An efficient nonlinear cardinal B-spline model for high tide forecasts at the Venice Lagoon

Wei, Hua‐Liang; Billings, S.A.

doi:10.5194/npg-13-577-2006

Cited by 34 publications

(17 citation statements)

References 27 publications

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“…Sobey (2006) shown that the normal mode decomposition approach is a useful analysis methodology in the evaluation of storm tide and tsunami hazard at a coastal site. During the last years, the techniques based on wavelet decompositions (Ró _ zyński and Reeve 2005), cardinal B-spline basic functions (Wei and Billings 2006), artificial neural networks (Chang and Lin 2006) were used in the investigations of water level variations at different time scales. Among these methods, the chaotic time series analysis of water level occupies a fitting place.…”

Section: Introductionmentioning

confidence: 99%

Signatures of low-dimensional chaos in hourly water level measurements at coastal site of Mariupol, Ukraine

Khokhlov

Глушков

Loboda

et al. 2007

Stoch Environ Res Risk Assess

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Variations of water levels in ports and estuaries are important for ship guidance and navigation and are influenced by a variety of factors. The hourly data that was collected from the coastal site at the Port of Mariupol, Ukraine during January-December 2005 were analysed with an objective to reveal features of chaotic behaviour. The concepts and methods of chaos theory (average mutual information, correlation dimension, false nearest neighbours, Lyapunov exponents) were applied. The manifestation of low-dimensional chaos was found in the time series. The possibility of nonlinear prediction was concluded.

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Section: Introductionmentioning

confidence: 99%

Signatures of low-dimensional chaos in hourly water level measurements at coastal site of Mariupol, Ukraine

Khokhlov

Глушков

Loboda

et al. 2007

Stoch Environ Res Risk Assess

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“…are given in Table 1 ( Wei and Billings, 2006b). For detailed discussions on cardinal B-splines and the associated wavelets, see Chui (1992).…”

Section: The Multi-wavelet Basis Functionsmentioning

confidence: 99%

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Wei

Billings

Liu

2010

IJMIC

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Abstract:A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The timevarying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method.

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“…For example, cardinal B-splines are an important class of basis functions and can be used for multi-resolution wavelet decompositions (Ahuja, Lertrattanapanich, & Bose, 2005). The B-spline function of mth order can be computed recursively according to de Boor (1978) and Chui and Wang (1992), and several low-order B-spline functions are provided in Wei and Billings (2006). Then the φ m l (·) can be expressed from the mth-order Bspline (B m ) with the scale j and shift indices l:…”

Section: Identification Of a Tv-narx Modelmentioning

confidence: 99%

Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models

Wei

Billings

2013

International Journal of Systems Science

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This paper introduces a new approach for nonlinear and non-stationary (time-varying) system identification based on timevarying nonlinear autoregressive moving average with exogenous variable (TV-NARMAX) models. The challenging model structure selection and parameter tracking problems are solved by combining a multiwavelet basis function expansion of the time-varying parameters with an orthogonal least squares algorithm. Numerical examples demonstrate that the proposed approach can track rapid time-varying effects in nonlinear systems more accurately than the standard recursive algorithms. Based on the identified time domain model, a new frequency domain analysis approach is introduced based on a time-varying generalised frequency response function (TV-GFRF) concept, which enables the analysis of nonlinear, non-stationary systems in the frequency domain. Features in the TV-GFRFs which depend on the TV-NARMAX model structure and time-varying parameters are investigated. It is shown that the high-dimensional frequency features can be visualised in a low-dimensional time-frequency space.

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An efficient nonlinear cardinal B-spline model for high tide forecasts at the Venice Lagoon

Abstract: Abstract. An efficient class of nonlinear models, constructed using cardinal B-spline (CBS) basis functions, are proposed for high tide forecasts at the Venice lagoon. Accurate short term predictions of high tides in the lagoon can easily be calculated using the proposed CBS models.

Cited by 34 publications

References 27 publications

Signatures of low-dimensional chaos in hourly water level measurements at coastal site of Mariupol, Ukraine

Signatures of low-dimensional chaos in hourly water level measurements at coastal site of Mariupol, Ukraine

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models

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