Traditional Principal Component Analysis Method Research Articles

Double-Layer Distributed and Integrated Fault Detection Strategy for Non-Gaussian Dynamic Industrial Systems.

Currently, with the increasing scale of industrial systems, multisensor monitoring data exhibit large-scale dynamic Gaussian and non-Gaussian concurrent complex characteristics. However, the traditional principal component analysis method is based on Gaussian distribution and uncorrelated assumptions, which are greatly limited in practice. Therefore, developing a new fault detection method for large-scale Gaussian and non-Gaussian concurrent dynamic systems is one of the urgent challenges to be addressed. To this end, a double-layer distributed and integrated data-driven strategy based on Laplacian score weighting and integrated Bayesian inference is proposed. Specifically, in the first layer of the distributed strategy, we design a Jarque-Bera test module to divide all multisensor monitoring variables into Gaussian and non-Gaussian blocks, successfully solving the problem of different data distributions. In the second layer of the distributed strategy, we design a dynamic augmentation module to solve dynamic problems, a K-means clustering module to mine local similarity information of variables, and a Laplace scoring module to quantitatively evaluate the structural retention ability of variables. Therefore, this double-layer distributed strategy can simultaneously combine the different distribution characteristics, dynamism, local similarity, and importance of variables, comprehensively mining the local information of the multisensor data. In addition, we develop an integrated Bayesian inference strategy based on detection performance weighting, which can emphasize the differential contribution of local models. Finally, the fault detection results for the Tennessee Eastman production system and a diesel engine working system validate the superiority of the proposed method.

High-dimensional robust principal component analysis and its applications

Principal component analysis method is one of the most widely used statistical procedures for data dimension reduction. The traditional principal component analysis method is sensitive to outliers since it is based on the sample covariance matrix. Meanwhile, the deviation of the principal component analysis based on the Minimum Covariance Determinant (MCD) estimation is significantly increased as the data dimension increases. In this paper, we propose a high-dimensional robust principal component analysis based on the Rocke estimator. Simulation studies and a real data analysis illustrate that the finite sample performance of the proposed method is significantly better than those of the existing methods.

Error Evaluation Method of Capacitive Voltage Transformer Based on Improved Principal Component Analysis

The capacitive voltage transformer is an important data source for electricity trading and is easily influenced by environmental factors during operation, resulting in decreased metering accuracy. Because the voltage data does not satisfy the Gaussian distribution, the accuracy of the traditional principal component analysis method is poor when evaluating the error of capacitive voltage transformers. This paper proposes an improved principal component analysis method based on the local outlier factor. First, principal component analysis is utilized to separate the primary voltage fluctuation and error change. Then, a new statistic is established by using the local outlier factor instead of the traditional statistic as an evaluation standard, which reduces the missed diagnosis and misdiagnosis caused by the data distribution characteristics. The experimental results show that the improved method is better than the traditional method in terms of the detection rate of transformer anomaly detection, can effectively detect the abnormal change of transformer error and is more suitable for capacitive voltage transformers in operation.

Study on the methods of feature extraction based on electromyographic signal classification.

Electromyography (EMG) is a form of biological information, which is used in many fields to help people study human muscle movement, especially in the study of bionic hands. EMG signals can be used to explain the activity at a certain moment through the signal changes of human muscles, and it is a very complex signal, so processing it is very important. The process of EMG signals can be divided into acquisition, pre-processing, feature extraction, and classification. Not all signal channels are useful in EMG acquisition, and it is important to select useful signals among them. Therefore, this study proposes a feature extraction method to extract the most representative two-channel signals from the eight-channel signals. In this paper, the traditional principal component analysis method and support vector machine feature elimination are used to extract signal channels. At the same time, a new method, correlation heat map, is proposed to implement feature extraction method by using three methods, and three classification algorithms of K-nearest neighbor, random forest, and support vector machine are used to verify. The results show that the classification accuracy of the proposed method is better than that of the other two traditional methods.

