Multiway Principal Components Analysis Research Articles

Using data analytics to accelerate biopharmaceutical process scale-up

In the biopharmaceutical industry, the selection of high-quality cell lines characterized by high productivity and stability over time plays a critical role for the development of processes meeting the desired quality and manufacturability criteria. Cell line selection involves their testing through subsequent stages at different process scales to progressively recreate the conditions of an industrial-scale bioreactor, from static micro-well plates, to shake flasks to reactors of increasing volumes and complexity. In this context both scale-up and scale-down are challenging due to the variety and quantity of data to mine and the scarcity of first-principles understanding on cells culture dynamics.This paper illustrates the use of advanced data-driven modeling where patterns across multiple scales are identified and interpreted to aid the cell line selection scale-up process. Methods such as multiway principal components analysis, Procrustes analysis and joint-Y projection to latent structures are used to characterize cell lines cross correlation and their dynamic behavior over time, and to carry out performance predictions across different scales. The approach has the potential to mature into a general framework to aid scale-up for cell-line selection and so drive acceleration in the development cycle of biopharmaceuticals through an optimal use of the available data acquisition platforms.

A Bottom-Up Approach for Data Mining in Bioaromatization of Beers Using Flow-Modulated Comprehensive Two-Dimensional Gas Chromatography/Mass Spectrometry

In this study, we report the combination of comprehensive two-dimensional gas chromatography (GC×GC) with multivariate pattern recognition through template matching for the assignment of the contribution of Brazilian Ale 02 yeast strain to the aroma profile of beer compared with the traditional Nottingham yeast. Volatile organic compounds (VOC) from two beer samples, which were fermented with these yeast strains were sampled using headspace solid-phase microextraction (HS-SPME). The aroma profiles from both beer samples were obtained using GC×GC coupled to a fast scanning quadrupole mass spectrometer. Data processing performed through multiway principal components analysis succeeded in separating both beer samples based on yeast strain. The execution of a simple and reliable procedure succeeded and identified 46 compounds as relevant for sample classification. Furthermore, the bottom-up approach spotted compounds found exclusively in the beer sample fermented with the Brazilian yeast, highlighting the bioaromatization properties introduced to the aroma profile by this yeast strain.

Tracing the geographical origin of burdock root based on fluorescent components using multi-way chemometrics techniques

Tracing the geographical origin of burdock root based on fluorescent components using multi-way chemometrics techniques were investigated in this work. Excitation emission spectra were obtained for 150 burdock root of different geographical origins by recording emission from 270 to 510nm with excitation in the range of 250–500nm. Multi-way principal components analysis (M-PCA), Multi-way partial least squares discriminant analysis (N-PLS-DA) and Parallel factor analysis coupling with partial least squares discriminant analysis (PARAFAC-PLS-DA) methods were used to decompose the excitation-emission matrices (EEM) datasets and classify the different burdock roots according to their geographical origins. M-PCA model showed the clustering tendency for the different geographical origin of burdock root samples. N-PLS-DA and PARAFAC-PLS-DA gave more detailed classification results. The accuracy of successful in prediction of the geographical origin of the 150 samples varied between 77.8% and 100% for N-PLS-DA model. For PARFAC-PLS-DA model, the accuracy of the 150 samples varied between 94.7% and 100%. Different figures of merit were used for comparing the classification ability of N-PLS-DA and PARAFAC-PLS-DA model. Comparing with the other two methods, the PARAFAC-PLS-DA classification model, constructed from PARAFAC model scores, got more accurate and reliable classification result. The result showed this method could be applied to trace the geographical origins of burdock root. Further, considering the relative concentration can be acquired by PARAFAC model, the interest of this model emerges from the fact that it maybe be promising to be used to distinguish the quality grade level of the burdock root samples.

