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Shield subway tunnel deformation detection based on mobile laser scanning
Automation in Construction 106 (2019) 102889
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Shield subway tunnel deformation detection based on mobile laser scanning a
b
Hao Cui , Xiaochun Ren , Qingzhou Mao a b
a,b,⁎
a
T
b
, Qingwu Hu , Wei Wang
School of Remote Sensing & Information Engineering, Wuhan University, Wuhan 430079, China State Key Laboratory of Rail Transit Engineering Informatization (FSDI), Xian 710043, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mobile laser scanning Shield subway tunnel Deformation detection Cross section Wavelet filtering Ellipse fitting
Shield subway tunnels are critical urban infrastructure and precise, rapid deformation detection method is required for the maintenance of these tunnels. A tunnel deformation detection system called Railway Mobile Measurement System (RMMS) was developed based on mobile laser scanning technique. Herein, detailed analysis is given to prove that profiles from the laser scanner can be seen as cross-sections of the tunnel and that the corresponding error can be ignored. A wavelet filtering algorithm was developed to filter the point cloud of tunnel ancillary facilities in the cross-section points. A subsequent ellipse fitting and deformation detection method is proposed. A cross-section location method for subway tunnels is also presented based on the greyscale image converted from the tunnel's point cloud. A tunnel ring segments seams detection method is proposed to detect tunnel ring segments dislocation. The accuracy of the system was verified in a subway tunnel in Wuhan, China with a total station. The accuracy of cross-section measurement was 1.5 mm, the repeatability of the overall and local deformation measurement was 0.5 and 0.9 mm, respectively. This system completely fulfils the accuracy requirement of railway tunnels deformation detection and its efficiency is significantly higher than that of the traditional method.
1. Introduction With the rapid development of infrastructure, an increasing number of subways have been built in China in the recent years. Most subways are constructed underground in tunnels excavated by shield tunneling machines. After excavation, these tunnels are mounted with precast concrete segments. The shape of newly built shield tunnels is circle, whereas these shield tunnels withstand huge stress from the earth, as time goes by, deformation of the tunnels will occur [1–3]. Severe deformation of subway tunnels will seriously threaten the operation of subways, so the deformation should be detected in the early stage and appropriate measures should be taken to prevent the deformation from getting worse. Fig. 1 shows an actual scene in a shield subway tunnel. There are many wires, pipes, and bolt holes on the inner wall of the tunnel, which interfere significantly with the detection of tunnel deformation. Moreover, subway tunnels are usually in operation all day long, and only a short skylight time in the early morning is spared for maintenance. Therefore, there are quite a few challenges in tunnel deformation detection and the method should be robust, accurate, and efficient. At present, tunnel deformation detection is mainly conducted using total stations or terrestrial laser scanners [4–7]. To detect tunnel deformation with a total station, some pre-set targets or points in the same ⁎
cross section of the tunnel are measured. The cross-section points are fitted to a circle and compared with the original design of the tunnel to detect deformation. The accuracy of total station is very high, but the low measurement speed limits overall efficiency and the number of cross-section points that can be measured. The insufficiency of crosssection points will have a negative effect on detecting deformation of the tunnel in small area. Terrestrial laser scanner provides accurate three-dimensional point cloud of the inner wall of a tunnel. The point cloud is very dense, and the scanning process takes only a few minutes. However, the point cloud will get sparse in faraway areas due to the incident angle. Therefore, multiple stations are needed to scan a long tunnel and all the stations must be registered together. Then the cross section of the tunnel must be extracted using algorithms. The following steps are just the same as those in the total station method. The whole deformation detection process with a terrestrial laser scanner is time consuming because multiple stations are scanned, and the computation cost of the massive point cloud is high. Many researchers have proposed different tunnel deformation detection methods based on point cloud. The key point of these methods is the extraction of cross-section points of the tunnel. The goal of their cross-section extraction algorithms is to make the cross-section orthogonal to the tunnel and they have tried different ways to achieve this. Xie and Lu [8] and Nuttens et al. [9] segmented the point cloud of a
Corresponding author at: School of Remote Sensing & Information Engineering, Wuhan University, Wuhan 430079, China. E-mail address: [email protected] (Q. Mao).
https://doi.org/10.1016/j.autcon.2019.102889 Received 23 September 2018; Received in revised form 12 May 2019; Accepted 20 June 2019 0926-5805/ © 2019 Elsevier B.V. All rights reserved.
Automation in Construction 106 (2019) 102889
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mobile laser scanning system cannot run at this high speed, the accuracy of the point cloud will drop dramatically. Some researchers have obtained tunnel cross-section points directly based on a mobile laser scanning system mounted on a custom trolley, to avoid the complicated processes of three-dimensional point cloud generation and cross-section points extraction. The company Amberg developed the GPR5000 clearance inspection trolley [24], which is equipped with a laser scanner, odometer, displacement sensor, and clinometer sensor. Their system can obtain a two-dimensional clearance map and cross section of the tunnel. Moreover, the Lecia company developed the SiTrack One mobile track scanning system [25] in which are integrated a Lecia P40 laser scanner, odometer, and high-end inertial measurement unit (IMU). This system can obtain point cloud of a tunnel with relative accuracy of 3–5 mm. High-end IMUs are used to obtain accurate position and posture. This leads to high cost and limits their wide application. Tan et al. [26,27] built a mobile laser scanning system for subway tunnels on an electronic trolley with a two-dimensional laser profiler and an odometer. The system can obtain the cross section of a tunnel directly and he proposed an algorithm that eliminates the point cloud of tunnel ancillary facilities in the tunnel. However, he did no further research on tunnel cross-sections. Du et al. [28] developed a mobile tunnel monitoring system called TS1, comprising a laser scanner, two odometers, a displacement sensor, and a custom trolley. Cross-section points of the tunnel were obtained directly; then, they were resampled, fitted to a circle, and compared with the original design of the tunnel. The result of tunnel deformation detection was verified using a total station. His method ignored the point cloud of tunnel ancillary facilities, and this has a negative effect on the accuracy. The original shape of subway tunnels excavated by shield tunneling machines is circular and the precast concrete segments are precisely mounted on the tunnels, so we can consider the cross section of newly built shield subway tunnels is a circle. Due to the effect of huge uneven underground stress, these tunnels will suffer from deformation and we conceive their cross sections will turn into an ellipse. In this case, the cross section of shield subway tunnels should be fit to an ellipse. Our experiment stands for this hypothesis. In this paper, a rigorous and efficient tunnel deformation detection system based on mobile laser scanning is presented. This tunnel deformation detection system consists of a high-precision two-dimensional laser profiler, an odometer, and a special-made trolley. The trolley is pushed forward manually on the rail track and is specially made to ensure that its pushing direction is parallel to the optical axis of the laser profiler. The cross section of the tunnel is obtained while the trolley is being pushed forward. Detailed analysis is given to prove that the cross-sections are orthogonal to the tunnel no matter whether the tunnel is straight or curved, and that the corresponding error can be ignored. A wavelet filtering algorithm is developed to eliminate the point cloud of tunnel ancillary facilities in the cross-section points. The filtered cross-section points are fitted to an ellipse. Then the fitting result is compared with the original design of the tunnel, after which the overall and local deformation result is obtained. To acquire the relative position of the cross section precisely, the point cloud of the tunnel is converted to a grayscale picture of which the grayscale value is determined by the reflectivity of the point cloud. The seams of the tunnel's inner wall ring are identified in the grayscale picture to locate the cross section. The accuracy of the system was verified in a subway tunnel using a total station and the rationality of ellipse fitting was verified as well.
Fig. 1. Actual scene of a shield subway tunnel.
tunnel into small segmentations and took the axis of the best fit cylinder to the segmentation as the tunnel axis. Then, they got the cross-section of the tunnel based on the cylinder axis. However, this method is not accurate enough for curved tunnels. Xu et al. [10] and Kang et al. [11] projected the point cloud of a tunnel to a horizontal plane and extracted the boundaries of the projected point cloud. The cross section was obtained by making a cutting plane vertical to the boundaries and projecting nearby points to the cutting plane. Puente et al. [12] proposed a cross-section extraction algorithm that calculated the normal vectors of the tunnel point cloud. The tunnel axis was determined by the normal vectors and the cutting plane was perpendicular to the tunnel axis. Pejić [13] use the vertical and horizontal positions of the rails alignment to get the cross section of railway tunnels point cloud. Since the noise of laser scanner on rail surface is very high, the rail positions are surveyed by total station and fitted to the designed elements of the rail alignment. This is an accurate and practical way to get the cross section of railway tunnels but surveying the rail position with total station is time consuming. Qiu and Cheng [14] generated a high-resolution digital elevation model (DEM) of a railway tunnel from terrestrial laser scanning data. The theoretical surface of a curved tunnel was reshaped into a developable surface and the cross section was defined on this surface. After the cross-section points of the tunnel were extracted, the next steps were very similar: these points were fitted to a circle or ellipse model and compared with the original design of the tunnel to find deformation. Although these researchers have spared no effort to make the cross-section orthogonal to the tunnel, error will inevitably accumulate with complicated calculation processes. Not to mention the heavy computational cost required by cross-section extraction. Compared to terrestrial laser scanning system, the mobile laser scanning system is more efficient and easier to deploy. A typical mobile laser scanning system consists of an inertial measurement unit (IMU), global positioning system (DGPS) antenna, an odometer, and one or more laser scanners [15–17]. Mobile laser scanning system has been widely used in three-dimensional point cloud acquisition in open spaces [18–21]. Some researchers have broadened the application of mobile laser scanning system to tunnel mapping. Puente et al. [22] obtained three-dimensional point cloud of a 2.5 km-long road tunnel in Spain using a mobile laser scanning system; then he proposed an algorithm to detect tunnel luminaires automatically. Arastounia [23] acquired point cloud of a 155 m-long subway tunnel using a mobile laser scanning system mounted on a rail car. He extracted the tunnel's main axis and cross sections; then created a preliminary model by fitting an ellipse to each extracted cross section. In these two cases, the mobile laser scanning systems run above 60 km/h to minimize the impact of GPS outage and to shorten the outage time. If the tunnel is too long or the
2. Materials 2.1. System integration The tunnel deformation detection system in this paper is called the Railway Mobile Measurement System (RMMS). RMMS integrates a twodimensional laser scanner, an odometer, a GPS antenna, an IMU, a 2
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0.0025 m long. Normally, the radius of a subway tunnel is 2.7 m. When R is 2.7 m and Ls is 0.0025 m, Serror is equal to 0.0012 mm according to Eq. (1). We drew the conclusion that the error from the spiral profiles can be ignored.
