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1、外文翻译部分：英文原文Mine-hoist fault-condition detection based onthe wavelet packet transform and kernel PCAAbstract: A new algorithm was developed to correctly identify fault conditions and accurately monitor fault development in a mine hoist. The new method is based on the Wavelet Packet Transform (WPT) an
2、d kernel PCA (Kernel Principal Component Analysis, KPCA). For non-linear monitoring systems the key to fault detection is the extracting of main features. The wavelet packet transform is a novel technique of signal processing that possesses excellent characteristics of time-frequency localization. I
3、t is suitable for analysing time-varying or transient signals. KPCA maps the original input features into a higher dimension feature space through a non-linear mapping. The principal components are then found in the higher dimension feature space. The KPCA transformation was applied to extracting th
4、e main nonlinear features from experimental fault feature data after wavelet packet transformation. The results show that the proposed method affords credible fault detection and identification.Key words: kernel method; PCA; KPCA; fault condition detection1 IntroductionBecause a mine hoist is a very
5、 complicated andvariable system, the hoist will inevitably generate some faults during long-terms of running and heavy loading. This can lead to equipment being damaged,to work stoppage, to reduced operating efficiency andmay even pose a threat to the security of mine personnel. Therefore, the ident
6、ification of running fault shas become an important component of the safety system. The key technique for hoist condition monitoring and fault identification is extracting information from features of the monitoring signals and then offering a judgmental result. However, there are many variables to
7、monitor in a mine hoist and, also , there are many complex correlations between thevariables and the working equipment. This introduce suncertain factors and information as manifested by complex forms such as multiple faults or associated faults, which introduce considerable difficulty to fault diag
8、nosis and identification1. There are currently many conventional methods for extracting mine hoist fault features, such as Principal Component Analysis(PCA) and Partial Least Squares (PLS)2. These methods have been applied to the actual process. However, these methods are essentially a linear transf
9、ormation approach. But the actual monitoring process includes nonlinearity in different degrees. Thus, researchers have proposed a series of nonlinearmethods involving complex nonlinear transformations. Furthermore, these non-linear methods are confined to fault detection: Fault variable separation
10、and fault identification are still difficult problems.This paper describes a hoist fault diagnosis featureexaction method based on the Wavelet Packet Transform(WPT) and kernel principal component analysis(KPCA). We extract the features by WPT and thenextract the main features using a KPCA transform,
11、which projects low-dimensional monitoring datasamples into a high-dimensional space. Then we do adimension reduction and reconstruction back to thesingular kernel matrix. After that, the target feature isextracted from the reconstructed nonsingular matrix.In this way the exact target feature is dist
12、inct and stable.By comparing the analyzed data we show that themethod proposed in this paper is effective.2 Feature extraction based on WPT andKPCA2.1 Wavelet packet transformThe wavelet packet transform (WPT) method3,which is a generalization of wavelet decomposition, offers a rich range of possibi
13、lities for signal analysis. The frequency bands of a hoist-motor signal as collected by the sensor system are wide. The useful information hides within the large amount of data. In general, some frequencies of the signal are amplified and some are depressed by the information. That is tosay, these b
14、roadband signals contain a large amountof useful information: But the information can not bedirectly obtained from the data. The WPT is a finesignal analysis method that decomposes the signalinto many layers and gives a etter resolution in thetime-frequency domain. The useful informationwithin the d
15、ifferent requency ands will be expressed by different wavelet coefficients after thedecomposition of the signal. The oncept of “energy information” is presented to identify new information hidden the data. An energy igenvector is then used to quickly mine information hiding within the large amount o
16、f data.The algorithm is: Step 1: Perform a 3-layer wavelet packet decomposition of the echo signals and extract the signal characteristics of the eight frequency components ,from low to high, in the 3rd layer. Step 2: Reconstruct the coefficients of the waveletpacket decomposition. Use 3 j S (j=0, 1
