Application of L‑M Algorithm with Trust Region Radius Strategy in Laser Tracer Multi‑Station Measurement

Hongfang Chen; Xingchen Yang; Ao Zhang; Zhaoyao Shi

doi:10.3788/CJL230440

Chinese Journal of Lasers, Volume. 50, Issue 14, 1404007(2023)

Application of L‑M Algorithm with Trust Region Radius Strategy in Laser Tracer Multi‑Station Measurement

Hongfang Chen^*, Xingchen Yang, Ao Zhang, and Zhaoyao Shi

Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China

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Figures & Tables(9)

Fig. 1. Multi-station measurement system of laser tracer

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Fig. 2. L-M algorithm flow for adding trust region radius strategy

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Fig. 3. Spatial distribution of the planned measurement points

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Fig. 4. Iterative process of laser tracer first station self-calibration. (a) L-M algorithm; (b) L-M algorithm with trust region radius strategy

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Fig. 5. Volume error of measuring points calculated by L-M algorithm

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Fig. 6. Volume error of measuring points calculated with L-M algorithm with trust region radius strategy

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Table 1. Theoretical coordinates of laser tracer station
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Table 1. Theoretical coordinates of laser tracer station
Station marker X /mm Y /mm Z /mm
1 -39.5209 -18.2952 -613.1806
2 513.0757 -48.5926 -613.1649
3 263.3054 -40.3469 -465.2685
4 265.0009 1306.7992 -613.4593

Table 2. Station coordinates solved by L-M algorithm with trust region radius strategy
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Table 2. Station coordinates solved by L-M algorithm with trust region radius strategy
Station marker X /mm Y /mm Z /mm
1 -39.5209 -18.2952 -613.1806
2 513.0757 -48.5926 -613.1648
3 263.3053 -40.3468 -465.2685
4 265.0008 1306.7792 -613.4593

Table 3. Number of iterations of L-M algorithm and L-M algorithm with trust region radius strategy
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Table 3. Number of iterations of L-M algorithm and L-M algorithm with trust region radius strategy
Station marker L-M algorithm L-M algorithm with trust region radius strategy
1 1727 9
2 1444 9
3 1128 9
4 1914 10

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Hongfang Chen, Xingchen Yang, Ao Zhang, Zhaoyao Shi. Application of L‑M Algorithm with Trust Region Radius Strategy in Laser Tracer Multi‑Station Measurement[J]. Chinese Journal of Lasers, 2023, 50(14): 1404007

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Paper Information

Category: Measurement and metrology

Received: Jan. 5, 2023

Accepted: Apr. 5, 2023

Published Online: Jul. 10, 2023

The Author Email: Chen Hongfang (chf0302@126.com)

DOI:10.3788/CJL230440

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Theoretical coordinates of laser tracer station

Table 1. Theoretical coordinates of laser tracer station

Table 2. Station coordinates solved by L-M algorithm with trust region radius strategy

Table 2. Station coordinates solved by L-M algorithm with trust region radius strategy

Table 3. Number of iterations of L-M algorithm and L-M algorithm with trust region radius strategy

Table 3. Number of iterations of L-M algorithm and L-M algorithm with trust region radius strategy