibration measurement. This study introduces the basic principle of the MIMO technique and the first Chinese made GB-MIMO interferometric radar. Experiments taken on a corner reflector and a high-speed railway bridge are respectively utilized to verify the vibration measurement ability of this novel type of GB-MIMO interferometric radar


Introduction
Deformation measurement is an important means of monitoring and warning landslide geological hazards.[1] Traditional deformation measurement equipment, including Global Navigation Satellite System (GNSS) receivers, fiber optic displacement sensors, total stations, and laser scanners, must be deployed in a contact manner or cannot operate all day.Ground-based interferometric radar has the technological advantages of all-weather, all-weather, high-precision, and large coverage.[2] Its deformation measurement rate can reach several minutes per time, which can significantly improve the deformation measurement ability and provide new equipment and important technical support for landslide disaster monitoring.[3] At the present stage, the mainstream product types of ground-based interferometric radar are ground-based real aperture radar (GB-RAR) and ground-based synthetic aperture radar (GB-SAR).Both of them use mechanical scanning to achieve imaging of large-scale scenes.The speed of mechanical scanning usually takes several minutes or even tens of minutes.A novel type of groundbased interferometric radar adopts the multiple-input multiple-output (MIMO) technology.[4][5]Through the special arrangement of multiple transmitting and receiving antennas, it can be equivalent to a specific array with a larger aperture.Using electronic beam scanning instead of common mechanical scanning, ground-based multiple-input multiple-output (GB-MIMO) interferometric radar can achieve fast acquisition of echo datasets at the second or even millisecond level, which can significantly improve the deformation measurement rate.[6] Structural health monitoring has become increasingly important with the large-scale construction of buildings and bridges.Vibration monitoring is an important approach to evaluate structural stability.[7] GB-RAR has been applied in the vibration monitoring of large structures, and can take data acquisition at sub-millisecond level.Based on the differential interferometry technique, GB-RAR can measure the micro-vibration as small as submillimeter level.However, GB-RAR has only onedimensional (1-D) range resolution, and scatters in the same resolution cell would be added together, which is rather hard for GB-RAR to accurately locate the position of the vibration pixels just with the 1-D range profile.[8] GB-MIMO interferometric radar has the abilities of 2-D high-resolution imaging and its image acquisition frequency can reach up to tens of hertz.The pixel number in a 2-D GB-MIMO interferometric radar image is much more than a 1-D GB-RAR range profile, which makes it better suitable for structural vibration monitoring.And has gradually shown its application potential in the field of structural health monitoring.Broussolle et al. has firstly proved the vibration measurement ability of GB-MIMO interferometric radar in 2014.[9] Pieraccini et al. has utilized a 4×4 radar array to measure bridge vibration and made comparisons with the measurement results of a GB-RAR system in 2019.[10] This paper firstly introduces the basic principle of the MIMO technique, and takes the first Chinese made GB-MIMO interferometric radar as an example to show its typical applications.The basic principle of implementing vibration measurement with the GB-MIMO interferometric radar is then introduced, and a validation experiment with a corner reflector as the measurement target is taken.Lastly, an experiment carried out on a high-speed railway bridge located on the Beijing Guangzhou high-speed railway is taken.

Basic principle
GB-MIMO interferometric radar utilizes multiple transmitting and receiving antennas to compose a specific geometrical structure and acquire a large aperture.Figure l shows a simplified scheme of MIMO radar, where M receiving antennas and N transmitting antennas are utilized to synthesize a MN virtual array.Taking the most basic uniform linear array as an example, and assuming these transmitting antennas are uniformly arranged in a linear pattern and the interval is d, then those receiving antennas should be also uniformly arranged and their neighboring interval is Md.In practical applications, to avoid the problem of imaging grating lobes, the neighboring interval of the equivalent virtual array should be small enough to satisfy the Nyquist criterion, and it is commonly smaller than half of the radar wavelength.For the Chinese made GB-MIMO interferometric radar, it utilizes 16 transmitting antennas to constitute two dense transmitting subarrays and 16 receiving antennas to constitute one sparse receiving subarray.An equivalent large aperture with 256 sampling intervals is synthesized.By adjusting system parameters such as pulse repetition time (PRT) and bandwidth, it can work in two modes including the deformation measurement mode and the vibration measurement mode.The deformation measurement mode is used to monitor deformations of the mountain slopes in figure 2. Its measurement rate is on the minute level and measurement accuracy can submillimeter level.The vibration measurement mode is used to monitor bridge and building vibrations.Its measurement rate can reach up to tens of Hz, and frequency measurement accuracy can reach a level of 0.1Hz.Table 1 shows the system parameters of the vibration measurement mode.

