A Descent Gradient Method and Its Global Convergence

Y Liu and C Storey(1992)proposed the famous LS conjugate gradient method which has good numerical results.However,the LS method has very weak convergence under the Wolfe-type line search.In this paper,we give a new descent gradient method based on the LS method.It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search.Finally,we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP^+method.

A modified three–term conjugate gradient method with sufficient descent property

A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.

Designing fuzzy inference system based on improved gradient descent method

The distribution of sampling data influences completeness of rule base so that extrapolating missing rules is very difficult. Based on data mining, a self-learning method is developed for identifying fuzzy model and extrapolating missing rules, by means of confidence measure and the improved gradient descent method. The proposed approach can not only identify fuzzy model, update its parameters and determine optimal output fuzzy sets simultaneously, but also resolve the uncontrollable problem led by the regions that data do not cover. The simulation results show the effectiveness and accuracy of the proposed approach with the classical truck backer-upper control problem verifying.

EFFICIENT GRADIENT DESCENT METHOD OFRBF NEURAL ENTWORKS WITHADAPTIVE LEARNING RATE

A new algorithm to exploit the learning rates of gradient descent method is presented, based on the second-order Taylor expansion of the error energy function with respect to learning rate, at some values decided by "award-punish" strategy. Detailed deduction of the algorithm applied to RBF networks is given. Simulation studies show that this algorithm can increase the rate of convergence and improve the performance of the gradient descent method.

A New Descent Nonlinear Conjugate Gradient Method for Unconstrained Optimization

In this paper, a new nonlinear conjugate gradient method is proposed for large-scale unconstrained optimization. The sufficient descent property holds without any line searches. We use some steplength technique which ensures the Zoutendijk condition to be held, this method is proved to be globally convergent. Finally, we improve it, and do further analysis.

Three New Hybrid Conjugate Gradient Methods for Optimization

In this paper, three new hybrid nonlinear conjugate gradient methods are presented, which produce suf?cient descent search direction at every iteration. This property is independent of any line search or the convexity of the objective function used. Under suitable conditions, we prove that the proposed methods converge globally for general nonconvex functions. The numerical results show that all these three new hybrid methods are efficient for the given test problems.

An Adaptive Learning Method for the Generation of Fuzzy Inference System from Data

Designing a fuzzy inference system(FIS)from data can be divided into two main phases:structure identification and parameter optimization.First,starting from a simple initial topology,the membership functions and system rules are defined as specific structures.Second,to speed up the convergence of the learning algorithm and lighten the oscillation,an improved descent method for FIS generation is developed.Furthermore, the convergence and the oscillation of the algorithm are system- atically analyzed.Third,using the information obtained from the previous phase,it can be decided in which region of the in- put space the density of fuzzy rules should be enhanced and for which variable the number of fuzzy sets that used to partition the domain must be increased.Consequently,this produces a new and more appropriate structure.Finally,the proposed method is applied to the problem of nonlinear function approximation.

PRP-Type Direct Search Methods for Unconstrained Optimization

Three PRP-type direct search methods for unconstrained optimization are presented. The methods adopt three kinds of recently developed descent conjugate gradient methods and the idea of frame-based direct search method. Global convergence is shown for continuously differentiable functions. Data profile and performance profile are adopted to analyze the numerical experiments and the results show that the proposed methods are effective.

基于优化快速搜索随机树算法的全局路径规划

为了改善传统快速搜索随机树(RRT)算法在全局路径规划中存在的平滑度差、具有潜在碰撞性等问题,提出了一种双重优化的RRT算法。在传统RRT算法基础上,引入自适应目标偏向策略以缩短采样时间,引入角度约束采样策略以适应车辆极限转角。得到初始路径后,建立二项优化函数(即降低路径曲率和远离障碍物),并将其作为基点进行梯度下降二次优化,生成可供车辆行驶、平滑性良好且碰撞概率低的路径,并进行仿真验证。结果表明:优化RRT算法相比于传统RRT算法、RRT-Connect算法和RRT算法,平均曲率分别降低了38.1%、36.4%和24.7%,曲率均方差分别降低了38.4%、38.4%和27.2%。

Sobolev Gradient Approach for Huxley and Fisher Models for Gene Propagation

The application of Sobolev gradient methods for finding critical points of the Huxley and Fisher models is demonstrated. A comparison is given between the Euclidean, weighted and unweighted Sobolev gradients. Results are given for the one dimensional Huxley and Fisher models.

