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.

A Kernel-Based Nonlinear Representor with Application to Eigenface Classification

This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.

Iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations

Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the iterative computation and increase the convergence rate and points out that this method is still effective. Even if the initial condition is discrete.

Numerical Solution of Nonlinear Mixed Integral Equation with a Generalized Cauchy Kernel

In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)). Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is powerful, effective and very simple.

Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel

In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.

含较少非线性非忠实不可约特征标的有限幂零群

有限群不可约特征标核的性质对群结构有重要的影响.刻画了非线性非忠实不可约特征标个数至多为2的有限幂零群的结构.

融合相似性度量加权核偏最小二乘的烷烃气体定量分析方法

烃类气体含量的有效监测是油气勘探开采过程中安全保障的重要环节。红外光谱法作为一种安全高效的检测方法,受到现场工程师的关注,但主要采用离线模型进行测量,无法较好应对现场复杂的工况及变化多样的非线性影响因素,导致离线模型不更新而难以维持较高的预测精度。为此,提出了一种融合相似性度量加权核偏最小二乘的即时学习建模策略。首先设计了一种多相似性度量准则融合的样本相似性判别依据,有效筛选历史样本用于在线建模,其次在局部PLS模型中引入非线性核函数,实现非线性特征的有效提取,弥补线性偏最小二乘模型的非线性处理能力。在构建的多组分混合气体红外光谱数据上的实验结果验证了该方法的有效性,拟合优度R2达到0.994 1,RMSE和MRE相比PLS模型分别提升了43.6%和85.8%,可有效用于烃类气体红外光谱定量分析模型的在线更新与高精度预测。

有限实验数据下工程结构概率建模及随机响应分析

为了研究实验数据下工程结构输入参数的概率建模以及依据所建模型的响应分析的问题,本文提出了一种实验数据下工程结构概率建模及随机响应求解的方法。依据Karhunen-Loeve展开和任意多项式混沌(aPC)展开理论,提出了一种基于核密度估计的新型随机模型;发展了结构随机响应的求解技术,并提出了用于随机响应aPC系数估计的D-optimal加权插值方法,实现了结构响应的高精度求解。研究表明:本文的研究为实验数据下工程结构的合理随机建模和高效响应分析提供了一个有效的框架,本文方法有效。

基于Kernel-SOM的非线性系统辨识及模型运行收敛性分析

该文提出基于核SOM(Kernel-SOM)的非监督非线性系统辨识方法。在辨识误差和系统初始输入误差同时存在的条件下,对Kernel-SOM辨识模型独立运行的收敛性进行了理论分析,并给出了辨识模型运行收敛的定理。数字仿真表明了所述方法的有效性及收敛定理的正确性。

Kernel-kNN:基于信息能度量的核k-最近邻算法

提出一种核k最近邻算法.首先给出用于最近邻学习的信息能度量方法,该方法克服了高维数据不便于用传统距离度量表示的困难,提高了数据间类别相似性和距离的一致性.在此基础上,将传统的kNN扩展为非线性形式,并采用半正定规划学习全局最优的度量矩阵.算法主要特点是:能较好地适用于高维数据,并有效提升kNN的分类性能.多个数据集的实验和分析表明,本文的Kernel-kNN算法与传统的kNN算法比较,在低维数据上,分类准确率相当;在高维数据上,分类性能有明显提高.

基于双层自适应集成残差主成分分析的复杂非线性过程监测

多元统计监测方法常使用正常数据选取特征,而现实过程中,不同的故障将影响不同的特征,并且这些特征可能随着时间和控制系统的作用而变化。当故障发生并随时间变化时,要想获得更好的故障检测能力,就需要聚集有效的故障敏感特征。本文提出了一种双层自适应集成残差主成分分析(AERPCA)模型,其子模型包含不同的特征,并突出地呈现一个或多个相关故障。首先,根据正常数据计算主成分分析(PCA)特征,利用不同特征构建线性子模型和相应的残差空间。考虑到残差空间的非线性特性及有效特征更为分散,采用核PCA(KPCA)提取不同的特征并组成同一残差空间下不同KPCA子模型。然后,利用贝叶斯方法获取集成KPCA子模型,完成各残差空间的划分和集成。最后,在主空间中获得多个线性子模型以及在残差空间中获得多个集成的非线性子模型后,利用滑动窗口确定当前时刻监控效果最好的模型。采用田纳西-伊士曼过程验证了AERPCA的有效性。

基于核密度估计的故障诊断信号非均匀量化方法

在工业物联网的某些故障诊断场景中,由于缺少电信网络覆盖,采集信号通过远距离无线电(Long Range Radio,LoRa)技术实现无线可靠回传,但其较低的传输速率会限制故障诊断的精度。针对LoRa窄带宽的技术限制,提出了采样频率和量化分辨率固定条件下的时域信号非均匀量化方案。首先,通过建立基于核密度估计(Kernel Density Estimation,KDE)的非参数拟合模型,重点研究了带宽受限场景中合适的核函数类型和带宽确定准则,拟合生成传感信号幅度的概率密度函数(Probability Density Function,PDF)。其次,以PDF为输入,以最小化量化噪声为目标函数,通过非线性规划,输出最佳的一组非均匀量化电平值。其特点在于针对出现频次最高的时域幅度,采用更小的量化间隔,实现量化噪声的最小化。最后,以轴流风机状态检测为例进行了实验,结果表明,基座松动和轴承故障对量化电平的影响更大。随着量化分辨率的增加,KDE量化逐渐趋近均匀量化,相较于高斯量化的优势逐渐缩小。因此,提出的KDE量化方案适合窄带宽条件下的非均匀量化,可提高信道利用率,并在传输带宽和量化噪声之间取得折中。

