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Wu Y, Peng S, Xie Q, et al. Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra. Spectrochim Acta A Mol Biomol Spectrosc. 2018;206:147-153doi: 10.1016/j.saa.2018.08.002.
Wu, Y., Peng, S., Xie, Q., & Xu, P. (2019). Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra. Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy, 206147-153. https://doi.org/10.1016/j.saa.2018.08.002
Wu, Yifan, et al. "Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra." Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy vol. 206 (2019): 147-153. doi: https://doi.org/10.1016/j.saa.2018.08.002
Wu Y, Peng S, Xie Q, Xu P. Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra. Spectrochim Acta A Mol Biomol Spectrosc. 2019 Jan 05;206:147-153. doi: 10.1016/j.saa.2018.08.002. Epub 2018 Aug 04. PMID: 30099311.
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Spectrochim Acta A Mol Biomol Spectrosc. 2019 Jan 05;206:147-153. doi: 10.1016/j.saa.2018.08.002. Epub 2018 Aug 04.

Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra.

Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy

Yifan Wu, Silong Peng, Qiong Xie, Pengcheng Xu

Affiliations

  1. Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100190, China.
  2. Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100190, China. Electronic address: [email protected].
  3. Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China.
  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China.

PMID: 30099311 DOI: 10.1016/j.saa.2018.08.002

Abstract

When using spectroscopic instrumentation for quantitative analysis of mixture, spectral intensity non-linearity and peak shift make it challenging for building calibration model. In this study, we investigated the performance of a nonlinear model, namely nonlinear least squares with local polynomial interpolation (NLSLPI). In NLSLPI, the parameters to be optimized are the concentrations of the components. Levenberg-Marquardt (L-M) method is used to solve the nonlinear-least-squares optimization problem and local polynomial interpolation is used to generate the nonlinear function for each component. We tested the robustness of NLSLPI on a computer-simulation dataset. We also compared NLSLPI, in terms of RMSEP, to partial least squares (PLS), classical least squares (CLS) and piecewise classical least squares (PCLS) on a real-world dataset. Experimental results demonstrate the effectiveness of the proposed method.

Copyright © 2018 Elsevier B.V. All rights reserved.

Keywords: Local polynomial interpolation; Nonlinear least squares; Quantitative analysis; Spectroscopy

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