基于核正则化Fisher判据的故障诊断

Fisher判据分析(FDA)是工业过程故障诊断的常用降维算法,但其无法提取数据中的非线性关系。基于核的FDA(KFDA)是对FDA的非线性推广,但在FDA和KFDA小样本情况下都会面临矩阵的病态问题,正则化技术是解决该问题的有效途径。推导一种转化为方程组求解并表示成对偶形式的核正则化FDA算法,给出其用于故障诊断的流程,并针对TE过程的故障数据进行仿真。     

局部Fisher判别分析算法及仿真研究*

复杂化工过程常被多种类型的故障损坏,正常的训练数据无法建立准确的操作模型。为了提高复杂化工过程中故障的检测和分类能力,传统无监督Fisher判别分析(Fisher Discriminant Analysis,FDA)算法无法在多模态故障数据中的应用,本文提出基于局部Fisher判别分析(Local Fisher Discriminant Analysis,LFDA)的故障诊断方法。首先计算训练数据的局部类内和类间离散度矩阵,寻找LFDA的投影方向;其次把训练数据和测试数据向投影向量上投影,提取特征向量;最后计算特征向量间的欧氏距离,运用KNN分类器进行分类。把提出的LFDA方法应用到Tennessee Eastman(TE)过程,监控结果表明,LFDA的效果好于FDA和核Fisher判别分析(Kernel Fisher Discriminant Analysis,KFDA),说明LFDA方法在分类及检测不同类的故障方面具有高准确性及高灵敏度的优势。     

Fast kernel Fisher discriminant analysis via approximating the kernel principal component analysis

Kernel Fisher discriminant analysis (KFDA) extracts a nonlinear feature from a sample by calculating as many kernel functions as the training samples. Thus, its computational efficiency is inversely proportional to the size of the training sample set. In this paper we propose a more approach to efficient nonlinear feature extraction, FKFDA (fast KFDA). This FKFDA consists of two parts. First, we select a portion of training samples based on two criteria produced by approximating the kernel principal component analysis (AKPCA) in the kernel feature space. Then, referring to the selected training samples as nodes, we formulate FKFDA to improve the efficiency of nonlinear feature extraction. In FKFDA, the discriminant vectors are expressed as linear combinations of nodes in the kernel feature space, and the extraction of a feature from a sample only requires calculating as many kernel functions as the nodes. Therefore, the proposed FKFDA has a much faster feature extraction procedure compared with the naive kernel-based methods. Experimental results on face recognition and benchmark datasets classification suggest that the proposed FKFDA can generate well classified features.     

一种用于人脸识别的非线性鉴别特征融合方法

最近，在人脸等图像识别领域，用于抽取非线性特征的核方法如核Fisher鉴别分析(KFDA)已经取得成功并得到了广泛应用，但现有的核方法都存在这样的问题，即构造特征空间中的核矩阵所耗费的计算量非常大．而且，抽取得到的单类特征往往不能获得到令人满意的识别结果．提出了一种用于人脸识别的非线性鉴别特征融合方法，即首先利用小波变换和奇异值分解对原始输入样本进行降雏变换，抽取同一样本空间的两类特征，然后利用复向量将这两类特征组合在一起，构成一复特征向量空间，最后在该空间中进行最优鉴别特征抽取．在ORL标准人脸库上的试验结果表明所提方法不仅在识别性能上优于现有的核Fisher鉴别分析方法，而且，在ORL人脸库上的特征抽取速度提高了近8倍．     

基于一种小波核优化学习的KSPP子空间故障特征提取*

针对电子系统故障诊断中有效特征提取困难,核属性约简方法中核函数与核参数选择繁琐等问题,提出了一种基于自优化小波核稀疏保持投影的子空间特征提取方法。通过对核极化准则的改进,使得新准则不仅可以处理多类别信息,而且可以保留同一类别数据间的局部结构特征。以墨西哥帽小波核函数为对象,基于改进的核评估准则构建优化目标函数,并采用粒子群优化算法进行核参数选择。将优化的小波核作为核稀疏保持投影的核函数,最终实现了在核子空间中对有效特征的提取。实验结果表明,相比于其它流形的子空间特征提取方法,提出的方法有效提升了分类精度,具有良好的泛化性能。     