Discrimination of geographical origin and detection of adulteration of kudzu root by fluorescence spectroscopy coupled with multi-way pattern recognition

In this work, fluorescence spectroscopy combined with multi-way pattern recognition techniques were developed for determining the geographical origin of kudzu root and detection and quantification of adulterants in kudzu root. Excitation-emission (EEM) spectra were obtained for 150 pure kudzu root samples of different geographical origins and 150 fake kudzu roots with different adulteration proportions by recording emission from 330 to 570nm with excitation in the range of 320–480nm, respectively. Multi-way principal components analysis (M-PCA) and multilinear partial least squares discriminant analysis (N-PLS-DA) methods were used to decompose the excitation-emission matrices datasets. 150 pure kudzu root samples could be differentiated exactly from each other according to their geographical origins by M-PCA and N-PLS-DA models. For the adulteration kudzu root samples, N-PLS-DA got better and more reliable classification result comparing with the M-PCA model. The results obtained in this study indicated that EEM spectroscopy coupling with multi-way pattern recognition could be used as an easy, rapid and novel tool to distinguish the geographical origin of kudzu root and detect adulterated kudzu root. Besides, this method was also suitable for determining the geographic origin and detection the adulteration of the other foodstuffs which can produce fluorescence.

Unsupervised classification of petroleum Certified Reference Materials and other fuels by chemometric analysis of gas chromatography-mass spectrometry data

As feedstocks transition from conventional oil to unconventional petroleum sources and biomass, it will be necessary to determine whether a particular fuel or fuel blend is suitable for use in engines. Certifying a fuel as safe for use is time-consuming and expensive and must be performed for each new fuel. In principle, suitability of a fuel should be completely determined by its chemical composition. This composition can be probed through use of detailed analytical techniques such as gas chromatography–mass spectroscopy (GC–MS). In traditional analysis, chromatograms would be used to determine the details of the composition. In the approach taken in this paper, the chromatogram is assumed to be entirely representative of the composition of a fuel, and is used directly as the input to an algorithm in order to develop a model that is predictive of a fuel’s suitability. When a new fuel is proposed for service, its suitability for any application could then be ascertained by using this model to compare its chromatogram with those of the fuels already known to be suitable for that application.In this paper, we lay the mathematical and informatics groundwork for a predictive model of hydrocarbon properties. The objective of this work was to develop a reliable model for unsupervised classification of the hydrocarbons as a prelude to developing a predictive model of their engine-relevant physical and chemical properties. A set of hydrocarbons including biodiesel fuels, gasoline, highway and marine diesel fuels, and crude oils was collected and GC–MS profiles obtained. These profiles were then analyzed using multi-way principal components analysis (MPCA), principal factors analysis (PARAFAC), and a self-organizing map (SOM), which is a kind of artificial neural network. It was found that, while MPCA and PARAFAC were able to recover descriptive models of the fuels, their linear nature obscured some of the finer physical details due to the widely varying composition of the fuels. The SOM was able to find a descriptive classification model which has the potential for practical recognition and perhaps prediction of fuel properties.

A New Method of On-Line Fault Monitoring Based on Nonlinear MPCA

Multiway principal components analysis (MPCA) is a linear model in nature, thus, limited when it is applied to batch process. In this paper, the linear model MPCA was complemented with an autoassociative neural network model in order to generate nonlinear principal components. The networks bottleneck layer outputs (nonlinear principal components) were made orthogonal. A method to estimate confidence limits based on a kernel probability density function was proposed since the nonlinear scores are no normally distributed. A statistic-like parameter () was proposed to evaluate on-line scores for new runs using the density estimated confidence bounds and replacing the statistic. The proposed method was applied to monitoring fed-batch streptomycete production, and the simulation results show that the nonlinear scores obtained with the autoassociative neural networks capture more process data variance than if obtained with a linear method and the density estimation method proved to be more reliable.

