Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds

Applied Spectroscopy
Peng ShanLiang Tang

Abstract

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance predi...Continue Reading

References

Mar 16, 2000·Journal of Accident & Emergency Medicine·M J CoatesM R James
Oct 31, 2008·Talanta·Roberto Kawakami Harrop GalvãoTeresa Cristina Bezerra Saldanha
Feb 14, 2009·Applied Spectroscopy·Patrick J CutlerPaul J Gemperline
May 4, 2013·Analytica Chimica Acta·Sandeep SharmaWouter Saeys

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Methods Mentioned

BETA
infrared spectroscopy

Software Mentioned

LBFGS
Matlab
Windows 7
LM
TLSP

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