基于算力-能量全分布式在线共享的5G网络负荷管理策略

5G与边缘计算等信息基础设施海量部署造成运营商用电成本上升,需推动边缘网络与电网的能量互动以节能降本。现有研究重点关注边缘网络参与日前经济调度,未考虑可再生能源和网络流量双重随机性造成的网络能量供需不平衡问题。针对强随机环境下的网络负荷管理问题,提出面向虚拟化边缘网络的能量实时管理策略。首先,以网络用能成本最小化为目标,构建联合网络资源管理、储能充放电与能量共享模型。其次,针对未来网络信息未知无法直接求解的问题,提出基于随机对偶次梯度法的在线管理策略。然后,针对资源共享涉及运营商隐私问题,提出全分布式的计算资源与能量协同共享算法。最后,仿真验证表明,所提在线算法在无需先验知识的前提下有效减少了5G边缘网络的用能成本。

集中供热系统水力热力耦合特性辨识方法研究

集中供热系统的运行能效主要受其水力热力特性的影响,换热站作为连接热源、热网和热用户的枢纽,是分析系统水力热力特性的关键,站内设备的长期运行性能衰减会导致供热系统整体能耗升高、能效下降,因此有必要对站内设备的运行性能进行诊断.基于换热站实测运行数据,分别采用最小二乘法和梯度下降对站内主要设备包括换热器、循环泵和调节阀的性能曲线进行了辨识,从而构建了集中供热系统的水力热力特性计算方法,全面分析了某典型换热站主要设备性能衰减情况和能耗水平,对主要设备运行性能进行了评估,并对设备维护的经济性和碳减排效果进行了计算.结果表明:换热站内主要设备性能存在不同程度衰减,其中换热器传热系数由1.00 kW/(m^(2)·K)下降至0.64 kW/(m^(2)·K),循环泵标况扬程由22.4 m下降至17.3 m,调节阀流通能力由183.0 t/h下降至82.4 t/h,且阀门整体开度较低,以上问题导致了系统整体能耗的增加;为消除气候变化对集中供热系统能耗分析的影响,结合度日数和实际供热面积,对系统能耗进行评价,与标准年相比,测试年采暖季同期平均热耗和电耗分别增加了0.86 GJ/(104 m^(2)·℃·d)和2.38 kW·h/(104 m^(2)·℃·d);对主要设备进行清洗和更换后,集中供热系统采暖季诊断时间内的同期累计电耗可降低16.3%,全生命周期内CO_(2)排放量可减少128.5 t.

基于改进Yolov5模型的纱筒余纱量检测方法

为实现针织圆纬机纱架上纱筒余纱量的实时检测,提出一种深度学习与传统图像处理相结合的检测方法。通过优化Yolov5的主干网络并加入Shuffle-Attention注意力机制,利用改进后模型在图像中检测并框出纱筒位置;然后利用透视变换、均值偏移、canny轮廓检测、闭操作等处理获取纱筒内外圆轮廓,设计基于梯度下降的圆拟合算法,拟合纱筒内外圆的轮廓,得到纱筒的内外圆半径;最后结合小孔成像的原理完成纱筒余纱量的测量。结果表明:改进后的Yolov5模型在纱筒检测精度上达到99.5%,检测速度可达20帧/s,同时模型参数减少至3.255×106可检测的最小纱筒余纱量为3 mm,当纱筒余纱量小于3 mm后,将其视为空筒,进行延时更换。本文算法拟合圆所花费时间是传统霍夫圆检测算法的1/4左右,因此可满足针织车间的实际应用需求。

基于分数阶偏微分的数字图像滤波去噪仿真

受多种因素影响,数字图像会呈现出不同程度的噪声图斑,导致图像质量、清晰度降低,加大了图像分析、检测、分割等难度,为此,提出基于偏微分方程的图像自适应滤波去噪算法。区分图像噪声点和非噪声点,检测图像的边缘特征,提高算法对边缘的保留能力;构建分数阶偏微分方程模型,通过模型完成对图像的自适应滤波去噪处理。选取含有不同程度的噪声图像对所提方法展开实验测试,结果表明,所提方法可以有效去除图像中的冗余噪声,使图像整体质量得到大幅度提升。

基于加权有界形变函数的可形变图像配准模型

可形变图像配准是图像处理领域中一个非常重要的课题,是计算机视觉中最基本的问题之一,也是医学图像分析的一个难题。文中研究了两幅单模态灰度图像之间的图像配准问题,充分考虑了参考图像的边缘信息,提出了一个新的基于加权有界形变函数的可形变图像配准模型。首次提出了加权的有界形变函数空间,给出了该空间的定义及相关结论,并从理论上证明了所提模型解的存在性。同时,利用梯度下降法设计了有效的算法进行数值求解,分别在合成图像和医学图像上进行数值实验。实验结果和定量评估结果表明,与对比模型相比,所提模型由于引入了控制函数且将加权有界形变函数作为正则项,得到了更精确的配准结果,特别是在图像边缘及一些细节处配准效果有明显提高。

