Multiblock Principal Component Analysis Research Articles

MBPCA-OS: an exploratory multiblock method for variables of different measurement levels. Application to study the immune response to SARS-CoV-2 infection and vaccination

Abstract Studying a large number of variables measured on the same observations and organized in blocks – denoted multiblock data – is becoming standard in several domains especially in biology. To explore the relationships between all these variables – at the block- and the variable-level – several exploratory multiblock methods were proposed. However, most of them are only designed for numeric variables. In reality, some data sets contain variables of different measurement levels (i.e., numeric, nominal, ordinal). In this article, we focus on exploratory multiblock methods that handle variables at their appropriate measurement level. Multi-Block Principal Component Analysis with Optimal Scaling (MBPCA-OS) is proposed and applied to multiblock data from the CURIE-O-SA French cohort. In this study, variables are of different measurement levels and organized in four blocks. The objective is to study the immune responses according to the SARS-CoV-2 infection and vaccination statuses, the symptoms and the participant’s characteristics.

A novel approach to combine spatial and spectral information from hyperspectral images

This article proposes a generic framework to process jointly the spatial and spectral information of hyperspectral images. First, sub-images are extracted. Then each of these sub-images follows two parallel workflows, one dedicated to the extraction of spatial features and the other dedicated to the extraction of spectral features. Finally, the extracted features are merged, producing as many scores as sub-images. Two applications are proposed, illustrating different spatial and spectral processing methods. The first one is related to the characterization of a teak wood disk, in an unsupervised way. It implements tensors of structure for the spatial branch, simple averaging for the spectral branch and multi-block principal component analysis for the fusion process. The second application is related to the early detection of apple scab on leaves. It implements co-occurrence matrices for the spatial branch, singular value decomposition for the spectral branch and multiblock partial least squares discriminant analysis for the fusion process. Both applications demonstrate the interest of the proposed method for the extraction of relevant spatial and spectral information and show how promising this new approach is for hyperspectral imaging processing.

HPLC-(Q)-TOF-MS-Based Study of Plasma Metabolic Profile Differences Associated with Age in Pediatric Population Using an Animal Model.

A deep knowledge about the biological development of children is essential for appropriate drug administration and dosage in pediatrics. In this sense, the best approximation to study organ maturation is the analysis of tissue samples, but it requires invasive methods. For this reason, surrogate matrices should be explored. Among them, plasma emerges as a potential alternative since it represents a snapshot of global organ metabolism. In this work, plasma metabolic profiles from piglets of different ages (newborns, infants, and children) obtained by HPLC–(Q)-TOF-MS at positive and negative ionization modes were studied. Improved clustering within groups was achieved using multiblock principal component analysis compared to classical principal component analysis. Furthermore, the separation observed among groups was better resolved by using partial least squares-discriminant analysis, which was validated by bootstrapping and permutation testing. Thanks to univariate analysis, 13 metabolites in positive and 21 in negative ionization modes were found to be significant to discriminate the three groups of piglets. From these features, an acylcarnitine and eight glycerophospholipids were annotated and identified as metabolites of interest. The findings indicate that there is a relevant change with age in lipid metabolism in which lysophosphatidylcholines and lysophoshatidylethanolamines play an important role.

Distributed Monitoring of Power System Oscillations Using Multiblock Principal Component Analysis and Higher-order Singular Value Decomposition

The primary goal in the analysis of hierarchical distributed monitoring and control architectures is to study the spatiotemporal patterns of the interactions between areas or subsystems. In this paper, a novel conceptual framework for distributed monitoring of power system oscillations using multi-block principal component analysis (MB-PCA) and higher-order singular value decomposition (HOSVD) is proposed to understand, characterize, and visualize the global behavior of the power system. The proposed framework can be used to evaluate the influence of a given area or utility on the oscillatory behavior, uncover low-dimensional structures from high-dimensional data, and analyze the effects of heterogeneous data on the modal characteristics and interpretation of power system. The metrics are then investigated to examine the relationships between the dynamic patterns and participation of individual data blocks in the global behavior of the system. Practical Application of these techniques is demonstrated by case studies of two systems: a 14-machine test system and a 5449-bus 635-generator equivalent model of a large power system.

