Displacement Conversion Algorithm and Performance Evaluation by Tunnel Tilt Meter Sensors 1

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1 Displacement Conversion Algorithm and Performance Evaluation by Tunnel Tilt Meter Sensors 1 Seung-Ki Ryu *, 2 Geun-Hyoung Park 1 Research Fellow, Korea Institute of Civil Engineering and Building Technology, Korea (*corresponding author) 2 Researchers, Korea Institute of Civil Engineering and Building Technology, Korea 1 skryu@kict.re.kr, 2 godpark@kict.re.kr ABSTRACT External environment factors affecting structure deformation such as pressure, load, and stress may cause ground collapse, and such hazard may induce a loss of human life. To detect the environmental changes, most of the safety inspection in tunnels has been performed by manual measurement with non-regular inspectors. Thus, regular monitoring of displacement data cannot be performed, which would lead to diverse problems such as inaccurate measurement of structure deformation, inspection cost increase by frequent inspections, and inspector accidents. Due to the problems mentioned earlier, it is very difficult to estimate hazardous situations with high accuracy. To address the problems, a strain gauge sensor has been employed for real-time measurement. However, the strain gauge sensor has limitations to produce displacement data. Thus, in this paper, we propose a new tunnel displacement measurement system using a tilt meter sensor. In our experiments, we tested our system in a modeled tunnel for approving system validity. Keywords: Tunnel, tilt meter, lateral displacement, displacement measurement, theodolite 1. INTRODUCTION The conditions of huge civil structures such as tunnels and subways should be accurately monitored in real-time. Moreover, the construction information such as ground deformation, load, stress, and underground water level is important for measuring the ground intensity and permeability. Various methodologies and devices have been used for monitoring the ground deformation under construction such as a tilt meter, a water level instrument, a settlement inspector, and a load cell. The general monitoring methods using a tilt meter sensor have been employed to measure the horizontal displacement, the soil relaxation area range, the ground subsidence under large scale construction, and the safety information of adjacent buildings and temporary structures. In this study, we reviewed the monitoring methods for the dynamic ground deformation under construction. Based on the reviewed methodologies, we propose a tunnel displacement monitoring system using a tilt meter sensor. Moreover, various experiments for our system verification are performed. We installed tilt meter sensors on our modeled tunnel with regular spacing and measured tilt angle data collected from each sensor. Our system generates tunnel displacement data using the collected tilt angle information. In addition, a new algorithm converting collected tilt angle data to displacement value is proposed. To evaluate the algorithm performance, we constructed a tunnel model. Randomly managed stress was applied to our tunnel model for producing dynamic tunnel deformation. We evaluated the accuracy of our monitoring system with various experiment environments. Seventeen tilt meter sensors were installed on the modeled tunnel with 4 cm spacing. We analyzed the measuring accuracy of tunnel displacement value by comparing the measured data and actual value when random stress is applied to certain points of our modeled tunnel. The tilt angle values collected from tilt meter sensors were used by conversion algorithm to produce displacement data. Thus, the conversion algorithm accuracy is very important to increase the accuracy of our system. We used a theodolite to produce reference displacement value that was compared with the displacement data from tilt meter sensors. 