Carlos M. Villa

Genetic Programming Transforms in Linear Regression Situations

The chapter summarizes the use of Genetic Programming (GP) inMultiple Linear Regression (MLR) to address multicollinearity and Lack of Fit (LOF). The basis of the proposed method is applying appropriate input transforms (model respecification) that deal with these issues while preserving the information content of the original variables. The transforms are selected from symbolic regression models with optimal trade-off between accuracy of prediction and expressional complexity, generated by multiobjective Pareto-front GP. The chapter includes a comparative study of the GP-generated transforms with Ridge Regression, a variant of ordinary Multiple Linear Regression, which has been a useful and commonly employed approach for reducing multicollinearity. The advantages of GP-generated model respecification are clearly defined and demonstrated. Some recommendations for transforms selection are given as well. The application benefits of the proposed approach are illustrated with a real industrial application in one of the broadest empirical modeling areas in manufacturing - robust inferential sensors. The chapter contributes to increasing the awareness of the potential of GP in statistical model building by MLR.

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.

Symbolic regression in multicollinearity problems

In this paper the potential of GP-generated symbolic regression for alleviating multicollinearity problems in multiple regression is presented with a case study in an industrial setting. The main advantage of this approach is the potential to produce a simple and stable polynomial model in terms of the original variables.

Symbolic Regression Model Comparison Approach Using Transmitted Variation

Model evaluation in symbolic regression generated by GP is of critical importance for successful industrial applications. Typically this model evaluation is achieved by a tradeoff between model complexity and R 2. The chapter introduces a model comparison approach based on the transmission of variation from the inputs to the output. The approach is illustrated with three different data sets from real industrial applications.