Kernel Principal Component Analysis Method Research Articles

Method of fault feature selection and fusion based on poll mode and optimized weighted KPCA for bearings

The health monitoring system for equipment is essential in the smooth proceeding of industrial production. However, the fault features to be detected in monitoring systems are generally selected through projects and expertise, which are not capable for complex and ever-changing fault information and may result in incomplete correspondence to the fault types emerged. To dig deeper for the effective features hidden in the data instead of selecting by experience, a feature selection and fusion method based on poll mode and optimized Weighted Kernel Principal Component Analysis (WKPCA) method is then proposed. Specifically, inspired by poll-mode and multi-criteria strategy, a multi-measure hierarchical model is designed to sort the fault features with high sensitivity, acquiring the feature subset with corresponding weight coefficient. Considering the variation in fault information collected by different sensors, the diagnosis rate in Extreme Learning Machine (ELM) is taken as the index for evaluation of each single sensor, then the sensitivity weight matrix of features extracted by multiple sensors is constructed after linear normalization. To integrate the feature information, WKPCA is applied for the weighted fusion of features, and Quantum Genetic Algorithm (QGA) is used to search for the kernel width parameter when the best separability in the samples under the fusion is reached. Finally, such samples are introduced to drive the diagnostic model of the monitoring system in rolling bearing. The experimental results show that, compared with the traditional feature selection and fusion methods, this method is capable for sorting out highly sensitive features with more fault information self-adaptively, and can improve the separability in the subset of fault samples effectively.

Deep neural learning based protein function prediction.

It is vital for the annotation of uncharacterized proteins by protein function prediction. At present, Deep Neural Network based protein function prediction is mainly carried out for dataset of small scale proteins or Gene Ontology, and usually explore the relationships between single protein feature and function tags. The practical methods for large-scale multi-features protein prediction still need to be studied in depth. This paper proposes a DNN based protein function prediction approach IGP-DNN. This method uses Grasshopper Optimization Algorithm (GOA) and Intuitionistic Fuzzy c-Means clustering (IFCM) based protein function modules extracting algorithm to extract the features of protein modules, utilizing Kernel Principal Component Analysis (KPCA) method to reduce the dimensionality of the protein attribute information, and integrating module features and attribute features. Inputting integrated data into DNN through multiple hidden layers to classify proteins and predict protein functions. In the experiments, the F-measure value of IGP-DNN on the DIP dataset reaches 0.4436, which shows better performance.

Sensitivity analysis of factors affecting motion reliability of manipulator and fault diagnosis based on kernel principal component analysis

AbstractAs an important index to quantitatively measure the motion performance of a manipulator, motion reliability is affected by many factors, such as joint clearance. The present research utilized a UR10 manipulator as the research object. A factor mapping model for influencing the motion reliability was established. The link flexibility factor, joint flexibility factor, joint clearance factor, and Denavit–Hartenberg (DH) parameters were comprehensively considered in this model. The coupling relationship among the various factors was concisely expressed. Subsequently, the nonlinear response surface method was used to calculate the reliability and sensitivity of the manipulator, which provided an applicable reference for its trajectory planning and motion control. In addition, a data-driven fault diagnosis method based on the kernel principal component analysis (KPCA) was used to verify the motion accuracy and sensitivity of the manipulator, and joint rotation failure was considered as an example to verify the accuracy of the KPCA method. This study on the motion reliability of the manipulator is of great significance for the current motion performance, adjusting the control strategy and optimizing the completion effect of the motion task of a manipulator.

Fault Diagnosis for PEMFC Water Management Subsystem Based on Learning Vector Quantization Neural Network and Kernel Principal Component Analysis

To solve the problem of water management subsystem fault diagnosis in a proton exchange membrane fuel cell (PEMFC) system, a novel approach based on learning vector quantization neural network (LVQNN) and kernel principal component analysis (KPCA) is proposed. In the proposed approach, the KPCA method is used for processing strongly coupled fault data with a high dimension to reduce the data dimension and to extract new low-dimensional fault feature data. The LVQNN method is used to carry out fault recognition using the fault feature data. The effectiveness of the proposed fault detection method is validated using the experimental data of the PEMFC power system. Results show that the proposed method can quickly and accurately diagnose the three health states: normal state, water flooding failure and membrane dry failure, and the recognition accuracy can reach 96.93%. Therefore, the method proposed in this paper is suitable for processing the fault data with a high dimension and abundant quantities, and provides a reference for the application of water management subsystem fault diagnosis of PEMFC.