基于PCA-KFCM的船舶柴油机故障诊断

为提高船舶柴油机故障诊断的准确率和深刻反映船舶柴油机的运行状况,结合主元分析(PCA)的特征提取优势和模糊核聚类(KFCM)具有较好聚类效果的特点,提出了一种新的船舶柴油机故障诊断方法。该方法首先利用主元分析对船舶柴油机故障的训练和测试数据集进行特征提取,消除了故障征兆之间的相关性;然后对经特征提取后的训练样本进行模糊核聚类,并用网格法确定其中的参数,得到聚类中心。通过计算测试样本集中各样本与聚类中心在高维特征空间中的欧氏距离,得出最终的故障诊断结果。对MAN B&W 10L90MC型船用柴油机的故障诊断结果验证了该方法的有效性。因此,应用提出的方法对船舶柴油机进行故障诊断具有重要的实际意义。     

基于PCA-KFCM的船舶柴油机故障诊断

为提高船舶柴油机故障诊断的准确率和深刻反映船舶柴油机的运行状况,结合主元分析(PCA)的特征提取优势和模糊核聚类(KFCM)具有较好聚类效果的特点,提出了一种新的船舶柴油机故障诊断方法。该方法首先利用主元分析对船舶柴油机故障的训练和测试数据集进行特征提取,消除了故障征兆之间的相关性;然后对经特征提取后的训练样本进行模糊核聚类,并用网格法确定其中的参数,得到聚类中心。最后通过计算测试样本集中各样本与聚类中心在高维特征空间中的欧氏距离,得出最终的故障诊断结果。对MAN B&W 10L90MC型船用柴油机的故障诊断结果验证了该方法的有效性。因此,应用提出的方法对船舶柴油机进行故障诊断具有重要的实际意义。     

Fuzzy discriminant analysis with kernel methods

A novel fuzzy nonlinear classifier, called kernel fuzzy discriminant analysis (KFDA), is proposed to deal with linear non-separable problem. With kernel methods KFDA can perform efficient classification in kernel feature space. Through some nonlinear mapping the input data can be mapped implicitly into a high-dimensional kernel feature space where nonlinear pattern now appears linear. Different from fuzzy discriminant analysis (FDA) which is based on Euclidean distance, KFDA uses kernel-induced distance. Theoretical analysis and experimental results show that the proposed classifier compares favorably with FDA.     

基于核Fisher判别分析的蛋白质氧链糖基化位点的预测

以各种窗口长度的蛋白质样本序列为研究对象,实验样本用稀疏编码方式编码,使用核Fisher判别分析(KFDA)的方法来预测蛋白质氧链糖基化位点。首先通过非线性映射(由核函数隐含定义)将样本映射到特征空间,然后在特征空间中用Fisher判别分析进行分类。进一步,用多数投票策略对各种窗口下的分类器进行组合以综合多个窗口的优势。实验结果表明,使用组合KFDA的方法预测的效果优于FDA和PCA以及单个KFDA分类器的预测效果,预测准确率为86.5%。     

Nonlinear feature extraction and classification of multivariate data in kernel feature space

Batch processes have played an essential role in the production of high value-added product of chemical, pharmaceutical, food, bio-chemical, and semi-conductor industries. For productivity and quality improvement, several multivariate statistical techniques such as principal component analysis (PCA) and Fisher discriminant analysis (FDA) have been developed to solve a fault diagnosis problem of batch processes. Fisher discriminant analysis, as a traditional statistical technique for feature extraction and classification, has been shown to be a good linear technique for fault diagnosis and outperform PCA based diagnosis methods. This paper proposes a more efficient nonlinear diagnosis method for batch processes using a kernel version of Fisher discriminant analysis (KFDA). A case study on two batch processes has been conducted. In addition, the diagnosis performance of the proposed method was compared with that of an existing diagnosis method based on linear FDA. The diagnosis results showed that the proposed KFDA based diagnosis method outperforms the linear FDA based method.     

