Computing correlation integral with the Euclidean distance normalized by the embedding dimension

Ning, Taikang; Tranquillo, Joe; Grare, Adam; Saraf, Ankita

doi:10.1109/icosp.2008.4697707

Cited by 7 publications

(2 citation statements)

References 18 publications

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“…Note that each variable is normalized and the sum is divided by the number of variables. Thus, this measure is expected to be less sensitive to the dimensionality of the decision variable space and to the domain of the variables (Ning et al, 2008). In the first iteration, the S multi-set is empty, so the DCS of each individual is infinity.…”

Section: Replacement Phase Of Vsd-moeamentioning

confidence: 99%

VSD-MOEA: A Dominance-Based Multiobjective Evolutionary Algorithm with Explicit Variable Space Diversity Management

Castillo

Segura

Coello

2022

Evolutionary Computation

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Most state-of-the-art Multi-Objective Evolutionary Algorithms (MOEAs) promote the preservation of diversity of objective function space but neglect the diversity of decision variable space. The aim of this paper is to show that explicitly managing the amount of diversity maintained in the decision variable space is useful to increase the quality of MOEAs when taking into account metrics of the objective space. Our novel Variable Space Diversity based MOEA (VSD-MOEA) explicitly considers the diversity of both decision variable and objective function space. This information is used with the aim of properly adapting the balance between exploration and intensification during the optimization process. Particularly, at the initial stages, decisions made by the approach are more biased by the information on the diversity of the variable space, whereas it gradually grants more importance to the diversity of objective function space as the evolution progresses. The latter is achieved through a novel density estimator. The new method is compared with state-of-art MOEAs using several benchmarks with two and three objectives. This novel proposal yields much better results than state-of-the-art schemes when considering metrics applied on objective function space, exhibiting a more stable and robust behavior.

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Section: Replacement Phase Of Vsd-moeamentioning

confidence: 99%

VSD-MOEA: A Dominance-Based Multiobjective Evolutionary Algorithm with Explicit Variable Space Diversity Management

Castillo

Segura

Coello

2022

Evolutionary Computation

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“…The correlation integral function of our LP filtered signal y * p is computed using the Grassberger-Procaccia method improved by [46] who normalize the Euclidean distance in Eq. (18) by the embedding dimension m. Figure 13 shows the resulting correlation integral function in logarithmic scale.…”

Section: Correlation Dimensionmentioning

confidence: 99%

Chaotic dynamics of large-scale structures in a turbulent wake

et al. 2017

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The dynamics of a 3D bimodal turbulent wake downstream a square-back Ahmed body are experimentally studied in a wind-tunnel through high-frequency wall pressure probes mapping the rear of the model and a horizontal 2D velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall pressure foot-print. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low frequencies dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well defined attractors. The low frequencies dynamics associated to the large-scale structures are then analyzed. The largest Lyapunov exponent is first estimated, leading to a low positive value characteristic of strange attractors and weak chaotic systems. Afterwards, analyzing the autocorrelation function of the time-series, we compute the correlation dimension, larger than two. The signal is finally transformed and analyzed as a telegraph signal showing that its dynamics correspond to a quasi-random telegraph signal. This is the first demonstration that the low frequencies dynamics of a turbulent 3D wake are not a purely stochastic process but rather a weak chaotic process exhibiting strange attractors. From the flowcontrol point of view, it also opens the path to more simple closed-loop flow control strategies aiming at the stabilization of the wake and the control of the dynamics of the wake barycenter.

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