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.

Pneumatic resistance network analysis and dimension optimization of high pressure electronic pneumatic pressure reducing valve

The structure and working principle of a self-deigned high pressure electronic pneumatic pressure reducing valve (EPPRV) with slide pilot are introduced.The resistance value formulas and the relationship between the resistance and pressure of three typical pneumatic resistances are obtained.Then,the method of static characteristics analysis only considering pneumatic resistances is proposed,the resistance network from gas supply to load is built up,and the mathematical model is derived from the flow rate formulas and flow conservation equations,with the compressibility of high pressure gas and temperature drop during the expansion considered in the model.Finally,the pilot spool displacement of 1.5 mm at an output pressure of 15MPa and the enlarging operating stroke of the pilot spool are taken as optimization targets,and the optimization is carried out based on genetic algorithm and the model mentioned above.The results show that the static characteristics of the EPPRV are significantly improved.The idea of static characteristics analysis and optimization based on pneumatic resistance network is valuable for the design of pneumatic components or system.

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.

A multi-objective optimization based on machine learning for dimension precision of wax pattern in turbine blade manufacturing

Wax pattern fabrication in the investment casting of hollow turbine blades directly determines the dimension accuracy of subsequent casting,and therefore significantly affects the quality of final product.In this work,we develop a machine learning-based multi-objective optimization framework for improving dimension accuracy of wax pattern by optimizing its process parameters.We consider two optimization objectives on the dimension of wax pattern,i.e.,the surface warpage and core offset.An active learning of Bayesian optimization is employed in data sampling to determine process parameters,and a validated numerical model of injection molding is used to compute objective results of dimension under varied process parameters.The collected dataset is then leveraged to train different machine learning models,and it turns out that the Gaussian process regression model performs best in prediction accuracy,which is then used as the surrogate model in the optimization framework.A genetic algorithm is employed to produce a non-dominated Pareto front using the surrogate model in searching,followed by an entropy weight method to select the most optimal solution from the Pareto front.The optimized set of process parameters is then compared to empirical parameters obtained from previous trial-and-error experiments,and it turns out that the maximum and average warpage results of the optimized solution decrease 26.0%and 20.2%,and the maximum and average errors of wall thickness compared to standard part decrease from 0.22 mm and 0.0517 mm using empirical parameters to 0.10 mm and 0.0356 mm using optimized parameters,respectively.This framework is demonstrated capable of addressing the challenge of dimension control arising in the wax pattern production,and it can be reliably deployed in varied types of turbine blades to significantly reduce the manufacturing cost of turbine blades.

Optimization design of the hydro-pneumatic suspension system for high clearance self-propelled sprayer using improved MOPSO algorithm

Large high clearance self-propelled sprayers were widely used in field plant protection due to their high-efficiency operation capabilities.Influenced by the characteristics of field operations such as high power,heavy weight,high ground clearance,and fast operation speed,the comprehensive requirements for the ride comfort,handling stability and road friendliness of the sprayer were increasingly strong.At the present stage,the chassis structure of the high clearance selfpropelled sprayer that attaches great importance to the improvement of comprehensive performance still has the problems of severe bumps,weak handling performance and serious road damage in complex field environments.Therefore,this paper proposes an optimization design method for hydro-pneumatic suspension system of a high clearance self-propelled sprayer based on the improved MOPSO(Multi-Objective Particle Swarm Optimization)algorithm,covering the entire process of configuration design,parameter intelligent optimization,and system verification of the high clearance self-propelled sprayer chassis.Specifically,chassis structure of the hydro-pneumatic suspension suitable for the high clearance self-propelled sprayer was designed,and a design method combining the improved MOPSO algorithm based on time-varying fusion strategy and adaptive update with the parameter optimization of hydro-pneumatic suspension based on this algorithm was proposed,and finally the software simulation and bench performance verification were carried out.The results show that the optimized hydropneumatic suspension has excellent vibration reduction effect,and the body acceleration,suspension dynamic deflection and tire deflection were increased by 16.5%,9.9%and 0.9%respectively,compared with those before optimization.The comprehensive performance of the hydro-pneumatic suspension designed in this study is better than that of the traditional suspension.

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.

多策略改进的猎人猎物优化算法及其应用

针对猎人猎物优化算法易陷入局部最优和收敛精度不足的问题,本文提出多策略改进的猎人猎物优化算法。该算法基于动态搜索思想,通过自适应机制从全局搜索转向局部开发;通过利用种群的历史信息来实施差分进化,从而增强种群的多样性;采用精英池策略和非线性步长相结合的方法,以防止算法陷入局部最优,并提升其收敛精度。在10个大规模(10 000维)测试函数上对改进后的算法和其他6种经典或最新的优化算法进行性能评估,结果显示,该算法在全局优化能力、寻优精度和稳定性方面均表现出色,能有效解决高维优化问题。最后,将多策略改进猎人猎物优化算法应用于三维无人机路径规划问题,仿真实验结果表明,该算法能求解到最优的无人机三维规划路径。

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.