Probabilistic bearing fault diagnosis using Gaussian process with tailored feature extraction

Deep learning methods recently have gained growing interests and are extensively applied in the data-driven bearing fault diagnosis. However, current deep learning methods perform the bearing fault diagnosis in the form of deterministic classification, which overlook the uncertainties that inevitably exist in actual practice. To tackle this issue, in this research, we develop a probabilistic fault diagnosis framework that can account for the uncertainty effect in prediction, which bears practical significance. This framework uses the Gaussian process classifier (GPC) as the mainstay, which fundamentally is built upon the Bayesian inference. To establish the high-fidelity GPC, the tailored feature extraction method can be adaptively determined through the cross validation-based grid search upon a prespecified method pool consisting of various kernel principal component analysis (KPCA) methods and stacked autoencoder. This adaptive strategy can ensure the adequate GPC model training to accurately characterize the complex nonlinear relations between the data features and respective faults. Systematic case studies using the publicly accessible experimental rolling bearing dataset, i.e., CWRU bearing dataset are carried out to validate this new framework. The results clearly illustrate the unique capability of this framework in handling uncertainties. It is also found that this framework outperforms other well-established machine learning and deep learning models in terms of accuracy and robustness. Moreover, the sensor fusion that combines the spatial vibration measurements appears to be an effective technique to further enhance the fault diagnosis performance. By fully leveraging the probabilistic feature of the framework, the future research endeavor, such as the extended fault diagnosis using limited fault labels will be facilitated.

Research on Prediction Method of Hydraulic Pump Remaining Useful Life Based on KPCA and JITL

Hydraulic pumps are commonly used; however, it is difficult to predict their remaining useful life (RUL) effectively. A new method based on kernel principal component analysis (KPCA) and the just in time learning (JITL) method was proposed to solve this problem. First, as the research object, the non-substitute time tac-tail life experiment pressure signals of gear pumps were collected. Following the removal and denoising of the DC component of the pressure signals by the wavelet packet method, multiple characteristic indices were extracted. Subsequently, the KPCA method was used to calculate the weighted fusion of the selected feature indices. Then the state evaluation indices were extracted to characterize the performance degradation of the gear pumps. Finally, an RUL prediction method based on the k-vector nearest neighbor (k-VNN) and JITL methods was proposed. The k-VNN method refers to both the Euclidean distance and angle relationship between two vectors as the basis for modeling. The prediction results verified the feasibility and effectiveness of the proposed method. Compared to the traditional JITL RUL prediction method based on the k-nearest neighbor algorithm, the proposed prediction model of the RUL of a gear pump presents a higher prediction accuracy. The method proposed in this paper is expected to be applied to the RUL prediction and condition monitoring and has broad application prospects and wide applicability.

Geographical discrimination of propolis using dynamic time warping kernel principal components analysis

The chemometric analysis of chromatographic data is commonly used for discriminating bee propolis based on their geographical origin. Traditional machine learning methods for this purpose include principal component analysis and hierarchical clustering. When viewed as a time-series, the key discriminatory features in chromatographic data are the peaks, which should have similar location patterns for the propolis of the same origin. However, the peaks between same-origin samples are not always exactly aligned. Without proper alignment, samples from the same origin may be perceived by the clustering method to be very different. In this paper, we propose a novel dynamic time warping kernel principal component analysis (DTW-KPCA) method for the chemometric discrimination of propolis. The proposed method uses a Gaussian dynamic time warping kernel to measure the similarity between chromatographic time-series which incorporates time-series alignment. Results show a better clustering of propolis samples compared to the currently used methods, as measured by the silhouette coefficient. Hence, the proposed method enables a more reliable clustering as to the origin of propolis samples.