Analysis of petroleum compositional similarity using multiway principal components analysis (MPCA) with comprehensive two-dimensional gas chromatographic data

The accurate establishment of oil similarity is a longstanding problem in petroleum geochemistry and a necessary component for resolving the architecture of an oil reservoir. Past limitations have included the excessive reliance on a relatively small number of biomarkers to characterize such complex fluids as crude oils. Here we use multiway principal components analysis (MPCA) on large numbers of specific chemical components resolved with comprehensive two-dimensional gas chromatography-flame ionization detection (GC × GC–FID) to determine the molecular relatedness of eight different maltene fractions of crude oils. MPCA works such that every compound eluting within the same first and second dimension retention time is quantitatively compared with what elutes at that same retention times within the other maltene fractions. Each maltene fraction and corresponding MPCA analysis contains upwards of 3500 quantified components. Reservoir analysis included crude oil sample pairs from around the world that were collected sequentially at depth within a single well, collected from multiple depths in the same well, and from different depths and different wells but thought to be intersected by the same permeable strata. Furthermore, three different regions of each GC × GC–FID chromatograms were analysed to evaluate the effectiveness of MPCA to resolve compositional changes related to the source of the oil generating sediments and its exposure to biological and/or physical weathering processes. Compositional and instrumental artefacts introduced during sampling and processing were also quantitatively evaluated. We demonstrate that MPCA can resolve multi-molecular differences between oil samples as well as provide insight into the overall molecular relatedness between various crude oils.

A systematic approach to data-driven modeling and soft sensing in a full-scale plant

The well-known mathematical modeling and neural networks (NNs) methods have limitations to incorporate the key process characteristics at the wastewater treatment plants (WWTPs) which are complex, non-stationary, temporal correlation, and nonlinear systems. In this study, a systematic methodology of NNs modeling which can be efficiently included in the key modeling information of the WWTPs is performed by selecting the temporal effect of the hydraulics based on multi-way principal components analysis (MPCA). The proposed method is applied for modeling wastewater quality of a full-scale plant, which is a Daewoo nutrient removal (DNR) process. Through the experimental results in a full-scale plant, the efficiency of the proposed method is evaluated and the prediction capability is highly improved by the inclusion of the hydraulics term due to the optimized structure of neural networks.

Controle multivariado de processos em batelada com duração variável

Processos em batelada são utilizados em diversos setores industriais (por exemplo, na manufatura de alimentos e fármacos). Nesses processos, matérias-primas são carregadas em uma unidade de processamento e submetidas a uma série de transformações até a obtenção do produto final. O desempenho do processo é descrito por variáveis, monitoradas ao longo da batelada. Dados resultantes desses processos tendem a apresentar uma estrutura de correlação e autocorrelação significativa, sendo usualmente monitorados usando cartas de controle baseadas na análise de componentes principais (CCPs). Neste artigo, investiga-se o caso especial, bastante freqüente na prática, de bateladas com duração variável, as quais não podem ser diretamente monitoradas através das CCPs. Para tanto, propõe-se uma nova estratégia de controle multivariado da qualidade. No procedimento proposto, bateladas não são alinhadas ou time warped relativamente a suas trajetórias, mas completadas utilizando um esquema de fácil implementação prática. Desta forma, preserva-se toda a informação sobre a variabilidade ao longo do eixo do tempo nos perfis das variáveis de processo. O conjunto de dados completados é analisado utilizando o método Statis e o monitoramento do desempenho da batelada é realizado diretamente nos gráficos de planos fatoriais, a partir dos quais cartas de controle não-paramétricas são derivadas. Um exemplo utilizando dados simulados ilustra a proposta metodológica.

Multivariate monitoring of fermentation processes with non-linear modelling methods

Multiway principal components analysis (MPCA) and parallel factor analysis (PARAFAC) are widely used in exploratory data analysis and multivariate statistical process control (MSPC). These models are linear in nature, thus, limited when non-linear relations are present in the data. Principal component analysis (PCA) can be extended to non-linear principal components analysis using autoassociative neural networks. In this paper, the network’s bottleneck layer outputs (non-linear components) were made orthogonal. A method to estimate confidence limits based on a kernel probability density function was proposed since these limits do not assume that the non-linear scores are normally distributed. A measure for the non-linear scores ( D NL) was presented here to monitor on-line the process replacing the well known Hotelling’s T 2 statistic. One hundred and two industrial fermentation runs were used to evaluate the performance of a non-linear technique for multivariate process statistical monitoring. Three process runs with faults were used to compare the error detection performance using a statistic for the non-linear scores and the residuals statistic (SPE).