基于前后逐段逼近的含多分支配电网单相接地故障测距方法

随着配电网的发展,T接分支的大量接入使得配电网结构复杂,传统测距算法通常忽略分支,测距精度变低,研究含多分支配电网单相接地故障测距具有重要意义。为此,提出一种基于前后逐段逼近的含多分支配电网单相接地故障精确测距方法。首先,分析分布参数模型,根据零序电压、电流关系,提出故障区段判别系数,判别最小故障区段。其次,利用最小故障区段两端的零序电压、电流建立故障测距函数,采用梯度下降法求解精确故障点。最后,在PSCAD仿真平台上对所述方法进行验证。结果表明,所提方法可确定故障最小区段,精确计算出故障点,并具有较强的耐受过渡电阻能力,能较好适应高渗透率分布式电源的接入。

求解一类非光滑凸优化问题的相对加速SGD算法

一阶优化算法由于其计算简单、代价小,被广泛应用于机器学习、大数据科学、计算机视觉等领域,然而,现有的一阶算法大多要求目标函数具有Lipschitz连续梯度,而实际中的很多应用问题不满足该要求。在经典的梯度下降算法基础上,引入随机和加速,提出一种相对加速随机梯度下降算法。该算法不要求目标函数具有Lipschitz连续梯度,而是通过将欧氏距离推广为Bregman距离,从而将Lipschitz连续梯度条件减弱为相对光滑性条件。相对加速随机梯度下降算法的收敛性与一致三角尺度指数有关,为避免调节最优一致三角尺度指数参数的工作量,给出一种自适应相对加速随机梯度下降算法。该算法可自适应地选取一致三角尺度指数参数。对算法收敛性的理论分析表明,算法迭代序列的目标函数值收敛于最优目标函数值。针对Possion反问题和目标函数的Hessian阵算子范数随变量范数多项式增长的极小化问题的数值实验表明,自适应相对加速随机梯度下降算法和相对加速随机梯度下降算法的收敛性能优于相对随机梯度下降算法。

基于梯度下降法的大房郢水库洪水预报模型参数率定及适用性研究

大房郢水库长期承担合肥市的防洪、供水任务,准确可靠地开展洪水预报对当地防汛抗旱工作具有重要意义。分别采用新安江模型和前期影响雨量(antecedent precipitation index,API)模型构建大房郢水库入库洪水预报模型,基于梯度下降法对模型参数进行优选,并以方案合格率作为评价指标,对2种模型在该水库的适用性进行分析。结果表明:新安江模型和API模型预报方案合格率均为90.7%,预报精度达到甲等;2种模型在不同预报项目中各有优势,对于洪峰和峰现时差,API模型预报效果更好,预报合格率分别为88.9%和100%,较新安江模型分别提高6.7%和5.9%;对于径流深,新安江模型预报效果更为理想,预报合格率可达94.4%,相对于API模型其提升幅度约13.3%。此外,API模型更适用于单式洪水预报,而新安江模型则更适用于复式洪水预报。研究成果可为提升大房郢水库入库洪水预报精度提供理论依据。

一种用于模块化CPC均衡充电的最优化策略

随着锂电池在工业及生活中的广泛应用,锂电池组均衡充电策略的高效性及快速性也变得愈发重要,因此构建单体电池与电池模块间CPC(cell-to-pack-to-cell)的均衡充电系统,以解决锂电池组快速均衡充电问题。首先,对均衡系统进行模块化处理,建立模块内和模块间的均衡电路;然后,提出1种用于均衡充电的最优化策略,对所提策略模型进行分层求解,顶层通过二分法来计算充电时间,底层通过梯度下降法来优化充电电流;最后,通过与非模块化均衡充电策略下的充电时间、均衡时间、单体电池端电压及均衡器承担电压进行仿真对比,验证了所提策略的可行性和有效性。

基于监督下降法的大地电磁二维反演及应用研究

传统的大地电磁二维反演方法较为成熟,但仍存在反演结果依赖初始模型和正则化参数选取、容易陷入局部极小值等问题。监督下降法是一种学习平均下降方向来预测数据残差的机器学习算法。本文尝试采用监督下降法解决传统的大地电磁二维反演存在的问题,基于监督下降法理论开发了大地电磁二维反演算法,设计理论模型合成算例验证了算法的正确性,并对西藏高原实测数据进行反演,检验了监督下降法的实用性。理论模型合成数据和实测数据反演结果表明,相较于传统的非线性共轭梯度反演,基于监督下降法的反演具有收敛速度快、反演效果好、抗噪能力强等特点。