Measurement Algorithm for Anti-Stress Cone Parameters of Cross-Linked Polyethylene Cable Joint Based on Three-Dimensional Point Cloud Processing

Lei Deng; Guihua Liu; Hao Deng; Junjie Huang; Binghong Zhou

doi:10.3788/CJL220785

Journals >Chinese Journal of Lasers >Volume 50 >Issue 6 >Page 0604003 > Article

Chinese Journal of Lasers
Vol. 50, Issue 6, 0604003 (2023)

Measurement Algorithm for Anti-Stress Cone Parameters of Cross-Linked Polyethylene Cable Joint Based on Three-Dimensional Point Cloud Processing

Lei Deng^1、2, Guihua Liu^1、2、*, Hao Deng^1、2, Junjie Huang^1、2, and Binghong Zhou^1、2

Author Affiliations

¹School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China

²Key Laboratory of Special Environment Robotics of Sichuan Province, Mianyang 621010, Sichuan, China

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DOI: 10.3788/CJL220785 Cite this Article Set citation alerts

Lei Deng, Guihua Liu, Hao Deng, Junjie Huang, Binghong Zhou. Measurement Algorithm for Anti-Stress Cone Parameters of Cross-Linked Polyethylene Cable Joint Based on Three-Dimensional Point Cloud Processing[J]. Chinese Journal of Lasers, 2023, 50(6): 0604003 Copy Citation Text

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Fig. 1. Flow of anti-stress cone of cable joint parameter measurement algorithm

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Fig. 2. Pseudocode of anti-stress cone of cable joint parameter measurement algorithm

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Fig. 3. Cable joint.(a) Structure diagram; (b) physical diagram; (c) point cloud data

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Fig. 4. Coordinate adjustment diagrams. (a) Before adjustment; (b) after adjustment

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Fig. 5. Diagram of obtaining target point cloud. (a) Joint point cloud; (b) circle fitting results of joint point cloud; (c) target point cloud fitting circle; (d) target point cloud

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Fig. 6. Change of cable joint fitting circle radius

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Fig. 7. Space division of cable joint point cloud.(a) Target point cloud; (b) strips division mode; (c) strips division results of figure (a); (d) an example of strip point cloud; (e) pieces division results of figure (a); (f) an example of piece

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Fig. 8. Analysis of piece points obtained by different space division methods. (a) Ours; (b) equal height division

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Fig. 9. Concave-convex decision diagrams. (a) Convex diagram;(b) concave diagram

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Fig. 10. Change of piece axis angle on strip point cloud

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Fig. 11. Diagram of strip point cloud formed by planes and surfaces

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Fig. 12. Calculation process diagram of starting point and ending point of anti-stress cone

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Fig. 13. Diagram of error correction based on residual estimation

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Fig. 14. Diagram of measured parameter of anti-stress cone

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Measuredparameter	Meaning	Calculation method
D_i	End diameter	Diameter of fitting circle at $Z_{4}$
D_o	Start diameter	Diameter of fitting circle at $Z_{3}$
H	Height	$Z_{4} - Z_{3}$
S	Slope length	$\sqrt[]{{[(D_{o} - D_{i}) / 2]}^{2} + H^{2}}$

Table 1. Explanation of measured parameters of anti-stress cone and their calculation methods

Joint	Index	Measured value of radius change				Measured value of ours
Joint	Index	D_i	D_o	S	H	D_i	D_o	S	H
Standard joint	x^* /mm	46.40	78.40	57.28	55.00	46.40	78.40	57.28	55.00
	x /mm	48.35	75.63	49.28	47.35	46.29	78.39	57.42	55.13
	e（x）/mm	-1.95	2.77	8.00	7.65	0.11	0.01	-0.14	-0.13
	e_r（x）/%	4.20	3.53	13.97	13.91	0.24	0.01	0.24	0.24
	Points	766310				766310
	Time /s	6.63				18.87
Artificial joint^①	x^* /mm	47.00	78.00	53.79	51.50	47.00	78.00	53.79	51.50
	x /mm	49.84	76.13	45.62	43.68	46.88	78.32	53.21	50.83
	e（x）/mm	-2.84	1.87	8.17	7.82	0.12	-0.32	0.58	0.67
	e_r（x）/%	6.04	2.40	15.18	15.18	0.26	0.41	1.08	1.30
	Points	814402				814402
	Time /s	7.14				19.85
Artificial joint^②	x^* /mm	45.50	77.50	59.68	57.50	45.50	77.50	59.68	57.50
	x /mm	46.62	74.87	52.69	50.76	45.97	77.21	59.28	57.19
	e（x）/mm	-1.12	2.63	6.99	6.74	-0.47	0.29	0.40	0.31
	e_r（x）/%	2.46	3.39	11.71	11.72	1.03	0.37	0.67	0.54
	Points	898623				898623
	Time /s	7.74				19.38