Batch process monitoring and its application to polymerization systems

AbstractSlight changes in raw material properties or operating conditions during critical periods of operation of batch and semi‐batch polymerization reactors may have a strong influence on reaction mechanism and impact final product quality. Online process monitoring, fault detection, fault diagnosis, and product quality prediction in real‐time ensure safe reactor operation and warn operators about excursions from normal operation that may lead to deterioration in product properties. Multivariate statistical process monitoring and quality prediction using multiway principal components analysis and multiway partial least squares have been successful in detecting abnormalities in process operation and product quality. When abnormal process operation is detected, fault diagnosis tools are used to determine the source cause of the deviation. Illustrative case studies are presented via simulated polyvinyl acetate polymerization.

A Method for Predicting Future Observations in the Monitoring of a Batch Process

Batch processes play an important role in the production of low-volume, high-value products such as polymers, pharmaceuticals, and biochemicals. Multiway Principal Components Analysis (MPCA), one of the multivariate projection methods, has been widely used for monitoring batch processes. One major problem in the on-line application of MPCA is that the input data matrix for MPCA is not complete until the end of the batch operation, and thus the unmeasured portion of the matrix (called the “future observations”) has to be predicted. In this paper we propose a new method for predicting the future observations of the batch that is currently being operated (called the “new batch”). The proposed method, unlike the existing prediction methods, makes extensive use of the past batch trajectories. The past batch trajectory which is deemed the most similar to the new batch is selected from the batch library and used as the basis for predicting the unknown part of the new batch. A case study on an industrial PVC batch process has been conducted. The results show that the proposed method results in more accurate prediction and has the capability of detecting process abnormalities earlier than the existing methods.

Translating third-order data analysis methods to chemical batch processes

Measurements collected from batch processes naturally produce a third-order or three-dimensional data form. The same structure also results when multiple samples are measured using hyphenated analysis techniques such as liquid chromatography with diode array detection. Analysis of third-order data by principal components analysis (PCA) is achieved by a nonunique rearrangement that produces a two-dimensional array. This preferentially models only one of the three orders present. In contrast, methods such as parallel factor analysis (PARAFAC) apply a particular decomposition that accounts for all three orders explicitly. The results from either approach should be related if data are to be interpreted reliably for applications to batch processes such as on-line monitoring and control. This work compares these two approaches from an applied point of view. To accomplish this objective, exemplary methods are selected from each type of analysis, parallel factor analysis (PARAFAC) and multiway principal components analysis (MPCA). These are employed to analyze data obtained during the manufacture of a condensation polymer in an industrial batch reactor.

Adaptive batch monitoring using hierarchical PCA

A new approach to monitoring batch processes using the process variable trajectories is presented. It was developed to overcome the need in the approach of Nomikos and MacGregor [P. Nomikos, J.F. MacGregor, Monitoring of batch processes using multi-way principal components analysis, Am. Inst. Chem. Eng. J. 40 (1994) 1361–1375; P. Nomikos, J.F. MacGregor, Multivariate SPC charts for batch processes, Technometrics 37 (1995) 41–59; P. Nomikos, J.F. MacGregor, Multi-way partial least squares in monitoring batch processes, Chemometrics Intell. Lab. Syst. 30 (1995) 97–108] for estimating or filling in the unknown part of the process variable trajectory deviations from the current time until the end of the batch. The approach is based on a recursive multi-block (hierarchical) PCA/PLS method which processes the data in a sequential and adaptive manner. The rate of adaptation is easily controlled with a parameter which controls the weighting of past data in an exponential manner. The algorithm is evaluated on industrial batch polymerization process data and is compared to the multi-way PCA/PLS approaches of Nomikos and MacGregor. The approach may have significant benefits when monitoring multi-stage batch processes where the latent variable structure can change at several points during the batch.

