Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes
This work describes a novel nonparametric identification method for estimating impulse responses of the general two-input single-output linear system with its target application to the individualization of an empirical model of type 1 diabetes. The proposed algorithm is based on correlation function...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9912406/ |
| _version_ | 1798021785395920896 |
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| author | Martin Dodek Eva Miklovicova Marian Tarnik |
| author_facet | Martin Dodek Eva Miklovicova Marian Tarnik |
| author_sort | Martin Dodek |
| collection | DOAJ |
| description | This work describes a novel nonparametric identification method for estimating impulse responses of the general two-input single-output linear system with its target application to the individualization of an empirical model of type 1 diabetes. The proposed algorithm is based on correlation functions and the derived generalization of the Wiener-Hopf equation for systems with two inputs, while taking the stochastic properties of the output measurements into account. Ultimately, this approach to solving the deconvolution problem can be seen as an alternative to widely used prediction error methods. To estimate the impulse response coefficients, the generalized least squares method was used in order to reflect nonuniform variances and nonzero covariances of the stochastic estimate of the cross-correlation functions, hence yielding the minimum variance estimator. Estimate regularization strategies were also involved, while three different types of penalties were applied. The combination of smoothing, stability, and causality regularization was proposed to improve the general validity of the estimate and also to lower its variance. The findings of this identification method are meant to be applied within an eventual predictive control synthesis for the artificial pancreas, so a procedure for transforming the nonparametric model into the transfer function-based parametric model was also described. A discussion on the results of a comprehensive simulation-based experiment concludes the paper. |
| first_indexed | 2024-04-11T17:20:22Z |
| format | Article |
| id | doaj.art-913c64c67ef14f7f93875743a2a6abbe |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T17:20:22Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-913c64c67ef14f7f93875743a2a6abbe2022-12-22T04:12:31ZengIEEEIEEE Access2169-35362022-01-011010636910638510.1109/ACCESS.2022.32124359912406Correlation Method for Identification of a Nonparametric Model of Type 1 DiabetesMartin Dodek0https://orcid.org/0000-0002-4118-4673Eva Miklovicova1https://orcid.org/0000-0002-4040-4697Marian Tarnik2Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, SlovakiaFaculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, SlovakiaFaculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, SlovakiaThis work describes a novel nonparametric identification method for estimating impulse responses of the general two-input single-output linear system with its target application to the individualization of an empirical model of type 1 diabetes. The proposed algorithm is based on correlation functions and the derived generalization of the Wiener-Hopf equation for systems with two inputs, while taking the stochastic properties of the output measurements into account. Ultimately, this approach to solving the deconvolution problem can be seen as an alternative to widely used prediction error methods. To estimate the impulse response coefficients, the generalized least squares method was used in order to reflect nonuniform variances and nonzero covariances of the stochastic estimate of the cross-correlation functions, hence yielding the minimum variance estimator. Estimate regularization strategies were also involved, while three different types of penalties were applied. The combination of smoothing, stability, and causality regularization was proposed to improve the general validity of the estimate and also to lower its variance. The findings of this identification method are meant to be applied within an eventual predictive control synthesis for the artificial pancreas, so a procedure for transforming the nonparametric model into the transfer function-based parametric model was also described. A discussion on the results of a comprehensive simulation-based experiment concludes the paper.https://ieeexplore.ieee.org/document/9912406/Correlation functiongeneralized least squares methodminimum variance estimatemultiple-input single-output systemsnonparametric modelregularization |
| spellingShingle | Martin Dodek Eva Miklovicova Marian Tarnik Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes IEEE Access Correlation function generalized least squares method minimum variance estimate multiple-input single-output systems nonparametric model regularization |
| title | Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes |
| title_full | Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes |
| title_fullStr | Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes |
| title_full_unstemmed | Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes |
| title_short | Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes |
| title_sort | correlation method for identification of a nonparametric model of type 1 diabetes |
| topic | Correlation function generalized least squares method minimum variance estimate multiple-input single-output systems nonparametric model regularization |
| url | https://ieeexplore.ieee.org/document/9912406/ |
| work_keys_str_mv | AT martindodek correlationmethodforidentificationofanonparametricmodeloftype1diabetes AT evamiklovicova correlationmethodforidentificationofanonparametricmodeloftype1diabetes AT mariantarnik correlationmethodforidentificationofanonparametricmodeloftype1diabetes |