水库群调度高维优化问题约束处理方法研究

随着水库群优化调度的调度规模的增加和调度时间步长的精细化,水库群调度高维优化问题的决策变量维度逐渐增加到数百数千维。在具有高维决策变量的梯级水库优化调度中,往往需要考虑多重复杂约束。现有传统优化方法在处理此类问题时难以找到有效可行解;而智能优化算法的多维度联动随机搜索,寻优空间大但寻优效率低。为此,本文提出了一种结合罚函数的嵌套DPSA–POA和智能算法的约束处理方法,将罚函数与DPSA–POA和智能算法嵌套,一方面可克服DPSA–POA收敛结果容易受初值影响和寻优空间狭窄的缺陷,另一方面可提升智能算法随机搜索策略的寻优效率。随后,本文以决策变量高达2 196维的赣江中游梯级水库群防洪优化调度问题为例开展分析,相关分析结果表明:1)结合罚函数嵌套DPSA–POA智能算法的3种约束处理方式,在不同来水情形下均能得到高维优化问题可行解;2)3种约束处理方式中,嵌套优化得到可行解后只进行DE优化的方式2收敛精度最高,计算时间约10 h;嵌套优化得到可行解后只进行DPSA–POA优化的方式3收敛精度次之,计算时间约1~3 h;3)现有可行解优先策略(SF)、随机排序策略(SR)、罚函数策略(PF)和ε–松弛约束策略(EC)配合现代智能算法,无法在不同来水情形下稳定收敛到可行解,且可行解的收敛精度相比本文提出的方法有明显差距。综上,本文提出的高维优化问题约束处理方法可有效解决水库群调度高维优化问题。

面向多目标优化的航空发动机装配特征选择

由于航空发动机装配工艺和试车工艺的复杂性,收集到的航空发动机装配数据的装配特征非常庞大,严重干扰了对航空发动机装配质量的准确预测,如何选择航空发动机装配的关键质量特征实现质量预测成为极具挑战性的问题。因此,针对航空发动机装配特征选择难题,本文提出面向多目标优化的航空发动机装配数据的两阶段特征选择方法。明确特征选择的优化目标,在第1阶段,基于最大相关最小冗余算法的相关特征选择过程,计算装配特征与试车指标的互信息值,筛选出与试车指标相关性最大的相关特征,并剔除有干扰影响的冗余特征。在第2阶段,通过引入种群初始化策略和自适应遗传算子,提出基于改进的二代非支配排序遗传算法的关键质量特征选择过程,得到航空发动机装配的关键质量特征子集的帕累托前沿。实验表明,本文所提出的两阶段特征选择方法比传统的方法有更好的适用性和有效性,实现了对航空发动机装配特征选择,提高了对航空发动机装配质量的预测准确率。

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.

基于神经辐射场算法的混合现实三维重建技术

针对目前在混合现实(MR)环境中高效率建立高质量三维(3D)模型的需求,基于神经辐射场算法(NeRF)的三维重建技术,提出了一种基于Laplacian算子的数据集优化算法。首先,围绕某线切割设备录制了一段1 min 51 s的视频,并采取等距提取视频帧的方式,获取了训练数据集;然后,使用Laplacian算子对数据集进行了优化,同时保留了原始数据集作为对比,使用了基于NeRF算法的重建方式与传统的基于COLMAP的稠密点云重建方式,分别对两组数据集进行了三维重建;最后,在重建精度与重建速度方面,对不同重建方式、不同重建数据集的重建结果进行了比较。研究结果表明:COLMAP稠密点云重建耗时是基于NeRF重建耗时的9.98倍,而相较于COLMAP稠密点云重建,使用NeRF重建方式的模型表面缺陷较少;此外,使用Laplacian算子优化的数据集的NeRF重建在峰值信噪比(PSNR)和结构相似性(SSIM)指标上分别提升了2.43%、0.72%,有利于提升重建模型的质量。研究结果支持混合现实技术在制造业数字化转型中的应用,可为其提供有益的参考。

改进NSGA-III求解高维多目标绿色柔性作业车间调度问题

为解决NSGA-III在求解上述模型存在初始解质量差与局部搜索效率低的问题,提出一种改进的NSGA-III(NSGA-III-TV)。基于MSOS编码,分别对OS和MS染色体采取不同混合初始化策略以提高初始解质量;基于关键路径,采用改进N6邻域结构进行邻域搜索,有效缩短完工时间并降低搜索盲目性,同时采用3种有效变异算子扩大算法搜索空间,提高后期收敛能力。结果表明:NSGA-III-TV在求解高维多目标柔性作业车间调度问题上具有较好的性能以及实用性,为企业生产制造车间的智能绿色转型升级提供了有力支持。

解决高维优化和特征选择问题的多策略改进麻雀搜索算法

为解决基本麻雀搜索算法(sparrow search algorithm,SSA)在求解高维复杂优化问题时存在收敛速度慢、容易陷入局部最优解及后期种群多样性变弱等问题,提出了一种基于海鸥优化算法算子和鲸鱼优化算法算子的改进麻雀搜索算法(improved sparrow search algorithm based on seagull optimization algorithm operator and whale optimization algorithm operator,SWSSA)。首先,该算法设计了自适应种群比例策略以增强种群在迭代过程中的多样性;其次,在局部搜索阶段融入鲸鱼优化算法气泡网捕食策略,增强麻雀搜索算法的局部搜索能力、加快收敛速度;然后,在追随者位置引入改进的海鸥优化算法算子降低算法陷入局部最优的概率。最后,选取了12个高维基准测试函数和16个UCI网站上的高维数据集进行仿真实验,将SWSSA与基本SSA、SSA变体版本、黄金正弦算法(golden sine algorithm,GSA)、蝴蝶算法(butterfly optimization algorithm,BOA)、黏菌算法(slime mold algorithm,SMA)、海鸥算法(seagull optimization algorithm,SOA),以及其他学者改进的算法进行比较。结果表明,本文提出的算法在12个测试函数上的收敛精度取得最优的比例达到了100%,在约95%的测试函数上收敛速度最快,在16个数据集中有9个数据集分类准确率最高和6个最佳特征子集数量最少。可见所提算法在处理高维函数优化和数据集特征选择问题上具有一定的优势。

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。