Measurement of Three-Dimensional Structural Displacement Using a Hybrid Inertial Vision-Based System
Abstract
:1. Introduction
2. The Proposed HIVBDM System Overview
3. Procedures and Designs of the Proposed HIVBDM System
3.1. Relative Displacement Measurements between the Camera and Structure Using a Stationary Camera
3.2. Relative Displacement Measurements between the Camera and Structure Using a Moving Camera
3.2.1. Camera Movement Compensation Using a Stationary Calibration Target
3.2.2. Camera Movement Compensation Using a Stationary Calibration Target with an Attached Tilt Sensor
4. Experimental Results
4.1. Implementation of the Camera Calibration Algorithm
4.2. Evaluations of the Relative Displacement Measurements between the Camera and Target Using a Stationary Camera
4.3. Evaluations of the Relative Displacement Measurements between the Camera and Target Using a Moving Camera
4.3.1. Evaluation on the Synthetic Target Displacements
4.3.2. Validation of Exact Camera Movements by Using a LVDT Sensor
4.3.3. Evaluation on the Long-Term Indoor Monitoring Process
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Symbol | Description |
---|---|
Input image sequence from time to time , | |
Camera coordinate system at time | |
Image plane at time | |
World coordinate system of the stationary structure at time | |
World coordinate system of the moving structure at time | |
World coordinate system of the camera at time | |
3 × 3 intrinsic camera parameter obtained from the stationary structure | |
1 × 4 camera distortion (warping) parameter obtained from the stationary structure | |
3 × 3 intrinsic camera parameter obtained from the moving structure | |
1 × 4 camera distortion (warping) parameter obtained from the moving structure | |
3 × 3 rotation matrix of the camera in the world coordinate system of the stationary structure at time | |
3 × 1 translation vector of the camera in the world coordinate system of the stationary structure at time | |
3 × 3 rotation matrix of the camera in the world coordinate system of the moving structure at time | |
3 × 1 translation vector of the camera in the world coordinate system of the moving structure at time | |
3 × 1 obtained difference of the camera rotation vector from time to time using an attached tilt sensor | |
3 × 3 obtained difference of the camera rotation matrix converted from using the Rodrigues formula | |
2 × 1 pixel-wise location of the detected feature points on the stationary calibration target at time | |
2 × 1 pixel-wise location of the detected feature points on the moving calibration target at time | |
3 × 1 spatial location of the detected feature points on the stationary calibration target at time | |
3 × 1 spatial location of the detected feature points on the moving calibration target at time | |
3 × 1 spatial location of the monitored point at time in the camera coordinate system at time | |
3 × 1 spatial location of the monitored point at time in the world coordinate system of the stationary structure at time | |
3 × 1 spatial location of the monitored point at time in the world coordinate system of the moving structure at time | |
3 × 1 measured structural displacement from time to time in the world coordinate system of the moving structure at time | |