Table 2. Measurement results of different methods

Joint	Index	Measured value of equal height division				Measured value of ours
Joint	Index	D_i	D_o	S	H	D_i	D_o	S	H
Standard joint	x^* /mm	46.40	78.40	57.28	55.00	46.40	78.40	57.28	55.00
	x /mm	47.16	76.36	55.56	53.60	46.29	78.39	57.42	55.13
	e（x）/mm	-0.76	2.04	1.72	1.40	0.11	0.01	-0.14	-0.13
	e_r（x）/%	1.64	2.60	3.00	2.55	0.24	0.01	0.24	0.24
	Points	766310				766310
	Time /s	18.36				18.87
Artificial joint^①	x^* /mm	47.00	78.00	53.79	51.50	47.00	78.00	53.79	51.50
	x /mm	47.87	76.84	52.66	50.63	46.88	78.32	53.21	50.83
	e（x）/mm	-0.87	1.16	1.13	0.87	0.12	-0.32	0.58	0.67
	e_r（x）/%	1.85	1.49	2.10	1.69	0.26	0.41	1.08	1.30
	Points	814402				814402
	Time/s	19.64				19.85
Artificial joint^②	x^* /mm	45.50	77.50	59.68	57.50	45.50	77.50	59.68	57.50
	x /mm	46.16	76.81	58.92	56.89	45.97	77.21	59.28	57.19
	e（x）/mm	-0.66	0.69	0.76	0.61	-0.47	0.29	0.40	0.31
	e_r（x）/%	1.45	0.89	1.27	1.06	1.03	0.37	0.67	0.54
	Points	898623				898623
	Time /s	19.43				19.38

Table 3. Measurement results for different space division methods

Joint	Index	Measured value before error correction				Measured value after error correction
Joint	Index	D_i	D_o	S	H	D_i	D_o	S	H
Standard joint	x^* /mm	46.40	78.40	57.28	55.00	46.40	78.40	57.28	55.00
	x /mm	46.29	78.39	57.42	55.13	46.29	78.39	57.42	55.13
	e（x）/mm	0.11	0.01	-0.14	-0.13	0.11	0.01	-0.14	-0.13
	e_r（x）/%	0.24	0.01	0.24	0.24	0.24	0.01	0.24	0.24
	Points	766310
	Time /s	18.87
Artificial joint^①	x^* /mm	47.00	78.00	53.79	51.50	47.00	78.00	53.79	51.50
	x /mm	47.46	77.36	51.45	49.23	46.88	78.32	53.21	50.83
	e（x）/mm	-0.46	0.64	2.34	2.27	0.12	-0.32	0.58	0.67
	e_r（x）/%	0.98	0.82	4.35	4.41	0.26	0.41	1.08	1.30
	Points	814402
	Time /s	19.85
Artificial joint^②	x^* /mm	45.50	77.50	59.68	57.50	45.50	77.50	59.68	57.50
	x /mm	46.36	76.06	57.12	55.16	45.97	77.21	59.28	57.19
	e（x）/mm	-0.86	1.44	2.56	2.34	-0.47	0.29	0.40	0.31
	e_r（x）/%	1.89	1.85	4.29	4.07	1.03	0.37	0.67	0.54
	Points	898623
	Time /s	19.38

Table 4. Measurement results before and after error correction

h /mm	H /mm	e（x）/mm	e_r（x）/%
0.1	55.61	-0.61	1.11
0.2	55.52	-0.52	0.95
0.3	55.43	-0.43	0.78
0.4	55.38	-0.38	0.69
0.5	55.25	-0.25	0.45
0.6	55.53	-0.53	0.96
0.7	55.74	-0.74	1.35
0.8	55.87	-0.87	1.58
0.9	56.01	-1.01	1.84
1.0	56.12	-1.12	2.04

Table 5. Effect of piece height h on algorithm accuracy

η /（°）	H /mm	e（x）/mm	e_r（x）/%
1	61.07	-3.57	6.21
2	60.17	-2.67	4.64
3	59.37	-1.87	3.25
4	58.40	-0.90	1.57
5	57.96	-0.46	0.80
6	57.18	0.32	0.56
7	56.62	0.88	1.53
8	56.13	1.37	2.38
9	55.47	2.03	3.53
10	54.10	3.40	5.91

Table 6. Effect of strip point cloud angle η on algorithm accuracy

D_th3	H /mm	e（x）/mm	e_r（x）/%
0.10	60.75	-3.25	5.65
0.15	59.83	-2.33	4.05
0.20	59.34	-1.84	3.20
0.25	58.63	-1.13	1.97
0.30	58.14	-0.64	1.11
0.35	57.96	-0.46	0.80
0.40	57.13	0.37	0.64
0.45	56.73	0.77	1.34
0.50	56.31	1.19	2.07
0.55	55.81	1.69	2.94

Table 7. Effect of threshold D_th3on algorithm accuracy

D_th4	H /mm	e（x）/mm	e_r（x）/%
0.10	61.03	-3.53	6.14
0.15	60.47	-2.97	5.17
0.20	59.67	-2.17	3.77
0.25	59.14	-1.64	2.85
0.30	58.66	-1.16	2.02
0.35	57.96	-0.46	0.80
0.40	57.36	0.14	0.24
0.45	56.78	0.72	1.30
0.50	56.21	1.29	2.24
0.55	55.73	1.77	3.08

Table 8. Effect of threshold D_th4on algorithm accuracy

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