An expectation–maximization algorithm for spectral reconstruction under the spectral hard model
Indirect Hard Modeling (IHM) is a physics-based evaluation method for the quantitative analysis of fluid compositions using spectroscopic techniques such as Raman spectroscopy. In this approach, mixture spectra are represented as a superposition of pure substance models, with each component describe...
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| Published in: | Chemometrics and intelligent laboratory systems Vol. 267; p. 105518 |
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| Abstract | Indirect Hard Modeling (IHM) is a physics-based evaluation method for the quantitative analysis of fluid compositions using spectroscopic techniques such as Raman spectroscopy. In this approach, mixture spectra are represented as a superposition of pure substance models, with each component described by a sum of parameterized peak functions. Nevertheless, the accuracy of the compositions prediction depends critically on user decisions regarding both the number of peak functions and the specific parameter adjustments employed. In this work, we apply an expectation–maximization (EM) based algorithm for generating spectral reconstructions of pure substance models that does not require the pre-specification of the number of peaks or any initial values. The efficient and fast performance of the used EM algorithm enables the fit of a given spectrum for an unknown number of peaks, based on a model selection criterion. In simulation studies, we demonstrate that this approach can recognize the true underlying function in settings of high noise, peak overlapping and background signals, yielding reliable results. In a validation study, the algorithm was tested using experimental data. It was integrated into an Indirect Hard Modeling framework and applied to three chemical test systems. The quality of the obtained results were in the range of other automated IHM model generating approaches while significantly reducing both time and computational effort.
•User-independent model generation for spectral evaluation using Indirect Hard Modeling.•Efficient and robust algorithm for generating pure substance models.•Automated modeling without specifying initial values.•Statistic based approach for spectral reconstruction. |
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| AbstractList | Indirect Hard Modeling (IHM) is a physics-based evaluation method for the quantitative analysis of fluid compositions using spectroscopic techniques such as Raman spectroscopy. In this approach, mixture spectra are represented as a superposition of pure substance models, with each component described by a sum of parameterized peak functions. Nevertheless, the accuracy of the compositions prediction depends critically on user decisions regarding both the number of peak functions and the specific parameter adjustments employed. In this work, we apply an expectation–maximization (EM) based algorithm for generating spectral reconstructions of pure substance models that does not require the pre-specification of the number of peaks or any initial values. The efficient and fast performance of the used EM algorithm enables the fit of a given spectrum for an unknown number of peaks, based on a model selection criterion. In simulation studies, we demonstrate that this approach can recognize the true underlying function in settings of high noise, peak overlapping and background signals, yielding reliable results. In a validation study, the algorithm was tested using experimental data. It was integrated into an Indirect Hard Modeling framework and applied to three chemical test systems. The quality of the obtained results were in the range of other automated IHM model generating approaches while significantly reducing both time and computational effort.
•User-independent model generation for spectral evaluation using Indirect Hard Modeling.•Efficient and robust algorithm for generating pure substance models.•Automated modeling without specifying initial values.•Statistic based approach for spectral reconstruction. |
| ArticleNumber | 105518 |
| Author | Kasterke, Marvin Kateri, Maria Kaufmann, Lea Brands, Thorsten |
| Author_xml | – sequence: 1 givenname: Marvin orcidid: 0000-0002-5984-6647 surname: Kasterke fullname: Kasterke, Marvin email: marvin.kasterke@ltt.rwth-aachen.de organization: Institute of Technical Thermodynamics, RWTH Aachen University, Germany – sequence: 2 givenname: Lea surname: Kaufmann fullname: Kaufmann, Lea organization: Institute of Statistics, RWTH Aachen University, Germany – sequence: 3 givenname: Maria surname: Kateri fullname: Kateri, Maria organization: Institute of Statistics, RWTH Aachen University, Germany – sequence: 4 givenname: Thorsten surname: Brands fullname: Brands, Thorsten organization: Institute of Technical Thermodynamics, RWTH Aachen University, Germany |
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| Cites_doi | 10.1016/S0003-2670(03)00944-9 10.1016/j.aca.2013.12.002 10.1016/S0584-8547(03)00037-5 10.1111/j.2517-6161.1977.tb01600.x 10.1214/aos/1176344136 10.1021/acs.iecr.7b03230 10.1016/j.fluid.2025.114344 10.1016/j.chemolab.2021.104419 10.1016/S0024-4937(00)00043-8 10.1366/0003702041655368 10.1016/j.chemolab.2007.11.004 10.1016/j.chemolab.2020.104076 10.1016/j.fluid.2018.08.006 10.1016/j.csda.2019.106846 10.1016/j.fluid.2022.113718 10.2174/2213385203666150219231836 10.1016/j.fluid.2014.08.032 |
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| Keywords | Raman spectroscopy Indirect hard modeling EM algorithm Probabilistic mixture model Spectral evaluation |
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