【正文】 ic information feature vectors are extracted through the process given above. Compared to other traditional methods, like the Hilbert transform, approaches based on the WPT analysis are more wele due to the agility of the process and its scientific deposition. Kernel principal ponent analysis The method of kernel principal ponent analysis applies kernel methods to principal ponent analysis[4–5]. 1, 1 , 2 , .. ., , 0 .MNkk kLe tx R k M x?? ? ??The principal ponent is the element at the diagonal after the covariance matrix，11 M TijjC x xM ?? ?has been diagonalized. Generally speaking, the first N values along the diagonal, corresponding to the large eigenvalues, are the useful information in the analysis. PCA solves the eigenvalues and eigenvectors of the covariance matrix. Solving the characteristic equation[6]: 11 ()M jjjc x xM?? ? ??? ? ?? （ 5） where the eigenvalues 0?? and the eigenvectors ? ?\0NR?? is essence of PCA. ? : 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: 11 ( ) ( )M TijJC x xM ?? ? ?? （ 6） Nonlinear principal ponent analysis can be considered to be principal ponent analysis ofC in the feature space, F. Obviously, all the eigenvalues of C( 0)?? and eigenvectors, V ?F \ {0} satisfy? V =C V . All of the solutions are in the subspace that transforms from ( ), 1, 2,...,jx i M?? ( ( ) ) ( ) , 1 , 2 , .. .,kkx V x C V k M? ? ??? （ 7） There is a coefficient i? Let 1 ()MiiiVx?? ??? （ 8） From Eqs.(6), (7) and (8) we can obtain: 111( ( ) ( ))1 (( ) ( )) ( ( ) ( ))Mi k jiMMi k j k jija x xa x x x xM???????? ? ? ???? （ 9） where k =1, 2, ….., M . Define A as an MM rank matrix. Its elements are: ( ) ( )ij i jA x x? ?? （ 10） From Eqs.(9) and (10), we can obtain M? Aa = 2A a . This is equivalent to: M? a =Aa . (11) Make 12.... M? ? ?? ? ? as A’s eigenvalues, and 12, ,..., M? ? ? ,as the corresponding eigenvector. We only need to calculate the test points’ projections on the eigenvectors kV that correspond to nonzero eigenvalues in F to do the principal ponent extraction. Defining this as k? it is given by: 1( ( ) ) ( ( ) )Mkki i kiVx xx??? ? ? ?? ? ? ?? (12) Principal ponent we need to know the exact form of the nonlinear image. Also as the dimension of the feature space increases the amount of putation goes up exponentially. Because Eq.(12) involves an innerproduct putation, ( ) ( )ixx?? according to the principles of HilbertSchmidt we can find a kernel function that satisfies the Mercer conditions and makes ( , ) ( ) ( )iiK x x x x? ? ?Then Eq.(12) can be written: 1( ( ) ) ( ( , ) )Mkki i kiV x K x x???? ? ?? (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 pletely determined by the choice of kernel function[ 7–8]. Description of the algorithm The algorithm for extracting target features in recognition of fault diagnosis is: Step 1: Extract the features by WPT。 Diagnosis,2021, 21(4): 258–262. [8] Zhao L J, Wang G, Li Y. Study of a nonlinear PCA fault detection and diagnosis method. Information and Control,2021, 30(4): 359–364. [9] Xiao J H, Wu J P. Theory and application study of feature extraction based on kernel. Computer Engineering,2021, 28(10): 36–38. 中文譯文 基于小波包變換和核主元分析技術(shù)的礦井提升機的自我故障檢測 摘要： 這是一種新的運算法，它能正確識別礦井提升機的故障并且準(zhǔn)確地監(jiān)測礦井提升機故障的 發(fā)展過程 。 KPCA就是將最初輸入的數(shù)據(jù)特征透過非線性映射映射到高維特征空間，然后在高維特征空間發(fā)現(xiàn)其主要組成部分。主成分分析 。因此，運行中故障的檢測已經(jīng)變成安全系統(tǒng)的一個重要組成部分。目前有許多傳統(tǒng)的方法可以提取礦井提升機故障特征，如主成分分析（ PCA）和偏最小二乘法（ PLS） 。因此我們的研究員已經(jīng)提出了 一系列涉及復(fù)雜的非線性變換非線性方法 。然后我們做了降維和重建并備份到奇異核矩陣。 2基于小波包變換和主成分分析技術(shù)的特征提取 小波包變換（小波包變換）方法 [ 3 ] ，這是一種小波的分解的概括， 為信號分析提供了很多可能。這就是說，這些寬帶信號包含大量有用的信息：但是從這些信息中不能直接獲得有用數(shù)據(jù)。 該算法是 ： 第 1步：將回波信號執(zhí)行 3層小波包分解，并提取 8個頻率成分的信號特