Robust Multivariate Statistical Process Monitoring via Stable Principal Component Pursuit

Variable contribution identification and visualization in multivariate statistical process monitoring

There are two problems in principal component analysis (PCA), which is widely employed in multivariate statistical process monitoring. On one hand, principal components selection according to the variance of the normal training dataset cannot represent the amount of fault information included in the online data. Thus, the useful fault information loss would exist and leads to poor monitoring performance. On the other hand, although the fault information contained in every principal component is different and the principal components are treated equally in traditional PCA-based methods. Then, some useful fault information would be suppressed. In order to reduce the dimension and preserve every original variable information as complete as possible at the same time, this paper selects key principal components using our previously proposed full variable expression method. Moreover, according to the accumulated reachability distance of the online data relative to that of the offline training data, those key principal components with large accumulated reachability distance are emphasized and weighted. Finally, the statistics are constructed to monitor the operation status, and the process monitoring performance of the proposed method is evaluated under an industrial process.

Defect detection is to find unexpected peak regions in an inspection image. Stable Principal Component Pursuit (SPCP) decomposes a given image into three matrices, low-rank, sparsity, and noise which are used for detecting defects. Each of them contains repeated pattern, spatially narrow abnormal elements which are regarded as defects, and small magnitude elements respectively. However, if the noise level of the image is spatially varied, it is hard to separate noise appropriately using naive SPCP. To overcome the difficulty, we propose a novel sliding-window based SPCP algorithm. First, a repeated pattern of each sliding-window is converted to a matrix for SPCP. The noise level based on rank-one approximation is then estimated, and the matrix decomposition is performed. Finally, the sparsity values of all sliding-windows are merged by averaging, and then the averaged term is used for defect detection. The experimental results show that our algorithm outperforms the traditional approaches.

In order to produce the goods with high quality, the industrial system is becoming more complex than before. Meanwhile, the plant is suffering from high potential risks and the faults within it is difficult to be detected. Researchers have made efforts to diagnose the possible faults occurred in the system to further prevent the process from being broken down. Model-based method is proposed at the beginning and it receives effective monitoring results indeed. However, the mathematic model of the system should be known as prior, and it is challenging to achieve the goal. On the other hand, the Multivariate Statistical Process Monitoring (MSPM) does not require that people have clearly understood the process model before carrying out the diagnosis method. Two approaches based on Principal Components Analysis (PCA) and Partial Least Squares (PLS) separately are included in the framework of MSPM. This paper firstly introduces PCA and PLS techniques, including the algorithms, the test statistic, and differences between them. Then the thesis proposes Benchmark Simulation Model No.1 (BSM1), which is used to testify the efficiency of the proposed methods. Finally, the simulation is carried out and the result is reported.

Robust statistical process monitoring

Compressed sensing can represent the sparse signal with a small number of measurements compared to Nyquist-rate samples. Considering the high-complexity of reconstruction algorithms in CS, recently compressive detection is proposed, which performs detection directly in compressive domain without reconstruction. Different from existing work that generally considers the measurements corrupted by dense noises, this paper studies the compressive detection problem when the measurements are corrupted by both dense noises and sparse errors. The sparse errors exist in many practical systems, such as the ones affected by impulse noise or narrowband interference. We derive the theoretical performance of compressive detection when the sparse error is either deterministic or random. The theoretical results are further verified by simulations.

Genome-wide association studies (GWAS) are susceptible to bias due to population stratification (PS). The most widely used method to correct bias due to PS is principal components (PCs) analysis (PCA), but there is no objective method to guide which PCs to include as covariates. Often, the ten PCs with the highest eigenvalues are included to adjust for PS. This selection is arbitrary, and patterns of local linkage disequilibrium may affect PCA corrections. To address these limitations, we estimate genomic propensity scores based on all statistically significant PCs selected by the Tracy-Widom (TW) statistic. We compare a principal components and propensity scores (PCAPS) approach to PCA and EMMAX using simulated GWAS data under no, moderate, and severe PS. PCAPS reduced spurious genetic associations regardless of the degree of PS, resulting in odds ratio (OR) estimates closer to the true OR. We illustrate our PCAPS method using GWAS data from a study of testicular germ cell tumors. PCAPS provided a more conservative adjustment than PCA. Advantages of the PCAPS approach include reduction of bias compared to PCA, consistent selection of propensity scores to adjust for PS, the potential ability to handle outliers, and ease of implementation using existing software packages.

Baselining network-wide traffic by time-frequency constrained Stable Principal Component Pursuit

The problem of recovering the low-rank and sparse components of a matrix is known as the stable principal component pursuit (SPCP) problem. It has found many applications in compressed sensing, image processing, and web data ranking. This paper proposes a generalized inexact Uzawa method for SPCP with nonnegative constraints. The main advantage of our method is that the resulting subproblems all have closed-form solutions and can be executed in distributed manners. Global convergence of the method is proved from variational inequalities perspective. Numerical experiments show that our algorithm converges to the optimal solution as other distributed methods, with better performances.