A Novel Method for Fault Diagnosis of the Two-Input Two-Output Nonlinear Mass-Spring-Damper System Based on NOFRF and MBPCA

For fault diagnosis of the two-input two-output mass-spring-damper system, a novel method based on the nonlinear output frequency response function (NOFRF) and multiblock principal component analysis (MBPCA) is proposed. The NOFRF is the extension of the frequency response function of the linear system to the nonlinear system, which can reflect the inherent characteristics of the nonlinear system. Therefore, the NOFRF is used to obtain the original fault feature data. In order to reduce the amount of feature data, a multiblock principal component analysis method is used for fault feature extraction. The least squares support vector machine (LSSVM) is used to construct a multifault classifier. A simplified LSSVM model is adopted to improve the training speed, and the conjugate gradient algorithm is used to reduce the required storage of LSSVM training. A fault diagnosis simulation experiment of a two-input two-output mass-spring-damper system is carried out. The results show that the proposed method has good diagnosis performance, and the training speed of the simplified LSSVM model is significantly higher than the traditional LSSVM.

Assessment of Biotechnologically Important Filamentous Fungal Biomass by Fourier Transform Raman Spectroscopy.

Oleaginous filamentous fungi can accumulate large amount of cellular lipids and biopolymers and pigments and potentially serve as a major source of biochemicals for food, feed, chemical, pharmaceutical, and transport industries. We assessed suitability of Fourier transform (FT) Raman spectroscopy for screening and process monitoring of filamentous fungi in biotechnology. Six Mucoromycota strains were cultivated in microbioreactors under six growth conditions (three phosphate concentrations in the presence and absence of calcium). FT-Raman and FT-infrared (FTIR) spectroscopic data was assessed in respect to reference analyses of lipids, phosphorus, and carotenoids by using principal component analysis (PCA), multiblock or consensus PCA, partial least square regression (PLSR), and analysis of spectral variation due to different design factors by an ANOVA model. All main chemical biomass constituents were detected by FT-Raman spectroscopy, including lipids, proteins, cell wall carbohydrates, and polyphosphates, and carotenoids. FT-Raman spectra clearly show the effect of growth conditions on fungal biomass. PLSR models with high coefficients of determination (0.83–0.94) and low error (approximately 8%) for quantitative determination of total lipids, phosphates, and carotenoids were established. FT-Raman spectroscopy showed great potential for chemical analysis of biomass of oleaginous filamentous fungi. The study demonstrates that FT-Raman and FTIR spectroscopies provide complementary information on main fungal biomass constituents.

Integrate weighted dependence and skewness based multiblock principal component analysis with Bayesian inference for large-scale process monitoring

In a large-scale process, variables are correlated, and are Gaussian and non-Gaussian coexisted. The decentralized monitoring methods divide variables into blocks and carry out local monitoring is aimed at reducing the process complexity. Recently, the weighted copula-correlation-based multiblock principal component analysis (WCMBPCA) considering the correlation degree and correlation patterns was proposed to monitor a correlated process. While its monitoring efficiency has been shown, the WCMBPCA method has some drawbacks: 1) monitoring performance relies on the selection of copula function; 2) computation time for the weight matrix is long; 3) without considering the distribution information. This study proposes a novel weight strategy for multiblock PCA by developing a measurement, which simultaneously estimates the dependence and skewness of data, such that the distribution information is additionally considered. The proposed weight matrix is based on the use of non-parametric ranks, prompting the short computation time. The experiment results from Tennessee Eastman (TE) process monitoring shows the average fault detection rate for the proposed method is 84.19% that outperforms regular PCA, dynamic PCA, multiblock PCA, and WCMBPCA. Moreover, the weight matrix calculation takes 0.000635 s for the proposed method, while 195.040282 s for WCMBPCA.

Multiblock metabolomics: An approach to elucidate whole-body metabolism with multiblock principal component analysis

Principal component analysis (PCA) is a useful tool for omics analysis to identify underlying factors and visualize relationships between biomarkers. However, this approach is limited in addressing life complexity and further improvement is required. This study aimed to develop a new approach that combines mass spectrometry-based metabolomics with multiblock PCA to elucidate the whole-body global metabolic network, thereby generating comparable metabolite maps to clarify the metabolic relationships among several organs. To evaluate the newly developed method, Zucker diabetic fatty (ZDF) rats (n = 6) were used as type 2 diabetic models and Sprague Dawley (SD) rats (n = 6) as controls. Metabolites in the heart, kidney, and liver were analyzed by capillary electrophoresis and liquid chromatography mass spectrometry, respectively, and the detected metabolites were analyzed by multiblock PCA. More than 300 metabolites were detected in the heart, kidney, and liver. When the metabolites obtained from the three organs were analyzed with multiblock PCA, the score and loading maps obtained were highly synchronized and their metabolism patterns were visually comparable. A significant finding in this study was the different expression patterns in lipid metabolism among the three organs; notably triacylglycerols with polyunsaturated fatty acids or less unsaturated fatty acids showed specific accumulation patterns depending on the organs.