Fault detection and diagnosis of the air handling unit via an enhanced kernel slow feature analysis approach considering the time-wise and batch-wise dynamics

Air handling unit (AHU) is a typical special batch control process, exhibiting strong nonlinear property and two-directional dynamic characteristics which are the time-wise and batch-wise dynamic characteristics. Specifically, the time-wise dynamic characteristic corresponds to the evolution of different operating modes caused by the underlying driving forces which vary slowly in each running day (a batch run), while the batch-wise dynamic characteristic relates to the dynamic variations and deviations among different running days (batch runs). In order to further improve the AHU FDD performance through capturing the underlying driving forces of the AHU system and tackling the batch-wise dynamic property between different batch runs, in this paper, an enhanced kernel slow feature analysis (SFA) based FDD scheme is developed to detect and identify the faults of the nonlinear AHU system. Firstly, a three-way data based kernel SFA (TBKSFA) approach is proposed to detect the faults. In the proposed TBKSFA approach, the kernel trick is adopted in the SFA to sufficiently deal with the nonlinearity and the time-wise dynamic characteristic, and the multiway data analysis is employed to cope with the batch-wise dynamics among different batch runs by converting the three-way training dataset into a variable-wise unfolding two-way matrix. In addition, to handle the tough problem of nonlinearly identifying the fault pattern, a novel kernel discriminant SFA (KDSFA) model is further built by combining the kernel SFA with the discriminant analysis method. In the fault pattern diagnosis process, the proposed KDSFA is pairwisely implemented on the normal and fault datasets to calculate the fault direction, and the fault is then identified by computing the similar degrees of its own fault direction and the historical fault directions. At last, experiments and comparisons on the FDD performance of the developed approach are made using the experimental data provided by ASHRAE Research Project RP-1312. To be specific, the proposed TBKSFA based fault detection method is compared with the popular kernel principal component analysis (KPCA) method, the closely related kernel SFA method and the emerging manifold learning based kernel locality preserving projections (KLPP) method. While the developed KDSFA based fault pattern diagnosis scheme is compared with the conventional jointed angle analysis technique, the strongly linked DSFA based method and the rising artificial neural networks based long short-term memory(LSTM) classifier. Experimental results demonstrate that significant improvements can be achieved by the proposed approach compared with some other popular methods.

A novel industrial process fault monitoring method based on kernel robust non-negative matrix factorization

Industrial processes are characterized by large amounts of nonlinear and noisy data, which pose a critical challenge to the accuracy and rapidity of fault detection. In this paper, an industrial process fault monitoring method based on kernel robust non-negative matrix factorization is proposed. This method uses the kernel technique to map the nonlinear data to high-dimensional linear space, where the local features of the sample will be extracted by the non-negative matrix factorization (NMF) method. However, noise signals will inevitably be mixed. Therefore, a sparse error matrix is introduced to isolate fault and noise information. Finally, a new monitoring statistics and a fault detection framework are constructed. On the TE platform, the algorithm proposed in this paper is compared with kernel principal component analysis and kernel NMF methods in nonlinear experiments and robustness experiments through two performance indicators: fault detection rate and fault delay. The results prove the effectiveness of the algorithm in this paper.

Manifold reduction techniques for the comparison of crank angle-resolved particle image velocimetry (PIV) data and Reynolds-averaged Navier-Stokes (RANS) simulations in a spark ignition direct injection (SIDI) engine

In this article, different manifold reduction techniques are implemented for the post-processing of Particle Image Velocimetry (PIV) images from a Spark Ignition Direct Injection (SIDI) engine. The methods are proposed to help make a more objective comparison between Reynolds-averaged Navier-Stokes (RANS) simulations and PIV experiments when Cycle-to-Cycle Variations (CCV) are present in the flow field. The two different methods used here are based on Singular Value Decomposition (SVD) principles where Proper Orthogonal Decomposition (POD) and Kernel Principal Component Analysis (KPCA) are used for representing linear and non-linear manifold reduction techniques. To the authors’ best knowledge, this is the first time a non-linear manifold reduction technique, such as KPCA, has ever been used in the study of in-cylinder flow fields. Both qualitative and quantitative studies are given to show the capability of each method in validating the simulation and incorporating CCV for each engine cycle. Traditional Relevance Index (RI) and two other previously developed novel indexes: the Weighted Relevance Index (WRI) and the Weighted Magnitude Index (WMI), are used for the quantitative study. The results indicate that both POD and KPCA show improvements in capturing the main flow field features compared to ensemble-averaged PIV experimental data and single cycle experimental flow fields while capturing CCV. Both methods present similar quantitative accuracy when using the three indexes. However, challenges were highlighted in the POD method for the selection of the number of POD modes needed for a representative reconstruction. When the flow field region presents a Gaussian distribution, the KPCA method is seen to provide a more objective numerical process as the reconstructed flow field will see convergence with an increasing number of modes due to its usage of Gaussian properties. No additional criterion is needed to determine how to reconstruct the main flow field feature. Using KPCA can, therefore, reduce the amount of analysis needed in the process of extracting the main flow field while incorporating CCV.