Fault detection in multimodal processes based on the local entropy double subspace

Recently, principal component analysis (PCA) and independent component analysis (ICA) have attracted increasing attention for fault detection in industrial processes. However, industrial processes usually have multimodal characteristics, in which case, the performance of traditional PCA and ICA methods is poor. A fault detection method based on the local entropy double subspace (LEDS) is proposed that effectively supervises the multimodal process with multiple steady modes. The proposed method uses the local probability density (LPD) to eliminate the multimodal characteristics of the data. Furthermore, local entropy (LE) is applied to mine the statistical information associated with the process data. The process variables are classified into Gaussian and non-Gaussian subspaces by the Kolmogorov–Smirnov (KS) test. PCA and ICA models are built in Gaussian and non-Gaussian subspaces, respectively, for fault detection. A Bayesian decision method is employed to transform the detection results into fault probabilities, and the detection results are combined with the final statistical information. This method effectively eliminates the multicentre structure of the data and improves the fault detection performance of traditional PCA and ICA. The proposed method is applied to the Tennessee Eastman multimodal process. The simulation results show that the fault detection rate of LEDS is better than the rates of traditional methods when the false alarm rate is low for most faults.

Manifold Regularized Principal Component Analysis Method Using L2,p-Norm

The main idea of principal component analysis (PCA) is to transform the problem of high-dimensional space into low-dimensional space, and obtain the output sample set after a series of operations on the samples. However, the accuracy of the traditional principal component analysis method in dimension reduction is not very high, and it is very sensitive to outliers. In order to improve the robustness of image recognition to noise and the importance of geometric information in a given data space, this paper proposes a new unsupervised feature extraction model based on l2,p-norm PCA and manifold learning method. To improve robustness, the model method adopts l2,p-norm to reconstruct the distance measure between the error and the original input data. When the image is occluded, the projection direction will not significantly deviate from the expected solution of the model, which can minimize the reconstruction error of the data and improve the recognition accuracy. To verify whether the algorithm proposed by the method is robust, the data sets used in this experiment include ORL database, Yale database, FERET database, and PolyU palmprint database. In the experiments of these four databases, the recognition rate of the proposed method is higher than that of other methods when p=0.5. Finally, the experimental results show that the method proposed in this paper is robust and effective.

Understanding Regional Background Ozone by Multiple Methods: A Case Study in the Shandong Region, China, 2018–2020

AbstractUprising ground‐level ozone (O3) and its regional pollution in Northern China are attracting more attention. Besides local precursor emissions and photochemistry, background ozone and long‐range transport also contribute significantly to O3 concentrations. To quantify the regional background O3 concentrations and their temporal and spatial variations, multiple methods, including the principal component analysis (PCA) and the Texas Commission on Environmental Quality (TCEQ) method, were applied as a case study in Shandong province in Northern China, where serious O3 pollution occurred frequently yet the background contributions have not been well quantified. We used four methods to quantify the regional background O3: Method 1 is PCA analysis with only ambient O3 data as input; Method 2 is PCA analysis considering O3 and meteorological parameters; Method 3 combines multiple linear regression and the traditional PCA method; and Method 4 is based on TCEQ and consists of the lowest MAD8 O3 measured to represent regional background O3 concentrations. Results derived from multiple methods show an overall consistent trend with 2018–2020 averaged regional background O3 (MDA8) of 41.5 ppb, accounting for 79.4% of the total O3 in the region. From 2018 to 2020, the changes in regional MDA8 O3 estimated by Methods 1–4 are −1.8, 0.7, −2.4, and 0.4 ppb, respectively. Clear seasonal variations in the regional background O3 are observed, showing a pattern of summer > spring > autumn > winter. In addition, the regional ozone contribution at coastal cities was larger than that for inland cities with local O3 contribution gradually increasing from coastal areas to inland areas. The 3‐year average sea‐land breeze contribution to summertime O3 in the eastern coastal cities was estimated to be around 2.1%, while the local photochemistry to O3 in the inland cities was about 29.7% during ozone pollution episodes, with maximum contribution estimated up to 55.8%. Overall, our study provides insights into the regional background ozone and local photochemistry in Northern China.

Whether dimensionality reduction techniques can improve the ability of sentiment proxies to predict stock market returns

In this study, we construct China's aggregate sentiment indicator (SsPCA) based on the method of Huang et al. (2021a), which employs a new dimension reduction method of scaled principal component analysis (PCA), to aggregate useful information from individual sentiment proxies, and further examine its return predictability for the Chinese stock market. The empirical evidence suggests that SsPCA significantly improves the prediction accuracy for stock market returns both in and out of the sample, and also obtains considerable economic gain for a mean-variance investor. Additionally, the forecasting effect of SsPCA is superior to that of SPCA and SPLS, evaluated using the traditional PCA and partial least square methods, respectively. Moreover, relative to the period of the bull market, SsPCA exhibits better ability in forecasting stock market returns during the bear market. Finally, special events, such as the outbreak of coronavirus disease 2019 (COVID-19), also affect the predictive performance of the sentiment indicator.