2. RELATED WORK 2.1 Monitoring System Generally, structure monitoring is to measure such as ground intensity, water permeability, ground deformation, load, stress, and water level in large scale structure constructions 1]. Various monitoring systems have been used in large scale constructions such as a tilt meter, a water level indicator, a piezo meter, a surface settlement indicator, a load cell, a strain gauge, and a crack gauge 2]. Herman is and Nesenbergs introduced a new grid shaped detection system using accelerometer sensor networks 3]. Moreover, they proposed specific clothes that can cure scoliosis by human posture awareness. Based on the studies, three-dimensional modeling methods that have an average error less than 1 cm are proposed. Hoshi et al. proposed a displacement monitoring device named three-dimensional capture sheet (3DCS) 4]. They showed the methods of calculating displacement value from position values for each link. An accelerometer sensor was equipped to collect the variation data of link roll and pitch angle. Park and Han proposed time domain reflecto meter (TDR) sensor-based detection system that uses electrical pulse and tunnel support measurement 5]. To measure the behavior of tunnel support, intensity and point conditions are prepared as similar as real field. The TDR data was compared to finite element analysis results in order to evaluate TDR sensor performance. The member force values of tunnel support were analyzed by sensor strain analysis with external stress. 48

2 2.2 Displacement Monitoring Displacement monitoring is performed using displacement measuring sensor systems in various environments such as structure constructions (a tunnel, a cut-slope, a retaining wall, and a dam) and building safety management (a tunnel and a bridge). The vibrating wire (VW) sensor based extensor meter is often used in structure constructions. It produces different output frequency based on the displacement size. The detection range is from to 5 mm, and minimum perforation diameter is 38 mm. The VW sensor-based extensometer includes a vibrating wire and a magnetic coil. The vibrating wire is fixed with proper tension. Ground displacement leads to anchor displacement, which changes the vibrating wire tension. At this time, the vibrating wire produces different resonance frequency according to the magnetization of magnetic coil. The signal is transmitted to an output device, and final results are displayed with certain numbers. Fig 1 shows the installation of anchor type of displacement instrumentation. 3. GROUND DISPLACEMENT MONITORING SYSTEMUSING A TILT METER 3.1 Tilt Meter Sensor Tunnel displacement data can be measured by analyzing the data collected from three-axis tilt meter sensors with regular spacing installation. As illustrated in Fig 2, if the three-axis tilt meter sensor is mounted on the serial structure, displacement data can be generated from tilt angle data by use of a conversion algorithm. Fig 2: Illustration of the serial structure Fig 1: Anchor type of displacement instrumentation The extensometer provides accurate detection. However, it can only measure displacement at the point where the sensor is installed. Thus, a large number of sensors is required to cover a wide detection zone. In addition, each sensor cable should be manually connected for measuring displacement because of wired communication methods. However, it provides higher detection accuracy than that of electric sensors. Moreover, permanent measurement is possible due to the waterproof and anti-sound functions. As the other type of monitoring systems, optical fiber sensors are used for measuring structure deformation. The diameter of an optical fiber is only 25 μm, which means that it is very light-weight and thin. Thus, an optical fiber sensor can be installed on any places without compromising structure functions. The optical fiber sensors, especially fiber Bragg grating (FBG) sensors, provide multi-points measurement. Thus, several different type of sensors can be made with different centroid wavelength. With the characteristics of the FBG sensor, it can provide high resolution sensingata single point, as well as wide area monitoring with distributed sensors. Fig 3: Serially connected tilt meters We connected tilt meters to each other as shown in Fig 3 for measuring three-axis tilt angle. These tilt meters are very closely connected for accurate and dense data. Each tilt meter includes MPU-915 that is a threeaxial MEMS gyroscope sensor. The MPU-915 has various advantages such as low costs, high performance, and small size. ATXmega16 microprocessor is equipped to our tilt meter board, and it is connected to a RS485 serial port. Thus, collected data can be transmitted to a remote terminal unit (RTU) in order to process and store the data. Table 1 depicts our tilt meter sensor specification. Table 1: Tilt meter specification Item Specification Sensor Type MEMS sensor Output Slope : x, y axis angle Sensing range -9 to 9 degree Resolution 1 / Sensitivity.1 Operating Temp. -4 to 8 o C 49