Multivariate Statistical Process Control in Batch Process Monitoring

Batch processing was widely practised long before the advent of the modern chemical industry. A number of limitations have inhibited the success of batch monitoring:- the finite duration of a batch, the presence of significant non-linearities, the lack of on-line sensors for measuring quality variables, the absence of steady-state operation, the difficulty of developing accurate mechanistic models and finally, process measurements are autocorrelated in time as well as being correlated with one another at any given time. Recent approaches to the monitoring of batch behaviour have been based on the extension of univariate statistical process control (SPC) philosophy to handle multivariate processes. These tools have been the statistical projection methods of principal components analysis (PCA) and projection to latent structures (PLS), and their extensions to batch operation, i.e. multiway PCA and PLS.In this paper, multiway PCR is applied to the monitoring of a batch polymerisation reactor and an industrial fed-batch fermentation process using two alternative approaches. These tools have been found to be an effective method for monitoring industrial processes when the data is of high dimension and ill-conditioned. Furthermore, they provide a useful modelling technique for predicting key quality variables which are either not measured on-line or else are monitored at a much slower frequency than the process variables.

Batch process monitoring for consistent production

A number of limitations have inhibited the success of batch process monitoring:- the finite and variable duration of a batch, the presence of significant non-linearities, the lack of on-line sensors for measuring quality variables, the absence of steady-state operation, the difficulty of developing accurate mechanistic models and process measurements that are autocorrelated in time as well as being correlated with one another. Recent approaches to the monitoring of batch behaviour have been based on extensions of the statistical projection methods of Principal Components Analysis (PCA) and Projection to Latent Structures (PLS) - multiway PCA and multiway PLS. These techniques form the bases of the multivariate statistical process control charts for batch process monitoring. The control limits for detecting when a process is moving out of control for multivariate SPC charts are based upon Hotelling's T 2 statistic. A new approach which allows the nominal data to dictate the form and shape of the bound, the M 2 statistic, is reviewed. Finally, an application of multivariate SPC and the impact the different confidence bounds have on process operation is highlighted by application to a batch methyl methacrylate polymerisation reactor.

Application of multi-way principal components analysis to nuclear waste storage tank monitoring

Multivariate statistical process control (MSPC) techniques for batch processes have been extended to monitoring a semi-batch process by focussing on periodic process set point changes. This procedure can be extended to continuous processes that have repeated upsets or perturbations. The MSPC technique was demonstrated for a nuclear waste storage tank that undergoes periodic agitation from a mixing pump. The procedure described here used multi-way principal components analysis to develop a statistical model of the process based on historical data. The model can be used to determine if changes have occurred in the system. At present this procedure is used off-line for monitoring but it could be implemented on-line.

Multi-way principal components analysis of a complex data array resulting from physicochemical characterization of natural waters

Multi-way principal components analysis (MPCA) is an efficient tool for reducing higher dimensional data arrays. Using the Kroonenberg algorithm — which originally was developed for three-dimensional data arrays but may be generalized to arbitrary dimensions in a straightforward manner — MPCA is applied to a complex example from the chemistry of waters. The data originated from the measurements of fifteen physicochemical parameters (variables) at ten different locations (objects) within some specific area of the Niger delta. These measurements were consistently recorded 22 times (occasions) in the course of a year. MPCA allows the detection of spatial and temporal factors of influence and the classification of the parameters considered according to these factors.

Multi-way principal components-and PLS-analysis

The Lohmöller–Wold decomposition of multi-way (three-way, four-way, etc.) data arrays is combined with the non-linear partial least squares (NIPALS) algorithms to provide multi-way solutions of principal components analysis (PCA) and partial least squares modelling in latent variables (PLS). The decomposition of a multi-way array is developed as the product of a score vector and a loading array, where the score vectors have the same properties as those of ordinary two-way PCA and PLS. In image analysis, the array would instead be decomposed as the product of a loading vector and an image score matrix. The resulting methods are equivalent to the method of unfolding a multi-way array to a two-way matrix followed by ordinary PCA or PLS analysis. This automatically proves the eigenvector and least squares properties of the multi-way PCA and PLS methods. The methodology is presented; the algorithms are outlined and illustrated with a small chemical example.