Decentralized dynamic process monitoring based on manifold regularized slow feature analysis

For large-scale process monitoring, traditional decentralized monitoring methods fail to discriminate real faults from normal operation deviations. This paper proposes a novel decentralized method for monitoring large-scale industrial processes by exploring serial correlations and local manifold structures of the data. A block division strategy based on maximal information coefficient-spectral clustering is proposed, which can divide the measured variables into several blocks without any prior knowledge. To extract inter-block relevance, multiblock principal component analysis is introduced to whiten the original variables. On this basis, we develop a new dimensionality reduction algorithm named manifold regularized slow feature analysis (MRSFA) to capture the temporal dynamics and local structure information in each block. Monitoring statistics are constructed based on the captured feature information to concurrently monitor the operation deviations and anomalous dynamics. To achieve decision fusion, the monitoring results derived from all blocks are combined through Bayesian inference. Two case studies on the Tennessee Eastman process and a real industrial process are carried out and the experimental results demonstrate the effectiveness of the proposed method.

Plant-Wide Process Monitoring Strategy Based on Complex Network and Bayesian Inference-Based Multi-Block Principal Component Analysis

In this work, a novel process monitoring method in a block-wised partitioning manor is proposed for plant-wide processes which can be partitioned into several sub-blocks and monitored parallelly. The focus of this method is to reduce the high complexity of global plant-wide process, while to improve the efficiency of local feature extraction. In this method, considering that not all process knowledge is available in the block division process strategy, a novel community discovery (CD) algorithms, based on the similarity of neighbor node weighted Louvain, is introduced into the framework of the multi-block Bayesian inference and principal component analysis (PCA) based plant-wide process monitoring scheme. Firstly, the complex network (CN) theory is used to establish the network topology structure for the global variables of the plant-wide process. Secondly, by analyzing the graph characteristic structure, considering the connection strength between nodes, a more reasonable sub-block division is conducted according to the improved Louvain algorithm. Then, PCA method is used to establish process monitoring model for each sub-block to obtain sub-block monitoring statistics. Finally, the total joint statistics is obtained through Bayesian inference for fault detection. The feasibility and effectiveness, in terms of the detection performance, of this method are demonstrated in a simulated plant-wide process by compared with other state-of-the-art PCA based monitoring methods.

Nonparametric Kullback-divergence-PCA for intelligent mismatch detection and power quality monitoring in grid-connected rooftop PV

In parallel to sustainable growth in solar fraction, continuous reductions in Photovoltaic (PV) module and installation costs fuelled a profound adoption of residential Rooftop Mounted PV (RMPV) installations already reaching grid parity. RMPVs are promoted for economic, social, and environmental factors, energy performance, reduced greenhouse effects and bill savings. RMPV modules and energy conversion units are subject to anomalies which compromise power quality and promote fire risk and safety hazards for which reliable protection is crucial. This article analyses historical data and presents a novel design that easily integrates with data storage units of RMPV systems to automatically process real-time data streams for reliable supervision. Dominant Transformed Components (TCs) are online extracted through multiblock Principal Component Analysis (PCA), most sensitive components are selected and their time-varying characteristics are recursively estimated in a moving window using smooth Kernel Density Estimation (KDE). Novel monitoring indices are developed as preventive alarms using Kullback-Leibler Divergence (KLD). This work exploits data records during 2015–2017 from thin-film, monocrystalline, and polycrystalline RMPV energy conversion systems. Fourteen test scenarios include array faults (line-to-line, line-to-ground, transient arc faults); DC-side mismatches (shadings, open circuits); grid-side anomalies (voltage sags, frequency variations); in addition to inverter anomalies and sensor faults.

