Fault detection in the Tennessee Eastman benchmark process using dynamic principal components analysis based on decorrelated residuals (DPCA

Dynamic Principal Components Analysis (DPCA) is an extension of Principal Components Analysis (PCA), developed in order to add the ability to capture the autocorrelative behaviour of processes, to the existent and well known PCA capability for modelling cross-correlation between variables. The simultaneous modelling of the dependencies along the "variable" and "time" modes, allows for a more compact and rigorous description of the normal behaviour of processes, laying the ground for the development of, for instance, improved Statistical Process Monitoring (SPM) methodologies, able to robustly detect finer deviations from normal operation conditions. A key point in the application of DPCA is the definition of its structure, namely the selection of the number of time-shifted replicates for each variable to include, and the number of components to retain in the final model. In order to address the first of these two fundamental design aspects of DPCA, and arguably the most complex one, we propose two new lag selection methods.The first method estimates a single lag structure for all variables, whereas the second one refines this procedure, providing the specific number of lags to be used for each individual variable. The application of these two proposed methodologies to several case studies led to a more rigorous estimation of the number of lags really involved in the dynamical mechanisms of the processes under analysis. This feature can be explored for implementing improved system identification, process monitoring and process control tasks that rely upon a DPCA modelling framework.

High‐dimensional and time‐dependent data pose significant challenges to Statistical Process Monitoring. Most of the high‐dimensional methodologies to cope with these challenges rely on some form of Principal Component Analysis (PCA) model, usually classified as nonadaptive and adaptive. Nonadaptive methods include the static PCA approach and Dynamic Principal Component Analysis (DPCA) for data with autocorrelation. Methods, such as DPCA with Decorrelated Residuals, extend DPCA to further reduce the effects of autocorrelation and cross‐correlation on the monitoring statistics. Recursive Principal Component Analysis and Moving Window Principal Component Analysis, developed for nonstationary data, are adaptive. These fundamental methods will be systematically compared on high‐dimensional, time‐dependent processes (including the Tennessee Eastman benchmark process) to provide practitioners with guidelines for appropriate monitoring strategies and a sense of how they can be expected to perform. The selection of parameter values for the different methods is also discussed. Finally, the relevant challenges of modeling time‐dependent data are discussed, and areas of possible further research are highlighted. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1478–1493, 2016

A new methodology is proposed for monitoring multi- and megavariate systems whose variables present significant levels of autocorrelation. The new monitoring statistics are derived after the preliminary generation of decorrelated residuals in a dynamic principal component analysis (DPCA) model. The proposed methodology leads to monitoring statistics with low levels of serial dependency, a feature that is not shared by the original DPCA formulation and that seriously hindered its dissemination in practice, leading to the use of other, more complex, monitoring approaches. The performance of the proposed method is compared with those of a variety of current monitoring methodologies for large-scale systems, under different dynamical scenarios and for different types of process upsets and fault magnitudes. The results obtained clearly indicate that the statistics based on decorrelated residuals from DPCA (DPCA-DR) consistently present superior performances regarding detection ability and decorrelation power and are also robust and efficient to compute.

In this article we address the general problem of monitoring the process cross-and auto-correlation structure through the incorporation of information about its internal structure in a pre-processing stage, where sensitivity enhancing transformations are applied to collected data. We have found out that the sensitivity of the monitoring statistics based on partial or marginal correlations in detecting structural changes is directly related to the nominal levels of the correlation coefficients during normal operation conditions (NOC). The highest sensitivities are obtained when the process variables involved are uncorrelated, a situation that is hardly met in practice. However, not all transformations perform equally well in producing uncorrelated transformed variables with enhanced detection sensitivities. The most successful ones are based on the incorporation of the natural relationships connecting the process variables. In this context, a set of sensitivity enhancing transformations are proposed, which are based on a network reconstruction algorithm. These new transformations make use of fine structural information of the variables connectivity and therefore are able to improve the detection capability to local changes in correlation, leading to better performances when compared to current marginal-based methods, namely those based on latent variables models, such as PCA or PLS. Moreover, a novel monitoring statistic for the transformed variables variance proved to be very useful in the detection of structural changes resulting from model mismatch. This statistic allows for the detection of multiple structural changes within the same monitoring scheme and with higher detection performances when compared to the current methods.

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A significant number of batch process monitoring methods have been proposed since the first groundbreaking approaches were published in the literature, two decades ago. The proper assessment of all the alternatives currently available requires a rigorous and robust assessment framework, in order to assist practitioners in their difficult task of selecting the most adequate approach for the particular situations they face and in the definition of all the optional aspects required, such as the type of preprocessing, infilling, alignment, etc. However, comparison methods currently adopted present several limitations and even some flaws that make the variety of studies available not easily generalizable or, in extreme situations, fundamentally wrong. Without a proper comparison tool decisions are made on a subjective basis and therefore are prone to be at least suboptimal. In this article we present a structured review of comparison methods and figures of merit adopted to assess batch process monitoring approaches, analyzing their strengths and limitations, as well as some common missuses. Furthermore, we propose a comparison and assessment methodology (CAM) and figures of merit that should be adopted in order to circumvent some of the limitations of the current procedures. We begin by addressing, in this article, the analysis of the methods' "detection strength". Detection strength regards the ability to correctly detect abnormal situations without resulting in excessive false alarms. We describe in detail how the comparison framework is implemented and illustrate its application in two case studies, encompassing a rich variety of testing scenarios (99 000 batch runs) and monitoring methods (2-way, 3-way, and dynamic methods, amounting to a total of 60 different combinations of methods and their variants). From this analysis, it stands out that the CAM methodology is suitable for comparing different monitoring methods, even when the number of methods and variants is very large. It provides simple, informative, and statisticalbased metrics to assess a given method's performance and is able to quantify the added value of alternative approaches. When applied to the two case studies considered, 2-way methods (with batch-wise unfolding) combined with missing data (MD) infilling and dynamic time warping (DTW) were found to provide adequate solutions. If a more parsimonious model is required, dynamic methods such as autoregressive principal components analysis (ARPCA) provide good alternatives and Tucker3 with current deviations (CD) infilling also presents an interesting performance for some fault scenarios. In general, no method can claim absolute supremacy in all faulty scenarios.