外文翻译部分：
英文原文
Mine-hoist fault-condition detection based on the wavelet packet transform and kernel PCA
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 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. 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 dimension 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 detection
1 Introduction
Because a mine hoist is a very 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 identification 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 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 diagnosis and identification[1]. 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 nonlinearmethods involving complex nonlinear transformations. Furthermore, these non-linear methods are confined to fault detection: Fault variable separation 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,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 distinct and stable.By comparing the analyzed data we show that themethod proposed in this paper is effective.
2 Feature extraction based on WPT and KPCA
2.1 Wavelet packet transform
The wavelet packet transform (WPT) method[3],which is a generalization of wavelet decomposition, offers a rich range of possibilities 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 broadband 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 different 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 of 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, …, 7) to denote the reconstructed signals of each frequencyband range in the 3rd layer. The total signal can thenbe denoted as:
s??S3j （1）
j?07Step 3: Construct the feature vectors of the echosignals of the GPR. When the coupling electromagneticwaves are transmitted underground they meetvarious
inhomogeneous media. 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, …, n), where n is the length of thesignal. Then we can get:
E3j??S3j(t)dt??xjk （2）
k?12n2Consider 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 feature vector:
1nD3j??(xjk?xjk) （3）
nk?12??7E?EStep 4: The 3 j E are often large so we normalize them. Assume that??3j?, ?J?0?2thus the derived feature vectors are, at last:
T=[E30/1,E31/1,.......,E36/1,E37/1] (4) The signal is decomposed by a wavelet packageand then the useful characteristic
information featurevectors are extracted through the process given above.Compared 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 analysis
The method of kernel principal component analysisapplies kernel methods to principal component analysis[4–5].
Letxk?R,k?1,2,...,M,?xk?0.The principalcomponent is the element at the
Nk?1M1diagonal afterthe covariance matrix，C?MTxx?ijhas beendiagonalized. Generally j?1Mspeaking, the first N valuesalong the diagonal, corresponding to the large
eigenvalues,are the useful information in the analysis.PCA solves the eigenvalues and eigenvectors of thecovariance matrix. Solving the characteristic equation[6]:
1???c??M?(xj?1Mj??)xj (5)
where the eigenvalues ??0,and the eigenvectors,??RN\\?0? 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 following form in the feature space:
1C?M??(x)?(x)ijJ?1MT (6)
Nonlinear principal component analysis can be