Randy J. Pell

Variable selection for multivariate calibration using a genetic algorithm: prediction of additive concentrations in polymer films from Fourier transform-infrared spectral data

Abstract Variable selection using a genetic algorithm is combined with partial least squares (PLS) for the prediction of additive concentrations in polymer films using Fourier transform-infrared (FT-IR) spectral data. An approach using an iterative application of the genetic algorithm is proposed. This approach allows for all variables to be considered and at the same time minimizes the risk of overfitting. We demonstrate that the variables selected by the genetic algorithm are consistent with expert knowledge. This very exciting result is a convincing application that the algorithm can select correct variables in an automated fashion.

Exploring process data with the use of robust outlier detection algorithms

Abstract To implement on-line process monitoring techniques such as principal component analysis (PCA) or partial least squares (PLS), it is necessary to extract data associated with the normal operating conditions from the plant historical database for calibrating the models. One way to do this is to use robust outlier detection algorithms such as resampling by half-means (RHM), smallest half volume (SHV), or ellipsoidal multivariate trimming (MVT) in the off-line model building phase. While RHM and SHV are conceptually clear and statistically sound, the computational requirements are heavy. Closest distance to center (CDC) is proposed in this paper as an alternative for outlier detection. The use of Mahalanobis distance in the initial step of MVT for detecting outliers is known to be ineffective. To improve MVT, CDC is incorporated with MVT. The performance was evaluated relative to the goal of finding the best half of a data set. Data sets were derived from the Tennessee Eastman process (TEP) simulator. Comparable results were obtained for RHM, SHV, and CDC. Better performance was obtained when CDC is incorporated with MVT, compared to using CDC and MVT alone. All robust outlier detection algorithms outperformed the standard PCA algorithm. The effect of auto scaling, robust scaling and a new scaling approach called modified scaling were investigated. With the presence of multiple outliers, auto scaling was found to degrade the performance of all the robust techniques. Reasonable results were obtained with the use of robust scaling and modified scaling.

Multiple outlier detection for multivariate calibration using robust statistical techniques

Abstract Outliers that are incorporated into a multivariate calibration model can significantly reduce the performance of the model. In the case of multiple outliers, the standard methods for outlier detection can fail to detect true outliers and even mistakenly identify good samples as outliers. Robust statistical methods are less sensitive to outliers and can provide a powerful tool for the reliable detection of multiple outliers. This paper examines the use of robust principal component regression (PCR) and iteratively reweighted partial least squares (PLS) for multiple outlier detection in an infrared spectroscopic application.

Genetic algorithms combined with discriminant analysis for key variable identification

Many trouble-shooting problems in process industries are related to key variable identification for classifications. The contribution charts, based on principal component analysis (PCA), can be applied for this purpose. Genetic algorithms (GAs) have been proposed recently for many applications including variable selection for multivariate calibration, molecular modeling, regression analysis, model identification, curve fitting, and classification. In this paper, GAs are incorporated with Fisher discriminant analysis (FDA) for key variable identification. GAs are used as an optimization tool to determine variables that maximize the FDA classification success rate for two given data sets. GA/FDA is a proposed solution for the variable selection problem in discriminant analysis. The Tennessee Eastman process (TEP) simulator was used to generate the data sets to evaluate the correctness of the key variable selection using GA/FDA, and the T2 and Q statistic contribution charts. GA/FDA correctly identifies the key variables for the TEP case studies that were tested. For one case study where the correlation changes in two data sets, the contribution charts incorrectly suggest that the operating conditions are similar. On the other hand, GA/FDA not only determines that the operating conditions are different, but also identifies the key variables for the change. For another case study where many key variables are responsible for the changes in the two data sets, the contribution charts only identifies a fraction of the key variables, while GA/FDA correctly identifies all of the key variables. GA/FDA is a promising technique for key variable identification, as is evidenced in successful applications at The Dow Chemical Company.