Serror =
R2 + Ls2 − R
(1)
Illustration of the second inherent error is shown in Fig. 3(b), which is the top view of the tunnel. The black lines on both sides indicate the inner wall of the tunnel and the blue dotted lines inside the tunnel indicate the rail tracks. Under normal conditions, the rail tracks are parallel to the tunnel in either a straight or turning area. However, position error of the trail tracks may occur in turning areas, leading to angle deviation between the rail tracks and the tunnel, eventually resulting in an error in the cross-section profiles. The angle deviation between the rail tracks and the tunnel can be work out using Eq. (2), where θ is the deviation angle, RT is the turning radius of the tunnel, and Ddev is the position error of the rail tracks in the tunnel. Suppose the position error of the rail tracks Ddev is 0.1 m. Since the position of the rail tracks is adjusted carefully, 0.1 m is a large deviation. According to the original design of the subway tunnel, its turning radius is RT 2000 m. The angle deviation θ between the real profile AB and optimal cross section CD in Fig. 3(b) is 0.57° under this condition. Then the error from rail track position error can be calculated using Eq. (3). In this equation, Perror is the error from rail tracks position error, rt is the radius of the tunnel, and θ is the deviation error calculated using Eq. (2). If the radius of the tunnel is 2.7 m, Perror will be 0.13 mm. Therefore, the inherent error from the position error of the rail track in tunnel turning areas can also be ignored.
Fig. 2. Hardware layout of the Railway Mobile Measurement System (RMMS).
control unit, and a power supply on a costumed trolley. Although there is an IMU and GPS antenna in this system, they are not used in the tunnel deformation detection process. The hardware layout of the RMMS is shown in Fig. 2. The laser scanner used in the RMMS is PROFILER 9012 from Z + F company. This laser scanner is a compact high-speed phase-based laser scanner with a 360° field of view. With its scan rate of more than 1 million points per second and maximum scan speed of 200 profiles/s, very short distances between profiles can be achieved even at high speed. Its accuracy is within 1 mm when the target distance is 25 m and its maximum range is 119 m. The reflectivity of the target can also be obtained during the scanning process. The trolley and mounting parts of the laser scanner are carefully designed to ensure that the pushing direction is parallel to the optical axis of the laser profiler. The odometer used in the RMMS is the Koyo TRD-2T/2TH incremental encoder with a maximum allowable speed of 5000 rpm. The distance can be worked out by the circumference of the wheel and number of pulses from the odometer. The control unit is in charge of control, time synchronization, and data storage for all the sensors, including the laser scanner, odometer, GPS antenna, and IMU. The trolley is suitable for railways or subways with a standard gauge of 1435 mm and it is quick and easy to assemble and disassemble. The trolley is a rigid structure to minimize change in its shape and it is pushed forward along the rail track manually. The calibration process was carried out on a section of rail track in the outdoors using a total station and several calibration boards.
RT ⎞ θ = arccos ⎛ ⎝ RT + Ddev ⎠
(2)
1 − 1⎞ Perror = rt ⎛ cos( θ) ⎝ ⎠
(3)
⎜
⎜
⎟
⎟
In this part, two types of inherent error, error from spiral profiles and error from position error of rail track in tunnel's turning area, were analyzed in detail. The maximum error of the former is 0.0012 mm and of the latter is 0.13 mm, both of which are much smaller than the distance resolution of the laser scanner. For this reason, these inherent errors can both be ignored. 3. Methodology The tunnel deformation detection system proposed in this study is based on mobile laser scanning technology. The cross-sections of the tunnel are obtained directly, and they go through a series of processes that include filtering, fitting, and locating. Next, the overall and local deformation results of the tunnel are calculated. The whole workflow of this study is shown in Fig. 4. First, a wavelet filtering algorithm to eliminate the point cloud of tunnel ancillary facilities in the cross-section points is proposed in Section 3.1. The ellipse fitting and result generation processes are presented in Section 3.2. Then, a cross section locating method based on the greyscale image generated by the tunnel point cloud is discussed in Section 3.3. Finally, a tunnel ring segments dislocation detection method is proposed in Section 3.4.
2.2. Error analysis Although profiles of the laser scanner can be seen as the approximate cross-section points of the tunnel after adjustment of mechanical structures, there is some inherent error. A detailed analysis of how the error occurs and how great the impact of the error will be is presented next. In general, there are two reasons for the inherent error: the spiral profiles and the position error of the rail tracks in the turning area of the tunnel. The illustration of the first error is shown in Fig. 3(a). EF indicates the trajectory of the laser scanner in the tunnel and O is a point on EF. The dotted spiral line is the top view of the laser profiles, segment CD is the diameter of the cross section measured by laser scanner, while segment GH is the actual diameter of the cross section. The error from the spiral is brought about by the distance error between CD and GH. This can be worked out using Eq. (1). In this equation, Serror is the error of the spiral profiles, R is the tunnel radius, and Ls is a quarter of the pitch of the spiral line. The laser scanner can obtain 200 profiles per second under working conditions and the operating speed of the system is two meters per second. Therefore, the pitch of the spiral line (segment AB in Fig. 3a) is 0.01 m; therefore, Ls (segment DH in this figure) is
3.1. Wavelet filtering algorithm for cross-section points The cross-section points generated by the laser scanner cannot be used directly because there are also many noise points from scanning tunnel ancillary facilities such as power lines or signal lines in the tunnel. Some researchers have attempted to filter out these noise points. Xie and Lu [8] filtered the point cloud of tunnel ancillary facilities by fitting a circle with the cross-section points, if the distance between the 3
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Fig. 3. Illustration of error analysis. (a) Error from spiral profiles; (b) Error from position error of rail track in tunnel turning area.
filters developed by Mallat [29]. The basic filter process is shown in Fig. 5. The input signal S is filtered through a pair of filters (one high pass and one low pass) and then down sampled to get a decomposed signal through each filter which is half the length of the input signal. The low frequency components are called approximation coefficients and the high frequency components are called detail coefficients. This is single-level signal decomposition, mathematically expressed as Eqs. (6) and (7), where X(n) is the original signal, h(n) and g(n) are the sample sequences or impulse responses, Yhp(k) and Ylp(k) are the outputs of the high-pass and low-pass filters, respectively, after subsampling by two.
cross-section points and fitting circle was larger than a certain threshold, these points were eliminated. Xu et al. [10] went further. He looped the fitting and eliminating processes until all the remaining points were within a certain threshold. The drawback of these methods is that, if there is deformation in the tunnel, the fitting circle may deviate from the cross-section points and normal cross-section points would be filtered. To overcome the drawback of previous methods and filter the crosssection points of the deformed tunnel, a cross-section points filtering algorithm based on discrete wavelet transform is proposed. The discrete wavelet function is given in Eq. (4), where a0 and b0 are constants, the scaling term is represented as a power of a0, and the translation term is a factor of a0m. Values of the parameters a0 and b0 are chosen as 2 and 1 respectively and is called as dyadic grid scaling. The dyadic grid wavelet is expressed in Eq. (5), where ψm, n(t) represents the wavelet coefficients at scale m and location n. This dyadic scaling scheme uses
ψm, n (t ) =
ψm, n (t ) =
1 a0m
(t − nb0 a0m ) a0m
m 1 (t − n2m) ψ = 2− 2 ψ (2−mt − n) 2m 2m
Fig. 4. Workflow chart of this study. 4
ψ∗
(4)
(5)
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Fig. 5. Block diagram of the filter analysis.
Fig. 6. Wavelet filtering algorithm for cross-section points. (a) Original cross-section points; (b) original cross-section points in polar coordinates; (c) the detail coefficient vector of (b); (d) threshold truncation process; (e) cross-section points in polar coordinates after threshold truncation; (f) (e) in Cartesian coordinates.
Yhp (k ) =
∑ X (n) g (2k − n) n
Ylp (k ) =
∑ X (n) h (2k − n) n
The proposed wavelet filtering algorithm can filter the point cloud of tunnel ancillary facilities effectively, regardless of the shape and deformation of the tunnel.
(6)
(7)
3.2. Ellipse fitting and deformation detection method
Detailed steps of the wavelet filtering algorithm are shown in Fig. 6. Fig. 6(a) is the upper part of a profile from the laser scanner, the lower part containing point cloud of rail tracks are discarded. As is seen from the point cloud, there is obvious deformation at the top of the tunnel. First, the original cross-section points are converted to polar coordinates, shown as Fig. 6(b). In this figure, the X-axis represents the ordinal number of the points, and the Y-axis is the distance between cross-section points and the center of the cross section. Then, single level discrete wavelet transform is applied to the cross-section points in polar coordinates, the detail coefficients vector of the input is shown in Fig. 6(c). As is shown in this figure, fluctuation of the Y value in Fig. 6(b) will lead to greater fluctuation in the detail coefficients vector. A threshold truncation process is carried out afterward. In Fig. 6(d), the red lines represent the thresholds, the value of upper one is 0.007 and that of lower one is −0.007. Cross-section points between the upper threshold truncation and adjacent lower threshold truncation are filtered. The filtering results in polar coordinates are shown in Fig. 6(e). Fig. 6(f) is the filtering result in Cartesian coordinates.
