Efficient Iterative Dynamic Kernel Principal ComponentAnalysis Monitoring Method for the Batch Process with Super-large-scaleData Sets

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

In the recognition of digital modulation signals, extracting the characteristics that more easily distinguish the source signals, and have better performance of the signal, the source signals can be identified by using these characteristics. This paper optimized the original 20 features using orthogonal experiment method, and then identified the signals by the neural network, finally compared its results with that of PCA(principal component analysis) and KPCA(kernel principal component analysis) methods. Experimental results show that orthogonal experiment method in Gaussian and multipath environment can optimize the selection of the features to achieve higher recognition rate than the original features. Orthogonal experiment method has a better ability than PCA and KPCA methods in the optimal choice of these 20 characteristics.

Torque tube is widely used on the offshore platform, and its quality plays an important role on the security of offshore platform. The cold bending forming process for torque tube production is nonlinear and dynamic seriously, with the fault types varied and complex, so the traditional PCA cannot get a good effect in the fault detection of cold bending forming. In this paper, a fault detection method based on dynamic kernel principal component analysis (DKPCA) algorithm is introduced to detect the faults of the cold bending forming. Eleven process variables were sampled from the actual manufacture process and used for fault diagnosis. PCA and DKPCA are used to carry out fault detection on the cold bending forming process, and the results show that the effect of DKPCA for fault detection is better than that of PCA. DKPCA can improve the detection effect greatly due to its advantage in nonlinear and dynamic characteristics, which can be applied widely in actual process.

Aimed at the nonlinear properties of analog circuits features , kernel Principal Component Analysis(KPCA) combined with Support Vector Machine(SVM) based diagnostic method for faults of analog circuit was proposed in this paper. Here, uses KPCA to reduce the irrelevant features. The KPCA method is used to extract the initial features. The SVM is then applied to the circuit after features extraction. It can be used as a new idea for Fault Diagnosis of Analog Circuits. To better verify the superiority of the proposed method, KPCA+SVM classification results were compared with the results of PCA+SVM. It is concluded that KPCA+SVM classifier achieved a better performance than PCA+SVM in the terms of the accuracy.

Fault discriminant enhanced kernel principal component analysis incorporating prior fault information for monitoring nonlinear processes

In this paper, we are going to propose an online radial basis function (RBF) neural network algorithm without any preprocessing step. Then a kernel principal component analysis (KPCA) is coupled with the proposed online RBF neural network algorithm. Indeed, the KPCA method is used as a preprocessing step to reduce the feature dimension which fed to the RBF neural network. Reducing memory requirements of the models makes RBF neural network training efficient and fast. These two proposed algorithms are applied, with success, for identification of a mobile robot position. The simulation results present that the used sigmoid function as a kernel, compared to other kernel functions, which gives an excellent model and a minimum mean square error.

This study proposes a diagnosis method for IGBT open circuit fault and sensor drift fault in CRH2 through ensemble empirical mode decomposition (EEMD) and an improved kernel principal component analysis (KPCA) way. EEMD is modified to reduce noise in the current and voltage signals. Subsequently, an improved KPCA method using weight matrix to highlighting fault information is developed to detect and diagnose the composite fault. Then the three-phase current averaging method is applied to perform fault location. Numerical simulation results verify the validity and availability of the composite fault detection method.

Aiming at complicated faults detection of distillation column industrial process, it has faced a grave challenge. In this paper, a new indiscernibility dynamic kernel principal component analysis (I-DKPCA) method is presented and applied to distillation column. Compared with traditional statistical techniques, I-DKPCA not only can capture nonlinear property and dynamic characteristic of processes but also can extract relevant variables from all the variables. Applying this new method to distillation column process (a hardware-in-the-loop simulation system), the results prove the proposed method has great advantages, that is, lower missing rate and higher detection rate for the faults, compared with KPCA and DPCA.

This paper proposes dynamic kernel principal components analysis (DKPCA) approach to bioprocesses monitoring. The basic idea of KPCA is to map the input data into a feature space first via a nonlinear mapping, and then perform a linear PCA in feature space F . The dynamic kernel matrix of DKPCA can capture the nonlinearity and the dynamics of bioprocesses. The proposed method was applied to the fault detection and diagnosis of a simulation benchmark of a biological treatment process. The simulation results clearly show the effectiveness of the proposed approach.

