Efficient Sensor Placement Optimization for Shape Deformation Sensing of Antenna Structures with Fiber Bragg Grating Strain Sensors
Abstract
:1. Introduction
2. Problem Statements
3. Deformation Reconstruction
3.1. Strain–Displacement Transformation
3.2. Relative Reconstruction Error Equation
4. Two-Stage Sensor Placement
4.1. Initial Sensor Placement at the First Stage
4.2. Sequential Sensor Placement at the Second Stage
4.3. Implementation Procedure
- (1)
- Specify the mode truncation number , the total sensor number and the allowed maximum reconstruction error . In addition, the measurable location set , the response reconstruction location set and the number of the candidate sensor locations are also determined.
- (2)
- Perform QR decomposition of the matrix using Equation (15), and select the first columns. The column numbers with respect to are extracted from the matrix , and we choose the initial sensor locations corresponding to the sequence of the elements with the value 1 in the unit conversion matrix .
- (3)
- Utilize Equation (18) to calculate the redundancy of information between all of the remaining candidate locations and the previously determined sensor locations.
- (4)
- Select an optimal sensor location satisfying Equation (20) from the current measurable location set.
- (5)
- Add the newly selected sensor location to the current sensor placement set , and update the current measurable location set and the allowable remaining sensor numbers in the second stage.
- (6)
- If the termination conditions are satisfied, the program is terminated, otherwise repeat the steps (3)~(6). In this paper, the termination conditions are as follows:
- (a)
- Whether the requirements of the specified reconstruction accuracy is satisfied;
- (b)
- Whether the allowed maximum sensor number is reached.
5. Numerical Experiment
5.1. FEM of the Antenna Experimental Platform
5.2. Superiority of Sensor Placement Method
6. Experimental Results
6.1. Experimental System
6.2. Reconstruction Results
6.3. Result Discussions
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Modal | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Frequency (Hz) | 0.45 | 1.47 | 2.78 | 5.05 | 6.03 | 6.40 | 8.52 |
Locations | RMSE (mm) | MAE (mm) | ARPE |
---|---|---|---|
Test point 1 | 0.0741 | 0.1587 | 3.43% |
Test point 2 | 0.3977 | 0.7240 | 5.22% |
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Zhou, J.; Cai, Z.; Zhao, P.; Tang, B. Efficient Sensor Placement Optimization for Shape Deformation Sensing of Antenna Structures with Fiber Bragg Grating Strain Sensors. Sensors 2018, 18, 2481. https://doi.org/10.3390/s18082481
Zhou J, Cai Z, Zhao P, Tang B. Efficient Sensor Placement Optimization for Shape Deformation Sensing of Antenna Structures with Fiber Bragg Grating Strain Sensors. Sensors. 2018; 18(8):2481. https://doi.org/10.3390/s18082481
Chicago/Turabian StyleZhou, Jinzhu, Zhiheng Cai, Pengbing Zhao, and Baofu Tang. 2018. "Efficient Sensor Placement Optimization for Shape Deformation Sensing of Antenna Structures with Fiber Bragg Grating Strain Sensors" Sensors 18, no. 8: 2481. https://doi.org/10.3390/s18082481
APA StyleZhou, J., Cai, Z., Zhao, P., & Tang, B. (2018). Efficient Sensor Placement Optimization for Shape Deformation Sensing of Antenna Structures with Fiber Bragg Grating Strain Sensors. Sensors, 18(8), 2481. https://doi.org/10.3390/s18082481