Many previous tunnel deformation detection methods based on point cloud had fitted the cross-section points to a circle and these methods were not rigorous enough. The original design of the cross section of subway tunnels is indeed a circle. Because subway tunnels come under huge uneven stress underground, as time goes by, the cross sections of subway tunnels become ellipses [1–3]. In this study, the cross-section points of the tunnel are fitted to an ellipse to get more comprehensive and detailed analysis of tunnel deformation. The length of the major axis of the fitted ellipse is related to the overall deformation of the tunnel. The longer the major axis is, the greater the overall deformation. The local deformation of the tunnel can be obtained by calculating the residual between the cross-section points and the fitted ellipse. To fit the cross section of the tunnel accurately, a stepwise ellipse fitting method is proposed. First, after wavelet filtering, the cross-section points are fitted to an ellipse following Taubin's [30] ellipse fitting method. Using the equation of the ellipse, its semi-major axis and semi5
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Fig. 7. Illustration of ellipse fitting and deformation detection method. (a) step-wise ellipse fitting; (b) deformation of the tunnel at different angles.
high-speed railways are located by mileage; therefore, multiple measurements can easily be aligned with the mileage of the cross-section points. However, facilities in subways are located by the number of rings on the inner wall of the tunnel. To locate the cross-section points of subway tunnels, rings on the inner wall should be identified and numbered. A cross-section locating method for subway tunnels is presented in this section. The laser scanner of the RMMS can obtain the reflectivity of the target, so, there is not only position information but also reflectivity information in the cross-section point cloud. First, the original laser profiles are converted to polar coordinates. Then a series of consecutive profiles are projected to a surface and generate a greyscale image based on the reflectivity of corresponding points. The generated greyscale image is shown in Fig. 8(a). We can see the seams of tunnel rings clearly in this image. To highlight the tunnel rings, the polar coordinate system starts and ends in the middle of the rail tracks. Therefore, rail tracks are located in the upper and lower parts of this image, as shown in the red frames. After that, the seams of the tunnel rings are identified by calculating the lateral gradient of the grayscale image. Finally, the tunnel rings are identified, numbered, and located based on their seams. The result is shown in Fig. 8(b), the red segments is the identified seams of tunnel rings and the number of rings is written on the tunnel rings. Through the cross-section locating process, accurate locations of the cross-section points in the subway tunnels can be obtained, and this ensures the alignment of the cross-section points from multiple measurements.
minor axis can be worked out using Eqs. (8)–(12). The equation of the ellipse indicated in Eq. (8). Xc in Eq. (9) and Yc in Eq. (10) represent x and y coordinate of the center of the ellipse respectively. The semimajor axis of the ellipse is represented as a in Eq. (11) and the semiminor axis as b in Eq. (12). Then, the residual between the cross-section points and the fitted ellipse is worked out, and the cross-section points with residual larger than 0.01 m are excluded. The rest of the crosssection points go through ellipse fitting and distance exclusion processes several times, until no point is excluded. The stepwise ellipse fitting method is shown in Fig. 7(a). In this figure, the red points indicate excluded points of which the residual from the fitting ellipse is larger than 0.01 m. The blue points are the fitting points of the ellipse and the green ring is part of the fitting ellipse. For this ellipse, the major axis is 5.5704 m and the minor axis is 5.3356 m. The original design of the tunnel was a circle with radius of 2.7 m and the major axis of this elliptical cross section is 0.1704 m longer than original design.
Ax 2 + Bxy + Cy 2 + Dx + Ey + 1 = 0
Xc =
Yc = a2 =
b2 =
BE − 2CD 4AC − B2
(8) (9)
BD − 2AE 4AC − B2
(10)
2(AXc2 + CYc2 + BXc Yc − 1) A+C+
(A − C )2 + B2
(11)
2(AXc2 + CYc2 + BXc Yc − 1) A+C−
(A − C )2 + B2
(12)
3.4. Tunnel ring segments dislocation detection method
After the ellipse fitting process, local deformation of the tunnel is worked out as well. To acquire accurate local deformation, auxiliary lines that start from the center of the ellipse are plotted. The deformation value is equal to the distance between the point nearest to the auxiliary line and the ellipse. Local deformations of the tunnel at different angles are shown in Fig. 7(b). Here, deformation is calculated from −10° to 190° every 10° clockwise. The red segments are auxiliary lines, and the deformation value and angle of auxiliary lines are labeled nearby. We can see from Fig. 7(b) that the top of the tunnel surface exhibits local deformation as much as 0.17 m in this section.
In fact, a tunnel ring is not a single component, it is riveted by serval precast concrete segments. The horizontal or oblique dark seems in the middle of tunnel rings in Fig. 8 are seams of precast concrete segments and the dark dots in this figure are holes of bolts that fit them together. Dislocation of the precast concrete segments may happen, which will have negative effect on the load-bearing structures of the tunnel, threating its safety. To detect dislocation of the precast concrete segments, it necessary to segment the tunnel rings and extract point cloud of the precast concrete segments. In the above section, tunnel ring seams are identified in greyscale image easily since they are vertical lines. However, the seams of precast concrete segments are difficult to identify in grayscale image since interference caused by the cables. Instead of identifying the seams directly, we propose an indirect method to identify them by detecting bolt holes.
3.3. Cross section locating method for subway shield tunnels Cross-section points can be located by adding the mileage of the starting point and that of the odometer. In an actual scene, facilities on 6
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Fig. 8. Greyscale image generated by reflectivity of tunnel's point cloud. (a) original greyscale image; (b) greyscale image after tunnel ring seam identification.
Fig. 9. Tunnel ring segments seams detection method. (a) Tunnel ring with oblique seams, (b) Tunnel ring with vertical seams. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
location of seams can be obtained as well. The bolt holes are not difficult to locate since their relative position with tunnel ring seams is fixed. Template matching method is used to locate precast concrete segments bolt holes and Fig. 9 show the results. Some bolt holes are obscured by ancillary facilities (such as wires and pipes) mounted on the ring, making them hard to detect. Because the distance between seams and bolt holes is a fixed value, the seams can still be located even though no paired bolt holes are found, as it shows in left part of Fig. 9(a). After seams of precast concrete segments are located, the dislocation between consecutive segments can easily detected by comparing the radial coordinate of points on both sides of the seams in polar coordinate.
Since the seams between tunnel rings are identified in Section 3.3, we divide the tunnel's point cloud into different rings and process them in turn. First, pick out the middle frame of cross-section points in a tunnel ring, processed them with wavelet filtering process in Section 3.1 and ellipse fitting process in Section 3.2. Next, set the midpoint of fitting ellipse as zeros point and convert the cross-section points of tunnel rings into polar coordinate system (The vertical downward direction is set as the polar axis). Then the cross-section points are converted into Euclidean coordinate system, with the position of crosssection in rail track direction as X coordinate, the angular coordinate of cross-section points in polar coordinate system multiply subway tunnel's standard diameter (2.75 m) as Y coordinate and the radial coordinate of cross-section points in polar coordinate as Z coordinate. Fig. 9(a), (b) shows the converted point cloud of two tunnel rings, the reflection intensity is also showed in the point cloud. There are two types of bolts in the tunnel rings, one type is used to riveted consecutive tunnel rings together (marked as yellow and green rectangle in Fig. 9), another type is used to riveted precast concrete segments together (marked as red and blue rectangles in Fig. 9). The segments seams are in the middle of a pair of bolts, if we detect the location of bolt holes, the
4. Experiment and results 4.1. Data acquisition The experiment was conducted in a subway tunnel in Wuhan, China. This subway line has been operating safely for six years. The 7
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become more like an ellipse rather than its original circular shape. The ellipse fitting of the cross sections is built on this conception, and we can prove it with the measured cross-section points from RMMS. The cross-section points of forward measurement of RMMS in Fig. 11(b) were selected, the lower part containing rail tracks and ground was removed, then the upper part was subjected to the wavelet filtering algorithm. The remaining part after wavelet filtering went through Taubin's [30] ellipse fitting method and least-square circle fitting method respectively. Absolute value of the residual between fitting ellipse (or circle) and each point was worked out. Their box plot is shown in Fig. 12. This figure is made up of 10 box plots corresponding to the selected cross sections and the ring numbers are listed under each box plot. The residual of ellipse fitting is in the left side of each box plot and the other side is the residual of circle fitting. The unit of ordinates is meters. The blue rectangle in each box plot stands for lower quartile to upper quartile of the residual and the red segment in the rectangle stand for median of residual. Black segments connected to the blue rectangle by dotted lines are lower and upper adjacent. Red cross above the blue rectangle is outlier value. We can see from Fig. 12 that the absolute value of ellipse fitting residual is less than that of circle fitting. So, we can draw a conclusion that the deformed subway shield tunnel is more like an ellipse.
inner wall of the tunnel is supported by rings and the original design of the tunnel is a 2.7 m radius circle. First, the RMMS was pushed back and forth for 200 m from the starting point. Then, cross-section points of the tunnel were measured using a total station to verify the accuracy of the deformation detection system. To select cross section points at the same location, the total station measured cross-sections in the middle of the inner wall rings. Finally, cross-sections of 10 consecutive rings were measured by total station and there were 20 points in each cross-section. The RMMS data were exported and processed afterward, and 2.4 billion points of the tunnel are obtained by this system. The scanning speed of the laser profiler was 200 rounds per second and the pushing speed of the trolley system was about 1 m/s. The distance between two adjacent cross-section points was about 5 mm and there were about 6000 points in a single frame. The operation of the RMMS, including installation and scanning, took about 16 min to complete. In the end, 396,762 cross-section profiles were obtained. However, it took the total station scanner 10 min to measure each cross section of the tunnel. The efficiency of the RMMS was significantly higher than that of total station, even disregarding the high density of point cloud in each cross section. Fig. 10(a) shows the data acquisition process by the RMMS. Fig. 10(b) is the three-dimensional cross-section point cloud of the tunnel acquired by the RMMS. The cross-sections that total station measured located at the middle of the tunnel rings and the measured points were all specially selected on the inner wall to avoid the interference of tunnel ancillary facilities. In each cross section, 20 points were measured by the total station. The seams of the tunnel rings were identified accurately by the method explained in Section 3.3, and the middle of a tunnel ring could be located easily. The cross section closest to the middle of a tunnel ring was considered the cross section in the middle. Because the distance between two adjacent cross-section points measured by the RMMS was only about 5 mm, the mileage error between cross-section points done by total station and those by the RMMS can be ignored. Fig. 11 shows cross-section points from the total station and from the RMMS. Fig. 11(a) shows the cross-section points measured by total station. Fig. 11(b) shows the corresponding cross-section points by forward measurement of the RMMS, and Fig. 11(c) shows the corresponding cross-section points by reverse measurement of the RMMS. The distance between two adjacent cross-sections was equal to the width of tunnel rings, which is 1.5 m.