The existing recommendation algorithms have lower robustness in facing of shilling attacks. Considering this problem, we present a robust recommendation algorithm based on kernel principal component analysis and fuzzy c-means clustering. Firstly, we use kernel principal component analysis method to reduce the dimensionality of the original rating matrix, which can extract the effective features of users and items. Then, according to the dimension-reduced rating matrix and the high correlation characteristic between attack profiles, we use fuzzy c-means clustering method to cluster user profiles, which can realize the effective separation of genuine profiles and attack profiles. Finally, we construct an indicator function based on the attack detection results to decrease the influence of attack profiles on the recommendation, and incorporate it into the matrix factorization technology to design the corresponding robust recommendation algorithm. Experiment results indicate that the proposed algorithm is superior to the existing methods in both recommendation accuracy and robustness.

There are some manufacturers of wet noodles that use hazardous substances to extend shelf life. Detection of formalin content in the noodles is still difficult for ordinary people to do. Standard chemical analysis tends to quantitatively analyze the elements or compounds in the sample. Qualitative analysis using Kernel Principal component analysis (K-PCA) can be done by detecting the aroma of wet noodles using electronic nose. Pure wet noodles and wet noodle mixed with 1%, 5%, 10%, 15% and 20% formalin solutions used as samples. With each sample was weighed with a mass of 20 grams and placed in a closed sample room. Using e-nose system with 5 gas sensors (TGS 2610, TGS 2620, TGS 2611, TGS 2602, and TGS 2600) and K-PCA with linear, polynomial, RBF and sigmoid methods, the samples were clustered. The results proved that pure wet noodles and wet noodles mixed by formalin can be clustered using the K-PCA method with a total variance of 98.83%. So that this e-nose can be used as an alternative instrument to detect the purity of wet noodles from the influence of harmful substances such as formalin.

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.

Application of KPCA combined with SVM in Raman spectral discrimination

The practical application of traditional data‐driven techniques for process monitoring encounters significant challenges due to the inherent nonlinear and dynamic nature of most industrial processes. Aiming at the problem of nonlinear dynamic process monitoring, a novel fault detection method based on dynamic kernel principal component analysis combined with weighted structural difference (DKPCA‐WSD) is proposed in this paper. Initially, the proposed method leverages a sophisticated nonlinear transformation to project the augmented matrix of the original input data into a high‐dimensional feature space, thereby facilitating the establishment of a DKPCA model. Subsequently, the WSD statistic is computed, utilizing a widely known sliding window technique, to quantify the mean and standard deviation differences across data structures. Ultimately, the WSD statistic is utilized for fault detection, completing the process monitoring task. By integrating the capability of DKPCA to capture nonlinear dynamic characteristics with the effectiveness of the WSD statistic in mitigating the impact of non‐Gaussian data distributions, DKPCA‐WSD significantly enhances the monitoring performance of traditional DKPCA in nonlinear dynamic processes. The proposed method is evaluated through a numerical case exhibiting nonlinear dynamic behaviors and a simulation model of a continuous stirred tank reactor. A comparative analysis with conventional methods, including principal component analysis (PCA), dynamic principal component analysis, KPCA, PCA similarity factor (SPCA), DKPCA, and moving window KPCA (MWKPCA), demonstrates that DKPCA‐WSD outperforms traditional fault detection techniques in nonlinear dynamic processes, offering a substantial improvement in monitoring performance.

Eigendecomposition of kernel matrix is an indispensable procedure in many learning and vision tasks. However, the cubic complexity O(N3) is impractical for large problem, where N is the data size. In this paper, we propose an efficient approach to solve the eigendecomposition of the kernel matrix W. The idea is to approximate W with W̄ that is composed of m 2 constant blocks. The eigenvectors of W̄, which can be solved in O(m3) time, is then used to recover the eigenvectors of the original kernel matrix. The complexity of our method is only O(mN + m 3), which scales more favorably than state-of-the-art low rank approximation and sampling based approaches (O(m2N + m3)), and the approximation quality can be controlled conveniently. Our method demonstrates encouraging scaling behaviors in experiments of image segmentation (by spectral clustering) and kernel principal component analysis.