Effective Resolution Enhancement of Infrared Microspectroscopic Data by Multiresponse Nonlinear Optimization

Computational methods are proposed and tested that enhance the spatial resolution of infrared microspectroscopic data collected from multilayer polymeric materials film structures. The data collected from such a structure with the use of an infrared microspectroscopic system are diffraction limited at approximately 10 μm (however, diffraction limits are wavelength dependent); therefore, layers of thickness less than approximately 10 μm give rise to spectra that are mixtures of spectra from surrounding layers. Some authors have even pointed out that this could be the case for areas sampled that were much greater than 10 μm. Factor analysis of the data matrix can reveal the number of spectrally different layers that are present, and the eigenvectors will give an abstract representation of the positional and wavelength information. An algorithm has been devised that uses layer boundary positions, aperture width, and aperture step size to model the positional information from such an experiment. The boundary layer positions may be used as adjustable parameters in a nonlinear optimization problem that fits the positional model to the abstract factor analysis positional data. This algorithm is applied to simulated and real data. Simulation results indicate superior performance in comparison with spectral matching to the raw data, and analysis of real data indicates consistent results as well as the ability to resolve unique spectral features when compared with results from more painstaking data collection experiments.

Multivariate curve resolution for understanding complex reactions

Chemometrics is applied to in situ infrared spectra collected from a complex reacting mixture to elucidate the reaction mechanism. A series of models beginning with simple peak area progressing to classical least squares then to multivariate curve resolution with nonnegative spectral and concentration profile constraints and finally to multivariate curve resolution with nonnegative constraints and spectral and concentration profile equality constraints are used. The logic used to develop from the simple models to the more complex models is discussed. An intermediate component is estimated, and for each of two of the chemical components, two pure component spectral profiles are required to accurately fit the validation data. The changing polarity of the system is believed to be responsible for the multiple pure spectra required for two single chemical components. A total of 11 components are used to accurately describe the reacting system. Copyright

In Situ Attenuated Total Reflectance Fourier Transform Infrared (ATR FT-IR) Spectroscopy Monitoring of 1,2-Butylene Oxide Polymerization Reaction by Using Iterative Concentration-Guided Classical Least Squares

There has been rapid growth in the application of in situ optical spectroscopy techniques for reaction and process monitoring recently in both academia and industry. Vibrational spectroscopies such as mid-infrared, near-infrared spectroscopy, and Raman spectroscopy have proven to be versatile and informative. Accurate determination of concentrations, based on highly overlapped spectra, remains a challenge. As an example, 1,2-butylene oxide (BO) polymerization, an important industrial reaction, initiated by propylene glycol (PG) and catalyzed by KOH, is studied in this work in a semi-batch fashion by using in situ attenuated total reflectance Fourier transform infrared spectroscopy (ATR FT-IR) monitoring. The weak BO absorbance, the constantly changing interference from the product oligomers throughout the course of the reaction, and the change in BO spectral features with system polarity posed challenges for quantitative spectral analysis based on conventional methods. An iterative concentration-guided classical least-squares (ICG-CLS) method was developed to overcome these challenges. Taking advantage of the concentration-domain information, ICG-CLS enabled the estimation of the pure oligomer product spectra at different stages of the semi-batch process, which in turn was used to construct valid CLS models. The ICG-CLS algorithm provides an in situ calibration method that can be broadly applied to reactions of known order. Caveats in its applications are also discussed.

Multivariate Analysis of Process Data Using Robust Statistical Analysis and Variable Selection

Abstract Historical plant data are useful in developing multivariate statistical models for on-line process monitoring, soft sensors, and process troubleshooting. For the first two purposes, historical data are used to build a model to capture the nonnal characteristics of the process. However, the presence of outliers can adversely affect the model. Various robust statistical techniques are investigated in this paper for outlier identification. For process troubleshooting and fault identification, it is crucial to identify the key process variables that are associated with the root causes. Genetic algorithms (GA) are incorporated with Fisher discriminant analysis (FDA) for this purpose. These techniques have been successfully applied at The Dow Chemical Company.