Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials
System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra s...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Electronics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-9292/11/19/3100 |
| _version_ | 1797479774609735680 |
|---|---|
| author | Michele Alessandrini Laura Falaschetti Giorgio Biagetti Paolo Crippa Claudio Turchetti |
| author_facet | Michele Alessandrini Laura Falaschetti Giorgio Biagetti Paolo Crippa Claudio Turchetti |
| author_sort | Michele Alessandrini |
| collection | DOAJ |
| description | System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives (NARX, NARMA). Different nonlinear estimators can be used for those algorithms, such as polynomials, neural networks or wavelet networks. This paper uses a different approach, named particle-Bernstein polynomials, as an estimator for SI. Moreover, unlike the mentioned algorithms, this approach does not operate in the time domain but rather in the spectral components of the signals through the use of the discrete Karhunen–Loève transform (DKLT). Some experiments are performed to validate this approach using a publicly available dataset based on ground vibration tests recorded from a real F-16 aircraft. The experiments show better results when compared with some of the traditional algorithms, especially for large, heterogeneous datasets such as the one used. In particular, the absolute error obtained with the prosed method is 63% smaller with respect to NARX and from 42% to 62% smaller with respect to various artificial neural network-based approaches. |
| first_indexed | 2024-03-09T21:51:38Z |
| format | Article |
| id | doaj.art-35e6e9b92f694100b63907e332600560 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-09T21:51:38Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-35e6e9b92f694100b63907e3326005602023-11-23T20:06:18ZengMDPI AGElectronics2079-92922022-09-011119310010.3390/electronics11193100Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein PolynomialsMichele Alessandrini0Laura Falaschetti1Giorgio Biagetti2Paolo Crippa3Claudio Turchetti4Department of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche 12, I-60131 Ancona, ItalyDepartment of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche 12, I-60131 Ancona, ItalyDepartment of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche 12, I-60131 Ancona, ItalyDepartment of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche 12, I-60131 Ancona, ItalyDepartment of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche 12, I-60131 Ancona, ItalySystem identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives (NARX, NARMA). Different nonlinear estimators can be used for those algorithms, such as polynomials, neural networks or wavelet networks. This paper uses a different approach, named particle-Bernstein polynomials, as an estimator for SI. Moreover, unlike the mentioned algorithms, this approach does not operate in the time domain but rather in the spectral components of the signals through the use of the discrete Karhunen–Loève transform (DKLT). Some experiments are performed to validate this approach using a publicly available dataset based on ground vibration tests recorded from a real F-16 aircraft. The experiments show better results when compared with some of the traditional algorithms, especially for large, heterogeneous datasets such as the one used. In particular, the absolute error obtained with the prosed method is 63% smaller with respect to NARX and from 42% to 62% smaller with respect to various artificial neural network-based approaches.https://www.mdpi.com/2079-9292/11/19/3100system identificationground vibrationnonlinear dynamic systemparticle-Bernstein polynomialsregression |
| spellingShingle | Michele Alessandrini Laura Falaschetti Giorgio Biagetti Paolo Crippa Claudio Turchetti Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials Electronics system identification ground vibration nonlinear dynamic system particle-Bernstein polynomials regression |
| title | Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials |
| title_full | Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials |
| title_fullStr | Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials |
| title_full_unstemmed | Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials |
| title_short | Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials |
| title_sort | nonlinear dynamic system identification in the spectral domain using particle bernstein polynomials |
| topic | system identification ground vibration nonlinear dynamic system particle-Bernstein polynomials regression |
| url | https://www.mdpi.com/2079-9292/11/19/3100 |
| work_keys_str_mv | AT michelealessandrini nonlineardynamicsystemidentificationinthespectraldomainusingparticlebernsteinpolynomials AT laurafalaschetti nonlineardynamicsystemidentificationinthespectraldomainusingparticlebernsteinpolynomials AT giorgiobiagetti nonlineardynamicsystemidentificationinthespectraldomainusingparticlebernsteinpolynomials AT paolocrippa nonlineardynamicsystemidentificationinthespectraldomainusingparticlebernsteinpolynomials AT claudioturchetti nonlineardynamicsystemidentificationinthespectraldomainusingparticlebernsteinpolynomials |