分段多向核主元分析的啤酒发酵过程故障检测

基于主元分析的故障诊断模型应用在非线性时变过程中具有局限性。基于间歇过程具有周期性这一特点,在非线性空间的数据提取中,将核变换理论引入其中,提出了一种改进的多向核主元分析故障诊断模型,该方法对于过程数据的非线性问题的解决和非线性信息的充分提取表现出很好的性能,使得非线性主元能够在高维特征空间中被快速提取。 对比实验结果表明,该方法对于缓慢时变的间歇过程具有很好的准确性与实时性。     

改进的核费舍判别分析法应用于故障诊断

化工过程采样数据具有强非线性和噪声,针对化工过程状态监控的问题,提出一种改进的核费舍判别分析法（KFDA）的故障诊断算法。首先采样数据经过小波变换方法去除噪声,去除噪声后的数据进行KFDA建模,然后在建模同时采用特征向量选择（FVS）算法降低复杂性。Tennessee Eastman process实验结果表明了该算法的有效性,同时该算法加强了KFDA故障诊断的准确性,并明显地减少了存储空间和运算时间。     

基于非线性电路频域核估计和神经网络的故障诊断

提出一种基于非线性电路频域核分析和神经网络的故障诊断方法．主要研究非线性系统频谱的获取,非线性系统频谱特征的提取及基于非线性系统频谱特征的故障诊断．利用Volterra频域核估计辨识非线性系统,通过系统广义频率响应函数的估算提取电路特征,将其预处理后作为递归神经网络的输入样本,利用神经网络的分类功能对电路的工作模式作出故障决策、最后。给出故障诊断实例验证了该方法的有效性．     

A novel fault diagnosis system using pattern classification on kernel FDA subspace

Recently, pattern recognition techniques have been applied for fault diagnosis. Principal component analysis (PCA) and kernel principal component analysis (KPCA) are introduced for feature extraction. However, those unsupervised learning methods have not incorporated the prior knowledge of process patterns. This paper proposes a novel fault diagnosis system to improve the performance of fault diagnosis. Kernel Fisher discriminant analysis (KFDA) is used in the first step for feature extraction, then Gaussian mixture model (GMM) and k-nearest neighbor (kNN) are applied for fault detection and isolation on the KFDA subspace. Since the performance of fault diagnosis system would be degraded in the fault detection stage, fault detection and identification are presented in a holistic manner without an intermediate step in the novel system. A case study of the Tennessee Eastman (TE) benchmark process indicates that the proposed methods are more efficient, compared to the traditional ones. Furthermore, as the performances of GMM and kNN are comparable, the data structure of the process should be checked beforehand, depending on which the optimal classifier can be selected.     

AKSNet: A novel convolutional neural network with adaptive kernel width and sparse regularization for machinery fault diagnosis

Convolutional kernels have significant affections on feature learning of convolutional neural network (CNN). However, it is still a challenging problem to determine appropriate kernel width. Moreover, some features learned by convolutional layers are still redundant and noisy. Thus, adaptive selection of kernel width and feature selection of feature maps are key techniques to improve feature learning performance of CNNs. In this paper, a new deep neural network (DNN) model, adaptive kernel sparse network (AKSNet) is proposed to extract multi-scale fault features from one-dimensional (1-D) vibration signals. Firstly, an adaptive kernel selection method is developed, where multiple branches with different kernels are used to extract multi-scale features from vibration signals. Channel-wise attention is developed to fuse features generated by these kernels to obtain different informative scales. Secondly, a spatial attention is used for dynamic receptive field to focus on salient region of feature maps. Thirdly, a sparse regularization layer is embedded in the deep network to further filter noise and highlight impaction of the feature maps. Finally, two cases are adopted to verify effectiveness of AKSNet-based feature learning for bearing fault diagnosis. Experimental results show that AKSNet can effectively extract features from multi-channel vibration signals and then improves fault diagnosis performance of the classifier significantly. AKSNet shows better recognition performance in comparison with that of shallow neural networks and other typical DNNs.     

