System identification using associated linear equations

Feijoo, J.A. Vázquez; Worden, Keith; Stanway, R.

doi:10.1016/s0888-3270(03)00078-5

Cited by 29 publications

(15 citation statements)

References 3 publications

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“…In [14] the parameter estimation is accomplished using a simple circle-fitting (based on the Nyquist plot of the mobility). The modal constant is obtained from the circle diameter D as…”

Section: Parameter Estimation Of a Structural Duffing Oscillator Withmentioning

confidence: 99%

“…This implies that the diameter should also be affected by k 3 in order to keep A constant. From (14) and (22), it is to be expected that the diameter D changes as the ratio of the apparent natural frequencies:…”

Section: Parameter Estimation Of a Structural Duffing Oscillator Withmentioning

confidence: 99%

“…According to (10), the input to the second-order ALE is y 2 1 , as y 0 can be considered part of the input-dependent system (the general methodology is described in [14]). Testing the system at the linear limit of 2.55 MN, one can generate y 1 from the identified (26), together with the full response to the input x.…”

Section: Nonlinear Identificationmentioning

confidence: 99%

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Analysis and control of nonlinear systems with DC terms

et al. 2009

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Although nonlinear systems with a DC term are quite often found, very little work has been done about the important effects that the DC term produces on the nonlinear system response.Some work can be found based on NARMAX model identification-this work identifies the system by NARMAX models and from them obtains the Higher-order Frequency Response Functions (HFRFs). From the HFRFs, the effects of the DC term on the nonlinear system can be predicted. This paper represents an extension of such a work; but here, other parametric models are used: the Associated Linear Equations (ALEs). This allows identification of the system directly from the frequency domain and the direct observation of the effect of the DC term. Because the model is parametric, it arguably allows one to explain the nonlinear system behaviour in a physical way.Also in this paper, the ALE-based identification scheme is extended to systems with DC, and it is explained how to construct Volterra inverses for such systems with the objective of implementing an openloop control of nonlinear systems.Unlike the situation for systems without DC, the pre-inverse and post-inverse Volterra systems differ from each other. In fact, the DC in the post-inverse cannot be eliminated in all the cases. The inverse strategies are tested on two simulated nonlinear systems: a Duffing oscillator and a Hammerstein model.

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“…In [14] the parameter estimation is accomplished using a simple circle-fitting (based on the Nyquist plot of the mobility). The modal constant is obtained from the circle diameter D as…”

Section: Parameter Estimation Of a Structural Duffing Oscillator Withmentioning

confidence: 99%

Section: Parameter Estimation Of a Structural Duffing Oscillator Withmentioning

confidence: 99%

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Analysis and control of nonlinear systems with DC terms

et al. 2009

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“…Similarly, for nonlinear system which can be described by the polynomial type nonlinear model (28), when the system subjected to a harmonic input and the driving frequency F ω coincides with one of the resonant frequencies of a NOFRF of the system, the magnitude of this NOFRF will reach a maximum (resonance) at a high order harmonic of F ω .…”

Section: Physical Implication Of the Resonant Frequencies Of Nofrfsmentioning

confidence: 99%

Resonances and resonant frequencies for a class of nonlinear systems

Peng

Lang

Billings

2007

Journal of Sound and Vibration

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Abstract:Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems.The effects of damping on the resonances and resonant frequencies are also analyzed.These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model.

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“…However, from Equation (1.3) it can be seen that a GFRF is multidimensional [7] [8], and may become difficult to measure, display and interpret in practice. Feijoo, Worden and Stanway [11]- [12] demonstrated that the Volterra series can be described by a series of associated linear equations (ALEs) whose corresponding associated frequency response functions (AFRFs) are easier to analyze and interpret than the GFRFs. According to Equation (1.4), the NOFRF is that it is one dimensional, and thus allows the analysis of nonlinear systems to be implemented in a convenient manner similar to the analysis of linear systems.…”

Section: The Concept Of Nonlinear Output Frequency Response Functionsmentioning

confidence: 99%

Non-linear output frequency response functions for multi-input non-linear Volterra systems

Peng

Lang

Billings

2007

International Journal of Control

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Abstract:The concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the nonlinear systems that can be described by a multi-input Volterra series model. A new algorithm is also developed to determine the output frequency range of nonlinear systems from the frequency range of the inputs. These results allow the concept of NOFRFs to be applied to a wide range of engineering systems. The phenomenon of the energy transfer in a two degree of freedom nonlinear system is studied using the new concepts to demonstrate the significance of the new results.

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System identification using associated linear equations

Cited by 29 publications

References 3 publications

Analysis and control of nonlinear systems with DC terms

Analysis and control of nonlinear systems with DC terms

Resonances and resonant frequencies for a class of nonlinear systems

Non-linear output frequency response functions for multi-input non-linear Volterra systems

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