Application of nonlinear PCA for fault detection in polymer extrusion processes

This paper describes the application of an improved nonlinear principal component analysis (PCA) to the detection of faults in polymer extrusion processes. Since the processes are complex in nature and nonlinear relationships exist between the recorded variables, an improved nonlinear PCA, which incorporates the radial basis function (RBF) networks and principal curves, is proposed. This algorithm comprises two stages. The first stage involves the use of the serial principal curve to obtain the nonlinear scores and approximated data. The second stage is to construct two RBF networks using a fast recursive algorithm to solve the topology problem in traditional nonlinear PCA. The benefits of this improvement are demonstrated in the practical application to a polymer extrusion process.     

Dynamic process fault monitoring based on neural network and PCA

A newly developed method, NNPCA, integrates two data driven techniques, neural network (NN) and principal component analysis (PCA), for process monitoring. NN is used to summarize the operating process information into a nonlinear dynamic mathematical model. Chemical dynamic processes are so complex that they are presently ahead of theoretical methods from a fundamental physical standpoint. NN functions as the nonlinear dynamic operator to remove processes' nonlinear and dynamic characteristics. PCA is employed to generate simple monitoring charts based on the multivariable residuals derived from the difference between the process measurements and the neural network prediction. It can evaluate the current performance of the process. Examples from the recent monitoring practice in the industry and the large-scale system in the Tennessee Eastman process problem are presented to help the reader delve into the matter.     

Validation of Nonlinear PCA

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours over-fitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.     

一种基于分级输入训练神经网络的非线性主元分析

基于输入训练神经网络的非线性主元分析（PCA）能够有效地提取过程变量的非线性主元,但是存在主元的个数不能通过网络训练确定,且各个主元重要程度在神经网络中无法区分等缺点，本文提出一种分级输入自调整神经网络,并进一步提出基于此网络的非线性PCA,通过多级输入自调整神经网络,将主元按顺序找出,且根据主元对过程数据的预测误差定量地确定出主元的个数,克服了上述缺点.     

A class of neural networks for independent component analysis

Independent component analysis (ICA) is a recently developed, useful extension of standard principal component analysis (PCA). The ICA model is utilized mainly in blind separation of unknown source signals from their linear mixtures. In this application only the source signals which correspond to the coefficients of the ICA expansion are of interest. In this paper, we propose neural structures related to multilayer feedforward networks for performing complete ICA. The basic ICA network consists of whitening, separation, and basis vector estimation layers. It can be used for both blind source separation and estimation of the basis vectors of ICA. We consider learning algorithms for each layer, and modify our previous nonlinear PCA type algorithms so that their separation capabilities are greatly improved. The proposed class of networks yields good results in test examples with both artificial and real-world data.     

基于误差模型的自适应鲁棒主成分分析

研究了改善主成分分析(PCA)算法鲁棒性的一种实现途径.通过对误差函数的建 模分析,得到一种改进的目标函数.提出一种新的在线自适应式的鲁棒PCA运算规则.该方 法基于单层线性神经网络(NN)结构,但是权值的训练算法是非线性的.从而在迭代训练中对 "劣点"样本加以适当处理来排除对运算精度和收敛性的影响.     

Image compression using principal component neural networks

Principal component analysis (PCA) is a well-known statistical processing technique that allows to study the correlations among the components of multivariate data and to reduce redundancy by projecting the data over a proper basis. The PCA may be performed both in a batch and in a recursive fashion; the latter method has been proven to be very effective in presence of high dimension data, as in image compression. The aim of this paper is to present a comparison of principal component neural networks for still image compression and coding. We first recall basic concepts related to neural PCA, then we recall from the scientific literature a number of principal component networks, and present comparisons about the structures, the learning algorithms and the required computational efforts, along with a discussion of the advantages and drawbacks related to each technique. The conclusion of our wide comparison among eight principal component networks is that the cascade recursive least-squares algorithm by Cichocki, Kasprzak and Skarbek exhibits the best numerical and structural properties.     

