Coupled-generalized nonlinear Schr¨odinger equations solved by adaptive step-size methods in interaction picture

We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.

Some new step-size rules for optimization problems

The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods. On the basis of the above three types of line search methods and the idea of the proximal point methods, a new class of step-size rules was proposed. Instead of a single objective function f, f ＋1/2（x - xk）^TBk（x-Xk） was used as the merit function in iteration k, where Sk is a given symmetric positive definite matrix. The existence of the steplength for the new rules was proved. Some convergence properties were also discussed.

An NLMS algorithm with optimized preparatory step-size parameters for SQUID-based MCG data processing

We present a new least-mean-square algorithm of adaptive filtering to improve the signal to noise ratio for magneto-cardiography data collected with high-temperature SQUID-based magnetometers. By frequently adjusting the adaptive parameter a go systematic optimum values in the course of the programmed procedure, the convergence is accelerated with a highest speed and the minimum steady-state error is obtained simultaneously. This algorithm may be applied to eliminate other non-steady relevant noises as well.

Variable step-size adaptive filtering algorithm based on an exponent sin function

This paper proposes a robust adaptive filter based on the exponent sin cost to improve the capability against Gaussian or multiple types of non-Gaussian noises of the adaptive filtering algorithm when dealing with time-varying/time-invariant linear systems function exponent sin(ExpSin).Then a variable step-size(VSS)-ExpSin algorithm is extended further.Besides,the stepsize,the convergence,and the steady-state performance of the proposed algorithm are validated experimentally.The Monte Carlo simulation results of linear system identification illustrate the principle and efficiency of this proposed adaptive filtering algorithm.Results suggest that the proposed adaptive filtering algorithm has superior performance when estimating the unknown linear systems under multiple-types measurement noises.

Optimal variable step-size LMS model and algorithm with independence assumption

To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.

A NEW STEP-SIZE SKILL FOR SOLVING A CLASS OF NONLINEAR PROJECTION EQUATIONS

In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.

VARIABLE STEP-SIZE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.

Step-size selection for split-step based nonlinear compensation with coherent detection in 112-Gb/s 16-QAM transmission

Non-uniform step-size distribution is implemented for split-step based nonlinear compensation in singlechannel 112-Gb/s 16 quadrature amplitude modulation （QAM） transmission. Numerical simulations of the system including a 20 × 80 km uncompensated link are performed using logarithmic step size distribution to compensate signal distortions. 50% of reduction in number of steps with respect to using constant step sizes is observed. The performance is further improved by optimizing nonlinear calculating position （NLCP） in case of using constant step sizes while NLCP optimization becomes unnecessary when using logarithmic step sizes, which reduces the computational effort due to uniformly distributed nonlinear phase for all successive steps.

On asymptotic properties of a constant-step-size sign-error algorithm for adaptive filtering

This work is devoted to asymptotic properties of a sign-error adaptive filtering algorithm with constant step size. Under much weaker conditions than those that appear in the literature, we obtain convergence and rate of convergence by using weak convergence methods. An example is provided to demonstrate the performance of the algorithm.

基于RRT^(*)-DR算法的机械臂避障路径规划

为使机械臂在障碍物环境下快速规划较优路径,提出了一种基于动态区域采样的改进RRT^(*)-DR路径规划算法,将整个规划过程分为快速探索路径和优化初始路径两个步骤。首先利用半目标导向扩展快速探索,找到连接起始点和目标点的路径。随后利用动态区域采样方法,始终在当前最优路径的周边范围内采样,优先密化当前最优路径附近的节点树,节省计算资源,使初始路径经过迭代快速向渐进最优路径收敛。同时,提出一种近障碍节点变步长机制,有选择性地缩短靠近障碍节点的扩展步长,可有效减少碰撞检测失败次数,提高算法效率。最后,在MATLAB和ROS系统下进行路径规划算法仿真,结果表明RRT^(*)-DR算法可在更短时间内实现路径规划,同时有效缩小路径代价。进一步通过实体机器人路径规划避障实验,验证了该算法的实用性和有效性。

