Kernel principal component analysis network for image classification

In order to classify nonlinear features with a linear classifier and improve the classification accuracy, a deep learning network named kernel principal component analysis network（ KPCANet） is proposed. First, the data is mapped into a higher-dimensional space with kernel principal component analysis to make the data linearly separable. Then a two-layer KPCANet is built to obtain the principal components of the image. Finally, the principal components are classified with a linear classifier. Experimental results showthat the proposed KPCANet is effective in face recognition, object recognition and handwritten digit recognition. It also outperforms principal component analysis network（ PCANet） generally. Besides, KPCANet is invariant to illumination and stable to occlusion and slight deformation.

NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS

In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.

FUZZY PRINCIPAL COMPONENT ANALYSIS AND ITS KERNEL-BASED MODEL

Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.

Kernel Generalization of Multi-Rate Probabilistic Principal Component Analysis for Fault Detection in Nonlinear Process

In practical process industries,a variety of online and offline sensors and measuring instruments have been used for process control and monitoring purposes,which indicates that the measurements coming from different sources are collected at different sampling rates.To build a complete process monitoring strategy,all these multi-rate measurements should be considered for data-based modeling and monitoring.In this paper,a novel kernel multi-rate probabilistic principal component analysis(K-MPPCA)model is proposed to extract the nonlinear correlations among different sampling rates.In the proposed model,the model parameters are calibrated using the kernel trick and the expectation-maximum(EM)algorithm.Also,the corresponding fault detection methods based on the nonlinear features are developed.Finally,a simulated nonlinear case and an actual pre-decarburization unit in the ammonia synthesis process are tested to demonstrate the efficiency of the proposed method.

Application of Particle Swarm Optimization to Fault Condition Recognition Based on Kernel Principal Component Analysis

Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.

Statistical Monitoring of Chemical Processes Based on Sensitive Kernel Principal Components

The kernel principal component analysis （KPCA） method employs the first several kernel principal components （KPCs）, which indicate the most variance information of normal observations for process monitoring, but may not reflect the fault information. In this study, sensitive kernel principal component analysis （SKPCA） is proposed to improve process monitoring performance, i.e., to deal with the discordance of T2 statistic and squared prediction error SVE statistic and reduce missed detection rates. T2 statistic can be used to measure the variation di rectly along each KPC and analyze the detection performance as well as capture the most useful information in a process. With the calculation of the change rate of T2 statistic along each KPC, SKPCA selects the sensitive kernel principal components for process monitoring. A simulated simple system and Tennessee Eastman process are employed to demonstrate the efficiency of SKPCA on online monitoring. The results indicate that the monitoring performance is improved significantly.

Comparison of Kernel Entropy Component Analysis with Several Dimensionality Reduction Methods

Dimensionality reduction techniques play an important role in data mining. Kernel entropy component analysis( KECA) is a newly developed method for data transformation and dimensionality reduction. This paper conducted a comparative study of KECA with other five dimensionality reduction methods,principal component analysis( PCA),kernel PCA( KPCA),locally linear embedding( LLE),laplacian eigenmaps( LAE) and diffusion maps( DM). Three quality assessment criteria, local continuity meta-criterion( LCMC),trustworthiness and continuity measure(T&C),and mean relative rank error( MRRE) are applied as direct performance indexes to assess those dimensionality reduction methods. Moreover,the clustering accuracy is used as an indirect performance index to evaluate the quality of the representative data gotten by those methods. The comparisons are performed on six datasets and the results are analyzed by Friedman test with the corresponding post-hoc tests. The results indicate that KECA shows an excellent performance in both quality assessment criteria and clustering accuracy assessing.

基于KPCA-CNN-DBiGRU模型的短期负荷预测方法

本文针对已有神经网络模型在短期负荷预测中输入维度过高、预测误差较大等问题,提出了一种结合核主成分分析、卷积神经网络和深度双向门控循环单元的短期负荷预测方法。先运用核主成分分析法对原始高维输入变量进行降维,再通过卷积深度双向门控循环单元网络模型进行负荷预测。以第九届全国电工数学建模竞赛试题A题中的负荷数据作为实际算例,结果表明所提方法较降维之前预测误差大大降低,与已有预测方法相比也有大幅的误差降低。