Robust principal component analysis by self-organizing rules basedon statistical physics approach

This paper applies statistical physics to the problem of robust principal component analysis (PCA). The commonly used PCA learning rules are first related to energy functions. These functions are generalized by adding a binary decision field with a given prior distribution so that outliers in the data are dealt with explicitly in order to make PCA robust. Each of the generalized energy functions is then used to define a Gibbs distribution from which a marginal distribution is obtained by summing over the binary decision field. The marginal distribution defines an effective energy function, from which self-organizing rules have been developed for robust PCA. Under the presence of outliers, both the standard PCA methods and the existing self-organizing PCA rules studied in the literature of neural networks perform quite poorly. By contrast, the robust rules proposed here resist outliers well and perform excellently for fulfilling various PCA-like tasks such as obtaining the first principal component vector, the first k principal component vectors, and directly finding the subspace spanned by the first k vector principal component vectors without solving for each vector individually. Comparative experiments have been made, and the results show that the authors' robust rules improve the performances of the existing PCA algorithms significantly when outliers are present.     

基于形态学与神经网络的骨髓细胞识别研究

针对骨髓细胞图像的特点，采用数学形态学的方法对图像进行了处理，获得了不同类型细胞核的准确边缘。对于获得的边缘图像，采用两级神经网络，利用基于神经网络的PCA算法获得图象的3个主分量，然后采用模拟退火算法和BP算法进行细胞的分类识别，获得了较好的识别效果。     

基于PCA和随机森林的故障趋势预测方法研究

故障预测和健康管理技术(PHM)在现代工程系统中能够在系统具备较高复杂度的情况下,有效保障其可靠性和安全性。在机械故障诊断中对于采集到的原始数据的高维特征量的处理较为复杂,并且在实际应用中趋势预测的精度要求较高,针对该问题提出一种基于主成分分析(PCA)与随机森林算法的轴承故障趋势预测方法。该方法利用PCA对提取的原始轴承数据特征量进行线性降维,并选取其中主成分特征量,输出非线性时间序列数据。原始数据经过PCA处理得到非线性时间序列,将该序列作为随机森林算法的输入进行故障趋势预测,并把预测结果与BP神经网络模型预测的结果进行对比,结果表明随机森林在故障趋势预测上在精度相较于BP神经网络有显著提高,是一种有效的故障趋势预测方法。     

基于PCA优化的神经网络飞机燃油消耗预测方法

针对传统方法存在的不足,提出了基于主成分分析法优化的Elman神经网络飞机燃油消耗预测方法。利用主成分分析法降低神经网络输入维数。构建主成分分析与Elman神经网络模型,进行基于飞参数据的实例分析,并将几种神经网络的预测效果进行了对比;提出了基于K-S检验法预测结果冗余修正法并进行了修正。误差指标和预测图像表明与主成分分析结合后Elman神经网络对飞机燃油消耗的预测性能优于其他传统神经网络,且K S检验法能够有效实现对预测结果的修正。     

Visualization of learning in multilayer perceptron networks using principal component analysis

This paper is concerned with the use of scientific visualization methods for the analysis of feedforward neural networks (NNs). Inevitably, the kinds of data associated with the design and implementation of neural networks are of very high dimensionality, presenting a major challenge for visualization. A method is described using the well-known statistical technique of principal component analysis (PCA). This is found to be an effective and useful method of visualizing the learning trajectories of many learning algorithms such as backpropagation and can also be used to provide insight into the learning process and the nature of the error surface.     

一种PCA算法及其应用

主成分分析是用于简化数据的一种技术，对于某些复杂数据就可应用主成分分析法对其进行简化。文中所用到的是一种连续统一的主分量分析法，它利用特征结构的正交性，提取出用于下一主分量的初始权向量，并且任何一种适用于线性前向反馈神经网络的主分量分析法都可作为此算法中的权修正等式。最后，将这种PCA法与普通PCA法运用于股票数据之中进行比较，结果对比证明用此方法提取出的数据比以前有所改进。     

Nonlinear autoassociation is not equivalent to PCA

A common misperception within the neural network community is that even with nonlinearities in their hidden layer, autoassociators trained with backpropagation are equivalent to linear methods such as principal component analysis (PCA). Our purpose is to demonstrate that nonlinear autoassociators actually behave differently from linear methods and that they can outperform these methods when used for latent extraction, projection, and classification. While linear autoassociators emulate PCA, and thus exhibit a flat or unimodal reconstruction error surface, autoassociators with nonlinearities in their hidden layer learn domains by building error reconstruction surfaces that, depending on the task, contain multiple local valleys. This interpolation bias allows nonlinear autoassociators to represent appropriate classifications of nonlinear multimodal domains, in contrast to linear autoassociators, which are inappropriate for such tasks. In fact, autoassociators with hidden unit nonlinearities can be shown to perform nonlinear classification and nonlinear recognition.     

