Nonlinear Parametric Identification Using Chaotic Data

Wouw, Nathan van de; Verbeek, G.; Campen, D.H. van

doi:10.1177/107754639500100303

Cited by 11 publications

(5 citation statements)

References 9 publications

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“…on the interval of data that is considered to be approximately periodic. The collection of unstable periodic orbits might be used for determining determinism, estimating the fractal dimension [19] or Lyapunov exponents [16], or identifying system parameters [20][21][22][23].…”

Section: Characterizing the Data In The Reconstructed Phase Spacementioning

confidence: 99%

Fractional Derivatives Applied to Phase-Space Reconstructions

Feeny

Lin

2004

Nonlinear Dyn

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The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.

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Section: Characterizing the Data In The Reconstructed Phase Spacementioning

confidence: 99%

Fractional Derivatives Applied to Phase-Space Reconstructions

Feeny

Lin

2004

Nonlinear Dyn

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“…The simplest form of objective function minimizes the Euclidean norm of the equation 37) where n is the number of DOF and m is the number of measured frequencies. The objective function J is minimized by solving 38) or…”

Section: Equation Error Methodsmentioning

confidence: 99%

“…System identification techniques based on time domain data have been developed for weakly nonlinear systems [37]. The NNUM is, to the author's knowledge, the first to use frequency response data to estimate the parameters of the model.…”

Section: Nonlinear Systemsmentioning

confidence: 99%

On model updating using neural networks

Atalla

Inman

1996

Adaptive Structures Forum

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Accurate models are necessary in critical applications. Key parameters in dynamic systems often change during their life cycle due to repair and replacement of parts or environmental changes. This dissertation presents a new approach to update system models, accounting for these changes. The approach uses frequency domain data and a neural network to produce estimates of the parameters being updated, yielding a model representative of the measured data.Current iterative methods developed to solve the model updating problem rely on minimization techniques to find the set of model parameters that yield the best match between experimental and analytical responses. Since the minimization procedure requires a fair amount of computation time, it makes the existing techniques infeasible for use as part of an adaptive control scheme correcting the model parameters as the system changes. They also require either mode shape expansion or model reduction before they can be applied, introducing errors in the procedure. Furthermore, none of the existing techniques has been applied to nonlinear systems.The neural network estimates the parameters being updated quickly and accurately without the need to measure all degrees of freedom of the system. This avoids the use of mode shape expansion or model reduction techniques, and allows for its implementation as part of an adaptive control scheme. The proposed technique is also capable of updating weakly nonlinear systems.Numerical simulations and experimental results show that the proposed method has good accuracy and generalization properties, and it is therefore, a suitable alternative for the solution of the model updating problem of this class of systems. iv I also wish to thank the following people for helping, supporting and encouraging me during these years:

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“…First we sought recurrences used for extracting unstable periodic orbits (UPOs) [26][27][28][29][30][31]. Recurrences are defined as instances for which |y n −y n+k | < ǫ, where y m is the reconstructed vector, and ǫ is a tolerance chosen by prescription.…”

Section: Characterization Of the Datamentioning

confidence: 99%

Fractional derivative reconstruction of forced oscillators

2008

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Fractional derivatives are applied in the reconstruction, from a single observable, of the dynamics of a Duffing oscillator and a two-well experiment. The fractional derivatives of time series data are obtained in the frequency domain. The derivative fraction is evaluated using the average mutual information between the observable and its fractional derivative. The ability of this reconstruction method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and fractal dimensions. The reconstruction is compared to the true phase space and the delay reconstruction in order to assess the reconstruction parameters and the quality of results.

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Nonlinear Parametric Identification Using Chaotic Data

Cited by 11 publications

References 9 publications

Fractional Derivatives Applied to Phase-Space Reconstructions

Fractional Derivatives Applied to Phase-Space Reconstructions

On model updating using neural networks

Fractional derivative reconstruction of forced oscillators

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