Monitoring Strategy for a Multistage Manufacturing Facility Using K-Means Clustering Technique

The article proposes a process monitoring strategy for a multistage manufacturing facility. In past, researchers have attempted to develop monitoring strategies for multistage processes using multi-block principal component analysis (MBPCA) which requires comprehensive process knowledge. But in most of the cases, the complete acquaintance with the process knowledge may not be possible. Hence, in such cases, a suitable clustering algorithm-based classification of process parameters may be performed. The current article proposes a methodology articulated via amalgamation of the K-means clustering algorithm and traditional MBPCA for monitoring of a process. K-means clustering algorithm is capable of clubbing the process parameters into relevant blocks without any prior process knowledge. In order to validate the devised strategy, a case study related to a multistage manufacturing facility engaged in production of rail blooms is considered. The outcome of the devised strategy has been compared with the outcome of regular MBPCA-based monitoring strategy which is used when the process knowledge is available.

Plant-wide process monitoring by using weighted copula–correlation based multiblock principal component analysis approach and online-horizon Bayesian method

Multiblock methods have been proposed to capture the complex characteristics of plant-wide monitoring due to the enlargement of process industries. These methods based on automatic sub-block division and copula–correlation, which simultaneously describe the correlation degree and correlation patterns, are designed for sub-block partition. However, the selection of variables for each sub-block through copula–correlation analysis requires a pre-defined cutoff parameter which is difficult to be determined without sufficient prior knowledge, and a “bad” parameter leads to a degraded performance. Therefore, a weighted copula-correlation-based multiblock principal component analysis (WCMBPCA) is proposed. First, the variables in each sub-block are obtained through the copula–correlation analysis-based weighted strategy rather than the cutoff parameter, which highly avoids information loss and prevents “noisy” information. Second, a PCA model is established in each sub-block. Third, a Bayesian inference strategy is used to merge the monitoring results of all sub-blocks. Finally, an online-horizon Bayesian fault diagnosis system is established to identify the fault type of the system based on the statistics of each sub-block. The average detection rate and the average diagnosis rate for numerical example are 77.85% and 98.95%, and that for TE example are 80.63% and 89.50%. Comparing with other candidate methods, the proposed method achieves excellent detection and diagnostic performance.

Decentralized monitoring for large‐scale process using copula‐correlation analysis and Bayesian inference–based multiblock principal component analysis

AbstractDue to the massive monitored samples and their features such as strong coupling and time delay in large‐scale industrial process, the decentralized monitoring methods, which divide the variables into several blocks and perform local monitoring in each subblock, have been brought up to handle the complex characteristics. However, most of the existing decentralized methods utilize the correlation degree among variables for block division, while the correlation patterns among variables are ignored. The missing of correlation pattern will influence the monitoring performance. To address this problem, the copula‐correlation analysis, which considers both the correlation degree and the correlation pattern, is adopted for block division; then the principal component analysis (PCA)–based method is used for subblock monitoring, and the Bayesian inference is introduced to achieve decision fusion of fault detection. The superiority and effectiveness of the proposed method are illustrated through comparison studies on a numerical example and the Tennessee Eastman (TE) benchmark process.

Stratified statistical monitoring strategy for a multi-product manufacturing facility with early detection approach

In this article, an attempt has been made to devise a multi layered or multi strata statistical process monitoring strategy. The stratification of the monitoring strategy implies to the key notion of carrying out model development and diagnosis of the detected fault in a hierarchical or stratified way. The nominal model that has been developed is a three strata or three level process representation based on the more illustrious two level multi-block principal component analysis. The article highlighted the issue of monitoring of multiple product portfolios via a single process representation or model; proposing new fault diagnostic approach encompassing the relative contribution of primary as well as associated characteristics towards the detected fault and lastly the article proposes a monitoring statistic for early detection of developing faults. The monitoring of all the product portfolios via a single unified model was done with the intention of cutting down on the resources mainly time and effort. The proposed diagnostic statistic encapsulated the contribution of associate characteristics where associate characteristics are the characteristics having significant correlation primary characteristics which are the main contributor towards the detected fault. The monitoring statistic used for early detection of the developing fault is a latent variable score based exponential weighted moving average (EWMA) chart. The unified model developed herein, the latent variable score based EWMA statistic proposed and the new fault diagnostic statistic devised were able to perform their functions satisfactorily with good model fit value, correct detection of developing fault and reasonably accurate diagnosis results. The devised monitoring strategy has been validated via a case study pertaining to an integrated steel plant (ISP).

Monitoring of an ingot making facility via principal component analysis and its variants

The ingots are a key intermediate product manufactured in the steel making industries. The article delves into the monitoring of the ingot manufacturing facility by making use of the multivariate process monitoring techniques. In order to deal with the various scenarios arising during the production of ingots, different variants viz. multi-block principal component analysis and multi-way principal component analysis are also employed to monitor the process and feed stock characteristics. A comparative analysis of the merits and demerits of the employed variants is also presented in the article based on the case study. On the basis of the findings it may be concluded that the decision regarding the methodology to be adopted depends upon a trade-off between the scope of application of the methodology and the ease of development.

