Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Multi-objective Optimal Design of High Frequency Probe for Scanning Ion Conductance Microscopy

Scanning ion conductance microscopy（SICM） is an emerging non-destructive surface topography characterization apparatus with nanoscale resolution. However, the low regulating frequency of probe in most existing modulated current based SICM systems increases the system noise, and has difficulty in imaging sample surface with steep height changes. In order to enable SICM to have the capability of imaging surfaces with steep height changes, a novel probe that can be used in the modulated current based bopping mode is designed. The design relies on two piezoelectric ceramics with different travels to separate position adjustment and probe frequency regulation in the Z direction. To fiarther improve the resonant frequency of the probe, the material and the key dimensions for each component of the probe are optimized based on the multi-objective optimization method and the finite element analysis. The optimal design has a resonant frequency of above 10 kHz. To validate the rationality of the designed probe, microstructured grating samples are imaged using the homebuilt modulated current based SICM system. The experimental results indicate that the designed high frequency probe can effectively reduce the spike noise by 26% in the average number of spike noise. The proposed design provides a feasible solution for improving the imaging quality of the existing SICM systems which normally use ordinary probes with relatively low regulating frequency.

Application for Optimization of New Soft Magnetic Material Motor by Taguchi Method

The application of new soft magnetic materials in permanent magnet motor can effectively reduce the loss of motor and improve the efficiency of motor. Taguchi method is a local multivariable and multi-objective optimization method widely used in various engineering problems, which can effectively improve the efficiency of engineering optimization. In this paper, based on a 25 kW, 1700 r/min three-phase permanent magnet motor, the relevant motor model is established in the finite element simulation software, and the relevant simulation analysis is carried out. Combined with Taguchi method optimization, the local optimal structure scheme is obtained. Through optimization, the motor can maintain high efficiency, reduce the cogging torque of the motor by 53.45%, reduce the torque ripple by 36.79%, and increase the torque generated by the permanent magnet per unit mass by 21.42%. Through this optimization, the overall performance of the motor has been significantly improved. The research content of this paper verifies the feasibility of the application of Taguchi method in the optimization of new soft magnetic material motor, provides a new idea for the optimization design of new soft magnetic material motor, and also provides a certain reference for the local multi-objective optimization of the electromagnetic structure of other similar motors.

一种求解高维优化问题的改进灰狼算法

为求解高维优化问题,提出基于反向学习和衰减因子的灰狼优化算法(grey wolf algorithm based on opposition learning and reduction factor,ORGWO).设计一种灰狼反向学习模型,模型考虑问题搜索边界信息和种群历史搜索信息,初始种群阶段增加反向学习,增强种群多样性.根据算法各个阶段不同特征引入衰减因子,平衡全局和局部勘探能力.选取8个高维函数和23个不同特征的优化函数对算法性能进行测试,进一步使用收敛性分析,寻优成功率,CPU时间,Wilcoxon秩和检验来评估改进算法,实验结果表明,ORGWO算法在求解高维问题上具有较好的精度,鲁棒性和更快的收敛速度.

三阶段自适应采样和增量克里金辅助的昂贵高维优化算法

代理辅助进化算法已广泛应用于求解代价高昂的多目标优化问题,但大多数由于代理模型的局限性而仅限于解决决策变量低维的问题。为了解决高维的昂贵多目标优化问题,提出了一种基于三阶段自适应采样策略的改进增量克里金辅助的进化算法。该算法使用改进的增量克里金模型来近似每个目标函数,此模型的超参数根据预测的不确定性进行自适应更新,降低计算复杂度的同时保证模型在高维上的准确性;此外,在模型管理方面提出一种三阶段自适应采样的策略,将采样过程分为不同的优化阶段以更有针对性的选择个体,能够首先保证收敛性,提高算法的收敛速度。为了验证算法的有效性,在包含各种特征的两组测试问题DTLZ(deb-thiele-laumanns-zitzler)、MaF(many-objective function)和路径规划实际工程问题上与最新的同类型算法进行实验对比,结果表明该算法在解决决策变量高维的昂贵多目标优化问题上具有较强的竞争力。

