Curvature and Bending Direction Error Correction Model of FBG Shape Sensor

Qiufeng Shang; Feng Liu

doi:10.3788/AOS231140

Acta Optica Sinica, Volume. 43, Issue 22, 2228002(2023)

Curvature and Bending Direction Error Correction Model of FBG Shape Sensor

Qiufeng Shang^1,2,3 and Feng Liu^1、*

¹Department of Electronic & Communication Engineering, North China Electric Power University, Baoding 071003, Hebei , China

²Hebei Key Laboratory of Power Internet of Things Technology, North China Electric Power University, Baoding 071003, Hebei , China

³Baoding Key Laboratory of Optical Fiber Sensing and Optical Communication Technology, North China Electric Power University, Baoding 071003, Hebei , China

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Abstract Get PDF(in Chinese)

Figures & Tables(14)

Fig. 1. Schematic diagram of sensor structure. (a) Cross section of detection point;(b)(c) schematic diagram of curvature and bending direction detection

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Fig. 2. Schematic diagram of spatial curve reconfiguration

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Fig. 3. Schematic diagram of laying angle deviation and calibration error of FBG. (a) Schematic diagram of FBG laying angle deviation;(b) schematic diagram of FBG calibration error

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Fig. 4. Optimization flow chart of the self-calibration mode

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Fig. 5. Simulation model of shape sensor. (a) Shape sensor;(b) sensor cross-section;(c) FBG simulation layout

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Fig. 6. Iteration curves of different optimization algorithms

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Fig. 7. Error correction results of curvature and bending direction. (a) Curvature;(b) bending direction

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Fig. 8. Packaging diagram of shape sensor. (a) Substrate-fiber holder; (b) schematic diagram of sensor section; (c) calibration tool; (d) FBG shape sensor

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Fig. 9. Calibration experiment. (a) Calibration experiment system diagram;(b) FBG calibration result

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Fig. 10. Shape reconfiguration experiment. (a) Arc; (b) hyperbola; (c) spiral

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Fig. 11. Shape reconfiguration results. (a) Arc; (b) hyperbola; (c) spiral

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Table 1. Laying angle deviation and calibration correction coefficient
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Table 1. Laying angle deviation and calibration correction coefficient
Data group Δθ_i/（°） H_i
FBGa FBGb FBGc FBGa FBGb FBGc
Data2 -10.14 -9.73 -4.96 0.98 0.98 1.03
Data3 4.92 9.65 4.93 1.02 0.99 0.98

Table 2. Laying angle deviation and calibration relationship correction coefficient of FBG at detection points

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Table 2. Laying angle deviation and calibration relationship correction coefficient of FBG at detection points

Detection point	FBGa		FBGb		FBGc
Detection point	$∆ θ$ /（°）	P	$∆ θ$ /（°）	P	$∆ θ$ /（°）	P
Point1	1.87	0.97	4.39	1.02	1.33	1.06
Point2	-3.50	1.03	-5.56	0.99	8.40	0.95
Point3	4.06	1.05	-9.70	1.02	1.79	1.01
Point4	5.28	0.97	7.81	0.97	-3.22	0.96
Point5	-8.30	1.11	-3.80	0.96	-5.83	1.04

Table 3. Reconfiguration errors of arc shapes with different curvatures

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Table 3. Reconfiguration errors of arc shapes with different curvatures

Curvature k/m^-1	Tail point reconfiguration error
	Uncorrected		Corrected
	Absolute error /mm	Relative error /%	Absolute error /mm	Relative error /%
2	10.80	2.54	3.96	0.85
10/6	11.43	2.46	4.25	0.91
10/7	11.66	2.51	4.43	0.95
1.25	11.72	2.52	4.38	0.94
10/9	10.67	2.29	4.61	0.99
1	12.50	2.69	5.34	1.15