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河南理工大学万方科技学院本科毕业论文附 录外文资料与中文翻译矿井提升机的小波变换和PCA诊断技术 摘要：提出了一种新的算法，以正确地确定故障情况，准确地监测出故障发生的矿井提升机。这种新方法是基于小波包变换和内核镇痛（核主复合成分分析，核主元分析） 。非线性监测系统故障检测的关键是提取他主要的特点。小波包变换是一种新型的信号处理技术，拥有出色的时频局部化特点。它适用于分析信号。核主元分析的原始输入功能进入了更高的层面，通过非线性映射出主成分，然后发现了多维特征空间。转变的核心主元用于提取分析主要的非线性特性实验数据，检测出小波包变换的故障特征。结果表明，该方法提供了可靠的故障检测鉴定。关键词：核方法、主成分分析、核主元分析、故障检测。1.简介 由于矿井提升机是一个非常复杂和可变系统，提升机在长期运行条件和重载过程中将不可避免地产生一些故障。这会导致设备损坏，停工，降低了作业效率，甚至可能威胁到矿井人员的安全。因此，确定运行故障的安全系统已成为一个重要组成部分。提升机的关键技术是状态监测与故障识别信息，监测信号的提取功能，然后提供一个判断的结果。然而，有许多变量，用于监测矿井提升机，也有许多复杂的变量和工作设备之间的相互关系。这里介绍的不确定因素和信息，表现出复杂的形式，如多故障或相关故障，其中引进相当困难的故障诊断与鉴定。目前有许多常规的提取方法，矿井提升机故障特征，如主成分分析（ PCA ）和（ PLS ） 。这些方法已应用于实际的过程。然而，这些方法基本上是一个线性变换的方法。但实际的监测过程中，包括不同程度的非线性。因此，研究人员已经提出了一系列的非线性方法的变革，涉及复杂的非线性。此外，这些非线性方法只限于故障检测：故障变量分离和故障识别仍有困难的问题。本文介绍了提升机故障诊断功能基于小波包变换（小波包变换）和核主成分分析（核主元分析）。我们提取的小波包变换的特点，然后提取物的主要特征变换利用核主元分析，该项目的样本监测数据到一个高维空间。然后我们做了降维和重建回到奇异核矩阵。在此之后，目标特征提取的重建非奇异矩阵。这样确定目标功能是独特的，稳定的。通过比较分析数据表明，提出了本文是有效的。2.基于特征提取的小波包变换和核主元分析2.1小波包变换 小波包变换方法，就是一个概括的小波分解，提供了丰富的各种可能性信号分析。频带升降器电机收集到的传感器信号系统是广泛的。大量的数据隐藏在实用的信息。一般情况下，一些频率的信号放大，有些不利的信息。这就是说，这些宽带信号包含了大量有用的信息：但是信息不能直接得到的数据。小波包变换是一个很好的信号分析方法的信号分解成许多层，并更好地解决在时频域。实用的信息在不同频段将表达不同的小波系数的分解后的信号。 “概念的能源信息”是以确定新的信息隐藏数据。能源特征向量，然后利用快速排雷信息隐藏了大量的数据。该算法是：第1步：执行3层小波包分解的回波信号和信号特征提取的8个频率组成部分，从低到高，在第三层。第2步：重构系数的小波包分解。使用（ j = 0 ， 1 ， . ， 7 ）来表示每个重建信号的频带范围内的第三层。总的信号就可以被命名为： (1)第3步：构建特征向量的回波信号的雷达。当电磁波的耦合传输他们满足各种地下非均匀介质。能源分布的回波信号在每个频带然后将不同。承担相应的能源的S3j（ j = 0 ， 1 ， . ， 7 ）可派代表作为E3j（ j = 0 ， 1 ， .7 ） 。规模分散点的重建信号是：S3j xjk(j=0, 1, , 7; k=1, 2, , n), 其中n是长度的信号。然后，我们可以得到：认为我们取得了只有3层小波包分解的回波信号。为了使每一个变化的更详细的频率成分的2阶统计特性的重建信号也视为一个特征向量：第4步：流行性往往大，所以我们正常化他们。假设，从而得出的特征向量是，最后：信号分解的小波包，然后有用的特征信息提取的特征向量是通过上述过程。相对于其他传统方法，如希尔伯特变换，方法基于小波包变换分析更欢迎由于敏捷的过程和它的科学分解。2.2版内核主成分分析 该方法的核心主成分分析方法，适用于核心主成分分析 4-5 。让主要组成部分是在对角线元素后，协方差矩阵，已被算好。一般而言，前n值沿对角线，相应的大特征值，是有用的信息的分析。常设仲裁法院解决了特征值和特征向量的协方差矩阵。求解特征方程 6 ：如果特征值和特征向量的本质，常设仲裁中介。让非线性变换，项目原始空间到特征空间，然后，协方差矩阵，原来的空间具有下列表格中的功能空间：（6）非线性主成分分析法可以被认为是主成分分析的C的功能空间，F. 显然，所有的特征值和特征向量. 所有的解决方案是在空间的变换由有一个系数.得（8）从（6）（7）（8）可以得出当k=1,2,M.A相当于M*M的乘机。其要点是：（10）从（9）（10）可以获得（11）作为A的特征值，作为相应的特征向量。 我们只需要计算测试点的预测的特征向量Vk对应的非零特征值的F这样做主要成分的提取.确定这是Bk，它是由：不难看出，如果我们解决了直接的主要组成部分，我们需要知道确切形式的非线性图像。还为层面的特征空间增加了计算量成倍上升。因为Eq12涉及党内产品计算， 根据原则的Hilbert -施密特我们能够找到一种内核功能，满足了条件，使。然后Eq12可以写作（13） 这里是特征向量的光，这样点的产品必须在原来的空间，但具体形式 （ x ）的需要不知道。映射， （ x ）和空间的特点，男，都完全取决于选择的核函数。2.3说明算法 该算法提取目标特征识别的故障诊断是： 第1步：提取特征的小波包变换; 第2步：计算核基质，钾，对每个样品，在原来的输入空间，和 第3步：计算后的核基质零意味着处理测绘数据的特征空间; 第4步：求解特征方程Ma =Aa;第5步：提取物的主要组成部分使用均衡器制定出一个新的载体。由于核函数用于满足现状,又是核主成分分析可以用来代替内在的产品在特徵空间。它不需要考虑的精确形式的非线性变形。. 这个映射函数可以非线性和尺寸的特征空间就会很高,但它可能会得到有效成分的主要特征,通过选择合适的内核函数和内核的参数.3结果与讨论这个角色的最常见的故障的矿井提升机的频率振动信号的装置。实验采用振动信号的矿井提升机作为测试数据。收集到的振动信号进行小波包变换首先处理。然后通过观察不同的时频能量分布在一个水平的小波包变换给出了原始数据表显示在表1中运行电动机的特点。在故障诊断模型,用于故障识别和分类。表1原故障数据表 实验测试了两部分:第一部分是性能的对比和主成分分析法(PCA)对特征提取核主成分分析的原始数据,即:分布投影的主要部件故障样本进行。第二部分是分类性能的比较,构建了以核主成分分析提取特征后或主成分分析法(PCA)。加权最小距离,用于分类标准进行比较,这也可以测试核主成分分析和主成分分析法(PCA)性能。 在第一部份的实验,300故障样本被用于比较和主成分分析法(PCA)对特征提取核主成分分析。简化的计算采用高斯核函数。 这个值,内核参数和3之间,0.8%区间数降低0.4时确定的尺寸。所以最好的正确分类率在这个维度的精确度是选粉机具有最好的分类结果。 在第二部分的实验,该分类识别特征提取了之后比较两个方面:进行加权最小距离或种群选择。