The world coordinate system is associated with the structure that is being monitored, and the world coordinate system only exists in the camera movement compensation. The structural displacements can only be calculated within the same coordinate system. |
Actual Static Target Displacements in X, Y and Z Directions | Static Target Displacement Measurements in X, Y and Z Directions | |||||||
---|---|---|---|---|---|---|---|---|
With Averaging Processing | Without Averaging Processing | |||||||
X | Y | Z | X | Y | Z | X | Y | Z |
0.000 | 0.000 | 0.000 | 0.008 | −0.029 | 0.304 | 0.006 | −0.043 | 0.555 |
1.588 | 0.000 | 0.000 | 1.719 | −0.043 | −0.729 | 1.727 | −0.039 | −0.797 |
3.175 | 0.000 | 0.000 | 3.491 | −0.131 | 0.273 | 3.480 | −0.111 | −0.138 |
6.350 | 0.000 | 0.000 | 6.831 | −0.133 | −0.672 | 6.829 | −0.034 | −2.090 |
12.700 | 0.000 | 0.000 | 13.066 | −0.296 | 0.140 | 13.075 | −0.266 | −0.595 |
25.400 | 0.000 | 0.000 | 26.063 | −0.575 | 1.266 | 26.061 | −0.541 | 0.740 |
50.800 | 0.000 | 0.000 | 51.224 | −1.039 | 3.476 | 51.175 | −1.029 | 3.432 |
RMSE of X Direction Static Target Measurements: | 0.397 () | 0.468 () | 1.457 () | 0.389 () | 0.453 () | 1.604 () | ||
X | Y | Z | X | Y | Z | X | Y | Z |
0.000 | 0.000 | 0.000 | 0.023 | 0.008 | 0.295 | −0.015 | −0.024 | 0.037 |
0.000 | 1.588 | 0.000 | −0.242 | 1.573 | −1.624 | −0.220 | 1.606 | −1.430 |
0.000 | 3.175 | 0.000 | −0.377 | 3.281 | −2.711 | −0.431 | 3.285 | −3.116 |
0.000 | 6.350 | 0.000 | −0.142 | 6.294 | −2.115 | −0.125 | 6.287 | −2.143 |
0.000 | 12.700 | 0.000 | −0.097 | 12.676 | −0.625 | −0.276 | 12.653 | −1.973 |
0.000 | 25.400 | 0.000 | −0.154 | 25.527 | −1.376 | −0.215 | 25.514 | −1.712 |
0.000 | 50.800 | 0.000 | −0.246 | 50.861 | −3.533 | −0.250 | 50.871 | −3.133 |
RMSE of Y Direction Static Target Measurements: | 0.212 () | 0.071 () | 2.046 () | 0.249 () | 0.073 () | 2.171 () | ||
X | Y | Z | X | Y | Z | X | Y | Z |
0.000 | 0.000 | 0.000 | 0.014 | 0.039 | −0.039 | −0.022 | 0.014 | −0.633 |
0.000 | 0.000 | 1.588 | −0.030 | 0.182 | 1.914 | −0.038 | 0.233 | 2.606 |
0.000 | 0.000 | 3.175 | −0.032 | 0.194 | 4.196 | −0.050 | 0.157 | 3.585 |
0.000 | 0.000 | 6.350 | −0.082 | 0.250 | 6.144 | −0.096 | 0.217 | 5.758 |
0.000 | 0.000 | 12.700 | −0.104 | 0.537 | 13.669 | −0.101 | 0.479 | 12.856 |
0.000 | 0.000 | 25.400 | −0.091 | 1.012 | 26.749 | −0.105 | 0.941 | 25.587 |
0.000 | 0.000 | 50.800 | −0.178 | 1.933 | 51.845 | −0.149 | 1.935 | 51.647 |
RMSE of Z Direction Static Target Measurements: | 0.092 () | 0.861 () | 0.849 () | 0.090 () | 0.844 () | 0.625 () |
Direction of Target Displacements | Test Number | |||
---|---|---|---|---|
X | 1 | −0.004 | 203.200 | −0.493 |
2 | −0.004 | 203.200 | −0.492 | |
3 | −0.004 | 203.200 | −0.493 | |
4 | −0.004 | 203.200 | −0.493 | |
5 | −0.004 | 203.200 | −0.495 | |
6 | −0.004 | 203.200 | −0.497 | |
7 | −0.004 | 203.200 | −0.501 | |
Y | 1 | −0.004 | 203.200 | −0.498 |
2 | −0.004 | 203.200 | −0.501 | |
3 | −0.004 | 203.200 | −0.509 | |
4 | −0.004 | 203.200 | −0.500 | |
5 | −0.004 | 203.200 | −0.499 | |
6 | −0.004 | 203.200 | −0.502 | |
7 | −0.004 | 203.200 | −0.504 | |
Z | 1 | −0.004 | 203.200 | −0.491 |
2 | −0.004 | 203.200 | −0.501 | |
3 | −0.004 | 203.200 | −0.499 | |
4 | −0.004 | 203.200 | −0.504 | |
5 | −0.004 | 203.200 | −0.497 | |
6 | −0.004 | 203.200 | −0.501 | |
7 | −0.004 | 203.200 | −0.496 |
Actual Static Target Displacements in X, Y and Z Directions | Static Target Displacement Measurements in X, Y and Z Directions | |||||||