3 3.2 Conversion Algorithm from Tilt Angle Data Our tilt meter sensors are mounted on the tunnel and connected to a serial communication port. External stress will be applied to center positioned tilt meter sensors, and the collected angle data will be converted to displacement data. Our conversion algorithm converts tilt angle data to displacement values, and the tunnel shape is visualized using the displacement values. The angle value (φ) of tilt meter sensor can be converted to x (s) and y (s)as follows. x (s) = cos φ y (s) = sin φ (1) If the tilt meter sensors are very close to each other, tunnel shape can be virtually reconstructed by linear approximation. If the sensors are not close, the curve data between tilt meter sensors will be interpolated as follows. x(t) = a x,3 t 3 + a x,2 t 2 + a x,1 t + a x, y(t) = a y,3 t 3 + a y,2 t 2 + a y,1 t + a y, (2) We assumed that the parameter s of equation (1) follows particle constant velocity model while the parameter t of equation (2) shows non-constant velocity. If the spacing between tilt meter sensors is not close, we assume that the tilt meter sensors move with nearly constant speed. Moreover, if two tilt meter sensors are placed to r() and r(1) positions, displacement value can be generated as follows. The spacing distance between tilt meter sensors cannot be guaranteed at the above equations. Thus, we performed numerical analysis ( {x (t)} 2 + {y (t)} 2 ), and k value can be represented as follows. k n+1 = k n l target ln (6) The calculated results mentioned earlier are optimal values. Thus, two end point coordinates are applied to x(1)and y(1). Since the angle value generated from first derivative may not match the angle value of tilt meter sensors, we produce a new curve data using Hermite spline. a x,3 a y, x () a x,2 a y,2 a x,1 a ] = x (1) ] y,1 1 x() a x, a y, 1 x(1) y () y (1) ] (7) y() y(1) Our conversion algorithm may induce certain error because we assumed that some parameters produce curve data between tilt meter sensors. The sensor coordinate errors are continuously accumulated, and as a result, the errors will be largerat the tilt meter sensor of the end point. Thus, the location information of tilt meter sensor sat the end point should be measured previously. Based on the location information, the error should be distributed to all tilt meter sensors. 4. SIMULATION WITH MODELED TUNNEL x () = k cos φ () y () = k sin φ () x (1) = k cos φ (1) y (1) = k sin φ (1) If second derivative of two end points is a zero natural spline and starting location is given, a new matrix can be generated as follows ] a x,3 a x,2 a x,1 a x, a y,3 a y,2 a ] = y,1 a y, x () x (1) x() (3) y () y (1) y () ] (4) 4.1 Modeled Tunnel To evaluate our system, we conducted tunnel simulator and tested our conversion algorithm. Fig 4 shows our modeled tunnel. In the experimental environment, tunnel deformation is made by outside pressure. For the accurate evaluation, any deformation from inside pressure is prevented. Our modeled tunnel has a 5.6 m diameter, and flexible bars are equipped on the tunnel with 1 m spacing. The end of each bar is fixed to ground. The center positioned bar of our modeled tunnel provides vertical movement. Equation (4) can be converted to equation (5) using a Pseudo Inverse method as follows. a x,3 a y,3 a x,2 a y,2 a x,1 a ] = y,1 a x, a y, x () 1/6 1/6 x (1) ] x() y () y (1) y() ] (5) Fig 4: Modeled Tunnel 5

4 We installed 17tilt meter sensors on the center positioned bar with 35 cm spacing as shown in Fig 4. As mentioned earlier, all tilt meter sensors are connected to a RS485 serial port. The tilt meter sensor 1 is connected to RTU for external data transmission. theodolite and the detection object. The theodolite can measure three-axis distance because theodolite lens can rotate 36 degree horizontally and vertically. The theodolite measures x, y, and z axis but typically two axes are used. The x-axis and y-axis represents north-south and east-west directions, respectively. The z-axis is used as ground elevation. We used a TC-18 theodolite from LEICA. It has 3x telescope,.3 million (mgon) angle measurement, 1 mm+2 ppm distance measurement, and 2.5 km maximum detection distance. In our experiment, as shown in Fig 5, we used reference target label marked as number. Based on the reference label, we measured displacement value of 17 tilt meter sensor points. The displacement data collected from tilt meter sensors is gathered at the same time. Fig 5: Tilt meter Test Diagram As depicted in Fig 5, we installed a cable between sensors 9 and 1 to create external stress that