4.3. Accuracy verification 4.3.1. Accuracy verification of the tunnel detection system by total station The cross-section points of the total station are fitted into ellipses by the method explained in Section 3.2. For the cross-section points of RMMS, the lower part containing rail tracks and ground was removed, then the remaining part was subjected to the wavelet filtering algorithm explained in Section 3.1 and fitted to an ellipse following the method in Section 3.2. The length of the semi-major axis of the fitting ellipse worked as an indicator verifying the accuracy of the RMMS. Length and deviation of the semi-major axis of the fitting ellipse from the total station and RMMS were calculated in each verifying ring, as shown in Table 1. The results of forward and reverse measurements of the RMMS were both verified by those from the total station. The deviation between the forward and reverse measurements of RMMS varied from −1.3 to 2.4 mm, and the Mean Absolute Deviation (MAD) between semi-major axis of the fitting ellipse from cross-section points by RMMS and total station was 1.2 mm for forward measurement and 1.5 mm for reverse measurement. Meanwhile, the accuracy requirement for subway tunnel deformation detection is ± 3 mm according to the “Standard for monitoring and measurement of urban rail transit
4.2. Residual comparison between ellipse and circle fitting We conceived that cross section of shield subway tunnels will
Fig. 10. Data acquisition process. (a) Data acquisition by RMMS; (b) point cloud measured by RMMS. 8
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Fig. 11. Cross-section points from total station and RMMS (different color stand for acquisition sequence of cross sections). (a) Cross-section points from total station; (b) Corresponding cross-section points by forward measurement of RMMS; (c) Corresponding cross-section points by reverse measurement of RMMS.
Fig. 12. Box plot of absolute value of the residual between ellipse (circle) fitting and cross section points from RMMS. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
structure”, which means that RMMS can completely fulfill the accuracy requirement of subway tunnels detection.
Table 1 Length and deviation of semi-major axis of the fitting ellipse from cross-section points obtained by total station and RMMS. Ring number
795 796 797 798 799 800 801 802 803 804
Total station (mm) 2737.2 2736.9 2738.8 2737.5 2738.6 2739.3 2738.9 2737.6 2738.4 2737.8
Forward (mm)
2735.9 2736.2 2739.5 2738.6 2736.7 2737.7 2737.2 2737.5 2736.9 2738.7
Reverse (mm)
2735.6 2736.1 2740.1 2738.3 2736.2 2737 2737.4 2738.5 2736.8 2739.1
Deviation of forward (mm)
Deviation of reverse (mm)
1.3 0.7 −0.7 −1.1 1.9 1.6 1.7 0.1 1.5 −0.9
1.6 0.8 −1.3 −0.8 2.4 2.3 1.5 −0.9 1.6 −1.3
4.3.2. Repeatability verification of overall and local deformation detection by RMMS itself The repeatability of the RMMS was verified by comparing the deformation results from forward and reverse measurement of consecutive tunnel rings. Both overall and local deformation results were verified. Fig. 13 shows the deviation between semi-major axis measured by RMMS in a round trip and the original design of the tunnel. The original design radius of the tunnel is 2.7 m; therefore, both the result of forward and reverse measurement by the RMMS were subtracted by the radius. As shown in this figure, the deviation between the forward and reverse measurement varied from −0.7 to 1 mm, and the mean absolute deviation and standard deviation between these two measurements 9
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Fig. 13. Comparison of deviation between semi-major axis measured by RMMS in a round trip and the original design of the tunnel.
Fig. 14. Local deformation measured by RMMS in forward and reverse measurement at different angles. (a) Local deformation at 60°; (b) local deformation at 80°; (c) local deformation at 100°; (d) local deformation at 120°.
mapping systems, like system that mounted on a (rail) car [22,23], RMMS is mounted on a costumed trolley, making it easier to be used in subway tunnels. Some existing tunnel mapping systems were also mounted on a trolley [24–28], but the trolley that RMMS used is a special designed quick disassembly structure and RMMS can operated normally without IMU or GPS. However, many aspects of this system could be improved. First, the RMMS was originally designed to conduct absolute position measurement in railways or subways, a task for which an IMU and a GPS antenna are essential. But for subway tunnel deformation detection, relative position analysis is a simpler way to fulfill the demand and there is no need to generate absolute point cloud of the tunnel. Removing the IMU and GPS antenna will make the system smaller, lighter, and most importantly, cheaper. This will expand the application of the RMMS in subway tunnel deformation detection. Furthermore, only the relative position of a subway tunnel is obtained by the RMMS in this paper; however, this system can acquire the absolute position of railway and subway tunnels with pre-arranged targets. Tunnel alignment detection can be done with its absolute point cloud; therefore, we will focus on the generation of the absolute point cloud of railway and subway tunnels in the future. Tunnel ring segments seams are detected indirectly in this work, but some of the seams are not detected successfully, since their bolt holes are completely or partial obscured by ancillary facilities mounted on the ring. We will focus on overcome this challenge by other method like combining three-dimensional shape and reflection intensity of tunnel rings, or deep learning technic. The laser scanner of the RMMS can acquire reflectivity of the target, if there are cracks or water leakage areas in the inner wall of the tunnel, the reflectivity of the point cloud in these areas will become significantly lower than in surrounding
was 0.42 and 0.53 mm, respectively. The RMMS showed high repeatability in overall deformation measurement. The local deformation detection results of the RMMS were also verified by comparing the deformation of the tunnel at several different angles. As mentioned in Section 3.2, local deformation is the residual between the nearest point to the auxiliary line of a certain angle and the fitting ellipse. The local deformation was calculated at 60°, 80°, 100°, and 120° of the forward and reverse measurement. Fig. 14 shows the local deformation measured by the RMMS in forward and reverse measurements at these angles. From this figure, we can see that the biggest standard deviation between forward and reverse measurements of the local deformation was 0.94 mm at 80°. This proves that the RMMS has high repeatability for local deformation measurement. 4.4. Verification of tunnel ring segments seams detection method The tunnel ring segments seams detection method is verified by processing point cloud of several continuous tunnel rings. The result is shown in Fig. 15, as is shown in this figure, some segments bolt holes are obscured by wires or pipes mounted on the ring, making it fails to locate the seams, as is shown in yellow rectangles. Besides these two parts, most segments bolt holes have been detected and the seams are located, lay a solid foundation for tunnel ring segments dislocation detection. 5. Discussion and future work The RMMS can achieve high accuracy and repeatability in subway tunnel deformation detection. Compared to other existing tunnel 10
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Fig. 15. Tunnel ring segments seams detection result.
Declaration of Competing Interest
areas. Thus, obvious dark patterns could be found in the greyscale image generated by reflectivity of the point cloud. Later, we will study the identification of cracks and water leakage based on the greyscale image of the railway tunnels. Finally, the RMMS system is now only suited for railways or subways with 1435 mm gauge tracks and must be pushed manually. In the future, we will develop an electric trolley that can run automatically in tunnels whether there are rail tracks there or not.
The authors declare no conflict of interest. Acknowledgments Work described in this paper was jointly supported by the Fundamental Research Funds for the Central Universities under Grant No. 2042017kf0235, National Key Research Program Grant No. 2016YFF0103502, and State Key Laboratory of Rail Transit Engineering Informatization (FSDI) Open Project Funding No. SKLK16-03.
6. Conclusions
References
A rigorous and efficient tunnel deformation detection system based on mobile laser scanning is presented in this paper. This tunnel deformation detection system integrates a high-precision two-dimensional laser profiler, an odometer, and a costumed trolley. While operating, the system is pushed forward manually on the rail track while the cross section of the tunnel is obtained simultaneously. Detailed analysis is performed to prove that profiles from the laser scanner can be seen as cross-sections of the tunnel and that the corresponding error can be ignored. A wavelet filtering algorithm is developed to eliminate the point cloud of tunnel ancillary facilities in the cross-section points. After that, the cross-section points are fitted to an ellipse. Then the fitting result is compared with the original design of the tunnel and the overall and local deformation result is obtained. To acquire the relative position of the cross section precisely, the point cloud of the tunnel is converted to a grayscale picture in which the grayscale values is determined by the reflectivity of the point cloud. The seams of the tunnel's inner wall rings are identified in the grayscale image and the rings are numbered to locate the cross section. Tunnel ring seams are detected indirectly by locating the bolt holes to detect tunnel ring segments dislocation. An experiment was carried out in a subway tunnel in Wuhan to verify the accuracy of the system. The system was pushed forward and forth for 200 m in this tunnel. Ten cross-sections of consecutive tunnel rings were measured using a total station and the corresponding crosssections measured by the RMMS were picked out for comparison. A residual comparison between ellipse and circle fitting of RMMS cross section points showed that ellipse is closer to the actual shape of deformed shield subway tunnel. The repeatability accuracy of overall and local deformation detection was also verified by comparing the deformation results of the cross-sections measured during this round trip. The tunnel ring segments seams detection method was verified by processing point cloud of several continuous tunnel rings. Finally, the accuracy of the cross-section measurement reached 1.5 mm, and the repeatability of the overall and local deformation measurements were 0.5 and 0.9 mm, respectively. This system exceeds the accuracy required for subway tunnel deformation detection and its efficiency is significantly higher than total station.