Application of Coupled LDA–KPCA and BO–MKRVM Model to Predict Coal and Gas Outbursts

This paper proposed a coupled model of effective feature extraction and optimized classifier, which can overcome the existing problems of coal and gas outbursts classification in the literatures. Firstly, we support the use of kernel principal component analysis and linear discriminant analysis methods to extract linear and nonlinear feature information from coal and gas outbursts influencing factors. Secondly, in order to realize the complementarity and correlation between coal and gas outbursts influencing factors, we perform parallel feature fusion to combine the extracted linear and nonlinear feature information. Thirdly, an improved classifier called BO–MKRVM has been proposed that combines mixed kernel relevance vector machine (MKRVM) and Bayesian optimization (BO) algorithm to predict coal and gas outbursts according to the extracted features. In BO–MKRVM model, an effective mixed kernel function which combines Gaussian kernel function and Sigmoid kernel function is proposed to improve the learning and generalization ability of the MKRVM classifier, then the BO and tenfold cross-validation are utilized to optimize kernel parameters and weight coefficients of MKRVM with strong global and local search capability, the proposed BO–MKRVM classifier is performed on coal and gas outbursts dataset. Compared with the single feature extraction method, the combination of linear and non-linear feature extraction methods can obtain complete feature information and contribute to the classification performance of outbursts. The mixed kernel function considers the characteristics of coal and gas outbursts sample data, which can also effectively improve the outbursts accuracy. After the MKRVM classifier is optimized by BO algorithm, the BO–MKRVM classifier has better fitting effect and generalization ability, and obtains higher accuracy with a lower time. The experimental results are obviously better than those of other classification models, which further verifies the applicability of the proposed coupled model.

Efficient Iterative Dynamic Kernel Principal Component Analysis Monitoring Method for the Batch Process with Super-large-scale Data Sets.

The Internet environment has provided massive data to the actual industrial production process. It not only has large amounts of data but also has a high data dimension, which brings challenges to the traditional statistical process monitoring. Aiming at the nonlinearity and dynamics of industrial large-scale high-dimensional data, an efficient iterative multiple dynamic kernel principal component analysis (IMDKPCA) method is proposed to monitor the complex industrial process with super-large-scale high-dimensional data. In KPCA, a new KKT matrix is first created by using kernel matrix K. According to the properties of the symmetric matrix, the newly constructed matrix has the same eigenvector as the original matrix K; hence, each column of the matrix K can be used as the input sample of the iteration algorithm. After iterative operation, the kernel principal component can be deduced fleetly without the eigen decomposition. Because the kernel matrix is not stored in the algorithm beforehand, it can effectively reduce the computation complexity of the kernel. Especially for a tremendous data scale, the traditional eigen decomposition technology is no longer appropriate, yet the presented method can be solved quickly. The autoregressive moving average (ARMA) time series model and kernel principal component analysis (KPCA) are combined to build the IDKPCA model for dealing with the dynamics and nonlinearity in the industrial process. Eventually, it is applied to monitor faults in the penicillin fermentation process and compared with MKPCA to certify the accuracy and applicability of the proposed method.

An Improved Fault Diagnosis Strategy for Process Monitoring Using Reconstruction Based Contributions

Air pollution has become the fourth leading cause of premature death on Earth. Air pollution causes poor health and death; about one case out of every ten deaths worldwide is caused by air pollution, which is six times more than malaria. Human activities are the main cause of air pollution, such as chemical industries, road traffic, and fossil fuel power plants. Over the span of several years, monitoring air quality has become an exigent and essential task. In order to limit the health impact of air pollution and to ensure safe operation of chemical processes, it is necessary to quickly detect and locate instrumentation defects. There are several process monitoring techniques in the literature. Among these techniques is the one selected for this work for the detection and location of sensor faults: the kernel principal component analysis (KPCA) method, which was selected for its primary advantages of easy employment and less necessity for prior knowledge. Using the KPCA method for monitoring nonlinear systems, the calculation cost and the memory size are related to the number of initial data. This is currently a major limitation of the KPCA method, especially in industrial environments. In order to remedy this limitation, in this paper we propose a new method of detection and localization. The key idea of this approach is to extend the method of localization based on the principle of reconstruction-based contributions (RBC) by downsizing the kernel matrix in the characteristic space. The proposed technique is named reconstruction-based contribution reduced rank kernel principal component analysis(RBC-RRKPCA). The approach is demonstrated using real air quality monitoring network data and simulated data from the Tennessee Eastman process (TEP) as a challenging benchmark problem. We also present a comparative study of the performances of the conventional diagnostic technique RBC-KPCA and the proposed technique RBC-RRKPCA. The results in this paper reveal that the proposed technique achieves the highest detection and localization accuracy.