基于SMOTE-IKPCA-SeNet深度迁移学习的小批量生产质量预测研究

随着智能制造技术的发展和客户个性化需求的增加,多品种小批量生产方式逐渐成为制造业的主流。面向大批量生产、以统计过程控制为核心的质量管理方式并不适用于小批量生产。针对复杂生产过程存在参数多、非线性和交互作用的问题,提出利用深度迁移学习的方式将历史生产数据作为源域迁移至小样本目标产品数据进行质量预测。首先,通过合成少数类过采样技术(synthetic minority over-sampling technique,SMOTE)和改进的核主成分分析(improved kernel principal component analysis,IKPCA)算法筛选源域和目标域的可迁移特征,这不仅兼顾了特征重要性和可迁移性,还减少了“负迁移”,提高了模型泛化能力;然后,采用结合通道注意力机制的卷积神经网络SeNet构建基于深度迁移学习的质量预测模型。仿真结果表明,随着目标域样本的增加,所提方法的预测准确性明显优于广泛采用的支持向量机建模方法。同时,所提可迁移特征筛选方法显著提高了深度迁移学习的质量预测效果,为复杂的小批量生产过程质量保证提供了新方法。

基于KPCA-PSO-ELM算法的地表水化学需氧量紫外-可见吸收光谱检测研究

化学需氧量(COD)是水质检测重要指标之一,反映水体有机物含量。传统的COD化学检测方法存在操作繁琐,等待时间长,二次污染等缺点。紫外-可见吸收光谱法是目前水体化学需氧量检测中应用最为广泛的方法之一,具有检测快速、无污染等特点。为了满足地表水化学需氧量快速、实时、在线监测等要求,采用紫外-可见吸收光谱进行测量,提出了内核主成分分析(KPCA)结合粒子群优化极限学习机(PSO-ELM)预测模型,满足当前对地表水化学需氧量快速、实时监测的要求。对光谱进行Savitzky-Golay(SG)滤波以降低随机噪声的影响;用积分光谱代替原光谱,以降低信号波动带来的影响;再将得到的光谱信息归一化,消除不同光谱数据量纲的影响。将预处理后的数据利用KPCA算法将全光谱数据压缩为5个特征,有效解决光谱信息冗余的问题;采用PSO算法对ELM的权重和偏置进行优化极大提高了模型的精度。对217个河流、长江及支流、湖库等地表水样本按照7∶3随机划分成训练集和测试集,并进行建模测试,其中训练集拟合优度(R2)为0.930 2、均方根误差(RMSE)为0.363 0 mg·L^(-1)、测试集拟合优度R2为0.931 9、均方根误差(RMSE)为0.400 7 mg·L^(-1)。为了验证提出的基于KPCA全光谱数据压缩方法对预测模型的提升效果,分别对比了主成分分析(PCA)、连续投影算法(SPA)、套索回归(LASSO)等特征处理算法。PCA-PSO-ELM模型的RMSE为0.715 1 mg·L^(-1)、 SPA-PSO-ELM模型的RMSE为0.473 7 mg·L^(-1)、 LASSO-PSO-ELM模型的RMSE为0.412 6 mg·L^(-1), KPCA-PSO-ELM模型较上述三种模型,RMSE分别降低了78.46%、 18.22%、 2.97%,结果表明KPCA是一种高效的光谱降维算法,能够有效消除光谱冗余信息,提升模型预测精度。基于KPCA-PSO-ELM预测模型结合紫外-可见吸收光谱可以实现对地表水COD快速、实时检测,为在线COD检测场景提供方法支撑。