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Contents lists available at ScienceDirect
Automation in Construction journal homepage: www.elsevier.com/locate/autcon
Shield subway tunnel deformation detection based on mobile laser scanning a
b
Hao Cui , Xiaochun Ren , Qingzhou Mao a b
a,b,⁎
a
T
b
, Qingwu Hu , Wei Wang
School of Remote Sensing & Information Engineering, Wuhan University, Wuhan 430079, China State Key Laboratory of Rail Transit Engineering Informatization (FSDI), Xian 710043, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mobile laser scanning Shield subway tunnel Deformation detection Cross section Wavelet filtering Ellipse fitting
Shield subway tunnels are critical urban infrastructure and precise, rapid deformation detection method is required for the maintenance of these tunnels. A tunnel deformation detection system called Railway Mobile Measurement System (RMMS) was developed based on mobile laser scanning technique. Herein, detailed analysis is given to prove that profiles from the laser scanner can be seen as cross-sections of the tunnel and that the corresponding error can be ignored. A wavelet filtering algorithm was developed to filter the point cloud of tunnel ancillary facilities in the cross-section points. A subsequent ellipse fitting and deformation detection method is proposed. A cross-section location method for subway tunnels is also presented based on the greyscale image converted from the tunnel's point cloud. A tunnel ring segments seams detection method is proposed to detect tunnel ring segments dislocation. The accuracy of the system was verified in a subway tunnel in Wuhan, China with a total station. The accuracy of cross-section measurement was 1.5 mm, the repeatability of the overall and local deformation measurement was 0.5 and 0.9 mm, respectively. This system completely fulfils the accuracy requirement of railway tunnels deformation detection and its efficiency is significantly higher than that of the traditional method.
1. Introduction With the rapid development of infrastructure, an increasing number of subways have been built in China in the recent years. Most subways are constructed underground in tunnels excavated by shield tunneling machines. After excavation, these tunnels are mounted with precast concrete segments. The shape of newly built shield tunnels is circle, whereas these shield tunnels withstand huge stress from the earth, as time goes by, deformation of the tunnels will occur [1–3]. Severe deformation of subway tunnels will seriously threaten the operation of subways, so the deformation should be detected in the early stage and appropriate measures should be taken to prevent the deformation from getting worse. Fig. 1 shows an actual scene in a shield subway tunnel. There are many wires, pipes, and bolt holes on the inner wall of the tunnel, which interfere significantly with the detection of tunnel deformation. Moreover, subway tunnels are usually in operation all day long, and only a short skylight time in the early morning is spared for maintenance. Therefore, there are quite a few challenges in tunnel deformation detection and the method should be robust, accurate, and efficient. At present, tunnel deformation detection is mainly conducted using total stations or terrestrial laser scanners [4–7]. To detect tunnel deformation with a total station, some pre-set targets or points in the same ⁎
cross section of the tunnel are measured. The cross-section points are fitted to a circle and compared with the original design of the tunnel to detect deformation. The accuracy of total station is very high, but the low measurement speed limits overall efficiency and the number of cross-section points that can be measured. The insufficiency of crosssection points will have a negative effect on detecting deformation of the tunnel in small area. Terrestrial laser scanner provides accurate three-dimensional point cloud of the inner wall of a tunnel. The point cloud is very dense, and the scanning process takes only a few minutes. However, the point cloud will get sparse in faraway areas due to the incident angle. Therefore, multiple stations are needed to scan a long tunnel and all the stations must be registered together. Then the cross section of the tunnel must be extracted using algorithms. The following steps are just the same as those in the total station method. The whole deformation detection process with a terrestrial laser scanner is time consuming because multiple stations are scanned, and the computation cost of the massive point cloud is high. Many researchers have proposed different tunnel deformation detection methods based on point cloud. The key point of these methods is the extraction of cross-section points of the tunnel. The goal of their cross-section extraction algorithms is to make the cross-section orthogonal to the tunnel and they have tried different ways to achieve this. Xie and Lu [8] and Nuttens et al. [9] segmented the point cloud of a
Corresponding author at: School of Remote Sensing & Information Engineering, Wuhan University, Wuhan 430079, China. E-mail address: [email protected] (Q. Mao).
https://doi.org/10.1016/j.autcon.2019.102889 Received 23 September 2018; Received in revised form 12 May 2019; Accepted 20 June 2019 0926-5805/ © 2019 Elsevier B.V. All rights reserved.
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mobile laser scanning system cannot run at this high speed, the accuracy of the point cloud will drop dramatically. Some researchers have obtained tunnel cross-section points directly based on a mobile laser scanning system mounted on a custom trolley, to avoid the complicated processes of three-dimensional point cloud generation and cross-section points extraction. The company Amberg developed the GPR5000 clearance inspection trolley [24], which is equipped with a laser scanner, odometer, displacement sensor, and clinometer sensor. Their system can obtain a two-dimensional clearance map and cross section of the tunnel. Moreover, the Lecia company developed the SiTrack One mobile track scanning system [25] in which are integrated a Lecia P40 laser scanner, odometer, and high-end inertial measurement unit (IMU). This system can obtain point cloud of a tunnel with relative accuracy of 3–5 mm. High-end IMUs are used to obtain accurate position and posture. This leads to high cost and limits their wide application. Tan et al. [26,27] built a mobile laser scanning system for subway tunnels on an electronic trolley with a two-dimensional laser profiler and an odometer. The system can obtain the cross section of a tunnel directly and he proposed an algorithm that eliminates the point cloud of tunnel ancillary facilities in the tunnel. However, he did no further research on tunnel cross-sections. Du et al. [28] developed a mobile tunnel monitoring system called TS1, comprising a laser scanner, two odometers, a displacement sensor, and a custom trolley. Cross-section points of the tunnel were obtained directly; then, they were resampled, fitted to a circle, and compared with the original design of the tunnel. The result of tunnel deformation detection was verified using a total station. His method ignored the point cloud of tunnel ancillary facilities, and this has a negative effect on the accuracy. The original shape of subway tunnels excavated by shield tunneling machines is circular and the precast concrete segments are precisely mounted on the tunnels, so we can consider the cross section of newly built shield subway tunnels is a circle. Due to the effect of huge uneven underground stress, these tunnels will suffer from deformation and we conceive their cross sections will turn into an ellipse. In this case, the cross section of shield subway tunnels should be fit to an ellipse. Our experiment stands for this hypothesis. In this paper, a rigorous and efficient tunnel deformation detection system based on mobile laser scanning is presented. This tunnel deformation detection system consists of a high-precision two-dimensional laser profiler, an odometer, and a special-made trolley. The trolley is pushed forward manually on the rail track and is specially made to ensure that its pushing direction is parallel to the optical axis of the laser profiler. The cross section of the tunnel is obtained while the trolley is being pushed forward. Detailed analysis is given to prove that the cross-sections are orthogonal to the tunnel no matter whether the tunnel is straight or curved, and that the corresponding error can be ignored. A wavelet filtering algorithm is developed to eliminate the point cloud of tunnel ancillary facilities in the cross-section points. The filtered cross-section points are fitted to an ellipse. Then the fitting result is compared with the original design of the tunnel, after which the overall and local deformation result is obtained. To acquire the relative position of the cross section precisely, the point cloud of the tunnel is converted to a grayscale picture of which the grayscale value is determined by the reflectivity of the point cloud. The seams of the tunnel's inner wall ring are identified in the grayscale picture to locate the cross section. The accuracy of the system was verified in a subway tunnel using a total station and the rationality of ellipse fitting was verified as well.
Fig. 1. Actual scene of a shield subway tunnel.
tunnel into small segmentations and took the axis of the best fit cylinder to the segmentation as the tunnel axis. Then, they got the cross-section of the tunnel based on the cylinder axis. However, this method is not accurate enough for curved tunnels. Xu et al. [10] and Kang et al. [11] projected the point cloud of a tunnel to a horizontal plane and extracted the boundaries of the projected point cloud. The cross section was obtained by making a cutting plane vertical to the boundaries and projecting nearby points to the cutting plane. Puente et al. [12] proposed a cross-section extraction algorithm that calculated the normal vectors of the tunnel point cloud. The tunnel axis was determined by the normal vectors and the cutting plane was perpendicular to the tunnel axis. Pejić [13] use the vertical and horizontal positions of the rails alignment to get the cross section of railway tunnels point cloud. Since the noise of laser scanner on rail surface is very high, the rail positions are surveyed by total station and fitted to the designed elements of the rail alignment. This is an accurate and practical way to get the cross section of railway tunnels but surveying the rail position with total station is time consuming. Qiu and Cheng [14] generated a high-resolution digital elevation model (DEM) of a railway tunnel from terrestrial laser scanning data. The theoretical surface of a curved tunnel was reshaped into a developable surface and the cross section was defined on this surface. After the cross-section points of the tunnel were extracted, the next steps were very similar: these points were fitted to a circle or ellipse model and compared with the original design of the tunnel to find deformation. Although these researchers have spared no effort to make the cross-section orthogonal to the tunnel, error will inevitably accumulate with complicated calculation processes. Not to mention the heavy computational cost required by cross-section extraction. Compared to terrestrial laser scanning system, the mobile laser scanning system is more efficient and easier to deploy. A typical mobile laser scanning system consists of an inertial measurement unit (IMU), global positioning system (DGPS) antenna, an odometer, and one or more laser scanners [15–17]. Mobile laser scanning system has been widely used in three-dimensional point cloud acquisition in open spaces [18–21]. Some researchers have broadened the application of mobile laser scanning system to tunnel mapping. Puente et al. [22] obtained three-dimensional point cloud of a 2.5 km-long road tunnel in Spain using a mobile laser scanning system; then he proposed an algorithm to detect tunnel luminaires automatically. Arastounia [23] acquired point cloud of a 155 m-long subway tunnel using a mobile laser scanning system mounted on a rail car. He extracted the tunnel's main axis and cross sections; then created a preliminary model by fitting an ellipse to each extracted cross section. In these two cases, the mobile laser scanning systems run above 60 km/h to minimize the impact of GPS outage and to shorten the outage time. If the tunnel is too long or the
2. Materials 2.1. System integration The tunnel deformation detection system in this paper is called the Railway Mobile Measurement System (RMMS). RMMS integrates a twodimensional laser scanner, an odometer, a GPS antenna, an IMU, a 2
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0.0025 m long. Normally, the radius of a subway tunnel is 2.7 m. When R is 2.7 m and Ls is 0.0025 m, Serror is equal to 0.0012 mm according to Eq. (1). We drew the conclusion that the error from the spiral profiles can be ignored.