80%的数据为训练和其他20%是用于测试。结果显示在表2和3。表2对比的辨识率的主成分分析和核主成分分析方法表3倍比较认可的主成分分析和核主成分分析方法 从表2、3,可以得出结论,从表2、3个核主成分分析需要更少的时间,比主成分分析法(PCA)的识别精度较高。4结论一个主成分分析提取方法使用内核过错。问题是先从一个非线性空间成为一个线性更高维度空间。然后更高维度特徵空间在以内部产品与核函数。从而解决这个复杂的计算问题,巧妙地克服困难的高维度和局部极小化。从实验数据,比较分析了传统主成分分析法(PCA)核主成分分析,极大地提高了特征提取和识别故障状态,效率。 参考文献1李布罗.损坏电机驱动系统故障检测。,2003年3月,18:50。2简索列特 故障监测与诊断的采矿设备。1994,(5):30 - 1332作证。3彭志科， 小波变换在机械状态监测和故障诊断研究。机械系统和信号处理,2003(17):74 - 221。4罗斯福,史蒂芬，使用核函数的非线性因素分析方法。麻萨诸塞州:麻省理工学院出版社,2000:568 - 406。5屯希,泰勒的使用核主成分分析的数据分布模型。模式识别,2003年,36(1):217 - 227。6穆勒克拉，尹浩然,等。介绍内核学习算法。国立台湾科技大学硕士论文,2001,12(2):32 - 34。7小卡文.支持向量机故障诊断。振动、测量及杂志,2001年,第21诊断(4):258 - 262。8赵小明,李勇的非线性主成分分析法(PCA)研究的故障检测和诊断方法。信息和控制,2001,(4):359 - 203。9胡小娇,理论与应用研究的特征提取基于核。计算机工程,2002,28(10):36 - 38。10Received 15 May 2008; accepted 20 July 2008 Projects 50674086 supported by the National Natural Science Foundation of China, BS2006002 by the Society Development Science and Technology Plan of Jiangsu Province and 20060290508 by the Doctoral Foundation of Ministry of Education of China Corresponding author. Tel: +86-516-83591702; E-mail address: xiasx Mine-hoist fault-condition detection based on the wavelet packet transform and kernel PCA XIA Shi-xiong, NIU Qiang, ZHOU Yong, ZHANG Lei School of Computer Science & Technology, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China Abstract: 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) and kernel PCA (Kernel Principal Compo-nent 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. It 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 dimen-sion feature space. The KPCA transformation was applied to extracting the 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 Introduction Because a mine hoist is a very complicated and variable 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 and may even pose a threat to the security of mine per-sonnel. Therefore, the identification of running faults has become an important component of the safety system. The key technique for hoist condition moni-toring and fault identification is extracting informa-tion from features of the monitoring signals and then offering a judgmental result. However, there are many variables to monitor in a mine hoist and, also, there are many complex correlations between the variables and the working equipment. This introduces uncertain factors and information as manifested by complex forms such as multiple faults or associated faults, which introduce considerable difficulty to fault diagnosis 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 transformation approach. But the actual monitoring process includes nonlinearity in different degrees. Thus, researchers have proposed a series of nonlinear methods involving complex nonlinear transforma-tions. Furthermore, these non-linear methods are con-fined to fault detection: Fault variable separation and fault identification are still difficult problems. This paper describes a hoist fault diagnosis feature exaction method based on the Wavelet Packet Trans-form (WPT) and kernel principal component analysis (KPCA). We extract the features by WPT and then extract the main features using a KPCA transform, which projects low-dimensional monitoring data samples into a high-dimensional space. Then we do a dimension reduction and reconstruction back to the singular kernel matrix. After that, the target feature is extracted from the reconstructed nonsingular matrix. In this way the exact target feature is distinct and sta-ble. By comparing the analyzed data we show that the method proposed in this paper is effective. 2 Feature extraction based on WPT and KPCA 2.1 Wavelet packet transform The wavelet packet transform (WPT) method3, which is a generalization of wavelet decomposition, offers a rich range of possibilities for signal analysis. J China Univ Mining & Technol 18 (2008) 05670570 JOURNAL OF CHINA UNIVERSITY OF MINING & TECHNOLOGY/locate/jcumt Journal of China University of Mining & Technology Vol.18 No.4 568The frequency bands of a hoist-motor signal as col-lected by the sensor system are wide. The useful in-formation 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 to say, these broadband signals contain a large amount of useful information: But the information can not be directly obtained from the data. The WPT is a fine signal analysis method that decomposes the signal into many layers and gives a better resolution in the time-frequency domain. The useful information within the different frequency bands will be ex-pressed by different wavelet coefficients after the decomposition of the signal. The concept of “energy information” is presented to identify new information hidden the data. An energy eigenvector is then used to quickly mine information hiding within the large amount of data. The algorithm is: Step 1: Perform a 3-layer wavelet packet decom-position 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 wavelet packet decomposition. Use 3 jS (j=0, 1, , 7) to denote the reconstructed signals of each frequency band range in the 3rd layer. The total signal can then be denoted as: ?=703jjSS (1) Step 3: Construct the feature vectors of the echo signals of the GPR. When the coupling electromag-netic waves are transmitted underground they meet various inhomogeneous media. The energy distribut-ing of the echo signals in each frequency band will then be different. Assume that the corresponding en-ergy of 3 jS (j=0, 1, , 7) can be represented as 3 jE(j=0, 1, , 7). The magnitude of the dispersed points of the reconstructed signal 3 jS is: jkx (j=0, 1, , 7; k=1, 2, , n), where n is the length of the signal. Then we can get: 22331( ) dnjjjkkESttx=? (2) Consider that we have made only a 3-layer wavelet package decomposition of the echo signals. To make the change of each frequency component more de-tailed the 2-rank statistical characteristics of the re-constructed signal is also regarded as a feature vector: 2311()njkjjkkDxxn=? (3) Step 4: The 3 jE are often large so we normalize them. Assume that 7230jjEE=?