空间光波前畸变校正中的元启发式SPGD算法

Meta-heuristic SPGD algorithm in spatial light wavefront distortion correction

为了改善传统随机并行梯度下降(Stochastic Parallel Gradient Descent,SPGD)算法收敛速度慢且容易陷入局部极值的问题,提出了一种元启发式随机并行梯度下降(Meta-Heuristic SPGD,MHSPGD)算法。该算法将SPGD算法和元启发式算法的开发与探索两步结合,首先利用SPGD算法的梯度下降搜索得到局部最优解,然后进行邻域搜索得到局部最优区域以外的可能最优解,通过所有解性能指标的比较来确定新的迭代起点。随着搜索范围的自适应扩展,该算法能够避免陷入局部极值并趋向收敛于全局最优。同时,为了避免重复搜索,建立了记忆表来记录迭代过程中产生的次最优解。搭建了无波前探测器自适应光学系统模型,运用所提算法对不同湍流强度下的波前畸变进行了仿真校正,并针对不同Zernike阶数的像差进行了仿真实验。在三种湍流强度下,MHSPGD算法所能达到的斯特列尔比(Strehl Ratio,SR)分别为0.7621、0.6554、0.3749,相比于SPGD算法分别提升了0.1%、2%和18.6%。此外,当畸变中含有较多高阶成分时,文中所提优化算法相比传统的SPGD算法,SR收敛到0.6所需的迭代次数减少了约47%,且SR收敛极限值也提升了约9.4%。结果表明:与三种主流优化算法相比,MHSPGD在保持较快收敛速度的同时,能够在各种湍流强度下达到更高的收敛极限,有效地解决了算法的局部收敛问题。

To improve the problem of slow convergence speed and ease of falling into the local extreme value of the traditional stochastic parallel gradient descent(SPGD) algorithm,a meta-heuristic SPGD(MHSPGD)algorithm is proposed.The proposed algorithm combines the exploration and exploitation of the metaheuristic algorithm with the SPGD algorithm.First,the gradient descent search of the SPGD algorithm is used to obtain the local optimal solution,and then the neighborhood search is carried out to obtain the possible optimal solution outside the local optimal region.The new starting point of iteration is determined by comparing the performance indexes of all solutions.With the adaptive expansion of the search range,the algorithm can avoid falling into the local extremum and tends to converge to the global optimum.At the same time,to avoid repeated searches,a memory table is established to save the suboptimal solution generated in the iterative process.The model of the wavefront sensor-less adaptive optics system was established,and the proposed algorithm was used to correct the wavefront distortion under different turbulence intensities.A simulation of distortions under different Zernike orders was also carried out.Under three turbulence intensities,the Strehl ratios(SR) of the MHSPGD algorithm are 0.762 1,0.655 4 and 0.374 9,which are 0.1%,2% and 18.6% higher than those of the SPGD algorithm.In addition,when the distortion contains more high-order components,compared with the traditional SPGD algorithm,the number of iterations required for SR convergence to 0.6 is reduced by approximately 47%,and the limit value of SR convergence is increased by approximately 9.4% for the proposed algorithm.The results show that compared with the three main optimization algorithms,MHSPGD can achieve a higher convergence limit under various turbulence intensities while maintaining a faster convergence rate,which means it effectively solves the problem of local convergence.