Application of Characteristic Model-Based Principal Component Analysis in Optimization of Flowmeter Parameters

In complex industrial processes, it is necessary to perform modeling analysis on some industrial systems and find and optimize the factors that have the greatest impact on the results, in order to achieve the optimization of the industrial systems. However, due to the high-level nature or complex working mechanism of complex industrial systems, traditional principal component analysis methods are difficult to apply. Therefore, this paper proposes a characteristic model-based principal component analysis (CMPCA) to perform principal component analysis on complex industrial systems. The differential pressure flowmeter is taken as an example to verify the effectiveness of the method. Flowmeter is an indispensable instrument in measurement, and its accuracy depends on its own structural parameters. However, the measurement accuracy of some flow meters is not high, and the measurement error is large, which affects the normal industrial production process. This method is used to analyze the influence of the structural parameters of the flowmeter on its measurement accuracy, and the four most important structural parameters are found and optimized. The measurement error of the Bitoba flowmeter is reduced from 1% to 0.2%, and the measurement repeatability is reduced from 0.3 to 0.06, which proves the effectiveness of the method.

Enhanced features in principal component analysis with spatial and temporal windows for damage identification

Principal component analysis (PCA) methods have been widely applied to damage identification in the long-term structural health monitoring (SHM) of infrastructure. Usually, the first few eigenvector components derived by PCA methods are treated as damage-sensitive features. In this paper, the effective method of double-window PCA (DWPCA) and novel features are proposed for better damage identification performance. In the proposed method, spatial and temporal windows are introduced to the traditional PCA method. The spatial windows are applied to group damage-sensitive sensors and exclude those sensors insensitive to damage, while the temporal window is applied to better discriminate eigenvectors between the damaged and healthy states. In addition, the length and directional angle of the eigenvector variation between the healthy and damaged states are used as the damage-sensitive features, instead of the components of the eigenvector variation used in previous studies. Numerical simulations based on a large-scale bridge reveal that the proposed features are successful in identifying the damage located far from sensors due to the use of both spatial and temporal windows as well as the length of the eigenvector variation. In addition, compared to the previous PCA and moving PCA methods, the novel features have higher sensitivity and resolution in damage identification.

Financial Risk Early-Warning Model Based on Kernel Principal Component Analysis in Public Hospitals

Public hospitals are facing the dual pressure of coping with external medical market competition and performing public health duties. Due to the influence of various risk factors, public hospitals are facing increasing financial risks. How to effectively prevent and control financial risks and maintain the normal operation and sustainable development of the hospital is a very important topic that needs to be studied in the development of public hospitals. Because the traditional principal component analysis method only pays attention to the global structural features and ignores the local structural features, a financial risk early-warning model based on improved kernel principal component analysis in public hospitals is proposed to improve the ability of risk assessment. The core ideas of the method in this paper for financial risk forecasting are as follows: the nonlinear features of the financial data are firstly extracted under different conditions, and then the feature matrix and the optimal feature vector are calculated to construct the distance statistics so as to determines the threshold by kernel density estimation; finally the Fisher discriminant analysis is used for similarity measurement to identify the risk types. Through experiments on the financial data of a number of public hospitals and listed companies, the experimental results verify the feasibility and effectiveness of the method used in this paper for financial risk analysis. This further shows that this research has a certain display significance.

Detecting subtle alteration information from ASTER data using a multifractal-based method: A case study from Wuliang Mountain, SW China

Remote sensing has been widely used to interpret hydrothermal alteration zones and it can support the geological field mapping, which is very useful for mineral exploration in inaccessible regions. However, the alteration information in covered terrains is usually not strong enough to be detected using traditional remote sensing methods, so how to efficiently detect subtle alteration information remains a challenging task. In this study, the multifractal theory-based Spectrum-Area (S-A) method is used for the processing of remote sensing data and the new method of “Principal Component Analysis (PCA) + S-A” is proposed as a tool to interpret hydrothermal alteration beneath covered areas. In order to test the efficiency of this method, the “PCA + S-A” method was compared with the traditionally used PCA method based on Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data. The Wuliang Mountain in the Yunnan Province of SW China, a rugged terrain with high altitudes and dense vegetation coverage, was selected as a case study to detect information on chlorite, epidote, biotite, and muscovite alteration, respectively. The following field survey and petrographic studies reveal that: (1) the average detection accuracy of the “PCA + S-A” method is 90.80%, 9.34% higher than that of the PCA method; (2) in the covered areas where the traditional PCA method cannot detect any subtle hydrothermal alteration, the “PCA + S-A” method can be successfully applied; and (3) in those areas where the fractional vegetation cover (FVC) is greater than 0.8, the detection of subtle hydrothermal alteration using the proposed method is inefficient, which requires further studies.