Serror =
R2 + Ls2 − R
(1)
Illustration of the second inherent error is shown in Fig. 3(b), which is the top view of the tunnel. The black lines on both sides indicate the inner wall of the tunnel and the blue dotted lines inside the tunnel indicate the rail tracks. Under normal conditions, the rail tracks are parallel to the tunnel in either a straight or turning area. However, position error of the trail tracks may occur in turning areas, leading to angle deviation between the rail tracks and the tunnel, eventually resulting in an error in the cross-section profiles. The angle deviation between the rail tracks and the tunnel can be work out using Eq. (2), where θ is the deviation angle, RT is the turning radius of the tunnel, and Ddev is the position error of the rail tracks in the tunnel. Suppose the position error of the rail tracks Ddev is 0.1 m. Since the position of the rail tracks is adjusted carefully, 0.1 m is a large deviation. According to the original design of the subway tunnel, its turning radius is RT 2000 m. The angle deviation θ between the real profile AB and optimal cross section CD in Fig. 3(b) is 0.57° under this condition. Then the error from rail track position error can be calculated using Eq. (3). In this equation, Perror is the error from rail tracks position error, rt is the radius of the tunnel, and θ is the deviation error calculated using Eq. (2). If the radius of the tunnel is 2.7 m, Perror will be 0.13 mm. Therefore, the inherent error from the position error of the rail track in tunnel turning areas can also be ignored.
Fig. 2. Hardware layout of the Railway Mobile Measurement System (RMMS).
control unit, and a power supply on a costumed trolley. Although there is an IMU and GPS antenna in this system, they are not used in the tunnel deformation detection process. The hardware layout of the RMMS is shown in Fig. 2. The laser scanner used in the RMMS is PROFILER 9012 from Z + F company. This laser scanner is a compact high-speed phase-based laser scanner with a 360° field of view. With its scan rate of more than 1 million points per second and maximum scan speed of 200 profiles/s, very short distances between profiles can be achieved even at high speed. Its accuracy is within 1 mm when the target distance is 25 m and its maximum range is 119 m. The reflectivity of the target can also be obtained during the scanning process. The trolley and mounting parts of the laser scanner are carefully designed to ensure that the pushing direction is parallel to the optical axis of the laser profiler. The odometer used in the RMMS is the Koyo TRD-2T/2TH incremental encoder with a maximum allowable speed of 5000 rpm. The distance can be worked out by the circumference of the wheel and number of pulses from the odometer. The control unit is in charge of control, time synchronization, and data storage for all the sensors, including the laser scanner, odometer, GPS antenna, and IMU. The trolley is suitable for railways or subways with a standard gauge of 1435 mm and it is quick and easy to assemble and disassemble. The trolley is a rigid structure to minimize change in its shape and it is pushed forward along the rail track manually. The calibration process was carried out on a section of rail track in the outdoors using a total station and several calibration boards.
RT ⎞ θ = arccos ⎛ ⎝ RT + Ddev ⎠
(2)
1 − 1⎞ Perror = rt ⎛ cos( θ) ⎝ ⎠
(3)
⎜
⎜
⎟
⎟
In this part, two types of inherent error, error from spiral profiles and error from position error of rail track in tunnel's turning area, were analyzed in detail. The maximum error of the former is 0.0012 mm and of the latter is 0.13 mm, both of which are much smaller than the distance resolution of the laser scanner. For this reason, these inherent errors can both be ignored. 3. Methodology The tunnel deformation detection system proposed in this study is based on mobile laser scanning technology. The cross-sections of the tunnel are obtained directly, and they go through a series of processes that include filtering, fitting, and locating. Next, the overall and local deformation results of the tunnel are calculated. The whole workflow of this study is shown in Fig. 4. First, a wavelet filtering algorithm to eliminate the point cloud of tunnel ancillary facilities in the cross-section points is proposed in Section 3.1. The ellipse fitting and result generation processes are presented in Section 3.2. Then, a cross section locating method based on the greyscale image generated by the tunnel point cloud is discussed in Section 3.3. Finally, a tunnel ring segments dislocation detection method is proposed in Section 3.4.
2.2. Error analysis Although profiles of the laser scanner can be seen as the approximate cross-section points of the tunnel after adjustment of mechanical structures, there is some inherent error. A detailed analysis of how the error occurs and how great the impact of the error will be is presented next. In general, there are two reasons for the inherent error: the spiral profiles and the position error of the rail tracks in the turning area of the tunnel. The illustration of the first error is shown in Fig. 3(a). EF indicates the trajectory of the laser scanner in the tunnel and O is a point on EF. The dotted spiral line is the top view of the laser profiles, segment CD is the diameter of the cross section measured by laser scanner, while segment GH is the actual diameter of the cross section. The error from the spiral is brought about by the distance error between CD and GH. This can be worked out using Eq. (1). In this equation, Serror is the error of the spiral profiles, R is the tunnel radius, and Ls is a quarter of the pitch of the spiral line. The laser scanner can obtain 200 profiles per second under working conditions and the operating speed of the system is two meters per second. Therefore, the pitch of the spiral line (segment AB in Fig. 3a) is 0.01 m; therefore, Ls (segment DH in this figure) is
3.1. Wavelet filtering algorithm for cross-section points The cross-section points generated by the laser scanner cannot be used directly because there are also many noise points from scanning tunnel ancillary facilities such as power lines or signal lines in the tunnel. Some researchers have attempted to filter out these noise points. Xie and Lu [8] filtered the point cloud of tunnel ancillary facilities by fitting a circle with the cross-section points, if the distance between the 3
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Fig. 3. Illustration of error analysis. (a) Error from spiral profiles; (b) Error from position error of rail track in tunnel turning area.
filters developed by Mallat [29]. The basic filter process is shown in Fig. 5. The input signal S is filtered through a pair of filters (one high pass and one low pass) and then down sampled to get a decomposed signal through each filter which is half the length of the input signal. The low frequency components are called approximation coefficients and the high frequency components are called detail coefficients. This is single-level signal decomposition, mathematically expressed as Eqs. (6) and (7), where X(n) is the original signal, h(n) and g(n) are the sample sequences or impulse responses, Yhp(k) and Ylp(k) are the outputs of the high-pass and low-pass filters, respectively, after subsampling by two.
cross-section points and fitting circle was larger than a certain threshold, these points were eliminated. Xu et al. [10] went further. He looped the fitting and eliminating processes until all the remaining points were within a certain threshold. The drawback of these methods is that, if there is deformation in the tunnel, the fitting circle may deviate from the cross-section points and normal cross-section points would be filtered. To overcome the drawback of previous methods and filter the crosssection points of the deformed tunnel, a cross-section points filtering algorithm based on discrete wavelet transform is proposed. The discrete wavelet function is given in Eq. (4), where a0 and b0 are constants, the scaling term is represented as a power of a0, and the translation term is a factor of a0m. Values of the parameters a0 and b0 are chosen as 2 and 1 respectively and is called as dyadic grid scaling. The dyadic grid wavelet is expressed in Eq. (5), where ψm, n(t) represents the wavelet coefficients at scale m and location n. This dyadic scaling scheme uses
ψm, n (t ) =
ψm, n (t ) =
1 a0m
(t − nb0 a0m ) a0m
m 1 (t − n2m) ψ = 2− 2 ψ (2−mt − n) 2m 2m
Fig. 4. Workflow chart of this study. 4
ψ∗
(4)
(5)
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Fig. 5. Block diagram of the filter analysis.
Fig. 6. Wavelet filtering algorithm for cross-section points. (a) Original cross-section points; (b) original cross-section points in polar coordinates; (c) the detail coefficient vector of (b); (d) threshold truncation process; (e) cross-section points in polar coordinates after threshold truncation; (f) (e) in Cartesian coordinates.
Yhp (k ) =
∑ X (n) g (2k − n) n
Ylp (k ) =
∑ X (n) h (2k − n) n
The proposed wavelet filtering algorithm can filter the point cloud of tunnel ancillary facilities effectively, regardless of the shape and deformation of the tunnel.
(6)
(7)
3.2. Ellipse fitting and deformation detection method
Detailed steps of the wavelet filtering algorithm are shown in Fig. 6. Fig. 6(a) is the upper part of a profile from the laser scanner, the lower part containing point cloud of rail tracks are discarded. As is seen from the point cloud, there is obvious deformation at the top of the tunnel. First, the original cross-section points are converted to polar coordinates, shown as Fig. 6(b). In this figure, the X-axis represents the ordinal number of the points, and the Y-axis is the distance between cross-section points and the center of the cross section. Then, single level discrete wavelet transform is applied to the cross-section points in polar coordinates, the detail coefficients vector of the input is shown in Fig. 6(c). As is shown in this figure, fluctuation of the Y value in Fig. 6(b) will lead to greater fluctuation in the detail coefficients vector. A threshold truncation process is carried out afterward. In Fig. 6(d), the red lines represent the thresholds, the value of upper one is 0.007 and that of lower one is −0.007. Cross-section points between the upper threshold truncation and adjacent lower threshold truncation are filtered. The filtering results in polar coordinates are shown in Fig. 6(e). Fig. 6(f) is the filtering result in Cartesian coordinates.