Facial emotion recognition using subband selective multilevel stationary wavelet gradient transform and fuzzy support vector machine

Facial emotion recognition finds a major role in affective computing. Recognizing emotion by facial expression is an extremely important activity to design control oriented and human computer interactive applications especially in cognitive science and neuroscience. For a precise and robust recognition, feature extraction is one of the major challenges in facial expression recognition system. Wavelet transform is one of the major key methods utilized for feature extraction in facial emotion recognition. In this paper, the statistical parameters from the proposed subband selective multilevel stationary wavelet gradient transform are calculated and are utilized as features for efficacious recognition of emotion. The features of the wavelet transform contain both spatial and spectral domain information which is best suited for identifying human emotions through facial expression. The introduction of gradient transform to find the gradient of subband avails to estimate the edges in images for the quality amelioration of subbands. The dimension reduction in the extracted features is done by using Pearson–kernel–principal component analysis method. The classification of emotion using the selected features is done by the proposed Gaussian membership function fuzzy SVM classifier. Experiments were performed on the well-known database for facial expression such as JAFEE database, CK + database and FG Net database and obtained promising emotion classification results.

Feature extraction of EEG signals based on functional data analysis and its application to recognition of driver fatigue state

Objective: Our objective is to study how to obtain features which can reflect the continuity and internal dynamic changes of electroencephalography (EEG) signals and study an effective method for fatigued driving state recognition based on the obtained features. Approach: A method of EEG signalfeature extraction based on functional data analysis is proposed. Combined with kernel principal component analysis method, the obtained features are applied to the recognition of driver fatigue state, and a corresponding recognition model of fatigued driving state is constructed. Main results: The recognition model is tested on the real collected driver fatigue EEG signals by selecting a suitable classifier. The test results show that the proposed driver fatigue state recognition method has good recognition effect, especially on the classifier based on decision tree, with an average accuracy of 99.50%. Significance: The extracted features well reflect the continuityand internal dynamic changes of the EEG signals, and it is of great significance and application value to study an effective method of fatigued driver state recognition based on the features.

Research on the application of improved SVM model in dam displacement and deformation prediction

Aiming at the influence of dam deformation on many factors, the kernel principal component analysis method is used to compare the factors affecting dam deformation, and the main factors affecting dam deformation are determined. The kernel function of support vector machine is selected, the main influence factor is input, the dam deformation is output, and the optimal parameters are obtained by grid search and cross-verification to establish the model. The deformation results are studied and analyzed, and the prediction effect is evaluated by absolute error and RMSE, and compared with the standard SVM model and the Prophet method based on time series. The results show that the accuracy of support vector machine model is improved obviously by optimizing parameters such as radius of kernel function and penalty factor through mesh optimization, and the prediction accuracy of nonlinear small sample data is significantly higher than that of time series method.

Fault detection and diagnosis of nonlinear dynamical processes through correlation dimension and fractal analysis based dynamic kernel PCA

A novel Dynamic Kernel PCA (DKPCA) method is developed for process monitoring in nonlinear dynamical systems. Classical DKPCA approaches still exhibit vague linearity assumptions to determine the number of principal components and to construct the dynamical structure. The optimal Static PCA (SPCA) and Dynamic PCA (DPCA) structures are constructed herein through the powerful theory of the nonlinear Fractal Dimension (FDim). While DKPCA offers a generic data-driven modelling of nonlinear dynamical systems, the fractal correlation dimension provides an intrinsic measure of the data complexity counting for the nonlinear dynamics and the chaotic behaviour. The proposed Fractal-based DKPCA (FDKPCA) integrates the two strategies to overcome SPCA/DPCA/DKPCA shortcomings, FDim allows verifying the degree of fitting and ensures optimal dimensionality reduction. The novel fault detection and diagnosis method is validated through seven applications using the Process Network Optimization (PRONTO) benchmark with real heterogeneous data, FDKPCA showed superior performance compared to contemporary approaches.