基于KPCA与KLPP及Wilks统计量的留兰香三维荧光数据特征提取与鉴别分析

为实现留兰香产地的快速鉴别,该研究提出了一种核主成分分析(kernel principal component analysis,KPCA)与核局部保持投影(kernel locality preserving projections,KLPP)及WilksΛ统计量序贯融合的特征波长提取策略,在此基础上鉴别5个产地的留兰香。首先,在采集5个产地300个留兰香样本的三维荧光数据后,运用三角形内插值法去除原始光谱中的瑞利散射和拉曼散射,并运用SG(Savitzky-Golay)对数据进行平滑预处理。然后,对预处理后的荧光光谱数据分别利用KPCA、KPCA+KLPP、KPCA+WilksΛ统计量、 KPCA+KLPP+WilksΛ统计量4种方法提取特征激发波长和特征发射波长。接着,按特征激发波长从小到大顺序将其对应的特征发射波长光谱值首尾相连转换成行向量;4种方法从300个样本中各得到1个300行的特征波长光谱值矩阵。再者,运用Fisher判别分析(fisher discriminant analysis,FDA)对特征波长光谱值矩阵进行数据可分性融合,生成可分性FD(fisher discriminant)变量。选取前4个累计判别能力达到99%的FD变量作为鉴别模型的输入向量。最后,用支持向量机(support vector machine,SVM)算法分析4个FD变量,分别得到对应于4种特征提取波长方法的FDA+SVM鉴别结果,其正确率分别为92.00%、96.00%、94.67%、100%。结果表明,所提出的KPCA+KLPP+WilksΛ统计量序贯融合的特征波长提取策略能够有效减少三维荧光光谱数据的冗余,并能表征原始荧光数据的信息特征,实现了5种留兰香产地的正确鉴别。该研究可为后续利用三维荧光光谱开展留兰香重要组分量化分析提供一定的基础。

基于KPCA特征量降维的风电并网系统暂态电压稳定性评估

针对电力系统暂态电压稳定性评估中所需特征量数据庞大,影响模型训练时间,降低计算效率等问题,提出了一种基于核主成分分析方法KPCA和CPSO-BP组合的风电并网系统暂态电压稳定性评估方法.首先根据输入特征采集原始特征集,采用核主成分分析算法对特征量进行非线性数据处理,提取出最优的特征集.然后将降维后的特征集作为CPSO-BP神经网络输入量进行监督学习,将得到的模型按照临界故障切除时间裕度值的大小进行分类,将分类后的样本进行风电并网系统的暂态电压稳定性评估和临界故障切除时间裕度值预测.仿真分析结果表明,对输入特征进行降维,保留重要输入特征量,剔除冗余特征量,不仅简化了模型,还提高了网络评估的准确性和计算效率.

基于KPCA-WOA-SVM的住宅工程造价预测

在项目决策阶段,准确预测住宅工程造价对提高工程项目决策的科学性至关重要,引入人工智能及机器技术能进一步提高预测的精准度。通过文献梳理,确定决策阶段住宅工程造价的影响指标,用核主成分分析(KPCA)对影响指标进行降维,利用鲸鱼优化算法(WOA)确定支持向量机(SVM)的惩罚参数与核参数,最终构建基于KPCA-WOA-SVM的住宅工程造价预测模型。采用江苏省近5年的70组住宅工程造价数据对模型进行验证,结果表明:与BP神经网络模型、SVM模型和WOA-SVM模型相比,KPCA-WOA-SVM模型预测精准度更高,适用性更好。

一种融合KPCA、FastICA及SVD的腹壁源胎儿心电 信号提取算法研究

目的:为实现从母体腹壁混合信号中提取高信噪比和波形清晰的胎儿心电信号,提出一种融合核主成分分析(kernel principal component analysis,KPCA)、快速独立成分分析(fast independent component analysis,FastICA)及奇异值分解(singular value decomposition,SVD)的胎儿心电信号提取算法。方法:首先,采用KPCA对母体心电信号进行降维,再利用改进的基于负熵的FastICA处理降维后的数据,得到独立成分。随后,引入样本熵进行信号通道选择,挑选出包含最多母体信息的信号通道。在选中的母体通道上进行SVD,得到母体心电信号的近似估计,再用腹壁源信号减去该信号得到胎儿心电的初步估计。最后,采用改进的基于负熵的FastICA成功分离出纯净的胎儿心电信号。在腹部和直接胎儿心电图数据库(Abdominal and Direct Fetal Electrocardiogram Database,ADFECGDB)和PhysioNet 2013挑战赛数据库中对提出的算法进行验证。结果:提出的算法在主观视觉效果和客观评价指标上都表现出优越的性能。在ADFECGDB数据库中,胎儿QRS复合波检测的敏感度、阳性预测值和F1值分别为99.74%、98.85%和99.30%;在PhysioNet 2013挑战赛数据库中,胎儿QRS复合波检测的敏感度、阳性预测值和F1值分别为99.10%、97.87%和98.48%。结论:融合KPCA、FastICA及SVD的胎儿心电信号提取算法在提取胎儿心电信号的同时有效处理了附加噪声,为胎儿疾病的早期诊断提供了有力支持。