结合非线性频谱与核主元分析的复杂系统故障诊断方法

传统非线性频谱分析方法对复杂系统进行故障诊断时,求解出的非线性频谱数据量庞大,不便于直接用于故障检测与分类识别.本文提出了一种非线性频谱特征与核主元分析(KPCA)结合的故障诊断方法,首先通过最小二乘算法估计出前3阶Volterra时域核,由多维傅立叶变换求取出广义频率响应函数,然后利用KPCA方法对谱数据进行压缩与提取谱特征,最后利用多分类最小二乘支持向量机进行多故障检测与识别.考虑到频谱数据具有非线性的特点,KPCA中的核函数选用由多项式函数与径向基函数构成的混合核函数,兼顾了局部特性与全局特性.论文基于非线性频谱数据,给出了核主元模型建立与在线故障诊断的具体算法.对非线性模拟电路和数控机床伺服传动系统进行了仿真实验,结果表明本文方法能够大幅度降低频谱数据维数,故障识别率高,是一种实用的故障诊断方法.     

正则化FDA的核化及与SVM的比较研究*

无论是Fisher判别分析（FDA）还是基于核的FDA（KFDA）,在小样本情况下都会面临矩阵的病态问题,正则化技术是解决该问题的有效途径。为了便于研究正则化FDA与支持向量机（SVM）的关系,推导了一种正则化FDA的核化算法。将约束优化问题转换为对偶的优化问题,得到了与SVM相似的形式,分析了该核化算法与SVM的联系。针对Tenessee-Eastman(TE)过程的故障诊断结果表明,正则化KFDA的诊断效果明显好于LS-SVM。     

一种基于空间变换的核Fisher鉴别分析

引入空间变换的思相想，提出了一种基于空间变换的核Fisher鉴别分析，与KFDA不同的是，该方法只需在一个较低维的空间内执行，从而较大幅度地降低了求解最优鉴别矢量集的计算量，提高了计算速度，在ORL标准人脸库上的试验结果验证了所提方法的有效性。     

Multi-layer radial basis function neural network based on multi-scale kernel learning

The conversion functions in the hidden layer of radial basis function neural networks (RBFNN) are Gaussian functions. The Gaussian functions are local to the kernel centers. In most of the existing research, the spatial local response of the sample is inaccurately calculated because the kernels have the same shape as a hypersphere, and the kernel parameters in the network are determined by experience. The influence of the fine structure in the local space is not considered during feature extraction. In addition, it is difficult to obtain a better feature extraction ability with less computational complexity. Therefore, this paper develops a multi-scale RBF kernel learning algorithm and proposes a new multi-layer RBF neural network model. For the samples of each class, the expectation maximization (EM) algorithm is used to obtain multi-layer nested sub-distribution models with different local response ranges, which are called multi-scale kernels in the network. The prior information of each sub-distribution is used as the connection weight between the multi-scale kernels. Finally, feature extraction is implemented using multi-layer kernel subspace embedding. The multi-scale kernel learning model can efficiently and accurately describe the fine structure of the samples and is fault tolerant to setting the number of kernels to a certain extent. Considering the prior probability of each kernel as the weight makes the feature extraction process satisfy the Bayes rule, which can enhance the interpretability of feature extraction in the network. This paper also theoretically proves that the proposed neural network is a generalized version of the original RBFNN. The experimental results show that the proposed method has better performance compared with some state-of-the-art algorithms.     

集成散度的MKL模型在模拟电路诊断中的应用

为提升模拟电路故障诊断精度,结合基于故障特征间一维模糊度的特征选择算法,提出一种新的多核超限学习机诊断模型。该模型通过设置虚拟的基核,将正则化参数融入基核权重求解过程中;同时,通过将特征空间类内散度集成到多核优化目标函数中,在最小化训练误差的同时,使得同一模式的故障样本更加集中,有效提升了故障模式间的辨识力。通过两个模拟电路诊断实例表明：相比于单核学习算法,所提方法可以显著提升诊断精度,并且可以将难以辨识的故障样本更加准确地隔离到相应模糊组中;相比于一般的多核学习算法,所提方法在取得相似诊断精度的同时,时间花费更少。