Robust High-Order Manifold Constrained Sparse Principal Component Analysis for Image Representation

In order to efficiently utilize the information in the data and eliminate the negative effects of outliers in the principal component analysis (PCA) method, in this paper, we propose a novel robust sparse PCA method based on maximum correntropy criterion (MCC) with high-order manifold constraints called the RHSPCA. Compared with the traditional PCA methods, the proposed RHSPCA has the following benefits: 1) the MCC regression term is more robust to outliers than the MSE-based regression term; 2) thanks to the high-order manifold constraints, the low-dimensional representations can preserve the local relations of the data and greatly improve the clustering and classification performance for image processing tasks; and 3) in order to further counteract the adverse effects of outliers, the MCC-based samples’ mean is proposed to better centralize the data. We also propose a new solver based on the half-quadratic technique and accelerated block coordinate update strategy to solve the RHSPCA model. Extensive experimental results show that the proposed method can outperform the state-of-the-art robust PCA methods on a variety of image processing tasks, including reconstruction, clustering, and classification, on outliers contaminated datasets.

Fault Detection on Big Data: A Novel Algorithm for Clustering Big Data to Detect and Diagnose Faults

With computer technology improving exponentially, data will grow incomprehensibly in size, complexity, and noise. However, latent within the data, valuable signals are hidden that, if discovered, can offer abundant information, such as fault detection. Traditionally, principal component analysis has been used to perform fault detection in large, multivariate systems. However, these methods often struggle to find the true origin, as they are susceptible to contribution smearing. In this work, a chemical plant system was analyzed and a novel cluster and detect method for fault detection utilizing machine-learning clustering algorithms was created in aim to improve fault detection time and diagnosis. Plant data containing complex variables were simulated, clustered into groups through a unique algorithm based upon correlations, and analyzed through principal component analysis as individual groups. This approach often resulted in quicker identification and more accurate diagnosis than the traditional principal component analysis method.

SuperPCA: A Superpixelwise PCA Approach for Unsupervised Feature Extraction of Hyperspectral Imagery

As an unsupervised dimensionality reduction method, principal component analysis (PCA) has been widely considered as an efficient and effective preprocessing step for hyperspectral image (HSI) processing and analysis tasks. It takes each band as a whole and globally extracts the most representative bands. However, different homogeneous regions correspond to different objects, whose spectral features are diverse. It is obviously inappropriate to carry out dimensionality reduction through a unified projection for an entire HSI. In this paper, a simple but very effective superpixelwise PCA approach, called SuperPCA, is proposed to learn the intrinsic low-dimensional features of HSIs. In contrast to classical PCA models, SuperPCA has four main properties. (1) Unlike the traditional PCA method based on a whole image, SuperPCA takes into account the diversity in different homogeneous regions, that is, different regions should have different projections. (2) Most of the conventional feature extraction models cannot directly use the spatial information of HSIs, while SuperPCA is able to incorporate the spatial context information into the unsupervised dimensionality reduction by superpixel segmentation. (3) Since the regions obtained by superpixel segmentation have homogeneity, SuperPCA can extract potential low-dimensional features even under noise. (4) Although SuperPCA is an unsupervised method, it can achieve competitive performance when compared with supervised approaches. The resulting features are discriminative, compact, and noise resistant, leading to improved HSI classification performance. Experiments on three public datasets demonstrate that the SuperPCA model significantly outperforms the conventional PCA based dimensionality reduction baselines for HSI classification. The Matlab source code is available at https://github.com/junjun-jiang/SuperPCA

Guided filter and principal component analysis hybrid method for hyperspectral pansharpening