基于OVMD-KPCA-RTH-GRU的短期光伏发电功率预测

针对光伏发电功率的随机性、波动性和非线性问题,提出了一种结合经红尾鵟(RTH)算法优化的变分模态分解(VMD)、核主成分分析(KPCA)和经RTH算法优化的门控循环单元(GRU)神经网络的光伏发电功率预测模型。首先,使用RTH算法对VMD和GRU神经网络的5个超参数进行优化;接着,应用优化后的VMD方法分解原始数据,以减少光伏数据的波动性和随机性;然后,采用KPCA方法降低数据维度,消除冗余;最后,利用经RTH优化的GRU神经网络模型进行时序建模。通过分析新疆某光伏电站的历史发电数据,并与GRNN、LSTM、GRU以及OVMD-GRU、OVMD-KPCA-GRU模型相比较,本模型的拟合优度高达98.96%,显示出更高的预测精度。

基于肌音信号的KPCAGASVM步态模式识别

外骨骼机器人发展迅速,基于生理信号的运动意图识别在人机协同控制研究中得以重视。针对肌电信号易受肌肉疲劳影响和采集要求高的缺点,提出一种基于肌音信号的核主成分分析和改进支持向量机(KPCAGASVM)的模式识别方案,对平地行走、上楼下楼和上坡下坡5种步态进行模式识别研究。基于遗传算法进行参数调优,其识别方案KPCAGASVM的识别准确率为97.33%,优于PCAGASVM和其他分类器。实验验证,基于肌音信号的KPCAGASVM为一种高效的步态运动识别方案。

基于KPCA-LSSVM的回采工作面瓦斯涌出量的预测

为了提高瓦斯涌出量预测精度,针对瓦斯涌出量影响因素具有线性重叠、高维非线性等问题,提出使用核主成分分析法(KPCA)对影响因素进行非线性降维。选取沈阳某矿30组样本数据,以前24组数据作为训练集,后6组数据作为测试集,将确定后的核主成分作为最小二乘支持向量机(LSSVM)的输入变量,建立KPCA-LSSVM预测模型,将预测结果与PCA-LSSVM、LSSVM、多元非线性回归、KPCA-BP神经网络、PCA-BP神经网络以及BP神经网络预测结果进行对比。以最大相对误差绝对值作为模型预测精度的评价指标。研究结果表明:当选取前4个核主成分时,即达到模型训练要求。KPCA-LSSVM模型的预测最大相对误差绝对值为5.89%,预测精度均优于其他6种对比模型。研究结果可为实现瓦斯涌出量高精度预测提供参考。

Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion （BIC） are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation （BP） network is applied whose input is multivar- iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis （LKPCA） model for incipient fault prognosis. The new method has been exemplified in a sim- ple nonlinear process and the complicated Tennessee Eastman （TE） benchmark process. The results indicate that the new method has suoerioritv in the fault prognosis sensitivity over other traditional fault prognosis methods.

基于WKPCA与IEDO-XGBoost的变压器故障诊断方法研究

针对变压器故障的特点,将加权核主成分分析技术与IEDO-XGBoost相结合,提出了一种新的变压器故障诊断模型。该方法主要将溶解气体分析技术与无编码比值法相结合,获取变压器的故障特征,利用WKPCA对其进行降维处理,并将归一化处理后的故障样本数据作为IEDO-XGBoost模型的输入,输出变压器故障诊断类型及其诊断准确率。选取20维变压器故障特征数据进行WKPCA降维处理,加快了模型的收敛速度;采用自适应正余弦策略和高斯变异策略对指数分布优化器算法进行改进,并用10个典型测试函数对改进后的指数分布优化算法性能进行了测试,结果表明改进后的指数分布优化算法具有更快的收敛速度和全局搜索能力。然后,利用改进的指数分布算法来确定XGBoost模型中的多个最优参数。仿真结果表明,该模型的诊断准确率为91.82%,分别比EDO-XGBoost、NGO-XGBoost、GJO-XGBoost、GWO-XGBoost和WOA-XGBoost故障诊断模型高2.73%、3.64%、5.46%、8.18%和10.91%,验证了本文所提方法能够有效提高变压器故障诊断性能。