Multivariate Statistical Projection Methods Research Articles

Statistical Monitoring of Wastewater Treatment Plants Using Variational Bayesian PCA

Multivariate statistical projection methods such as principal component analysis (PCA) are the most common strategy for process monitoring in wastewater treatment plants (WWTPs). Such monitoring strategies can indeed recognize faults and achieve better control performance for fully observed data sets but can be more difficult in the case of having missing data. This study presents a variational Bayesian PCA (VBPCA) based methodology for fault detection in the WWTPs. This methodology not only is robust against missing data but also reconstructs missing data. Furthermore, a novel historical data preprocess method is proposed to deal with diurnal behaviors in the WWTPs with fast sample rate. These methodologies have been validated by process data collected from two WWTPs with different process characteristics and different sample rates. The results showed that the proposed methodology is capable of detecting sensor faults and process faults with good accuracy under different scenarios (highly and lowly instr...

Multivariate statistical projection methods to perform robust feature extraction and classification in surface grading

We present an innovative way to simultaneously perform feature extraction and classification for the quality-control issue of surface grading by applying two multivariate statistical projection methods: SIMCA and PLS-DA. These tools have been applied to compress the color texture data that describe the visual appearance of surfaces (soft color texture descriptors) and to directly perform classification using statistics and predictions from the projection models. Experiments have been carried out using an extensive ceramic images database (VxC TSG) comprised of 14 different models, 42 surface classes, and 960 pieces. A factorial experimental design evaluated all the combinations of several factors affecting the accuracy rate. These factors include the tile model, color representation scheme (CIE Lab, CIE Luv, and RGB), and compression/classification approach (SIMCA and PLS-DA). Moreover, a logistic regression model is fitted from the experiments to compute accuracy estimates and study the effect of the factors on the accuracy rate. Results show that PLS-DA performs better than SIMCA, achieving a mean accuracy rate of 98.95%. These results outperform those obtained in a previous work where the soft color texture descriptors in combination with the CIE Lab color space and the k-NN classifier achieved an accuracy rate of 97.36%.

Multivariate projection methods applied to flotation columns

On line monitoring and diagnosis systems of process operating performance are becoming important part of industrial programs, leading to improve process operation and therefore product quality over time. In processes, such as flotation, a large number of input variables, highly correlated, are presented. These characteristics usually pose more difficulties in modelling the process for monitoring and diagnosis purposes. Multivariate statistical projection methods have been proposed to effectively deal with these situations. The application of these ideas to a column flotation process is discussed here. In this work, the detection of measurement problems in relevant variables, and the identification of the set of variables responsible for driving the process outside its normal operating region, are demonstrated. Furthermore, the use of these techniques gave considerable information for the correction of the operating problem.

Flotation Column Monitoring and Control Based on PLS Models

Today, massive amounts of data are being collected routinely on hundred of variables at high frequency. However, many important variables, such as concentrate and tailings grades are available only infrequently in flotation processes. To effectively monitor flotation columns one must utilize all the information contained in routine measurements. The main difficulties are the dimensionality and the fact that process operating variables are often highly correlated and collinear. Multivariate statistical projection methods have been proposed to treat these situations. These ideas are demonstrated using simulation studies on flotation columns.

Analysis, Monitoring and Fault Diagnosis of Industrial Processes Using Multivariate Statistical Projection Methods

Multivariate statistical procedures based on various versions of principle component analysis (PCA), and partial least squares (PLS), have recently been proposed for the analysis monitoring and diagnosis of industrial processes. These methods are capable of treating processes with large numbers of highly correlated process and quality variables, and can easily handle missing data. The only information needed to exploit them is a good database on historical process operations.In this paper, industrial experiences with these methods based on recent applications in many different industries are presented. Both continuous and batch processes are treated. Multi-block methods are shown to be very useful for treating large continuous processes or multistage batch operations, and multi-way methods are used to treat batch processes where one has time-varying trajectory data on many variables.

Process analysis, monitoring and diagnosis, using multivariate projection methods

Multivariate statistical methods for the analysis, monitoring and diagnosis of process operating performance are becoming more important because of the availability of on-line process computers which routinely collect measurements on large numbers of process variables. Traditional univariate control charts have been extended to multivariate quality control situations using the Hotelling T2 statistic. Recent approaches to multivariate statistical process control which utilize not only product quality data (Y), but also all of the available process variable data (X) are based on multivariate statistical projection methods (principal component analysis, (PCA), partial least squares, (PLS), multi-block PLS and multi-way PCA). An overview of these methods and their use in the statistical process control of multivariate continuous and batch processes is presented. Applications are provided on the analysis of historical data from the catalytic cracking section of a large petroleum refinery, on the monitoring and diagnosis of a continuous polymerization process and on the monitoring of an industrial batch process.

Statistical process control of multivariate processes

With process computers routinely collecting measurements on large numbers of process variables, multivariate statistical methods for the analysis, monitoring and diagnosis of process operating performance have received increasing attention. Extensions of traditional univariate Shewhart, CUSUM and EWMA control charts to multivariate quality control situations are based on Hotelling's T 2 statistic. Recent approaches to multivariate statistical process control which utilize not only product quality data (Y), but also all of the available process variable data (X) are based on multivariate statistical projection methods (Principal Component Analysis (PCA) and Partial Least Squares (PLS)). This paper gives an overview of these methods, and their use for the statistical process control of both continuous and batch multivariate processes. Examples are provided of their use for analysing the operations of a mineral processing plant, for on-line monitoring and fault diagnosis of a continuous polymerization process and for the on-line monitoring of an industrial batch polymerization reactor.

Statistical Process Control of Multivariate Processes

With process computers routinely collecting measurements on large numbers of process variables, multivariate statistical methods for the analysis, monitoring and diagnosis of process operating performance have received increasing attention. Extensions of traditional univariate Shewhart, CUSUM and EWMA control charts to multivariate quality control situations are based on Hotelling’s T2 statistic. Recent approaches to multivariate statistical process control which utilize not only product quality data (Y), but also all of the available process variable data (X) are based on multivariate statistical projection methods (Principal Component Analysis (PCA) and Projection to Latent Structures (PLS)). This paper gives an overview of these methods, and their use in the statistical process control of multivariate processes.

Process monitoring and diagnosis by multiblock PLS methods

AbstractSchemes for monitoring the operating performance of large continuous processes using multivariate statistical projection methods such as principal component analysis (PCA) and projection to latent structures (PLS) are extended to situations where the processes can be naturally blocked into subsections. The multiblock projection methods allow one to establish monitoring charts for the individual process subsections as well as for the entire process. When a special event or fault occurs in a subsection of the process, these multiblock methods can generally detect the event earlier and reveal the subsection within which the event has occurred. More detailed diagnostic methods based on interrogating the underlying PCA/PLS models are also developed. These methods show those process variables which are the main contributors to any deviations that have occurred, thereby allowing one to diagnose the cause of the event more easily. These ideas are demonstrated using detailed simulation studies on a multisection tubular reactor for the production of low‐density polyethylene.