Identification of a class of nonlinear systems under stationary non-Gaussian excitation

Ralston, Jonathon; Zoubir, Abdelhak M.; Boashash, Boualem

doi:10.1109/78.558490

Cited by 41 publications

(16 citation statements)

References 22 publications

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“…Fourier transforming (7) with respect to v leads to Cyx (w) = G(w)Cxx(w) + G2(w) f Cxxx(A, w)dA , (8) where the key result to note is that G2 (w) has separated from the integral term.8 This separability result does not occur for the kernels of the Volterra series,10'13 nor for any other non-trivial subset of the Volterra series in the non-Gaussian case. The form of the Hammerstein model is thus appropriate.…”

Section: Stationary Non-gaussian Excitationmentioning

confidence: 99%

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<title>Identification of a class of time-invariant and time-varying nonlinear systems under non-Gaussian excitation</title>

1995

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We consider the identification of nonlinear systems when the excitation is a non-Gaussian process. Closed form expressions are found for a class of nonlinear time-invariant as well as for time-varying systems which are excited by stationary and non-stationary inputs, respectively. The nonlinear model used represents a subset of the Volterra series, judiciously chosen so that closed form expressions can be resolved for non-Gaussian inputs. Nonlinear coherence functions are also derived in closed form. Estimation issues are discussed. Two examples are given to illustrate the general results.

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Section: Stationary Non-gaussian Excitationmentioning

confidence: 99%

“…Using the sliced cumulant notation as in (5), we have for (8) and (9) the equivalent representations…”

Section: Stationary Non-gaussian Excitationmentioning

confidence: 99%

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<title>Identification of a class of time-invariant and time-varying nonlinear systems under non-Gaussian excitation</title>

1995

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“…Such systems have also been considered, for example, in [2], as well as in [3], where the model is referred to as Manuscript [3], and distillation columns [4]. Also worth mentioning are single-sided electromagnetically controlled oscillators [5].…”

Section: Introductionmentioning

confidence: 99%

Design of Truncated Maximum Length Ternary Signals Where Their Squared Versions Have Uniform Even Harmonics

Tan

2007

IEEE Trans. Automat. Contr.

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The design of pseudo-random maximum length (PRML) ternary signals with properties suitable for identification of generalized quadratic Hammerstein models is considered. For such an application, it is desirable for the signal to have odd harmonics uniform and even harmonics suppressed, with its squared version having odd harmonics suppressed and even harmonics uniform. To date, the only class of signal known to possess such harmonic properties comprises of PRML ternary signals based on Galois field GF(3), and its extension fields. In this note, theoretical conditions for a PRML signal to possess these properties are derived and imposed on the design of signals based on higher odd fields to generate truncated PRML signals that fulfill the required specifications.Index Terms-Frequency domain design, Hammerstein models, maximum length signals, perturbation signals, pseudo-random signals, system identification.

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“…Hammerstein series are composed of many conventional Hammerstein models in parallel, and therefore each branch comprises a static polynomial nonlinearity followed by a linear dynamic system [1]. Hammerstein series model has the low parametric complexity and computational consumption of model extraction.…”

Section: Introductionmentioning

confidence: 99%

A Model of Second Order Hammerstein Series for Nonlinear System

Jin¹,

Lu²

2016

Advances in Computer Science Research

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Abstract. In this paper, modeling a weakly nonlinear system whose nonlinearity is up to the second order is studied. During this task a second order Hammerstein series model is used because it can lead to a trade-off between computational cost and generalization ability. To extract such model form measured input-output data, a nonparametric algorithm based on the minimum mean square error criterion is proposed. The polyspectrum up to order 4 is used to determine the Hammerstein kernels, while the input is a random multi-sine signal. Finally the proposed modeling method is validated on simulated system.

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Identification of a class of nonlinear systems under stationary non-Gaussian excitation

Cited by 41 publications

References 22 publications

<title>Identification of a class of time-invariant and time-varying nonlinear systems under non-Gaussian excitation</title>

<title>Identification of a class of time-invariant and time-varying nonlinear systems under non-Gaussian excitation</title>

Design of Truncated Maximum Length Ternary Signals Where Their Squared Versions Have Uniform Even Harmonics

A Model of Second Order Hammerstein Series for Nonlinear System

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