Vibration Measurement of GB-MIMO Interferometric Radar
In order to realize vibration measurement, GB-MIMO interferometric radar quickly collects echo signals at frequencies of several tens of Hz, and the total collection time is a few minutes to tens of minutes.Then the echo datasets are processed with the back-projection imaging algorithm to acquire a series of 2-D high resolution radar images and the image number can reach tens of thousands.Figure 3 shows the sketch diagram of the GB-MIMO interferometric radar images, which constructs a threedimensional (3-D) data matrix in the range, azimuth and time domain.Those pixels suitable for the vibration measurement are selected with specific criteria such as amplitude dispersion (ADI) and signal-to-noise (SNR) ratio.As shown in Fig. 3, a pixel sequence is extracted and then the vibration measurement can be taken with the differential interferometry and power spectrum estimation methods.[11]  x y can be modeled as follows: where  is the wavelength， , x y i i  is the complex scattering coefficient, , ( ) x y R t is the distance between the measurement pixel and radar ai time t , and clu S is the static clutter.[13] After static clutter suppression and interferometry processing, the interferometric phase sequence A typical spectrum method such as the Welch method can be utilized to estimate the vibration frequency.Other dynamic parameters such as deflection, damping ratio, and vibration mode can be further estimated with other methods.[14][15]

Corner reflector experiment
The measurement target of GB-MIMO interferometric radar is a corner reflector (CR).Under the control of a vibration calibrator, the CR is set to vibrate in a sinusoidal form with the vibration frequency of 10 Hz and vibration amplitude of 1mm.The experimental scenario was selected on the fourth floor platform of the experimental building at Beijing Institute of Technology, with the CR located approximately 10 meters from the radar center.Using the BP imaging algorithm to process and image radar echoes, the imaging result in cartesian coordinate is shown in figure .

High speed railway bridge experiment
The experimental scenario is selected from a part of the Beijing Guangzhou High Speed Railway located in the Beijing RV Park.The Beijing Guangzhou high-speed railway is a simply supported box girder bridge, with a bridge span of about 30m.The GB-MIMO interferometric radar was set in a side view angle to observe the bridges.The total data collection time was 109 seconds, and approximately 5000 images were acquired.Fig. 6 shows the photo the measurement scenario and the radar image.The bridge deck of the Beijing Guangzhou high-speed railway is smooth with weak scattering.There are special locations at the bridge pier connection where strong scattering occurs.In the 50th to 55th seconds of data collection, an 8-car high-speed train passed by.When the high-speed train passed by, the bridge showed an overall deflection change, and the vibration form was forced vibration.The vibration amplitude generated by the excitation was large, and after the excitation, the bridge returned to a stable stage.Select a pixel on the bridge (35.8m, 87.2m) in figure .6, as shown in Fig. 7. From the vibration displacement sequence, it can be seen that the high-speed rail undergoes vibration changes after observation.After conducting vibration analysis, the point has a vibration frequency of 1.98Hz in the frequency domain, which is a strong vibration frequency.

Conclusion
This study introduces the basic principle of the MIMO technique and the first Chinese made GB-MIMO interferometric radar.Experiments taken on a CR and a high-speed railway bridge are respectively utilized to verify the vibration measurement ability of this novel type of GB-MIMO interferometric radar.For the CR, its vibration amplitude measurement error is 0.1mm, and the vibration frequency is 0.2Hz.For the high-speed railway bridge, the time period during which a highspeed rail passed can be identified from the vibration displacement sequence, and a forced vibration frequency of 1.98Hz can be measured.

Figure 3 .
Figure 3. Sketch diagram of the GB-MIMO interferometric radar images The complex sequence

Table 1 .
System parameters of the vibration measurement mode