Fault Isolation by Partial Dynamic Principal Component Analysis in Dynamic Process

Principal component analysis （PCA） is a useful tool in process fault detection, but offers little support on fault isolation. In this article, structured residual with strong isolation property is introduced. Although it is easy to get the residual by transformation matrix in static process, unfortunately, it becomes hard in dynamic process under control loop. Therefore, partial dynamic PCA（PDPCA） is proposed to obtain structured residual and enhance the isolation ability of dynamic process monitoring, and a compound statistic is introduced to resolve the problem resulting from independent variables in every variable subset. Simulations on continuous stirred tank reactor （CSTR） show the effectiveness of the proposed method.

Fast Tensor Principal Component Analysis via Proximal Alternating Direction Method with Vectorized Technique

This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.

Loss-of-Main Monitoring and Detection for Distributed Generations Using Dynamic Principal Component Analysis

In this paper, our previous work on Principal Component Analysis (PCA) based fault detection method is extended to the dynamic monitoring and detection of loss-of-main in power systems using wide-area synchrophasor measurements. In the previous work, a static PCA model was built and verified to be capable of detecting and extracting system faulty events;however the false alarm rate is high. To address this problem, this paper uses a well-known ‘time lag shift’ method to include dynamic behavior of the PCA model based on the synchronized measurements from Phasor Measurement Units (PMU), which is named as the Dynamic Principal Component Analysis (DPCA). Compared with the static PCA approach as well as the traditional passive mechanisms of loss-of-main detection, the proposed DPCA procedure describes how the synchrophasors are linearly auto- and cross-correlated, based on conducting the singular value decomposition on the augmented time lagged synchrophasor matrix. Similar to the static PCA method, two statistics, namely T2 and Q with confidence limits are calculated to form intuitive charts for engineers or operators to monitor the loss-of-main situation in real time. The effectiveness of the proposed methodology is evaluated on the loss-of-main monitoring of a real system, where the historic data are recorded from PMUs installed in several locations in the UK/Ireland power system.

Kernel Generalization of Multi-Rate Probabilistic Principal Component Analysis for Fault Detection in Nonlinear Process

In practical process industries,a variety of online and offline sensors and measuring instruments have been used for process control and monitoring purposes,which indicates that the measurements coming from different sources are collected at different sampling rates.To build a complete process monitoring strategy,all these multi-rate measurements should be considered for data-based modeling and monitoring.In this paper,a novel kernel multi-rate probabilistic principal component analysis(K-MPPCA)model is proposed to extract the nonlinear correlations among different sampling rates.In the proposed model,the model parameters are calibrated using the kernel trick and the expectation-maximum(EM)algorithm.Also,the corresponding fault detection methods based on the nonlinear features are developed.Finally,a simulated nonlinear case and an actual pre-decarburization unit in the ammonia synthesis process are tested to demonstrate the efficiency of the proposed method.

FUZZY PRINCIPAL COMPONENT ANALYSIS AND ITS KERNEL-BASED MODEL

Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.

Principal component analysis and cluster analysis based orbit optimization for earth observation satellites

This paper proposes a design optimization method for the multi-objective orbit design of earth observation satellites, for which the optimality of orbit performance indices with different units, such as: total coverage time, the frequency of coverage, average time per coverage and maximum coverage gap, etc. is required simultaneously. By introducing index normalization method to convert performance indices into dimensionless variables within the range of [0, 1], a design optimization method based on the principal component analysis and cluster analysis is proposed, which consists of index normalization method, principal component analysis, multiple-level cluster analysis and weighted evaluation method. The results of orbit optimization for earth observation satellites show that the optimal orbit can be obtained by using the proposed method. The principal component analysis can reduce the total number of indices with a non-independent relationship to save computing time. Similarly, the multiple-level cluster analysis with parallel computing could save computing time.

DYNAMIC VARIATIONS OF WATER QUALITY IN TAIHU LAKE AND MULTIVARIATE ANALYSIS OF ITS INFLUENTIAL FACTORS

Dynamic variation of water quality in Meiliang Bay and part of West Taihu Lake has been analysed based on data from 1991 to 1992. Principal Component Analysis is used to reveal the mutual relationships of various factors. It is shown that there existis an obvious spatial and temporal variation in the main factors of water quality. Annual values of TP, CON, TN, Chl-a and conductivity decrease evidently from inner Meiliang Bay to the outer from north to south. TP and TN fluctuate seasonally with much higher value in winter. This is particularly true for the mouth of Liangxi River. In addition, the Chl-1 has a synchronous variation with water temperature, although being lagged a little, and closely relates to TP and TN. Finally, the results from Principal Component Analysis show that TP, TN, SS (or SD), water temperature and Chl-a are the most influential factors to water qualuty in this area, and both suspensions and algae can contribute to transparency to Taihu Lake.