=?, thus the derived feature vectors are, at last: 30313637/, /, ., /, /EE EEEE EE=T (4) The signal is decomposed by a wavelet package and then the useful characteristic information feature vectors are extracted through the process given above. Compared to other traditional methods, like the Hil-bert transform, approaches based on the WPT analy-sis are more welcome due to the agility of the process and its scientific decomposition. 2.2 Kernel principal component analysis The method of kernel principal component analysis applies kernel methods to principal component analy-sis45. Let1, 1, 2, , , 0MNkkkxRkMx=?. The prin-cipal component is the element at the diagonal after the covariance matrix, T11Mijjx xM=?C, has been diagonalized. Generally speaking, the first N values along the diagonal, corresponding to the large eigen-values, are the useful information in the analysis. PCA solves the eigenvalues and eigenvectors of the covariance matrix. Solving the characteristic equa-tion6:11()Mjjjxv xM=?C (5) where the eigenvalues 0 and the eigenvectors 0NR is essence of PCA. Let the nonlinear transformations, :NRF, xX, project the original space into feature space, F. Then the covariance matrix, C, of the original space has the following form in the feature space: T11( )()MijjxxM=?C (6) Nonlinear principal component analysis can be considered to be principal component analysis of Cin the feature space, F. Obviously, all the eigenvalues of C (0) and eigenvectors, 0VF satisfy VV= C. All of the solutions are in the subspace that transforms from ( ), 1, 2, , ixiM=?: ()(), 1, 2, , kkxVxV kM =?C (7) There is a coefficient i. Let 1( )MiiiVx=? (8) From Eqs.(6), (7) and (8) we can obtain: XIA Shi-xiong et al Mine-hoist fault-condition detection based on the wavelet packet 569111()( )1 ()()()( )MikiiMMikjjiijaxxaxxxxM=? (9)where1, 2, , kM=?. Define A as an MM rank matrix. Its elements are: ( )()ijijA?xx= (10) From Eqs.(9) and (10), we can obtain 2Maa=AA. This is equivalent to: M aa=A (11) Make 12M? as As eigenvalues, and 12, , , M? as the corresponding eigenvector. We only need to calculate the test points projec-tions on the eigenvectors kV that correspond to nonzero eigenvalues in F to do the principal compo-nent extraction. Defining this as k, it is given by: 1( )( )( )MkkiikiVxxx=? (12) It is easy to see that if we solve for the direct prin-cipal component we need to know the exact form of the non-linear image. Also as the dimension of the feature space increases the amount of computation goes up exponentially. Because Eq.(12) involves an inner-product computation, ( )( )ixx, accord-ing to the principles of Hilbert-Schmidt we can find a kernel function that satisfies the Mercer conditions and makes ( , )( )( )iiK x xxx=. Then Eq.(12) can be written: 1( )( , )MkkiikiVxx x=?K (13) Here is the eigenvector of K. In this way the 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 func-tion78. 