A correlation function for choosing time delays in phase portrait reconstructions

Kember, G.; Fowler, A. C.

doi:10.1016/0375-9601(93)90653-h

Cited by 63 publications

(40 citation statements)

References 8 publications

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“…Similar conclusions can be found in reference [10], while the proposed method here applies singular entropy instead of using linear SVF function. S and the comparisons with SVF method.…”

Section: 1supporting

confidence: 83%

“…Martinerie considered that it's more meaningful to estimate m and L simultaneously with a time window [9], and Kember proposed the recipe of correlation function termed singular value fraction (SVF) to choose proper time delay [10]. Such methods as high-order correlation [11], nonlinear correlation functions [12], and singular value spectrum entropy [13] are also proposed to overcome the deficiency of autocorrelation function.…”

Section: Introductionmentioning

confidence: 99%

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Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method

2016

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Abstract.The method of Delays is commonly used in state space reconstruction of chaotic time series, and the quality of attractor reconstruction of phase space is sensitive to the choice of embedding parameters, i.e. embedding dimension and time delay. In this paper, singular entropy (SE) is applied to choose the optimal time delay in reconstructed dynamical system, and the comparisons of relevant results are made with the correlation function method by using singular value fraction (SVF). The robustness of singular entropy algorithm is further discussed, and it shows the advantage of the proposed method. The reconstructed state of the system at each discrete time i is

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“…Similar conclusions can be found in reference [10], while the proposed method here applies singular entropy instead of using linear SVF function. S and the comparisons with SVF method.…”

Section: 1supporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method

2016

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“…A more computationally effective algorithm based on the expansion of the area for all pairwise planar projections of the embedded attractors is presented in [11]. Similar approaches based on the spatial properties of phase spaces include the average displacement method [10], the SVF method [12], and the wavering product [13] method.…”

Section: Introductionmentioning

confidence: 99%

Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

et al. 2018

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A simple and effective algorithm for the identification of optimal time delays based on the geometrical properties of the embedded attractor is presented in this paper. A time series synchronization measure based on optimal time delays is derived. The approach is based on the comparison of optimal time delay sequences that are computed for segments of the considered time series. The proposed technique is validated using coupled chaotic Rössler systems.

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“…where τ is the delay time and m is the embedding dimension [52]. Even if their values are not uniquely determined, these two parameters are crucial in the algorithm efficiency and result accuracy during the reconstruction state.…”

Section: State Reconstruction: Embedding Parametersmentioning

confidence: 99%

A Dynamic Fuzzy Controller to Meet Thermal Comfort by Using Neural Network Forecasted Parameters as the Input

et al. 2014

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Heating, ventilating and air-conditioning (HVAC) systems are typical non-linear time-variable multivariate systems with disturbances and uncertainties. In this paper, an approach based on a combined neuro-fuzzy model for dynamic and automatic regulation of indoor temperature is proposed. The proposed artificial neural network performs indoor temperatures forecasts that are used to feed a fuzzy logic control unit in order to manage the on/off switching of the HVAC system and the regulation of the inlet air speed. Moreover, the used neural network is optimized by the analytical calculation of the embedding parameters, and the goodness of this approach is tested through MATLAB. The fuzzy controller is driven by the indoor temperature forecasted by the neural network module and is able to adjust the membership functions dynamically, since thermal comfort is a very subjective factor and may vary even in the same subject. The paper shows some experimental results, through a real implementation in an embedded prototyping board, of the proposed approach in terms of the evolution of the inlet air speed injected by the fan coils, the indoor air temperature forecasted by the neural network model and the adjusting of the membership functions after receiving user feedback.

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A correlation function for choosing time delays in phase portrait reconstructions

Cited by 63 publications

References 8 publications

Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method

Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method

Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

A Dynamic Fuzzy Controller to Meet Thermal Comfort by Using Neural Network Forecasted Parameters as the Input

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