make random tunnel deformation. Our tilt meter sensors measure a tilt angle variation when the cable is pulled. All sensors have their own label number from 1 to 17. Fig 6 shows a theodolite target label to measure accurate tunnel displacement value produced by theodolite. We equipped the label to all tilt meter sensors. Fig 6: Theodolite Target Label 4.2 Experimental Environment A theodolite generates distance data by measuring the time taken to receive a reflected laser. The time is directly proportional to the distance between the Fig 7: Theodolite measurement with external stress In this study, we progressed our experiment according to following procedure. a. Tilt meter sensors and a theodolite measure displacement data without any external stress. The theodolite collects data from 18 points including the reference label point. The tilt meter sensors gather data from 17 points. b. Tilt meter sensors and a theodolite measure data with 1 mm, 2 mm, 3 mm, and 4 mm cable pulling. 5. SIMULATION RESULT In this paper, the data from the theodolite and the tilt meter sensors are marked as measured data (MD) and calculated data (CD). Fig 8 depicts displacement data with different pulling distance based on MD. As expected, large displacement occurs at the points of sensors 9 and 1 because of the position of the pulling cable. Fig 9 shows displacement data based on CD. The results were generated by our conversion algorithm. The overall displacement values are similar to MD. 51

5 Fig 8: Measured Data from a Theodolite Fig 9: Calculated Data from Tilt meter Sensors Table 2 shows comparison results of MD and CD. In this table, is the difference between MD and CD. The difference at sensor 9 point showed the largest displacement values that were 1.7 mm, 1.1 mm, 1. mm, and 1.6 mm. Fig 1 depicts the difference value between MD and CD. In this figure, sensors 2, 3 and 4 show larger displacement than other sensors. However, all difference values are less than 3 mm except the case of 3 mm pulling distance. The big difference of 3 mm pulling distance case at sensors 2, 3, and 4 is because of minor simulation error. From the overall analysis from Table 2 and Fig 1, we can say that our tilt meter sensor system has high accuracy and sufficient performance to be applied to real field. Table 2: Comparison results of MD and CD 1mm 2mm 3mm 5mm Spot M C Δ M C Δ M C Δ M C Δ

6 project of Ministry of Science, ICT and Future Planning department of Korea ] REFERENCES 1] J.Dunicliff, Geotechnical instrumentation for monitoring field performance, John wiley and Son s, Fig 1: Displacement difference between MD and CD 6. CONCLUSIONS Converting from tilt angle values to displacement values is important in physical monitoring systems. In this study, we showed a new method to measure tunnel displacement by use of tilt meter sensors. Our conversion method from tilt angle values to displacement values can be summarized as follows. a. Install the tilt meter sensors on the tunnel with regular spacing. b. Measure three-axis values from tilt meter sensors and distance data between the sensors. c. Produce tunnel displacement data using our conversion algorithm. Based on our experimental results, we can summarize that our system has sufficient accuracy to be applied to real field. Moreover, our system showed that small devices with easy maintenance such as our tilt meter sensors can provide accurate displacement measurement. ACKNOWLEDGMENT This research was supported by a grant, Development of High-reliable USN Sensor Node and Data Analysis System for Ground Collapsing Prevention 2] Controls Testing equipment Ltd., 3] A. Hermanis and K. Nesenbergs, Grid shaped accelerometer network for surface shape recognition, In proceedings of the Electronics Conference (BEC), Oct ] T. Hoshi, S. Ozaki, and H. Shinoda, Threedimensional shape capture sheet using distributed triaxial accelerometers, In proceedings of the 4 th International Conference on Networked Sensing Systems, Jun 27. 5] M. Park and H. Han, Model Experiments and Behavior Analyses of The Tunnel Support Using TDR Sensor, Journal of Korean Geo- Environmental Society, Vol.12, No.9, 211. AUTHOR PROFILES Seung-Ki Ryu received the degree in electrical engineering at the ChungBuk National University in Korea. Currently, he is a research fellow at Korea Instituteof Civil Engineering and Building Technology. Hisresearch interest covers intelligent transportation systems, information technology, ubiquitous city, construction ITconvergence and logistics. 53