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| Naji, M. |
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| Mohamed, Tarek |
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| Ertürk, Emre |
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| Azevedo, Nuno Monteiro |
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Pintelon, Rik
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Publications (7/7 displayed)
- 2021Best Linear Time-Varying Approximation of a General Class of Nonlinear Time-Varying Systemscitations
- 2021An operando ORP-EIS study of the copper reduction reaction supported by thiourea and chlorides as electrorefining additivescitations
- 2020Local bending stiffness identification of beams using simultaneous Fourier-series fitting and shearography (vol 443, pg 764, 2019)
- 2019Local bending stiffness identification of beams using simultaneous Fourier-series fitting and shearographycitations
- 2010Odd random phase multisine EIS as a detection method for the onset of corrosion of coated steel
- 2007Practical aspects of continuous-time modelling from noisy observations
- 2004Electrochemical impedance spectroscopy in the presence of non-linear distortions and non-stationary behaviour Part I: theory and validation
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article
Best Linear Time-Varying Approximation of a General Class of Nonlinear Time-Varying Systems
Abstract
This article presents a method for estimating a linear time-varying approximation of a general class of nonlinear time-varying (NLTV) systems. It starts from noisy measurements of the response of the NLTV system to a special class of periodic excitation signals. These measurements are subject to measurement noise, process noise, and a trend. The proposed method is a two-step procedure. First, the disturbing noise variance is quantified. Next, using this knowledge, the linear time-varying dynamics are estimated together with the NLTV distortions. The latter are split into even and odd contributions. As a result, the signal-to-nonlinear-distortion ratio is quantified. It allows one to decide whether or not a linear approximation is justifiable for the application at hand. The two-step algorithm is fully automatic in the sense that the user only has to choose upper bounds on the number of basis functions used for modeling the response signal. The obtained linear time-varying approximation is the best in the sense that the difference between the actual nonlinear response and the response predicted by the linear approximation is uncorrelated with the input. Therefore, it is called the best linear time-varying approximation (BLTVA). Finally, the theory is validated on a simulation example and illustrated on two measurement examples: the crystallographic pitting corrosion of aluminum and copper electrorefining.