DYNAMIC VARIATIONS OF WATER QUALITY IN TAIHU LAKE AND MULTIVARIATE ANALYSIS OF ITS INFLUENTIAL FACTORS

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An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Identification and analysis of serum samples by surface-enhanced Raman spectroscopy combined with characteristic ratio method and PCA for gastric cancer detection

This study aimed to explore the application of surface-enhanced Raman scattering(SERS)in the rapid diagnosis of gastric cancer.The SERS spectra of 68 serum samples from gastric cancer patients and healthy volunteers were acquired.The characteristic ratio method(CRM)and principal component analysis(PCA)were used to differentiate gastric cancer serum from normal serum.Compared with healthy volunteers,the serum SERS intensity of gastric cancer patients was relatively high at 722 cm^(-1),while it was relatively low at 588,644,861,1008,1235,1397,1445 and 1586 cm^(-1).These results indicated that the relative content of nucleic acids in the serum of gastric cancer patients rises while the relative content of amino acids and carbohydrates decreases.In PCA,the sensitivity and specificity of discriminating gastric cancer were 94.1%and 94.1%,respectively,with the accuracy of 94.1%.Based on the intensity ratios of four characteristic peaks at 722,861,1008 and 1397 cm^(-1),CRM presented the diagnostic sensitivity and specificity of 100%and 97.4%,respectively,and the accuracy of 98.5%.Therefore,the three peak intensity ratios of I_(722)/I_(861),I_(722)/I_(1008)and I_(722)/I_(1397)can be considered as biologicalfingerprint information for gastric cancer diagnosis and can rapidly and directly reflect the physiological and pathological changes associated with gastric cancer development.This study provides an important basis and standards for the early diagnosis of gastric cancer.

Nonlinear Dynamic Analysis of MPEG-4 Video Traffic

The main research motive is to analysis and to veiny the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/f^β and periodic characteristics.The priraeipal compohems analysis of the reconstructed space dimension shows only several principal components can be the representation of all dimensions. The correlation dimension analysis proves its fractal characteristic. To accurately compute the largest Lyapunov exponent, the video traffic is divided into many parts.So the largest Lyapunov exponent spectrum is separately calculated using the small data sets method. The largest Lyapunov exponent spectrum shows there exists abundant nonlinear chaos in MPEG-4 video traffic. The conclusion can be made that MPEG-4 video traffic have complex nonlinear be havior and can be characterized by its power spectral density,principal components, correlation dimension and the largest Lyapunov exponent besides its common statistics.

Principal Component-Discrimination Model and Its Application

Having researched for many years, seismologists in China presented about 80 earthquake prediction factors which reflected omen information of earthquake. How to concentrate the information that the 80 earthquake prediction factors have and how to choose the main factors to predict earthquakes precisely have become one of the topics in seismology. The model of principal component-discrimination consists of principal component analysis, correlation analysis, weighted method of principal factor coefficients and Mahalanobis distance discrimination analysis. This model combines the method of maximization earthquake prediction factor information with the weighted method of principal factor coefficients and correlation analysis to choose earthquake prediction variables, applying Mahalanobis distance discrimination to establishing earthquake prediction discrimination model. This model was applied to analyzing the earthquake data of Northern China area and obtained good prediction results.

Water Quality Analysis of Fuping Section of the Shichuan River Based on Different Evaluation Methods

In order to study the water quality of the Shichuan River basin in Fuping,Shaanxi Province,based on improved Nemerow index method,comprehensive pollution index method and principal component analysis method,eight water quality indexes such as pH,dissolved oxygen(DO),total dissolved solids(TDS),COD,total hardness,total phosphorus,total nitrogen and Zn in three monitoring sections of Fuping section of the Shichuan River in Shaanxi Province were detected and analyzed.The results show that the water quality of the surface water in the Shichuan River basin is gradeⅢorⅣwater,that is,the water is slightly polluted and moderately polluted.It is necessary to monitor the water quality after regulation and clarify the main factors causing the water pollution.