Many previous tunnel deformation detection methods based on point cloud had fitted the cross-section points to a circle and these methods were not rigorous enough. The original design of the cross section of subway tunnels is indeed a circle. Because subway tunnels come under huge uneven stress underground, as time goes by, the cross sections of subway tunnels become ellipses [1–3]. In this study, the cross-section points of the tunnel are fitted to an ellipse to get more comprehensive and detailed analysis of tunnel deformation. The length of the major axis of the fitted ellipse is related to the overall deformation of the tunnel. The longer the major axis is, the greater the overall deformation. The local deformation of the tunnel can be obtained by calculating the residual between the cross-section points and the fitted ellipse. To fit the cross section of the tunnel accurately, a stepwise ellipse fitting method is proposed. First, after wavelet filtering, the cross-section points are fitted to an ellipse following Taubin's [30] ellipse fitting method. Using the equation of the ellipse, its semi-major axis and semi5
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Fig. 7. Illustration of ellipse fitting and deformation detection method. (a) step-wise ellipse fitting; (b) deformation of the tunnel at different angles.
high-speed railways are located by mileage; therefore, multiple measurements can easily be aligned with the mileage of the cross-section points. However, facilities in subways are located by the number of rings on the inner wall of the tunnel. To locate the cross-section points of subway tunnels, rings on the inner wall should be identified and numbered. A cross-section locating method for subway tunnels is presented in this section. The laser scanner of the RMMS can obtain the reflectivity of the target, so, there is not only position information but also reflectivity information in the cross-section point cloud. First, the original laser profiles are converted to polar coordinates. Then a series of consecutive profiles are projected to a surface and generate a greyscale image based on the reflectivity of corresponding points. The generated greyscale image is shown in Fig. 8(a). We can see the seams of tunnel rings clearly in this image. To highlight the tunnel rings, the polar coordinate system starts and ends in the middle of the rail tracks. Therefore, rail tracks are located in the upper and lower parts of this image, as shown in the red frames. After that, the seams of the tunnel rings are identified by calculating the lateral gradient of the grayscale image. Finally, the tunnel rings are identified, numbered, and located based on their seams. The result is shown in Fig. 8(b), the red segments is the identified seams of tunnel rings and the number of rings is written on the tunnel rings. Through the cross-section locating process, accurate locations of the cross-section points in the subway tunnels can be obtained, and this ensures the alignment of the cross-section points from multiple measurements.
minor axis can be worked out using Eqs. (8)–(12). The equation of the ellipse indicated in Eq. (8). Xc in Eq. (9) and Yc in Eq. (10) represent x and y coordinate of the center of the ellipse respectively. The semimajor axis of the ellipse is represented as a in Eq. (11) and the semiminor axis as b in Eq. (12). Then, the residual between the cross-section points and the fitted ellipse is worked out, and the cross-section points with residual larger than 0.01 m are excluded. The rest of the crosssection points go through ellipse fitting and distance exclusion processes several times, until no point is excluded. The stepwise ellipse fitting method is shown in Fig. 7(a). In this figure, the red points indicate excluded points of which the residual from the fitting ellipse is larger than 0.01 m. The blue points are the fitting points of the ellipse and the green ring is part of the fitting ellipse. For this ellipse, the major axis is 5.5704 m and the minor axis is 5.3356 m. The original design of the tunnel was a circle with radius of 2.7 m and the major axis of this elliptical cross section is 0.1704 m longer than original design.
Ax 2 + Bxy + Cy 2 + Dx + Ey + 1 = 0
Xc =
Yc = a2 =
b2 =
BE − 2CD 4AC − B2
(8) (9)
BD − 2AE 4AC − B2
(10)
2(AXc2 + CYc2 + BXc Yc − 1) A+C+
(A − C )2 + B2
(11)
2(AXc2 + CYc2 + BXc Yc − 1) A+C−
(A − C )2 + B2
(12)
3.4. Tunnel ring segments dislocation detection method
After the ellipse fitting process, local deformation of the tunnel is worked out as well. To acquire accurate local deformation, auxiliary lines that start from the center of the ellipse are plotted. The deformation value is equal to the distance between the point nearest to the auxiliary line and the ellipse. Local deformations of the tunnel at different angles are shown in Fig. 7(b). Here, deformation is calculated from −10° to 190° every 10° clockwise. The red segments are auxiliary lines, and the deformation value and angle of auxiliary lines are labeled nearby. We can see from Fig. 7(b) that the top of the tunnel surface exhibits local deformation as much as 0.17 m in this section.
In fact, a tunnel ring is not a single component, it is riveted by serval precast concrete segments. The horizontal or oblique dark seems in the middle of tunnel rings in Fig. 8 are seams of precast concrete segments and the dark dots in this figure are holes of bolts that fit them together. Dislocation of the precast concrete segments may happen, which will have negative effect on the load-bearing structures of the tunnel, threating its safety. To detect dislocation of the precast concrete segments, it necessary to segment the tunnel rings and extract point cloud of the precast concrete segments. In the above section, tunnel ring seams are identified in greyscale image easily since they are vertical lines. However, the seams of precast concrete segments are difficult to identify in grayscale image since interference caused by the cables. Instead of identifying the seams directly, we propose an indirect method to identify them by detecting bolt holes.
3.3. Cross section locating method for subway shield tunnels Cross-section points can be located by adding the mileage of the starting point and that of the odometer. In an actual scene, facilities on 6
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Fig. 8. Greyscale image generated by reflectivity of tunnel's point cloud. (a) original greyscale image; (b) greyscale image after tunnel ring seam identification.
Fig. 9. Tunnel ring segments seams detection method. (a) Tunnel ring with oblique seams, (b) Tunnel ring with vertical seams. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
location of seams can be obtained as well. The bolt holes are not difficult to locate since their relative position with tunnel ring seams is fixed. Template matching method is used to locate precast concrete segments bolt holes and Fig. 9 show the results. Some bolt holes are obscured by ancillary facilities (such as wires and pipes) mounted on the ring, making them hard to detect. Because the distance between seams and bolt holes is a fixed value, the seams can still be located even though no paired bolt holes are found, as it shows in left part of Fig. 9(a). After seams of precast concrete segments are located, the dislocation between consecutive segments can easily detected by comparing the radial coordinate of points on both sides of the seams in polar coordinate.
Since the seams between tunnel rings are identified in Section 3.3, we divide the tunnel's point cloud into different rings and process them in turn. First, pick out the middle frame of cross-section points in a tunnel ring, processed them with wavelet filtering process in Section 3.1 and ellipse fitting process in Section 3.2. Next, set the midpoint of fitting ellipse as zeros point and convert the cross-section points of tunnel rings into polar coordinate system (The vertical downward direction is set as the polar axis). Then the cross-section points are converted into Euclidean coordinate system, with the position of crosssection in rail track direction as X coordinate, the angular coordinate of cross-section points in polar coordinate system multiply subway tunnel's standard diameter (2.75 m) as Y coordinate and the radial coordinate of cross-section points in polar coordinate as Z coordinate. Fig. 9(a), (b) shows the converted point cloud of two tunnel rings, the reflection intensity is also showed in the point cloud. There are two types of bolts in the tunnel rings, one type is used to riveted consecutive tunnel rings together (marked as yellow and green rectangle in Fig. 9), another type is used to riveted precast concrete segments together (marked as red and blue rectangles in Fig. 9). The segments seams are in the middle of a pair of bolts, if we detect the location of bolt holes, the
4. Experiment and results 4.1. Data acquisition The experiment was conducted in a subway tunnel in Wuhan, China. This subway line has been operating safely for six years. The 7
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become more like an ellipse rather than its original circular shape. The ellipse fitting of the cross sections is built on this conception, and we can prove it with the measured cross-section points from RMMS. The cross-section points of forward measurement of RMMS in Fig. 11(b) were selected, the lower part containing rail tracks and ground was removed, then the upper part was subjected to the wavelet filtering algorithm. The remaining part after wavelet filtering went through Taubin's [30] ellipse fitting method and least-square circle fitting method respectively. Absolute value of the residual between fitting ellipse (or circle) and each point was worked out. Their box plot is shown in Fig. 12. This figure is made up of 10 box plots corresponding to the selected cross sections and the ring numbers are listed under each box plot. The residual of ellipse fitting is in the left side of each box plot and the other side is the residual of circle fitting. The unit of ordinates is meters. The blue rectangle in each box plot stands for lower quartile to upper quartile of the residual and the red segment in the rectangle stand for median of residual. Black segments connected to the blue rectangle by dotted lines are lower and upper adjacent. Red cross above the blue rectangle is outlier value. We can see from Fig. 12 that the absolute value of ellipse fitting residual is less than that of circle fitting. So, we can draw a conclusion that the deformed subway shield tunnel is more like an ellipse.
inner wall of the tunnel is supported by rings and the original design of the tunnel is a 2.7 m radius circle. First, the RMMS was pushed back and forth for 200 m from the starting point. Then, cross-section points of the tunnel were measured using a total station to verify the accuracy of the deformation detection system. To select cross section points at the same location, the total station measured cross-sections in the middle of the inner wall rings. Finally, cross-sections of 10 consecutive rings were measured by total station and there were 20 points in each cross-section. The RMMS data were exported and processed afterward, and 2.4 billion points of the tunnel are obtained by this system. The scanning speed of the laser profiler was 200 rounds per second and the pushing speed of the trolley system was about 1 m/s. The distance between two adjacent cross-section points was about 5 mm and there were about 6000 points in a single frame. The operation of the RMMS, including installation and scanning, took about 16 min to complete. In the end, 396,762 cross-section profiles were obtained. However, it took the total station scanner 10 min to measure each cross section of the tunnel. The efficiency of the RMMS was significantly higher than that of total station, even disregarding the high density of point cloud in each cross section. Fig. 10(a) shows the data acquisition process by the RMMS. Fig. 10(b) is the three-dimensional cross-section point cloud of the tunnel acquired by the RMMS. The cross-sections that total station measured located at the middle of the tunnel rings and the measured points were all specially selected on the inner wall to avoid the interference of tunnel ancillary facilities. In each cross section, 20 points were measured by the total station. The seams of the tunnel rings were identified accurately by the method explained in Section 3.3, and the middle of a tunnel ring could be located easily. The cross section closest to the middle of a tunnel ring was considered the cross section in the middle. Because the distance between two adjacent cross-section points measured by the RMMS was only about 5 mm, the mileage error between cross-section points done by total station and those by the RMMS can be ignored. Fig. 11 shows cross-section points from the total station and from the RMMS. Fig. 11(a) shows the cross-section points measured by total station. Fig. 11(b) shows the corresponding cross-section points by forward measurement of the RMMS, and Fig. 11(c) shows the corresponding cross-section points by reverse measurement of the RMMS. The distance between two adjacent cross-sections was equal to the width of tunnel rings, which is 1.5 m.