Monitoring of an ingot making facility via principal component analysis and its variants

The ingots are a key intermediate product manufactured in the steel making industries. The article delves into the monitoring of the ingot manufacturing facility by making use of the multivariate process monitoring techniques. In order to deal with the various scenarios arising during the production of ingots, different variants viz. multi-block principal component analysis and multi-way principal component analysis are also employed to monitor the process and feed stock characteristics. A comparative analysis of the merits and demerits of the employed variants is also presented in the article based on the case study. On the basis of the findings it may be concluded that the decision regarding the methodology to be adopted depends upon a trade-off between the scope of application of the methodology and the ease of development.

Automated multivariate analysis of multi-sensor data submitted online: Real-time environmental monitoring.

A pilot study demonstrating real-time environmental monitoring with automated multivariate analysis of multi-sensor data submitted online has been performed at the cabled LoVe Ocean Observatory located at 258 m depth 20 km off the coast of Lofoten-Vesterålen, Norway. The major purpose was efficient monitoring of many variables simultaneously and early detection of changes and time-trends in the overall response pattern before changes were evident in individual variables. The pilot study was performed with 12 sensors from May 16 to August 31, 2015. The sensors provided data for chlorophyll, turbidity, conductivity, temperature (three sensors), salinity (calculated from temperature and conductivity), biomass at three different depth intervals (5–50, 50–120, 120–250 m), and current speed measured in two directions (east and north) using two sensors covering different depths with overlap. A total of 88 variables were monitored, 78 from the two current speed sensors. The time-resolution varied, thus the data had to be aligned to a common time resolution. After alignment, the data were interpreted using principal component analysis (PCA). Initially, a calibration model was established using data from May 16 to July 31. The data on current speed from two sensors were subject to two separate PCA models and the score vectors from these two models were combined with the other 10 variables in a multi-block PCA model. The observations from August were projected on the calibration model consecutively one at a time and the result was visualized in a score plot. Automated PCA of multi-sensor data submitted online is illustrated with an attached time-lapse video covering the relative short time period used in the pilot study. Methods for statistical validation, and warning and alarm limits are described. Redundant sensors enable sensor diagnostics and quality assurance. In a future perspective, the concept may be used in integrated environmental monitoring.

Supervised Multiblock Analysis in R with the ade4 Package

This paper presents two novel statistical analyses of multiblock data using the R language. It is designed for data organized in (K + 1) blocks (i.e., tables) consisting of a block of response variables to be explained by a large number of explanatory variables which are divided into K meaningful blocks. All the variables - explanatory and dependent - are measured on the same individuals. Two multiblock methods both useful in practice are included, namely multiblock partial least squares regression and multiblock principal component analysis with instrumental variables. The proposed new methods are included within the ade4 package widely used thanks to its great variety of multivariate methods. These methods are available on the one hand for statisticians and on the other hand for users from various fields in the sense that all the values derived from the multiblock processing are available. Some relevant interpretation tools are also developed. Finally the main results are summarized using overall graphical displays. This paper is organized following the different steps of a standard multiblock process, each corresponding to specific R functions. All these steps are illustrated by the analysis of real epidemiological datasets.

Fault Analysis Of Process System Using Multi Block Principal Component Analysis

This research looks into the issues of the quality improvement based on process control instead of product control using multivariate statistical process contro. A deterministic model of a proton exchange membrane fuel cell (PEM-FC) power plant was used as a case study to represent a multi variable or mukti equipment system. A three-step approach is proposed which can be classified into fault detection, fault isolation, and faulr diagnosis. The fault detection and the isolation utilize the multivariate analysis and yhe contro chart method , which uses the series multi-block principal component analysis of extended of PCA method. The series block principal component abalysis is solved using the non linear iteration partial least squares (NIPALS) algorithm. The SB-PCA can advangeouly incorporate the control chart, namely, T2 Hotelling control chart. In the fault diagnosis chart, the normalized variable method was successfully applied in this study with promising results. As a conclution, the result of this study demonstrated the potentials of multivariate statistical process control in solving fault detection and diagnosis problem for multi variable and multi equipment system.Keywords : statistical process control, principal component, fault analysis