基于高维多目标序贯三支决策的恶意代码检测模型

针对传统基于二支决策的恶意代码检测方法在面对动态环境中的复杂海量数据时,没有考虑在信息不充足条件下进行决策产生影响的问题,本文提出了一种基于卷积神经网络的序贯三支决策恶意代码检测模型。通过卷积神经网络对样本数据进行特征提取并构建多粒度特征集,引入序贯三支决策理论对恶意代码进行检测。为改善检测模型整体性能,避免阈值选取的主观性,本文在上述模型的基础上,同时考虑模型的综合分类性能、决策效率和决策风险代价建立高维多目标序贯三支决策模型,并采用高维多目标优化算法对模型进行求解。仿真结果表明,模型在保证检测性能的同时,有效地提升了决策效率,降低了决策时产生风险代价,更好地拟合了真实动态检测环境。

An Ant Colony Optimization Based Dimension Reduction Method for High-Dimensional Datasets

In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection （ACO-S） is proposed for high-dimensional datasets. Because microarray datasets comprise tens of thousands of features （genes）, they are usually used to test the dimension reduction techniques. ACO-S consists of two stages in which two well-known ACO algorithms, namely ant system and ant colony system, are utilized to seek for genes, respectively. In the first stage, a modified ant system is used to filter the nonsignificant genes from high-dimensional space, and a number of promising genes are reserved in the next step. In the second stage, an improved ant colony system is applied to gene selection. In order to enhance the search ability of ACOs, we propose a method for calculating priori available heuristic information and design a fuzzy logic controller to dynamically adjust the number of ants in ant colony system. Furthermore, we devise another fuzzy logic controller to tune the parameter （q0） in ant colony system. We evaluate the performance of ACO-S on five microarray datasets, which have dimensions varying from 7129 to 12000. We also compare the performance of ACO-S with the results obtained from four existing well-known bionic optimization algorithms. The comparison results show that ACO-S has a notable ability to＂ generate a gene subset with the smallest size and salient features while yielding high classification accuracy. The comparative results generated by ACO-S adopting different classifiers are also given. The proposed method is shown to be a promising and effective tool for mining high-dimension data and mobile robot navigation.

畅流活水净化动力学行为分析

针对河道和湖泊水质净化处理问题,从水动力学方面优化水体自身的水质净化能力,基于FLUENT软件分别建立二维和三维水动力模型,模拟注水过程中流场的变化,以流场中流速、压力以及湍流强度为指标,研究不同注水位置对水质自净化过程的影响。结果表明:在深度方向上,随着进水口位置的下移,流场活跃范围减小,死区增多;在流动方向,流动距离越远,流场湍流强度越大;在宽度方向,流场流速,压力和湍流强度均以中间进水口的纵向截面对称,流速主要集中在进水口主流区,以及末端的回流处。进水口越接近上部,对于水体的自净化促进效果越好,建议采用上部注水方式来促进河道自净化。研究结果可对促进河道水质自净化提供参考和建议。

求解高维函数的果蝇免疫协同优化算法

果蝇是一种仅依赖其先天性免疫应答机制,即可高效抵御外来入侵者的简单生物。受此免疫机理的启发,论文将模拟果蝇先天性免疫机理设计种群划分及各子群的进化模块,尝试探讨果蝇免疫协同优化算法。该设计思想简洁易懂,内外循环的平衡以及协同思想的设计,使得在保证算法优化效果的前提下,很大程度上提高了算法效率。大量实验表明,该算法在寻优能力、搜索效率及对高维函数的优化方面均具有明显优势。

基于PCA和ICA模式融合的非高斯特征检测识别

针对无人船(Unmanned surface vehicle,USV)航行位姿观测数据的非高斯性/高斯性判别问题,提出一种基于主成分分析(Principal component analysis,PCA)和独立成分分析(Independent component analysis,ICA)模式融合的非高斯特征检测识别方法.首先,采用基于标准化加权平均和信息熵的数据预处理方法.其次,引入混合加权核函数并使用灰狼优化(Grey wolf optimization,GWO)算法进行参数优化,以提高PCA方法的准确性.同时,该算法采用一种新的非线性控制因子策略,提高全局和局部搜索能力.最后,建立了一种基于ICA和PCA联合的相关性分析方法来实现多维数据的降维,在降维数据的基础上综合T型多维偏度峰度检验法和KS(Kolmogorov-Smirnov)检验法进行非高斯性/高斯性特征检测识别.该方法考虑了非线性非高斯的噪声对降维结果精确度的影响,有效降低了多维数据非高斯检测的复杂度,同时也为后续在实际USV位姿估计等应用中提供了保障.实验表明,该方法具有较高的准确性和稳定性,可为USV航行位姿观测数据处理提供支持.

