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Blind source separation in the context of deterministic signals
Published in Marcio Eisencraft, Romis Attux, Ricardo Suyama, Chaotic Signals in Digital Communications, 2018
Diogo C. Soriano, Ricardo Suyama, Rafael A. Ando, Romis Attux, Leonardo T. Duarte
More specifically, the recurrence plot is created by determining a binary distance matrix that indicates which states in the reconstructed attractor are closer (in terms of a threshold distance є) to one another. This can be performed by generating the reconstructed state x(k) and building an N × N matrix, where the element (i, j) will be a black dot (or a bit 1 from the binary alphabet (0, 1)) whenever x(i) is sufficiently close to x(j), i.e., whenever ||x(i) – x(j)|| < ε. Formally, the recurrence matrix Ri,j can be defined as [17] () Ri,j=Θ(ε−‖x(i)−x(j)‖),
Precast segmental bridge construction in seismic zones
Published in Fabio Biondini, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Resilience and Sustainability, 2012
Fabio Biondini, Dan M. Frangopol
where e is a threshold value representing the specific length scale of focus and |M| takes the Euclidean distance of the m-dimensional vector. By using the Heaviside function 0(·), the values of RjJ· are 1 or 0 depending on whether the distance between points x(i) and xj) is less than or greater than a threshold value e, respectively. A plot of the recurrence matrix is referred to as the recurrence plot. In the case of a single observed variable x(n) the familiar delay coordinate approach can be used. Delay coordinate reconstruction is the standard first step in most nonlinear time series analysis and proceeds by forming the reconstructed dynamics
Trend and seasonality features extraction with pre-trained CNN and recurrence plot
Published in International Journal of Production Research, 2023
Fernanda Strozzi, Rossella Pozzi
The Recurrence Plot (RP) calculates the recurrence of the time series in the state space and depicts this information through coloured points and lines in 2D images. The RP of time series has proven to bring to human sight features that are not visible for 1D series. Research has started applying together RP and CNN but little research, e.g. Li, Kang, and Li (2020) have considered the context of time series forecasting. Even though results are promising, these studies are few, do not cover the whole forecasting process, and often overlook alternative methods that could be easier to apply for practitioners.
Dynamic Characterization of a Ducted Inverse Diffusion Flame Using Recurrence Analysis
Published in Combustion Science and Technology, 2018
Uddalok Sen, Tryambak Gangopadhyay, Chandrachur Bhattacharya, Achintya Mukhopadhyay, Swarnendu Sen
where is the number of data points in the reconstructed phase space, is the Heaviside function, is the maximum distance between two points in the phase space that can be called recurrent, and is the sampling rate of data capturing. In the present work, the distance between two trajectories is calculated using the -norm. Hence, is a square symmetric matrix having only 0 and 1 as elements. For obtaining the recurrence plot from , the zeros are represented as white dots and the ones are represented as black dots. Since = 1, the principal diagonal of any recurrence plot is composed entirely of black dots and is commonly referred to as the line of identity (LOI). The recurrence plot for a periodic signal is composed of diagonal lines parallel to the LOI where the vertical (or horizontal) spacing between the lines represents the time period. A quasiperiodic system, however, is represented by lines parallel to the LOI having unequal vertical spacings (Zou, 2007). Disconnected short segments represent departure from periodicity due to noise or chaos, whereas vertical lines in the recurrence plot denote intermittent steady behavior or laminar states. Recurrence plots for random data, on the other hand, consists of black and white dots randomly dispersed on the plane. Recent studies have shown the usefulness of RQA in various diverse applications, such as flow regime identification in multiphase flow situations (Górski et al., 2015; Llop et al., 2015; Mosdorf and Górski, 2015), financial market analysis (Bastos and Caiado, 2011; Nakano et al., 2015), and biomedical systems (Schlenker et al., 2016; Yan et al., 2016), among others. Recurrence plots have also been used in combustion studies (Gotoda et al., 2015; Kabiraj et al., 2015; Kinugawa et al., 2016; Nair and Sujith, 2015b; Sen et al., 2016; Yang et al., 2015, 2016), revealing several interesting dynamical features. This calls for a similar analysis in the present study as well. In the present work, was chosen as 20% of the attractor size for constructing the recurrence plots.