东营凹陷八面河地区古近系沙四段湖相白云岩测井识别及应用

湖相白云岩储层岩石组分复杂、结构多样,利用测井资料对白云岩岩性进行识别具有重要意义。为了解决传统测井方法工作量大和识别精度低等问题,提出利用蛛网图-交会图-主成分分析法融合的方法,构建岩性敏感因子交会图,开展湖相白云岩岩性综合识别。研究结果表明:①东营凹陷八面河地区古近系沙四段主要由颗粒云岩、微晶云岩、泥晶云岩、砂岩和页岩等组成,其中,颗粒云岩、微晶云岩和页岩为主要岩石类型。②优选6类特征参数分析不同岩石类型蛛网图和交会图的差异,其中,GR和AC可有效区分颗粒云岩,SP对砂岩具有较好的识别效果,在蛛网图与交会图的识别成果基础上,应用主成分分析法对测井参数进行标准化处理,构建出累计方差贡献率为90.75%的主成分F1和F2,建立岩性判别模型,综合识别岩性。③通过产能与取心井验证,岩性识别准确度高达85.4%,明确研究区颗粒云岩在西部以SW—NE走向呈条带状分布,向南部和北部过渡为微晶云岩和泥晶云岩,东部则以不规则分布的砂岩为主。

A new image processing method for discriminating internal layers from radio echo sounding data of ice sheets via a combined robust principal component analysis and total variation approach

Discriminating internal layers by radio echo sounding is important in analyzing the thickness and ice deposits in the Antarctic ice sheet.The signal processing method of synthesis aperture radar(SAR)has been widely used for improving the signal to noise ratio(SNR)and discriminating internal layers by radio echo sounding data of ice sheets.This method is not efficient when we use edge detection operators to obtain accurate information of the layers,especially the ice-bed interface.This paper presents a new image processing method via a combined robust principal component analysis-total variation(RPCA-TV)approach for discriminating internal layers of ice sheets by radio echo sounding data.The RPCA-based method is adopted to project the high-dimensional observations to low-dimensional subspace structure to accelerate the operation of the TV-based method,which is used to discriminate the internal layers.The efficiency of the presented method has been tested on simulation data and the dataset of the Institute of Electronics,Chinese Academy of Sciences,collected during CHINARE 28.The results show that the new method is more efficient than the previous method in discriminating internal layers of ice sheets by radio echo sounding data.

基于主成分及聚类分析的板栗品质综合评价

为建立一种适宜的板栗资源果实品质评价方法,本研究以25个板栗品种为研究对象,选取21项品质指标进行测定,通过主成分分析结合相关性分析、描述性统计分析的方法筛选影响板栗品质的核心评价指标,基于熵权法对核心指标赋予权重,并建立灰色关联度评价模型。结果表明,不同品种板栗多项指标存在显著差异(P<0.05),且多个指标间存在显著相关性,主成分分析确立了水分、直链淀粉与支链淀粉含量的比值(Ratio of amylose to amylopectin,AA)、总黄酮、好果率、果形指数、硬度、可溶性糖和还原糖为核心指标,熵权法计算核心指标的权重分别为14.08%、14.64%、15.64%、7.74%、9.41%、9.11%、18.90%、10.48%。灰色关联度分析结果表明,丹栗1号、丹东9113和qX-005综合品质列前三位。经聚类分析将25个品种板栗分为4类,第一类板栗适宜开发功能性饮品;第二类板栗适合取仁加工,制作罐头、果脯等产品,或加工成板栗粉用于面包、饼干等产品的制作;第三类板栗可作为优质的食品原料;第四类板栗适宜炒食,也适宜作为直售坚果。本研究结果为板栗优质资源筛选及品种的选育提供参考,也为各品种的综合利用提供了理论依据。

Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

Cycle temporal algorithm-based multivariate statistical methods for fault diagnosis in chemical processes

Multivariate statistical process monitoring methods are often used in chemical process fault diagnosis.In this article,(I)the cycle temporal algorithm(CTA)combined with the dynamic kernel principal component analysis(DKPCA)and the multiway dynamic kernel principal component analysis(MDKPCA)fault detection algorithms are proposed,which are used for continuous and batch process fault detections,respectively.In addition,(II)a fault variable identification model based on reconstructed-based contribution(RBC)model that paves the way for determining the cause of the fault are proposed.The proposed fault diagnosis model was applied to Tennessee Eastman(TE)process and penicillin fermentation process for fault diagnosis.And compare with other fault diagnosis methods.The results show that the proposed method has better detection effects than other methods.Finally,the reconstruction-based contribution(RBC)model method is used to accurately locate the root cause of the fault and determine the fault path.