Infrared and Laser Engineering, Volume. 53, Issue 9, 20240257(2024)
Staged adaptive optimization of SPGD algorithm in laser coherent beam combining
Figures & Tables(14)
Fig. 3. The iteration curves of the evaluation function for the traditional SPGD algorithm at different gain coefficients
Fig. 4. The iteration curves of the evaluation function for the Staged SPGD algorithm at different initial gain coefficients
Fig. 5. The iteration curves of the evaluation function for the two algorithms at different perturbation voltages
Fig. 6. The iteration curves of the evaluation function for the Staged SPGD algorithm at different gradient update factors
Fig. 7. Comparison of the number of iteration steps as the algorithm converges. (a) SPGD; (b) Adaptive gain SPGD; (c) Staged SPGD
Fig. 8. Iteration curves for five algorithmic evaluation functions. (a) 19 elements; (b) 37 elements; (c) 61 elements; (d) 91 elements
Fig. 9. Comparison of the number of iterations of the five algorithms when converging at different number of beams
Fig. 10. The distribution of the number of iterations at the convergence of the five algorithms
Fig. 11. The average
Table 1. Staged SPGD algorithm process
View tableView in ArticleTable 1. Staged SPGD algorithm process
Staged SPGD algorithm 1) Set Set initial gain coefficient $ {\gamma ^{\left( 0 \right)}} $ $ {{\boldsymbol{u}}^{\left( 0 \right)}} = \left\{ {0, \cdot \cdot \cdot ,0} \right\} $ $ {J^{\left( 0 \right)}} $ 2) For n=1,2,···,T do 3) Generation of random perturbation voltage $ \delta {{\boldsymbol{u}}^{\left( n \right)}} = \left( {\delta u_1^{\left( n \right)},\delta u_2^{\left( n \right)},...\delta u_N^{\left( n \right)}} \right) $ $ \left| {\delta {\boldsymbol{u}}} \right| = 1 $ 4) Apply a positive disturbance voltage $ {\boldsymbol{u}}_ + ^{\left( n \right)} = {{\boldsymbol{u}}^{\left( {n - 1} \right)}} + \delta {{\boldsymbol{u}}^{\left( n \right)}} $ 5) Obtain the performance evaluation function $ J_ + ^{\left( n \right)} $ $ \delta J_ + ^{\left( n \right)} = J_ + ^{\left( n \right)} - {J^{\left( {n - 1} \right)}} $ 6) Apply a negative disturbance voltage $ {\boldsymbol{u}}_ - ^{\left( n \right)} = {{\boldsymbol{u}}^{\left( {n - 1} \right)}} - \delta {{\boldsymbol{u}}^{\left( n \right)}} $ 7) Obtain the performance evaluation function $ J_ - ^{\left( n \right)} $ $ \delta J_ - ^{\left( n \right)} = J_ - ^{\left( n \right)} - {J^{\left( {n - 1} \right)}} $ 8) Calculate the change in the performance evaluation function $ \delta {J^{\left( n \right)}} = J_ + ^{\left( n \right)} - J_ - ^{\left( n \right)} $ 9) Determine if $ {J^{\left( {n - 1} \right)}} < 0.6 $ ① $ {\gamma ^{\left( n \right)}} = \left| {{\gamma ^{\left( {n - 1} \right)}} - \left| {\delta {J^{\left( n \right)}}} \right| \times {J^{\left( {n - 1} \right)}}} \right| $ ② $ {\gamma ^{\left( n \right)}} = {\gamma ^{\left( 0 \right)}} \times \left\{ {\exp \left[ { - \left( {{J^{\left( {n - 1} \right)}}} \right)} \right]} \right\} $ 10) Determine if $ {{\mathrm{sign}}} \left( {\delta J_ + ^{\left( n \right)}} \right) + {{\mathrm{sign}}} \left( {\delta J_ - ^{\left( n \right)}} \right) < 0 $ ① Update the control voltage $ {{\boldsymbol{u}}^{\left( n \right)}} = {{\boldsymbol{u}}^{\left( {n - 1} \right)}} + {\gamma ^{\left( n \right)}}\delta {{\boldsymbol{u}}^{\left( n \right)}}\delta {J^{\left( n \right)}} $ ② Update the control voltage $ {{\boldsymbol{u}}^{\left( n \right)}} = {{\boldsymbol{u}}^{\left( {n - 1} \right)}} + C{\gamma ^{\left( n \right)}}\delta {{\boldsymbol{u}}^{\left( n \right)}}\dfrac{{J_ + ^{\left( n \right)} - J_ - ^{\left( n \right)}}}{{\left| {J_ + ^{\left( n \right)} - J_ - ^{\left( n \right)} + \varepsilon } \right|}} $ 11) Obtain the performance evaluation function $ {J^{\left( n \right)}} $ 12) End For
Table 2. Parameter settings for each algorithm
View tableView in ArticleTable 2. Parameter settings for each algorithm
Algorithm Parameter settings Staged SPGD γ(0) = 4 , C = 0.25 , |δ u | = 1Adm SPGD γ(0) = 0.6 , ρ = 1 , p = 0.3 , |δ u | = 1Piecewise SPGD γ= 4 , |δ u (0)|= π/3Exp SPGD γ(0) = 4 , α = 0 , |δ u | = 1SPGD γ= 2 , |δ u | = 1
Table 3. Comparison of algorithm iteration times
View tableView in ArticleTable 3. Comparison of algorithm iteration times
Algorithm Iteration number Algorithm iteration time/s Staged SPGD 1000 4.97 60 0.30 SPGD 1000 4.91 95 0.47
Tools
Get Citation
Copy Citation Text
Wenhui ZHENG, Jiaqin QI, Wenjun JIANG, Guiyuan TAN, Qiqi HU, Huaien GAO, Jiazhen DOU, Jianglei DI, Yuwen QIN. Staged adaptive optimization of SPGD algorithm in laser coherent beam combining[J]. Infrared and Laser Engineering, 2024, 53(9): 20240257
Paper Information
Category:
Received: Jun. 8, 2024
Accepted: --
Published Online: Oct. 22, 2024
The Author Email:
© Copyright 2018-2021 | Chinese Laser Press.
All Rights Reserved 沪ICP备15018463号-20