4.3. Accuracy verification 4.3.1. Accuracy verification of the tunnel detection system by total station The cross-section points of the total station are fitted into ellipses by the method explained in Section 3.2. For the cross-section points of RMMS, the lower part containing rail tracks and ground was removed, then the remaining part was subjected to the wavelet filtering algorithm explained in Section 3.1 and fitted to an ellipse following the method in Section 3.2. The length of the semi-major axis of the fitting ellipse worked as an indicator verifying the accuracy of the RMMS. Length and deviation of the semi-major axis of the fitting ellipse from the total station and RMMS were calculated in each verifying ring, as shown in Table 1. The results of forward and reverse measurements of the RMMS were both verified by those from the total station. The deviation between the forward and reverse measurements of RMMS varied from −1.3 to 2.4 mm, and the Mean Absolute Deviation (MAD) between semi-major axis of the fitting ellipse from cross-section points by RMMS and total station was 1.2 mm for forward measurement and 1.5 mm for reverse measurement. Meanwhile, the accuracy requirement for subway tunnel deformation detection is ± 3 mm according to the “Standard for monitoring and measurement of urban rail transit
4.2. Residual comparison between ellipse and circle fitting We conceived that cross section of shield subway tunnels will
Fig. 10. Data acquisition process. (a) Data acquisition by RMMS; (b) point cloud measured by RMMS. 8
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Fig. 11. Cross-section points from total station and RMMS (different color stand for acquisition sequence of cross sections). (a) Cross-section points from total station; (b) Corresponding cross-section points by forward measurement of RMMS; (c) Corresponding cross-section points by reverse measurement of RMMS.
Fig. 12. Box plot of absolute value of the residual between ellipse (circle) fitting and cross section points from RMMS. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
structure”, which means that RMMS can completely fulfill the accuracy requirement of subway tunnels detection.
Table 1 Length and deviation of semi-major axis of the fitting ellipse from cross-section points obtained by total station and RMMS. Ring number
795 796 797 798 799 800 801 802 803 804
Total station (mm) 2737.2 2736.9 2738.8 2737.5 2738.6 2739.3 2738.9 2737.6 2738.4 2737.8
Forward (mm)
2735.9 2736.2 2739.5 2738.6 2736.7 2737.7 2737.2 2737.5 2736.9 2738.7
Reverse (mm)
2735.6 2736.1 2740.1 2738.3 2736.2 2737 2737.4 2738.5 2736.8 2739.1
Deviation of forward (mm)
Deviation of reverse (mm)
1.3 0.7 −0.7 −1.1 1.9 1.6 1.7 0.1 1.5 −0.9
1.6 0.8 −1.3 −0.8 2.4 2.3 1.5 −0.9 1.6 −1.3
4.3.2. Repeatability verification of overall and local deformation detection by RMMS itself The repeatability of the RMMS was verified by comparing the deformation results from forward and reverse measurement of consecutive tunnel rings. Both overall and local deformation results were verified. Fig. 13 shows the deviation between semi-major axis measured by RMMS in a round trip and the original design of the tunnel. The original design radius of the tunnel is 2.7 m; therefore, both the result of forward and reverse measurement by the RMMS were subtracted by the radius. As shown in this figure, the deviation between the forward and reverse measurement varied from −0.7 to 1 mm, and the mean absolute deviation and standard deviation between these two measurements 9
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Fig. 13. Comparison of deviation between semi-major axis measured by RMMS in a round trip and the original design of the tunnel.
Fig. 14. Local deformation measured by RMMS in forward and reverse measurement at different angles. (a) Local deformation at 60°; (b) local deformation at 80°; (c) local deformation at 100°; (d) local deformation at 120°.
mapping systems, like system that mounted on a (rail) car [22,23], RMMS is mounted on a costumed trolley, making it easier to be used in subway tunnels. Some existing tunnel mapping systems were also mounted on a trolley [24–28], but the trolley that RMMS used is a special designed quick disassembly structure and RMMS can operated normally without IMU or GPS. However, many aspects of this system could be improved. First, the RMMS was originally designed to conduct absolute position measurement in railways or subways, a task for which an IMU and a GPS antenna are essential. But for subway tunnel deformation detection, relative position analysis is a simpler way to fulfill the demand and there is no need to generate absolute point cloud of the tunnel. Removing the IMU and GPS antenna will make the system smaller, lighter, and most importantly, cheaper. This will expand the application of the RMMS in subway tunnel deformation detection. Furthermore, only the relative position of a subway tunnel is obtained by the RMMS in this paper; however, this system can acquire the absolute position of railway and subway tunnels with pre-arranged targets. Tunnel alignment detection can be done with its absolute point cloud; therefore, we will focus on the generation of the absolute point cloud of railway and subway tunnels in the future. Tunnel ring segments seams are detected indirectly in this work, but some of the seams are not detected successfully, since their bolt holes are completely or partial obscured by ancillary facilities mounted on the ring. We will focus on overcome this challenge by other method like combining three-dimensional shape and reflection intensity of tunnel rings, or deep learning technic. The laser scanner of the RMMS can acquire reflectivity of the target, if there are cracks or water leakage areas in the inner wall of the tunnel, the reflectivity of the point cloud in these areas will become significantly lower than in surrounding
was 0.42 and 0.53 mm, respectively. The RMMS showed high repeatability in overall deformation measurement. The local deformation detection results of the RMMS were also verified by comparing the deformation of the tunnel at several different angles. As mentioned in Section 3.2, local deformation is the residual between the nearest point to the auxiliary line of a certain angle and the fitting ellipse. The local deformation was calculated at 60°, 80°, 100°, and 120° of the forward and reverse measurement. Fig. 14 shows the local deformation measured by the RMMS in forward and reverse measurements at these angles. From this figure, we can see that the biggest standard deviation between forward and reverse measurements of the local deformation was 0.94 mm at 80°. This proves that the RMMS has high repeatability for local deformation measurement. 4.4. Verification of tunnel ring segments seams detection method The tunnel ring segments seams detection method is verified by processing point cloud of several continuous tunnel rings. The result is shown in Fig. 15, as is shown in this figure, some segments bolt holes are obscured by wires or pipes mounted on the ring, making it fails to locate the seams, as is shown in yellow rectangles. Besides these two parts, most segments bolt holes have been detected and the seams are located, lay a solid foundation for tunnel ring segments dislocation detection. 5. Discussion and future work The RMMS can achieve high accuracy and repeatability in subway tunnel deformation detection. Compared to other existing tunnel 10
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Fig. 15. Tunnel ring segments seams detection result.
Declaration of Competing Interest
areas. Thus, obvious dark patterns could be found in the greyscale image generated by reflectivity of the point cloud. Later, we will study the identification of cracks and water leakage based on the greyscale image of the railway tunnels. Finally, the RMMS system is now only suited for railways or subways with 1435 mm gauge tracks and must be pushed manually. In the future, we will develop an electric trolley that can run automatically in tunnels whether there are rail tracks there or not.
The authors declare no conflict of interest. Acknowledgments Work described in this paper was jointly supported by the Fundamental Research Funds for the Central Universities under Grant No. 2042017kf0235, National Key Research Program Grant No. 2016YFF0103502, and State Key Laboratory of Rail Transit Engineering Informatization (FSDI) Open Project Funding No. SKLK16-03.
6. Conclusions
References
A rigorous and efficient tunnel deformation detection system based on mobile laser scanning is presented in this paper. This tunnel deformation detection system integrates a high-precision two-dimensional laser profiler, an odometer, and a costumed trolley. While operating, the system is pushed forward manually on the rail track while the cross section of the tunnel is obtained simultaneously. Detailed analysis is performed to prove that profiles from the laser scanner can be seen as cross-sections of the tunnel and that the corresponding error can be ignored. A wavelet filtering algorithm is developed to eliminate the point cloud of tunnel ancillary facilities in the cross-section points. After that, the cross-section points are fitted to an ellipse. Then the fitting result is compared with the original design of the tunnel and the overall and local deformation result is obtained. To acquire the relative position of the cross section precisely, the point cloud of the tunnel is converted to a grayscale picture in which the grayscale values is determined by the reflectivity of the point cloud. The seams of the tunnel's inner wall rings are identified in the grayscale image and the rings are numbered to locate the cross section. Tunnel ring seams are detected indirectly by locating the bolt holes to detect tunnel ring segments dislocation. An experiment was carried out in a subway tunnel in Wuhan to verify the accuracy of the system. The system was pushed forward and forth for 200 m in this tunnel. Ten cross-sections of consecutive tunnel rings were measured using a total station and the corresponding crosssections measured by the RMMS were picked out for comparison. A residual comparison between ellipse and circle fitting of RMMS cross section points showed that ellipse is closer to the actual shape of deformed shield subway tunnel. The repeatability accuracy of overall and local deformation detection was also verified by comparing the deformation results of the cross-sections measured during this round trip. The tunnel ring segments seams detection method was verified by processing point cloud of several continuous tunnel rings. Finally, the accuracy of the cross-section measurement reached 1.5 mm, and the repeatability of the overall and local deformation measurements were 0.5 and 0.9 mm, respectively. This system exceeds the accuracy required for subway tunnel deformation detection and its efficiency is significantly higher than total station.
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