一种混合多策略改进的麻雀搜索算法

针对麻雀搜索算法SSA求解目标函数最优解时具有过早收敛、在多峰条件下易陷入局部最优和在高维情况下求解精度不足等问题,提出了一种混合多策略改进的麻雀搜索算法MISSA。考虑到算法初始解的质量很大程度上会影响整个算法的收敛速度与精度,引入精英反向学习策略,扩大算法的搜索区域,提升初始种群的质量和多样性;对步长进行分阶段控制,以提高算法的求解精度;通过在跟随者的位置中加入Circle映射参数与余弦因子,提高算法的遍历性与搜索能力;采用自适应选择机制在麻雀个体位置更新中加入Lévy飞行,增强算法寻优和跳出局部最优的能力。将改进后的算法与麻雀搜索算法及其他算法在13个测试函数上进行对比,并进行Friedman检验。实验结果表明,改进后的麻雀搜索算法能够有效提高寻优精度与收敛速度,并在高维问题中也具备较高的稳定性。

融合三维螺旋运动和混合反向学习策略的改进鹈鹕优化算法

针对鹈鹕优化算法收敛速度较慢、初始化过程随机产生初始种群导致种群多样性差,在后期易陷入局部最优等问题,提出了一种融合三维螺旋飞行和混合反向学习策略的鹈鹕优化算法。首先使用Gauss映射初始化种群,提高种群多样性;其次利用三维螺旋飞行和混合最优最差反向学习策略,加强算法跳出局部最优的能力;最后,引入自适应平衡因子与自适应步长,提出鹈鹕坠落策略,以模拟捕食过程中群体的微小变化。最后,通过12个基准函数和实际案例对IPOA(improved pelican optimization algorithm)进行测试,并与8个仿生算法进行对比,测试结果与Wilcoxon符号秩和检验结果均表明IPOA收敛精度与稳定性等各项性能都有所提升,具有明显优势。

脉冲噪声下AUV水声通信盲均衡算法模拟仿真

针对存在琢稳定分布噪声的水声信道中传统常数模盲均衡算法(constant modulus algorithm,CMA)无法稳定收敛的问题,提出一种基于模拟退火粒子群算法优化的变步长分数低阶盲均衡算法(SAPSO-VSS-FLOSCMA),该算法将FLOSCMA的代价函数作为SAPSO算法的适应度函数,利用SAPSO算法搜索全局最优解代替盲均衡器的初始权向量,降低了FLOSCMA算法的稳态误差,并采用双曲正切函数调节FLOSCMA算法的步长因子加快算法的收敛速度。水声信道仿真结果表明,与CMA和FLOSCMA算法相比,SAPSO-VSS-FLOSCMA算法在收敛速度和稳态误差方面均得到提高,且误码率更低。

基于功率预测的自适应变步长MPPT算法研究

最大功率点跟踪技术(Maximum Power Point Tracking, MPPT)是光伏发电系统中关键技术研究的热点之一。针对传统扰动观察法跟踪速度和精度无法兼顾的问题,文中提出了一种以功率变化量为步长控制量的自适应变步长扰动观察法,通过判断功率变化趋势,对远离最大功率点,采用大步长逼近;靠近最大功率点,采用小步长逼近。建立太阳能光伏电池数学模型得到其输出特性曲线,再利用MATLAB/Simulink搭建基于Boost电路的MPPT仿真模型,最后经仿真验证了所提出算法的稳定性、快速性和准确性,它比传统算法具有更好的MPPT暂态性能。

基于改进人工鱼群算法的无人机三维航迹规划

无人机航迹规划算法中,针对传统人工鱼群算法(Artificial Fish Swarm Algorithm,AFSA)存在易陷入局部最优、优化效率不佳等问题,引入了步长衰减函数,提出了一种自适应步长的人工鱼群算法(Adaptive Step Size Artificial Fish Swarm Algorithm,AS-AFSA),实现航迹规划中全局与局部收敛的自适应;进一步给出了人工鱼权重优化策略,提高人工鱼群算法的收敛速度与精度。仿真结果表明,改进人工鱼群算法在无人机航迹规划情景下表现优异,迭代次数相同条件下,航迹代价相较于狼群算法(Wolf Colony Algorithm,WCA)优化了4.5%,相较于传统人工鱼群算法优化了2.5%。