On-Line Batch Process Monitoring Using Multiway Kernel Partial Least Squares

An approach for batch processes monitoring and fault detection based on multiway kernel partial least squares(MKPLS) was presented.It is known that conventional batch process monitoring methods,such as multiway partial least squares(MPLS),are not suitable due to their intrinsic linearity when the variations are nonlinear.To address this issue,kernel partial least squares(KPLS) was used to capture the nonlinear relationship between the latent structures and predictive variables.In addition,KPLS requires only linear algebra and does not involve any nonlinear optimization.In this paper,the application of KPLS was extended to on-line monitoring of batch processes.The proposed batch monitoring method was applied to a simulation benchmark of fed-batch penicillin fermentation process.And the results demonstrate the superior monitoring performance of MKPLS in comparison to MPLS monitoring.

Selective ensemble modeling based on nonlinear frequency spectral feature extraction for predicting load parameter in ball mills

Strong mechanical vibration and acoustical signals of grinding process contain useful information related to load parameters in ball mills. It is a challenge to extract latent features and construct soft sensor model with high dimensional frequency spectra of these signals. This paper aims to develop a selective ensemble modeling approach based on nonlinear latent frequency spectral feature extraction for accurate measurement of material to ball volume ratio. Latent features are first extracted from different vibrations and acoustic spectral segments by kernel partial least squares. Algorithms of bootstrap and least squares support vector machines are employed to produce candidate sub-models using these latent features as inputs. Ensemble sub-models are selected based on genetic algorithm optimization toolbox. Partial least squares regression is used to combine these sub-models to eliminate collinearity among their prediction outputs. Results indicate that the proposed modeling approach has better prediction performance than previous ones.

Hellinger distance based probability distribution approach to performance monitoring of nonlinear control systems

Control performance monitoring has attracted great attention in both academia and industry over the past two decades. However, most research efforts have been devoted to the performance monitoring of linear control systems, without considering the pervasive nonlinearities(e.g. valve stiction) present in most industrial control systems. In this work, a novel probability distribution distance based index is proposed to monitor the performance of non-linear control systems. The proposed method uses Hellinger distance to evaluate change of control system performance. Several simulation examples are given to illustrate the effectiveness of the proposed method.

Online Contribution Rate Based Fault Diagnosis for Nonlinear Industrial Pro cesses

在过去的十年，核主管部件分析(KPCA ) 在监视区域的数据驱动的过程相当流行地出现了。庞大的工作被做了显示出它的简洁，可行性，和有效性。然而，核诡计的介绍使直接为差错诊断采用传统的贡献阴谋不可能。在这份报纸，根据重游并且分析存在， KPCA 相关的诊断来临，新贡献率基于方法被建议它能清楚地解释有缺点的变量。而且，为联机非线性的诊断的一个计划被建立。最后，连续搅动的坦克反应堆(CSTR ) 上的案例研究基准被使用存取新方法论的有效性，在有传统的线性方法的比较也被包含的地方。

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

基于核密度估计法的大跨度非对称悬索桥碰撞概率分析

为了对随机地震作用下大跨度非对称悬索桥的梁端碰撞概率进行评估,基于OpenSEES建立了一座典型实例桥的三维非线性有限元模型,综合考虑了地震动与模型参数的双重随机特性,采用拉丁超立方抽样与核密度估计方法建立了桥梁碰撞概率模型,并验证了该方法的有效性,最后分析了桥梁结构随机参数、伸缩缝宽度及非线性阻尼器对悬索桥梁端碰撞概率的影响。分析结果表明:若忽略桥梁结构参数的不确定性可能会高估桥梁的碰撞概率,其最大误差可达122%;大震作用下非线性阻尼器可以显著减小桥梁的碰撞概率,且阻尼器的减震效果随着伸缩缝宽度增大而越加明显;当PGA<0.7g时,通过设置阻尼器不仅可以减小悬索桥的碰撞力峰值,而且可以减少梁端碰撞次数;当PGA>0.7g时,阻尼器对碰撞次数影响较小,但能明显降低其碰撞力。

基于核函数-Wiener过程的轧辊非线性退化建模与剩余寿命预测

在轧钢生产过程中,由于磨损等原因,长时间复杂工况运行下的轧辊工作性能会呈现逐步衰退的特征.考虑轧辊工作环境具有工况复杂、随机干扰强等特点,提出基于核函数-Wiener过程(KWP)退化模型,使用Wiener过程刻画轧辊退化趋势的强随机性特征,引入核函数捕捉轧辊的非线性退化路径,推导贝叶斯框架下参数估计的解析表达式,并构造轧辊可工作转动量的健康指标,进一步预测轧辊剩余寿命(RUL).结合某钢铁公司1580热轧生产线现场数据,所构建模型拟合优度达到0.989,剩余寿命预测误差低于4.7%,相较常见机器学习算法取得了更好效果,有助于提高设备运转效率与安全性并实现视情维护.