多输入傅里叶神经网络及其麻雀搜索优化

鉴于反向传播(BP)神经网络存在灵敏度高但收敛速度慢,以及已有傅里叶神经网络不具备多输入数据特征提取能力,借助多个傅里叶神经网络构建能接收多维数据的堆叠神经网络,进而将其与多层感知器融合,获得基于梯度下降的多输入傅里叶神经网络。结合此神经网络获取全局最优参数值难的因素,通过在麻雀搜索算法中引入Cat混沌映射、动态种群规模调节机制及参数自适应调节方案,提出改进型麻雀搜索算法,并将其应用于多输入傅里叶神经网络的参数优化及高维函数优化问题的求解。理论分析可得,所提算法的计算复杂度主要由种群规模和优化问题的维度决定。比较性的数值实验表明,所获神经网络提取多源数据特征的能力和泛化能力强,同时所提算法处理高维优化问题具有明显优势且收敛速度快。

Aerodynamic multi-objective integrated optimization based on principal component analysis

Based on improved multi-objective particle swarm optimization（MOPSO） algorithm with principal component analysis（PCA） methodology, an efficient high-dimension multiobjective optimization method is proposed, which, as the purpose of this paper, aims to improve the convergence of Pareto front in multi-objective optimization design. The mathematical efficiency,the physical reasonableness and the reliability in dealing with redundant objectives of PCA are verified by typical DTLZ5 test function and multi-objective correlation analysis of supercritical airfoil,and the proposed method is integrated into aircraft multi-disciplinary design（AMDEsign） platform, which contains aerodynamics, stealth and structure weight analysis and optimization module.Then the proposed method is used for the multi-point integrated aerodynamic optimization of a wide-body passenger aircraft, in which the redundant objectives identified by PCA are transformed to optimization constraints, and several design methods are compared. The design results illustrate that the strategy used in this paper is sufficient and multi-point design requirements of the passenger aircraft are reached. The visualization level of non-dominant Pareto set is improved by effectively reducing the dimension without losing the primary feature of the problem.

Model Updating for High Speed Aircraft in Thermal Environment Using Adaptive Weighted-Sum Methods

Model updating for aircraft in a high temperature environment(HTE)is proposed based on the hierarchical method.With this method,the problem can be decomposed into temperature field updating and dynamic structural updating.In order to improve the estimation accuracy,the model updating problem is turned into a multi-objective optimization problem by constructing the objective function which combined with residues of modal frequency and effective modal mass.Then the metamodeling,support vector regression(SVR)is introduced to improve the optimization efficiency,and the solution can be determined by adaptive weighted-sum method(AWS).Finally,the proposed method is tested on a finite element(FE)model of a reentry vehicle model.The results show that the multi-objective model updating method in HTE can identify the input parameters of the temperature field and structure with good accuracy.

解决高维优化和特征选择的多策略改进正弦余弦算法

针对基本正弦余弦算法(sine cosine algorithm,SCA)求解高维复杂优化问题时存在精度低、收敛慢和易陷入局部最优等缺点,提出一种改进的SCA(improved sine cosine algorithm,iSCA)。首先,该算法设计出一种基于倒S形函数的非线性转换参数规则替代原有线性策略,从而实现从全局搜索到局部搜索的良好过渡;其次,嵌入个体历史最佳信息修改位置搜索方程以指导寻优过程,进一步改善算法的解精度和加快收敛;最后,引入翻筋斗觅食机制生成新的位置以增加群体多样性,从而降低算法陷入局部最优的概率。选取10个高维基准测试函数、10个UCI高维数据集和2个风电机组故障数据集进行仿真实验,并与基本SCA、MSCA(memoryguided SCA)和I-GWO(improved grey wolf optimizer)算法比较,结果表明,iSCA算法在精度和收敛指标上均优于其他比较方法。

求解高维复杂函数的改进飞蛾扑火算法

提出一种融合自适应动态扰动系数和分段可调节搜索策略的飞蛾扑火优化算法(a moth-flame optimization algorithm with adaptive dynamic disturbance coefficient and piecewise adjustable search strategy,ADMFO),求解高维复杂函数优化问题。通过自适应动态扰动系数策略来提高算法的全局搜索能力,避免算法陷入局部最优;通过分段可调节搜索策略来平衡全局探索和局部开发的比重,以此实现更好的寻优策略。对15个单峰和多峰复杂高维基准函数进行寻优实验,与粒子群算法、正弦余弦算法、蝴蝶算法、灰狼算法和其他4种改进算法进行对比。实验结果表明,ADMFO算法具有更好的寻优精度和稳定性。

