This manuscript describes a methodology for measuring the first-order Volterra kernel of a discrete-time nonlinear system, that is, the impulse response for small signal amplitudes of the nonlinear system. In the proposed approach, multiple linear identifications are performed using the same excitation signal multiplied by different gains, and the first-order Volterra kernel is obtained from a polynomial interpolation of the measured values. Any linear identification method proposed in the literature can be used with this approach. The proposed approach is a multiple variance (MV) method that, in contrast to all other MV methods, aims to estimate one of the kernels of the Volterra model, the first-order kernel, with high precision. The manuscript discusses the proposed methodology, determines the mean square deviation (MSD) due to noise of the measured coefficients, and the value of the optimal gains that minimize the MSD. Remarkably, it is shown in the manuscript that the optimal gains assume only a reduced set of values that depends on the order of nonlinearity. The optimal number of measurements is also determined. The conditions under which the proposed methodology is more convenient than the classical linear methods are discussed. The experimental results demonstrate the proposed methodology and its strengths.
A Polynomial Multiple Variance Method for Impulse Response Measurement
Alberto Carini
;Riccardo Forti;
2023-01-01
Abstract
This manuscript describes a methodology for measuring the first-order Volterra kernel of a discrete-time nonlinear system, that is, the impulse response for small signal amplitudes of the nonlinear system. In the proposed approach, multiple linear identifications are performed using the same excitation signal multiplied by different gains, and the first-order Volterra kernel is obtained from a polynomial interpolation of the measured values. Any linear identification method proposed in the literature can be used with this approach. The proposed approach is a multiple variance (MV) method that, in contrast to all other MV methods, aims to estimate one of the kernels of the Volterra model, the first-order kernel, with high precision. The manuscript discusses the proposed methodology, determines the mean square deviation (MSD) due to noise of the measured coefficients, and the value of the optimal gains that minimize the MSD. Remarkably, it is shown in the manuscript that the optimal gains assume only a reduced set of values that depends on the order of nonlinearity. The optimal number of measurements is also determined. The conditions under which the proposed methodology is more convenient than the classical linear methods are discussed. The experimental results demonstrate the proposed methodology and its strengths.File | Dimensione | Formato | |
---|---|---|---|
2023 SIGPRO Carini Forti Orcioni.pdf
Open Access dal 04/02/2025
Tipologia:
Bozza finale post-referaggio (post-print)
Licenza:
Copyright Editore
Dimensione
571.1 kB
Formato
Adobe PDF
|
571.1 kB | Adobe PDF | Visualizza/Apri |
1-s2.0-S0165168423000348-main.pdf
accesso aperto
Tipologia:
Documento in Versione Editoriale
Licenza:
Creative commons
Dimensione
2.18 MB
Formato
Adobe PDF
|
2.18 MB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.