Process monitoring multivariate modelling

Several statistics from the models can be used to monitor the performance of the controller. Square prediction error (SPE) gives an indication of the quality of the PLS model. If the correlation of all variables remains the same, the SPE value should be low, and indicate that the model is operating within the limits for which it was developed. Hotelling s 7 provides an indication of where the process is operating relative to the conditions used to develop the PLS model, while the Q statistic is a measure of the variability of a sample s response relative to the model. Thus the use of a multivariate model (PCA or PLS) within a control system can provide information on the status of the control system. 

A bioprocess system has been monitored using a multi-analyzer system with the multivariate data used to model the process.27 The fed-batch E. coli bioprocess was monitored using an electronic nose, NIR, HPLC and quadrupole mass spectrometer in addition to the standard univariate probes such as a pH, temperature and dissolved oxygen electrode. The output of the various analyzers was used to develop a multivariate statistical process control (SPC) model for use on-line. The robustness and suitability of multivariate SPC were demonstrated with a tryptophan fermentation. 

The book follows a rational presentation structure, starting with the fundamentals of univariate statistical techniques and a discussion on the implementation issues in Chapter 2. After stating the limitations of univariate techniques, Chapter 3 focuses on a number of multivariate statistical techniques that permit the evaluation of process performance and provide diagnostic insight. To exploit the information content of process measurements even further. Chapter 4 introduces several modeling strategies that are based on the utilization of input-output process data. Chapter 5 provides statistical process monitoring techniques for continuous processes and three case studies that demonstrate the techniques. 

L Xie, U Kruger, D Lieftucht, T Littler, Q Chen, and S-Q Wang. Statistical monitoring of dynamic multivariate processes - Part 1. Modeling autocorrelation and cross-correlation. Ind. Engg. Chem. Research, 45 1659—1676, 2006. 

The first efforts towards real-time and in-line monitoring of CO2 absorption processes focused on the use of Fourier transform infrared (FTIR) spectroscopy in combination with a multivariate model. Geers et al. (3) successfully applied this methodology to a solvent consisting of an equimolar solution of p-alanine and potassium hydroxide. They predicted the concentrations of the amine, of absorbed CO2 and SO2, and also included the effect of NO2 in their analysis. 

Einbu et al. (4) also assessed the use of a combination of FTIR spectroscopy and a multivariate model for composition predictions, but applied to a CO2 absorption process using aqueous MEA. They constructed a model based on a very extensive calibration set of 86 samples, covering MEA concentration of 10 to 80 wt% and CO2 eoneentration of 0.0 to 0.5 mol CO2 per mol amine. Based on these calibration samples, the model was calculated to have a relative predictive uncertainty of 1.4% for MEA and 3.0% for CO2. It has also successfully been use for continuous in-line monitoring of an operating pilot plant, but no quantitative results for the prediction accuracy ate given. 

Combinations of in-line measurement techniques with multivariate modelling show promising properties for nse as real-time monitoring applications of the liqnid composition in acid gas absorption processes. Both spectroscopic and non-spectroscopic analytical techniques can be nsed. Althongh the first developments were mostly aimed at predicting CO2 and amine concentrations in post-combustion CO2 capture processes, recent developments are also directing into applications involving acid gas removal from natural gas and the use of solvents that inclnde mixtures of two active components. 

Calibration Most process analyzers are designed to monitor concentration and/or composition. This requires a calibration of the analyzer with a set of prepared standards or from well-characterized reference materials. The simple approach must always be adopted first. For relatively simple systems the standard approach is to use a simple linear relationship between the instrument response and the analyte/ standard concentration [27]. In more complex chemical systems, it is necessary to adopt either a matrix approach to the calibration (still relying on the linearity of the Beer-Lambert law) using simple regression techniques, or to model the concentration and/or composition with one or more multivariate methods, an approach known as chemometrics [28-30]. 

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