基于神经网络的非线性PCA方法

由于普通的主元分析（PCA）方法无法提取数据中的非线性相关特性,本文提出了一种基于神经网络的非线性PCA（NIPCA）方法,不仅提取了高维原始数据的线性信息还能提取非线性信息。在此基础上进一步提出了样本中显著误差及劣点的检测方法,从而支持对其进行合理剔除或是修正,仿真试验表明它能有效地减小误差点对网络训练精度的影响,大大增强了算法的鲁棒性。     

基于小波变换核主元分析和多支持向量机的过程监控

针对过程工业数据中所含的噪声和干扰信号、过程工业的非线性及基于主元分析(Principal Component Analysis,PCA)的统计性能监控法由于不用过程机理模型的信息从而对故障诊断问题难以在理论上作系统分析的缺陷,提出基于小波变换核主元分析和多支持向量机的过程监控方法,该方法首先采用基于小波变换的收缩阈值去噪法对建模数据进行预处理,以有效抑制过程数据中所含的噪声和干扰信号,然后利用核主元分析来进行故障特征的提取,从而提高非线性统计过程监控的准确性;最后提出多支持向量机用来对故障的来源进行分类,以避免求解核主元空间到原始空间的逆映射.将该方法应用到对TE(Tennessee Eastman,TE)过程的监控,表明了所提出方法的有效性,为过程的监控和故障诊断提供了一个新的方法.     

A globally convergent learning algorithm for PCA neural networks

Principal component analysis (PCA) by neural networks is one of the most frequently used feature extracting methods. To process huge data sets, many learning algorithms based on neural networks for PCA have been proposed. However, traditional algorithms are not globally convergent. In this paper, a new PCA learning algorithm based on cascade recursive least square (CRLS) neural network is proposed. This algorithm can guarantee the network weight vector converges to an eigenvector associated with the largest eigenvalue of the input covariance matrix globally. A rigorous mathematical proof is given. Simulation results show the effectiveness of the algorithm.     

Nonlinear identification of a gasoline HCCI engine using neural networks coupled with principal component analysis

Homogeneous charge compression ignition (HCCI) is a futuristic combustion technology that operates with high efficiency and reduced emissions. HCCI combustion is characterized by complex nonlinear dynamics which necessitates the use of a predictive model in controller design. Developing a physics based model for HCCI involves significant development times and associated costs arising from developing simulation models and calibration. In this paper, a neural networks (NN) based methodology is reported where black box type models are developed to predict HCCI combustion behavior during transient operation. The NN based approach can be considered a low cost and quick alternative to the traditional physics based modeling. A multi-input single-output model was developed each for indicated net mean effective pressure, combustion phasing, maximum in-cylinder pressure rise rate and equivalent air–fuel ratio. The two popular architectures namely multi-layer perceptron (MLP) and radial basis network (RBN) models were compared with respect to design, prediction performance and overall applicability to the transient HCCI modeling problem. A principal component analysis (PCA) is done as a pre-processing step to reduce input dimension thereby reducing memory requirements of the models. Also, PCA reduces the cross-validation time required to identify optimal model hyper-parameters. On comparing the model predictions with the experimental data, it was shown that neural networks can be a powerful approach for non-linear identification of a complex combustion system like the HCCI engine.     

基于PCA/SOFM混合神经网络的矢量量化

针对自组织特征映射(SOFM)神经网络应用于矢量量化具有收敛速度慢、计算量大等缺点,本文提出了一种基于PCA/SOFM混合神经网络的矢量量化的算法,先用主元分析(PCA)线性神经网络对输入矢量进行降维处理,再用SOFM神经网络进行矢量量化。通过调整SOFM神经网络的学习函数、邻域权值及初始码书对网络进行优化。实验表明,改进算法缩短了图像压缩的时间,提高了码书的性能。     

A novel neural-network approach of analog fault diagnosis based on kernel discriminant analysis and particle swarm optimization

Kernel principal component analysis (KPCA) and kernel linear discriminant analysis (KLDA) are two commonly used and effective methods for dimensionality reduction and feature extraction. In this paper, we propose a KLDA method based on maximal class separability for extracting the optimal features of analog fault data sets, where the proposed KLDA method is compared with principal component analysis (PCA), linear discriminant analysis (LDA) and KPCA methods. Meanwhile, a novel particle swarm optimization (PSO) based algorithm is developed to tune parameters and structures of neural networks jointly. Our study shows that KLDA is overall superior to PCA, LDA and KPCA in feature extraction performance and the proposed PSO-based algorithm has the properties of convenience of implementation and better training performance than Back-propagation algorithm. The simulation results demonstrate the effectiveness of these methods.