---|---|---|---|---|---|---|---|---|
Using a Stationary Calibration Target | Using a Stationary Calibration Target with an Attached Tilt Sensor | |||||||
X | Y | Z | X | Y | Z | X | Y | Z |
0.000 | 0.000 | 0.000 | 1.080 | −1.699 | 0.119 | −0.479 | −0.722 | 0.961 |
1.588 | 0.000 | 0.000 | 3.603 | −2.122 | −1.106 | 1.567 | −1.117 | 2.857 |
3.175 | 0.000 | 0.000 | 5.335 | −1.836 | −5.351 | 3.071 | −0.705 | 1.565 |
6.350 | 0.000 | 0.000 | 8.644 | −1.567 | −7.531 | 6.223 | −0.297 | 1.860 |
12.700 | 0.000 | 0.000 | 16.007 | −1.801 | −9.846 | 13.529 | −0.238 | 2.762 |
25.400 | 0.000 | 0.000 | 28.718 | −2.634 | −8.425 | 26.260 | −1.079 | 3.055 |
50.800 | 0.000 | 0.000 | 52.625 | −2.233 | −10.061 | 50.478 | −0.088 | 4.479 |
RMSE of X direction static target measurements: | 2.403 () | 2.014 () | 7.129 () | 0.505 () | 0.715 () | 2.726 () | ||
X | Y | Z | X | Y | Z | X | Y | Z |
0.000 | 0.000 | 0.000 | 0.800 | −1.376 | 7.145 | −0.650 | −0.551 | −0.205 |
0.000 | 1.588 | 0.000 | 0.014 | 1.159 | 8.397 | −1.203 | 1.973 | −0.906 |
0.000 | 3.175 | 0.000 | 0.034 | 3.214 | 7.902 | −0.991 | 4.133 | −1.670 |
0.000 | 6.350 | 0.000 | 0.592 | 6.752 | 8.507 | −0.995 | 7.271 | −1.464 |
0.000 | 12.700 | 0.000 | −0.270 | 12.276 | 7.621 | −1.248 | 13.300 | −1.944 |
0.000 | 25.400 | 0.000 | 0.297 | 25.588 | 6.175 | −1.069 | 26.253 | −3.710 |
0.000 | 50.800 | 0.000 | −3.449 | 47.445 | 79.469 | −1.872 | 50.712 | −5.650 |
RMSE of Y direction static target measurements: | 1.365 () | 1.399 () | 30.863 () | 1.198 () | 0.688 () | 2.810 () | ||
X | Y | Z | X | Y | Z | X | Y | Z |
0.000 | 0.000 | 0.000 | 1.186 | 13.767 | −32.499 | −0.493 | −0.561 | 1.866 |
0.000 | 0.000 | 1.588 | 3.476 | 13.146 | −36.111 | −0.051 | 0.073 | 6.874 |
0.000 | 0.000 | 3.175 | 3.578 | 13.274 | −35.506 | −0.016 | 0.329 | 8.474 |
0.000 | 0.000 | 6.350 | 0.013 | −1.480 | 13.960 | −0.259 | 0.744 | 11.423 |
0.000 | 0.000 | 12.700 | 0.386 | −0.532 | 21.522 | 0.429 | 1.845 | 18.657 |
0.000 | 0.000 | 25.400 | 1.671 | 0.013 | 32.823 | 1.523 | 3.438 | 29.354 |
0.000 | 0.000 | 50.800 | 1.359 | 2.609 | 57.991 | 2.406 | 7.088 | 53.406 |
RMSE of Z direction static target measurements: | 2.107 () | 8.846 () | 24.542 () | 1.109 () | 3.081 () | 4.522 () |
Test Number | Error (%) | |||||
---|---|---|---|---|---|---|
1 | 4.900 | 236.538 | 0.018 | 3.048 | 2.849 | 6.54% |
2 | 9.800 | 236.538 | 0.037 | 6.350 | 5.857 | 7.77% |
3 | 4.900 | 295.275 | 0.028 | 5.588 | 5.425 | 2.92% |
4 | 9.800 | 295.275 | 0.058 | 11.938 | 11.444 | 4.14% |
5 | 4.900 | 358.775 | 0.039 | 9.906 | 9.401 | 5.10% |
6 | 9.800 | 358.775 | 0.082 | 20.574 | 19.695 | 4.27% |
Please note that the error percentage is defined as . |
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Zhang, X.; Zeinali, Y.; Story, B.A.; Rajan, D. Measurement of Three-Dimensional Structural Displacement Using a Hybrid Inertial Vision-Based System. Sensors 2019, 19, 4083. https://doi.org/10.3390/s19194083
Zhang X, Zeinali Y, Story BA, Rajan D. Measurement of Three-Dimensional Structural Displacement Using a Hybrid Inertial Vision-Based System. Sensors. 2019; 19(19):4083. https://doi.org/10.3390/s19194083
Chicago/Turabian StyleZhang, Xinxiang, Yasha Zeinali, Brett A. Story, and Dinesh Rajan. 2019. "Measurement of Three-Dimensional Structural Displacement Using a Hybrid Inertial Vision-Based System" Sensors 19, no. 19: 4083. https://doi.org/10.3390/s19194083