改进藤壶配尾优化算法求解高维连续优化问题

为增强藤壶配尾优化算法(barnacles mating optimizer,BMO)的全局探索性能和局部寻优精度,融合藤壶幼虫的沉降附着行为与正反向递减铸型策略提出一种改进藤壶配尾优化算法(improved BMO,IBMO)并将其用于求解高维连续优化问题。沉降附着行为模型受自然界藤壶幼虫随潮浮游、螺旋沉降的行为启发所构建,以增加种群多样性并改善算法的全局探索性能。正反向递减铸型策略借鉴反向学习思想并融入递减调控机制修正传统藤壶优化算法的精子铸型过程,以扩增种群的局部搜索域并改善算法的局部开采性能。实验结果表明,两种策略可分别有效改善藤壶优化算法的全局探索和局部开采性能;同时,所提IBMO算法相较于其他新近智能算法则表现出更高收敛精度、更强算法稳健性和良好高维适用性等。

大功率高频变压器三维温升计算及优化设计方法

三维温升计算是大功率高频变压器(HFT)建模中的难点问题,准确、快速的热模型对于HFT的优化设计和稳定运行有着重要意义。目前,普遍采用降维方式建立集总参数热网络模型,其计算精度易受结构参数影响,在宽参数范围寻优中难以实现准确的热点预测。该文基于有限差分方法(FDM)构建了HFT三维热模型,并对离散化误差及其控制方法进行分析。借助有限元仿真对三维热模型的参数适应性进行详细校验,包括结构尺寸、损耗密度及散热条件,校验结果表明,该模型在宽参数范围内的最大误差小于10%。以10 kHz、150 kW变压器为例进行优化设计,单次三维温升计算平均耗时2.8 ms,最优设计边界上的最高温升计算误差低于5.5%。根据优化设计结果加工150 kW变压器原型样机并进行额定功率测试,最高温升计算误差为3%。

信息迁移多任务优化共生生物搜索算法

针对现有共生生物搜索(SOS)算法只能求解单个任务,以及信息负迁移影响多任务优化(MTO)性能这两个难题,提出一个信息迁移多任务优化共生生物搜索(ITMTSOS)算法。首先基于多种群演化MTO框架,根据任务个数设置相应数量种群;然后各种群独立运行基本SOS算法,当某一种群连续若干代停滞进化时,引入个体自身最优经验和邻域最优个体以形成知识模块并将该模块迁移至该种群个体进化过程中;最后对ITMTSOS算法时间和空间复杂度进行分析。仿真实验结果表明,ITMTSOS算法同时求解多个不同形态高维函数时均能快速收敛至全局极值解0,与单任务SOS算法相比,平均运行时间最多缩短约25.25%;而在同时求解多维0/1背包问题和师生匹配问题时,所提算法在测试集weing1和weing7上的最优适应值与目前测试集公布的最优结果相比分别提高了22767和22602,师生最优匹配差和平均匹配差的绝对值分别下降了26和33,平均运行时间约缩短了7.69%。

改进成分分析的差分隐私高维数据发布方法

针对高维数据发布中“维度灾难”所导致发布结果可用性较差的问题,提出一种改进成分分析的差分隐私高维数据发布方法ICAHDP。ICAHDP通过引入属性重要度来优化PCA,利用优化算法对数据进行降维,减少时间和空间的开销。该算法在数据发布的过程中引入基于互信息的评价机制,确定最优的主成分个数。考虑到高维数据中可能存在多个敏感属性,ICAHDP引入敏感属性偏好,结合最优匹配理论,设计敏感属性分级保护策略来满足个性化的差分隐私保护策略。实验表明,ICAHDP不仅保证了发布数据的隐私性,而且很大程度地提升了数据的准确性和实用性。

多策略改进的持续爆破算法

为解决持续爆破算法寻优精度低、易陷入局部最优等问题,提出一种多策略改进的持续爆破算法。在阶段寻优过程中,基于历史阶段最优解提出新的动态爆破半径,提高算法的寻优精度;通过对阶段最优解进行反向变异提高算法跳出局部最优的能力。通过阶段局部最优解向阶段最优解的方向移动的策略更新种群位置,实现种群信息的有效交互。实验结果表明,改进算法的寻优精度和收敛速度明显提升,在求解高维函数优化问题时也有较好的寻优表现。