Source Diagnosis of Solid Oxide Fuel Cell System Oscillation Based on Data Driven

The solid oxide fuel cell (SOFC) is a new energy technology that has the advantages of low emissions and high efficiency. However, oscillation and propagation often occur during the power generation of the system, which causes system performance degradation and reduced service life. To determine the root cause of multi-loop oscillation in an SOFC system, a data-driven diagnostic method is proposed in this paper. In our method, kernel principal component analysis (KPCA) and transfer entropy were applied to the system oscillation fault location. First, based on the KPCA method and the Oscillation Significance Index (OSI) of the system process variable, the process variables that were most affected by the oscillations were selected. Then, transfer entropy was used to quantitatively analyze the causal relationship between the oscillation variables and the oscillation propagation path, which determined the root cause of the oscillation. Finally, Granger causality (GC) analysis was used to verify the correctness of our method. The experimental results show that the proposed method can accurately and effectively locate the root cause of the SOFC system’s oscillation.

Mapping the Galactic Disk with the LAMOST and Gaia Red Clump Sample. I. Precise Distances, Masses, Ages, and 3D Velocities of ∼140,000 Red Clump Stars

Abstract We present a sample of ∼140,000 primary red clump (RC) stars of spectral signal-to-noise ratios higher than 20 from the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) Galactic spectroscopic surveys, selected based on their positions in the metallicity-dependent effective temperature–surface gravity and color–metallicity diagrams, supervised by high-quality Kepler asteroseismology data. The stellar masses and ages of those stars are further determined from the LAMOST spectra, using the kernel principal component analysis method and are trained with thousands of RCs in the LAMOST–Kepler fields with accurate asteroseismic mass measurements. The purity and completeness of our primary RC sample are generally higher than 80%. For the mass and age, a variety of tests show typical uncertainties of 15% and 30%, respectively. Using over 10,000 primary RCs with accurate distance measurements from the parallaxes of Gaia Data Release 2 (DR2), we recalibrate the K s absolute magnitudes of primary RCs by, for the first time, considering both the metallicity and age dependencies. With the the new calibration, distances are derived for all the primary RCs, with a typical uncertainty of 5–10%, which is even better than the values yielded by the Gaia parallax measurements for stars beyond 3–4 kpc. The sample covers a significant volume of the Galactic disk of 4 ≤ R ≤ 16 kpc, , and −20 ≤ ϕ ≤ 50°. Stellar atmospheric parameters, line-of-sight velocities, and elemental abundances derived from the LAMOST spectra and proper motions of Gaia DR2 are also provided for the sample stars. Finally, the selection function of the sample is carefully evaluated in the color–magnitude plane for different sky areas. The sample is publicly available at 10.5281/zenodo.3875974.

Comprehensive evaluation of robotic global performance based on modified principal component analysis

The multivariate statistical method such as principal component analysis based on linear dimension reduction and kernel principal component analysis based on nonlinear dimension reduction as the modified principal component analysis method are commonly used. Because of the diversity and correlation of robotic global performance indexes, the two multivariate statistical methods principal component analysis and kernel principal component analysis methods can be used, respectively, to comprehensively evaluate the global performance of PUMA560 robot with different dimensions. When using the kernel principal component analysis method, the kernel function and parameters directly have an effect on the result of comprehensive performance evaluation. Because kernel principal component analysis with polynomial kernel function is time-consuming and inefficient, a new kernel function based on similarity degree is proposed for the big sample data. The new kernel function is proved according to Mercer’s theorem. By comparing different dimension reduction effects of principal component analysis method, the kernel principal component analysis method with polynomial kernel function, and the kernel principal component analysis method with the new kernel function, the kernel principal component analysis method with the new kernel function could deal more effectively with the nonlinear relationship among indexes, and its calculation result is more reasonable for containing more comprehensive information. The simulation shows that the kernel principal component analysis method with the new kernel function has the advantage of low time consuming, good real-time performance, and good ability of generalization.