17、, , 7) to denote the reconstructed signals of each frequencyband range in the 3rd layer. The total signal can thenbe denoted as: （1）Step 3: Construct the feature vectors of the echosignals of the GPR. When the coupling electromagneticwaves are transmitted underground they meetvarious inhomogeneous m
18、edia. The energy distributing of the echo signals in each frequency band willthen be different. Assume that the corresponding energyof 3 j S (j=0, 1, , 7) can be represented as3 j E (j=0, 1, , 7). The magnitude of the dispersedpoints of the reconstructed signal 3 j S is: jk x (j=0,1, , 7; k=1, 2, ,
19、n), where n is the length of thesignal. Then we can get: （2）Consider that we have made only a 3-layer waveletpackage decomposition of the echo signals. To makethe change of each frequency component more detailedthe 2-rank statistical characteristics of the reconstructedsignal is also regarded as a f
20、eature vector: （3）Step 4: The 3 j E are often large so we normalize them. Assume that, thus the derived feature vectors are, at last:T= (4) The signal is decomposed by a wavelet packageand then the useful characteristic information featurevectors are extracted through the process given above.Compare
21、d to other traditional methods, like the Hilberttransform, approaches based on the WPT analysisare more welcome due to the agility of the processand its scientific decomposition.2.2 Kernel principal component analysisThe method of kernel principal component analysisapplies kernel methods to principa
22、l component analysis45.The principalcomponent is the element at the diagonal afterthe covariance matrix，has beendiagonalized. Generally speaking, the first N valuesalong the diagonal, corresponding to the large eigenvalues,are the useful information in the analysis.PCA solves the eigenvalues and eig
23、envectors of thecovariance matrix. Solving the characteristic equation6: (5)where the eigenvalues ,and the eigenvectors, is essence of PCA.Let the nonlinear transformations, : RN F ,x X , project the original space into feature space,F. Then the covariance matrix, C, of the original space has the fo
24、llowing form in the feature space: (6)Nonlinear principal component analysis can beconsidered to be principal component analysis ofin the feature space, F. Obviously, all the igenvaluesof C and eigenvectors, V F 0 satisfyV = V . All of the solutions are in the subspacethat transforms from (7)There i
25、s a coefficient Let (8)From Eqs.(6), (7) and (8) we can obtain: (9)where k =1, 2, ., M . Define A as an MM rankmatrix. Its elements are:From Eqs.(9) and (10), we can obtainM Aa = A2a . This is equivalent to:M Aa = Aa .Make as As eigenvalues, and, as the corresponding eigenvector.We only need to calc
26、ulate the test points projectionson the eigenvectorsthat correspond tononzero eigenvalues in F to do the principal componentextraction. Defining this asit is given by: (12)principalcomponent we need to know the exact form of the non-linear image. Also as the dimension of the feature space increases
27、the amount of computation goes up exponentially. Because Eq.(12) involves an inner-product computation, according to the principles of Hilbert-Schmidt we can find a kernel function that satisfies the Mercer conditions and makesThen Eq.(12) canbe written:Here is the eigenvector of K. In this way the
28、dot product must be done in the original space but the specific form of (x) need not be known. The mapping, (x) , and the feature space, F, are all completely determined by the choice of kernel function 78.2.3 Description of the algorithmThe algorithm for extracting target features in recognition of
29、 fault diagnosis is:Step 1: Extract the features by WPT; Step 2: Calculate the nuclear matrix, K, for each sample, in the original input space, andStep 3: Calculate the nuclear matrix after zero-mean processing of the mapping data in feature space;Step 4: Solve the characteristic equation M a = Aa ;
30、Step 5: Extract the k major components using Eq.(13) to derive a new vector. Because the kernel function used in KPCA met the Mercer conditions it can be used instead of the inner product in feature space. It is not necessary to consider the precise form of the nonlinear transformation. The mapping
31、function can be non-linear and the dimensions of the feature space can be very high but it is possible to get the main feature components effectively by choosing a suitable kernel function and kernel parameters9. 3 Results and discussionThe character of the most common fault of a mine hoist was in t
32、he frequency of the equipment vibration signals. The experiment used the vibration signals ofa mine hoist as test data. The collected vibration signals were first processed by wavelet packet. Then through the observation of different time-frequencyenergy distributions in a level of the wavelet packe