2.3 Description of the algorithmThe algorithm for extracting target features in rec-ognition of fault diagnosis is: Step 1: Extract the features by WPT; Step 2: Calculate the nuclear matrix, K, for each sample, (1, 2, , )NixRiN=?, in the original in-put space, and ( )()ijijKxx=; Step 3: Calculate the nuclear matrix after zero-mean processing of the mapping data in feature space; Step 4: Solve the characteristic equation M aa=A; 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 con-sider the precise form of the nonlinear transformation. The mapping function can be non-linear and the di-mensions of the feature space can be very high but it is possible to get the main feature components effec-tively by choosing a suitable kernel function and kernel parameters9. 3 Results and discussion The character of the most common fault of a mine hoist was in the frequency of the equipment vibration signals. The experiment used the vibration signals of a mine hoist as test data. The collected vibration sig-nals were first processed by wavelet packet. Then through the observation of different time-frequency energy distributions in a level of the wavelet packet we obtained the original data sheet shown in Table 1 by extracting the features of the running motor. The fault diagnosis model is used for fault identification or classification. Table 1 Original fault data sheet Eigenvector (104) E50E51E41E31E21E11Fault style1166.4951.34980.13612 0.08795 0.19654 0.25780F12132.7141.24600.10684 0.07303 0.12731 0.19007F13112.251.53530.21356 0.09543 0.16312 0.16495F14255.031.95740.44407 0.31501 0.33960 0.28204F25293.112.65920.66510 0.43674 0.27603 .027473F26278.842.46700.49700 0.44644 0.28110 0.27478F27284.122.30140.29273 0.49169 0.27572 0.23260F38254.221.53490.47248 0.45050 0.28597 0.28644F39312.742.43370.42723 0.40110 0.34898 0.24294F310304.122.60140.77273 0.53169 0.37281 0.27263F411314.222.53490.87648 0.65350 0.32535 0.29534F412302.742.83370.72829 0.50314 0.38812 0.29251F4Experimental testing was conducted in two parts: The first part was comparing the performance of KPCA and PCA for feature extraction from the origi-nal data, 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-neighbor criteria were used for classifica-tion comparison, which can also test the KPCA and PCA performance. In the first part of the experiment, 300 fault sam-ples were used for comparing between KPCA and PCA for feature extraction. To simplify the calcula-tions a Gaussian kernel function was used: Journal of China University of Mining & Technology Vol.18 No.4 57022( , )( ), ( )exp2xyx yxy?=?K (10) The 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 experiment, the classifi-ers recognition rate after feature extraction was ex-amined. Comparisons were done two ways: the minimum 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. Table 2 Comparing the recognition rate of the PCA and KPCA methods (%) PCA KPCA Minimum distance 91.4 97.2 Nearest-neighbor 90.6 96.5 Table 3 Comparing the recognition times of the PCA and KPCA methods (s) Times of extractionTimes of classificationTotal timesPCA 216.4 38.1 254.5 KPCA129.5 19.2 148.7 From Tables 2 and 3, it can be concluded from Ta-bles 2 and 3 that KPCA takes less time and has rela-tively higher recognition accuracy
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