On-line principal component analysis with application to process modeling

Principal component analysis and hierarchical cluster analysis were applied to investigate physicochemical and instrumental textural properties of fresh kashar cheese. Four different principal components sufficiently explained the variability in the cheese samples. In addition, hierarchical cluster analysis was performed to group the kashar cheese samples regarding physicochemical and instrumental textural properties. Instrumental textural properties indicated greater variability than chemical composition of cheese samples. Principal component analysis revealed that color parameters were positively correlated with textural and chemical parameters. The results of this study revealed that other parameters rather than chemical composition would be effective on the instrumental textural properties. It was proved that principal component analysis was a very effective statistical tool to determine quality of cheese samples. According to the principal component analysis and hierarchical cluster analysis results, the attributes defining the kashar cheese samples were determined to be primarily the texture profile analysis parameters.

Groundwater is considered as one of the most important sources for water supply in Iran. The Fasa Plain in Fars Province, Southern Iran is one of the major areas of wheat production using groundwater for irrigation. A large population also uses local groundwater for drinking purposes. Therefore, in this study, this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis (CA), Discriminant Analysis (DA), and Principal Component Analysis (PCA). Water quality data was monitored at 22 different wells, for five years (2009-2014) with 10 water quality parameters. By using cluster analysis, the sampling wells were grouped into two clusters with distinct water qualities at different locations. The Lasso Discriminant Analysis (LDA) technique was used to assess the spatial variability of water quality. Based on the results, all of the variables except sodium absorption ratio (SAR) are effective in the LDA model with all variables affording 92.80% correct assignation to discriminate between the clusters from the primary 10 variables. Principal component (PC) analysis and factor analysis reduced the complex data matrix into two main components, accounting for more than 95.93% of the total variance. The first PC contained the parameters of TH, Ca2+, and Mg2+. Therefore, the first dominant factor was hardness. In the second PC, Cl-, SAR, and Na+ were the dominant parameters, which may indicate salinity. The originally acquired factors illustrate natural (existence of geological formations) and anthropogenic (improper disposal of domestic and agricultural wastes) factors which affect the groundwater quality.

In this paper, a multivariate statistical process monitoring technique based on bottleneck auto-associative neural network is applied on a water treatment plant. First, the nonlinear principal component analysis (NLPCA) is carried out in order to identify and analyze the relationships among the correlated variables in the process by compressing multidimensional data set, extracting the original data from the principal components and then the squared prediction error is evaluated to find the erroneous data samples. So, the information obtained using this intelligent tool is used for diagnosis. The obtained results on realistic data demonstrate the effectiveness of the applied technique for monitoring water treatment plants.

This study integrated conventional statistical tools with neighbourhood linkage to propose the statistical diagnosis approach. Fourteen monitoring wells in Kaohsiung Science Park were selected as study case, and lab data of routine groundwater analysis including pH, EC, hardness, TDS, TOC, ammonia, nitrate, nitrite, chloride, sulphate, fluoride, phenols, Fe, Mn, As, and temperature were subjected to principal component and cluster analysis. Principal component analysis (PCA) was utilized to reflect those chemical data with the greatest correlation, and PCA results identified five major principal components (PCs) representing 74.6% of cumulative variance. Based on the monitoring data between 2005 and 2008, the extracted information from the PCA mirrored the potential sources of groundwater contamination as acid leakage, arsenic dissolution, salinization, mineralization, and fluoride release. Cluster analysis (CA) was used to evaluate the similarities of water quality in groundwater samples, and five clusters were assigned in two-step clustering for corresponding with the number of PCs, i.e. the potential sources of groundwater contamination. The interpreted facts from CA illustrated that the classified monitoring wells in each cluster properly match up with the identified processes. With the aid of neighbourhood linkage, the domain of groundwater contamination can be spatially outlined by mapping the neighbouring wells within the identical cluster. Therefore, the nature of underlying processes affecting groundwater quality was explored by statistical diagnosis.

In this letter, we focus on a device free localization (DFL) system which is based on logistic regression model using received signal strength (RSS) measurements in each link as training and testing data. To reduce the computational complexity of the logistic regression model prediction and improve the localization accuracy by reduction of the redundant training features, we obtain principal component using the measured RSS data through principal component analysis (PCA). Moreover, to overcome the imbalanced data problem, the number of training data belonging to major class is decreased through the sampling technique based on the distance between the reference points. The modified logistic regression model is derived from Bayesian formula based prior correction method due to the change in the ratio of the major and the minor classes in sampled training data. By substituting the transformed principal components of testing dataset to the probability model with the optimal regression coefficients, the localization probabilities of a target are computed at every reference point.