多导联心电图识别的稳定步长ResNet深度网络

针对经典的ResNet深度神经网络对一维多导联心电图图像进行识别、分类时,因原始图像的维度较高导致提取到的深度特征维度高,造成全连接层训练出现收敛速度慢和过拟合的问题,在ResNet的全连接层提出一种稳定步长动量训练算法,通过引入近似二阶梯度信息增强动量法的寻优能力和加速收敛速度;利用连续2次迭代的参数变化量和梯度信息自适应调整步长,构造边界函数对步长的大小进行限制,以防止步长过大或过小而影响收敛稳定性,使用动量项对参数的更新方向进行修正。在CPSC2018心电图数据集上的实验结果表明:所提算法训练的ResNet取得的F 1分数、准确率、精确度分别达到0.859、97.4%、87.9%,收敛速度和整体分类指标值优于其他相比较的方法。

基于sigmoid-sinh分段函数的变步长FxLMS算法

为改善滤波-x最小均方(filtered-x least mean square,FxLMS)算法在噪声主动控制时无法兼顾收敛速度和稳态误差的问题,提出了基于sigmoid-sinh分段函数的FxLMS(SSFxLMS)算法,并引入蚁狮算法对SFxLMS(sigmoid filtered-x least mean square)、ShFxLMS(sinh filtered-x least mean square)、SSFxLMS算法的参数进行优化。分别采用高斯白噪声和实测簇绒地毯织机噪声为输入信号,采用FxLMS、SFxLMS、ShFxLMS、SSFxLMS算法进行噪声主动控制仿真,对比分析这4种算法的性能。结果表明:与其他3种算法相比,采用SSFxLMS算法对高斯白噪声和簇绒地毯织机噪声进行控制时,误差信号的平均绝对值更小,平均降噪量与收敛速度也有大幅度提升。由此可知,SSFxLMS算法有效改善了FxLMS算法无法兼顾收敛速度和稳态误差的问题,研究结果为噪声主动控制算法设计提供了一定的参考。

基于RRT^(*)改进的移动机器人路径规划算法

针对RRT^(*)算法在复杂环境路径规划中存在的盲目搜索、冗余节点及路径较长等问题,提出一种融合树扩展策略和采样策略的改进RRT^(*)算法(AF-RRT^(*))。通过创造父节点改进RRT^(*)扩展树的结构,缩小路径长度;引入自适应探索,增加采样导向的选择性,减少路径搜索时间,同时不会陷入局部最优陷阱;通过动态步长,减少冗余节点。仿真结果表明,AF-RRT^(*)算法在多种环境下,路径获取效率和路径质量均优于RRT^(*)和F-RRT^(*)。消融实验验证了AF-RRT^(*)算法和算法各功能模块的有效性。

基于随机噪声和自适应步长的快速对抗训练方法

当前对抗训练(AT)及其变体被证明是防御对抗攻击的最有效方法,但生成对抗样本的过程需要庞大的计算资源,导致模型训练效率低、可行性不强;快速AT(Fast-AT)使用单步对抗攻击代替多步对抗攻击加速训练过程,但模型鲁棒性远低于多步AT方法且容易发生灾难性过拟合(CO)。针对这些问题,提出一种基于随机噪声和自适应步长的Fast-AT方法。首先,在生成对抗样本的每次迭代中,通过对原始输入图像添加随机噪声增强数据;其次,累积训练过程中每个对抗样本的梯度,并根据梯度信息自适应地调整对抗样本的扰动步长;最后,根据步长和梯度进行对抗攻击,生成对抗样本用于模型训练。在CIFAR-10、CIFAR-100数据集上进行多种对抗攻击,相较于N-FGSM(Noise Fast Gradient Sign Method),所提方法在鲁棒准确率上取得了至少0.35个百分点的提升。实验结果表明,所提方法能避免Fast-AT中的CO问题,提高深度学习模型的鲁棒性。