33、t we obtained the original data sheet shown in Table 1 by extracting the features of the running motor. Thefault diagnosis model is used for fault identification or classification.Experimental testing was conducted in two parts: The first part was comparing the performance of KPCA and PCA for featur
34、e extraction from the originaldata, namely: The distribution of the projection of the main components of the tested fault samples. The second part was comparing the performance of the classifiers, which were constructed after extracting features by KPCA or PCA. The minimum distance and nearest-neigh
35、bor criteria were used for classification comparison, which can also test the KPCA and PCA performance. In the first part of the experiment, 300 fault samples were used for comparing between KPCA and PCA for feature extraction. To simplify the calculations a Gaussian kernel function was used: 10The
36、value of the kernel parameter, , is between 0.8 and 3, and the interval is 0.4 when the number of reduced dimensions is ascertained. So the best correct classification rate at this dimension is the accuracy of the classifier having the best classification results. In the second part of the experimen
37、t, the classifiers recognition rate after feature extraction was examined. Comparisons were done two ways: theminimum distance or the nearest-neighbor. 80% of the data were selected for training and the other 20% were used for testing. The results are shown in Tables 2 and 3.From Tables 2 and 3, it
38、can be concluded from Tables 2 and 3 that KPCA takes less time and has relatively higher recognition accuracy than PCA.4 ConclusionsA principal component analysis using the kernel fault extraction method was described. The problem is first transformed from a nonlinear space into a linearlinearhigher
39、 dimension space. Then the higher dimension feature space is operated on by taking the inner product with a kernel function. This thereby cleverly solves complex computing problems and overcomes the difficulties of high dimensions and local minimization. As can be seen from the experimental data, co
40、mpared to the traditional PCA the KPCA analysis has greatly improved feature extraction and efficiency in recognition fault states. References1 Ribeiro R L. Fault detection of open-switch damage involtage-fed PWM motor drive systems. IEEE TransPower Electron, 2003, 18(2): 587593.2 Sottile J. An over
41、view of fault monitoring and diagnosisin mining equipment. IEEE Trans Ind Appl, 1994, 30(5):13261332.3 Peng Z K, Chu F L. Application of wavelet transform inmachine condition monitoring and fault diagnostics: areview with bibliography. Mechanical Systems and SignalProcessing, 2003(17): 199221.4 Roth
42、 V, Steinhage V. Nonlinear discriminant analysisusing kernel function. In: Advances in Neural InformationProceeding Systems. MA: MIT Press, 2000: 568574.5 Twining C, Taylor C. The use of kernel principal componentanalysis to model data distributions. PatternRecognition, 2003, 36(1): 217227.6 Muller
43、K R, Mika S, Ratsch S, et al. An introduction tokernel-based learning algorithms. IEEE Trans on NeuralNetwork, 2001, 12(2): 181.7 Xiao J H, Fan K Q, Wu J P. A study on SVM for faultdiagnosis. Journal of Vibration, Measurement & Diagnosis,2001, 21(4): 258262.8 Zhao L J, Wang G, Li Y. Study of a nonli
44、near PCA faultdetection and diagnosis method. Information and Control,2001, 30(4): 359364.9 Xiao J H, Wu J P. Theory and application study of featureextraction based on kernel. Computer Engineering,2002, 28(10): 3638.中文译文基于PCA技术核心的打包和变换的矿井提升机失误的发现摘要： 一个新的运算法则被正确的运用于证明和监视矿井提升机的过失情况。这种方法是基于小浪小包变换（WPT）
45、和PCA为核心基础的。（KPCA，核心校长成份分析）因为非线性监听系统主要是通过主要特征来发现和吸取系统过失的。小浪小包变换是处理时间-频率局限性的优良特性信号的新技术。它对分析改变时间或短暂的信号是适当的。KPCA 透过最初的输入的非线性映射映射特征进入较高的尺寸特征空间。主要的成份然后在较高的尺寸特征空间被发现。KPCA 变形被适用于从实验的过失特征小浪后的数据小包变形吸取主要的非线性特征。结果表示，被提议的方法负担可信的过失发现和确认。关键词：核心方法;主成分分析;核主元分析;故障检测1介绍因为我的矿井提升机是一个非常复杂的可变性比较大的系统，升高不可避免的产生错误和长时间的超载。这些都
46、有可能损坏设备，操作终端，甚至降低工作效率，对我们员工的安全带来威胁。因此，流动错误的确认一直被认为是安全系统的一个重要组成部分。对于升高情况的测试和监听只要是依靠探取监听信号和他的结果的信息特征。但是，在那里矿井提升的高度检测和工作设备之间有许多复杂的相互关系。这些因素和数据的引进可以当作有很多部分显示形成许多错误和失误。这错误的介绍和确认会给我们带来相当多的困难认识。现在，很多利用我的技术发现现有提升机缺点的方法在许多传统的方法中扮演着重要的角色。比如主要成份分析（PCA）和部分最少广场（PLS）。这些方法已经被熟练的运用于我们的实际生产中来。但是这些方法在本质上是接近的。然而在实际工作中
47、的监视设备往往发、生非线性的。因此我们的研究员已经计划了包括浮躁的非线性变形等一系列的无线发现技术。此外，这些非线性方法限制了错误的发现，现在这些错误的分离和缺点的确认依然是一个困难的所在。这篇论文是基于小浪小包变换 （WPT）和核心校长成份分析 （KPCA）的矿井提升机的失误确认方法。我们吸取 WPT和 thenextract 的特征使用 KPCA 变换，计划低空间的监听 datasamples 进入高空间的空间主要部份特征。接着我们做到尺寸的减少 然后进行核心点阵式尺寸的重建。之后我们的目标是重建特征和非反常的点阵式尺寸。这样我们得到的是清楚又稳定的目标特征。基于此我们表示，这种方法在这次
48、计划中分析出来的数据是有效的。2基于小波包变换的特征提取核心单元的分析 2.1小波包变换小波包变换（小波包变换）方法 3 ，这是一个小波的概括分解，提供了的很多可能性分析，传感系统的信号频带的升降器点击收集到的信号是非常广泛的。这些信息中隐藏了大量的使用信息。一般情况下，一些平率信号的扩大包含不好的信息。这就是说，这些宽带信号包含大量有用的信息：但是信息不能获得的数据。然而小波包变换是一个很好的信号分析方法，分解许多层并给出了一个见上书决议时间频域。实用的信息在不同的发展战略将不同的小波系数后的信号。该信号的提出，是以确定新的信息隐藏数据。能源然后用于排雷信息隐藏的算法是：第1步：执行3层小波包分
