Reconfiguration Error Correction Model for an FBG Shape Sensor Based on the Sparrow Search Algorithm
Abstract
:1. Introduction
2. FBG Shape Sensing Error Model
2.1. Curvature Error and Bending Direction Error Correction Model
2.2. Error Correction Model Verification and Analysis
3. Experiment
3.1. Experimental System and Sensor Calibration
3.2. Optimization Model
- Enter the measured curvatures ka, kb, and kc for FBG a, FBG b, and FBG c in the fixed curvature state, respectively.
- Initialize the inputs and set the placement angles θ1, θ2, and θ3 of the FBG sensor. In this paper, θ1 = 90°, θ2 = 210°, and θ3 = 330°.
- Set the FBG calibration direction deviation Δθi and placement angle deviation Δαi, and Δθi and Δαi are randomly assigned and coded within a certain range.
- Δθi and Δαi are substituted into Equation (10) to obtain the theoretical curvatures k1, k2, and k3, and are optimized using Chebyshev-SSA.
- The optimal parameters of Δθi and Δαi are output when the value of the fitness function ∆k is minimized or at the end of the iteration. Otherwise, steps (3) to (5) are repeated.
3.3. Shape Reconfiguration
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Data Group | Data2 | Data3 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Bending direction/° | 80 | 90 | 200 | 210 | 330 | 80 | 90 | 200 | 210 | 330 | |
Rmax/% | Uncorrected | 2.2 | 2.7 | 2.6 | 1.9 | 0.8 | 2.8 | 2.8 | 1.3 | 0.7 | 2.0 |
Corrected | 0.4 | 0.6 | 0.1 | 0.06 | 0.4 | 0.2 | 0.1 | 0.3 | 0.2 | 0.5 |
Detection Point | Placement Angle Deviation/° | Calibration Direction Deviation/° | ||||
---|---|---|---|---|---|---|
FBGa | FBGb | FBGc | FBGa | FBGb | FBGc | |
Point1 | 0 | −3.9 | 7.5 | 3.9 | 12.5 | 2.2 |
Point2 | 7.5 | −4.5 | 4.3 | 1.6 | −8.0 | 1.8 |
Point3 | 2 | 5.3 | −6.1 | −9.2 | 8.4 | −7.4 |
Point4 | −4.1 | 10.5 | 5.8 | 11.2 | −4.3 | 8.1 |
Point5 | 2.3 | 14.8 | 9.4 | 9.1 | 9.2 | −3.5 |
Radius of Curvature r/mm | Tail Point Reconfiguration Error | |||
---|---|---|---|---|
Uncorrected Error | Corrected Error | |||
Absolute Error/mm | Relative Error/% | Absolute Error/mm | Relative Error/% | |
600 | 11.80 | 2.54 | 4.63 | 0.99 |
700 | 11.66 | 2.51 | 5.23 | 1.13 |
800 | 11.72 | 2.52 | 4.38 | 0.94 |
900 | 10.67 | 2.29 | 4.21 | 0.91 |
1000 | 12.50 | 2.69 | 5.65 | 1.22 |
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Shang, Q.; Liu, F. Reconfiguration Error Correction Model for an FBG Shape Sensor Based on the Sparrow Search Algorithm. Sensors 2023, 23, 7052. https://doi.org/10.3390/s23167052
Shang Q, Liu F. Reconfiguration Error Correction Model for an FBG Shape Sensor Based on the Sparrow Search Algorithm. Sensors. 2023; 23(16):7052. https://doi.org/10.3390/s23167052
Chicago/Turabian StyleShang, Qiufeng, and Feng Liu. 2023. "Reconfiguration Error Correction Model for an FBG Shape Sensor Based on the Sparrow Search Algorithm" Sensors 23, no. 16: 7052. https://doi.org/10.3390/s23167052