Hyperspectral (HS) pansharpening aims to generate a fused HS image with high spectral and spatial resolution through integrating an HS image with a panchromatic (PAN) image. A guided filter (GF) and principal component analysis (PCA) hybrid HS pansharpening method is proposed. First, the HS image is interpolated and the PCA transformation is performed on the interpolated HS image. The first principal component (PC1) channel concentrates on the spatial information of the HS image. Different from the traditional PCA method, the proposed method sharpens the PAN image and utilizes the GF to obtain the spatial information difference between the HS image and the enhanced PAN image. Then, in order to reduce spectral and spatial distortion, an appropriate tradeoff parameter is defined and the spatial information difference is injected into the PC1 channel through multiplying by this tradeoff parameter. Once the new PC1 channel is obtained, the fused image is finally generated by the inverse PCA transformation. Experiments performed on both synthetic and real datasets show that the proposed method outperforms other several state-of-the-art HS pansharpening methods in both subjective and objective evaluations.

Gearbox Fault Diagnosis Based on a Novel Hybrid Feature Reduction Method

The dimensionality reduction of the high-dimensional feature space is a critical part for data preprocessing, which directly affects the accuracy of fault diagnosis. In this paper, a novel hybrid algorithm named principal component locally linear embedding (PCLLE) is introduced to compress the original high-dimensional feature. This approach combines the optimization objectives of the principal component analysis (PCA) and locally linear embedding (LLE), which attempts to find a mapping that meets the optimization goals of PCA and LLE at the same time. It is applied on the gearbox fault diagnosis. In the experiment, the extracted fault-sensitive feature is compressed by PCLLE method. Then, the compressed feature is embedded with five classifiers for fault detection. To evaluate the performance of the proposed new method, the traditional PCA and LLE methods are introduced for comparison. Experimental results show that the PCLLE algorithm has good performance during the classification process compared with the traditional PCA and LLE method.

Research on the Application and Comparison of PCA & 2DPCA in Face Recognition

Face recognition technology considers one of the hot spots in the field of pattern recognition, and it is also one of the difficulties in the field of pattern recognition. In this paper, the principal component analysis (PCA) algorithm and its application in the face recognition technology has been studied primarily. Firstly, discusses the traditional 1DPCA algorithm. Secondly, based on the previously mentioned 1DPCA algorithm, the 2DPCA algorithm, which improves algorithm, is put forward. Simulation results showed that the 2DPCA method is superior to the traditional PCA method for its avoidance of the transformation from image array to one-dimensional vector. The programmable procedures of 1DPCA and 2DPCA designed in the thesis have high recognition rate, and pose theoretically important influence and application value.

Fault detection based on weighted difference principal component analysis

AbstractRecently, multivariate statistical methods, such as principal component analysis (PCA), have drawn increasing attention for fault detection applications in industrial processes. However, industrial processes typically have complex multimodal and nonlinear characteristics. In these situations, the traditional PCA method performs poorly due to its assumption that the process data are linear and unimodal. To improve fault detection performance in nonlinear and multimode industrial processes, this paper proposes a new fault detection method based on weighted difference principal component analysis (WDPCA). Weighted difference principal component analysis first eliminates the multimodal and nonlinear characteristics of the original data by using the weighted difference method. Then, PCA is applied to the preprocessed data, neglecting the influences of multimodality and nonlinearity. Two numerical examples and an industrial application in a semiconductor manufacturing process are used to verify the effectiveness of WDPCA. The simulation results demonstrate that WDPCA shows better fault detection performance than the PCA, kernel principal component analysis (KPCA), independent component analysis (ICA), k‐nearest neighbor rule (kNN), and local outlier factor (LOF) methods.

Incipient Sensor Fault Diagnosis Using Moving Window Reconstruction-Based Contribution

Reconstruction-based contribution (RBC) is widely used for fault isolation and estimation in conjunction with principal component analysis (PCA)-based fault detection. Correct isolation can be guaranteed by RBC for single-sensor faults with large magnitudes. However, the incipient sensor fault diagnosis problem is not well handled by traditional PCA and RBC methods. In this paper, the limitations of traditional PCA and RBC methods for incipient sensor fault diagnosis are illustrated and analyzed. Through the introduction of a moving window, a new strategy based on the PCA model is presented for incipient fault detection. Regarding incipient fault isolation and estimation, a new contribution analysis method called moving window RBC is proposed to enhance the isolation performance and estimation accuracy. Rigorous fault detectability and isolability analyses of the proposed methods are provided. In addition, effects of the window width on fault detection, isolation, and estimation are discussed. Simulation ...