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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

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TLDR
In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract
A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

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Journal ArticleDOI

Cosine window-based boundary processing method for EMD and its application in rubbing fault diagnosis

TL;DR: Simulative and experimental studies verified that the proposed method can enormously decrease the boundary distortion of EMD and is useful in rubbing fault diagnosis of rotor system.
Journal ArticleDOI

Successive variational mode decomposition

TL;DR: In this paper, a new method is introduced, namely successive variational mode decomposition (SVMD), which extracts the modes successively and does not need to know the number of modes.
Journal ArticleDOI

Remaining useful life and state of health prediction for lithium batteries based on empirical mode decomposition and a long and short memory neural network

TL;DR: This work combined the empirical mode decomposition (EMD) method and backpropagation long-short-term memory (B-LSTM) neural network (NN) to develop SOH estimation and RUL prediction models that have high robustness, good accuracy, and applicability.
Journal ArticleDOI

Recent Developments in Chaotic Time Series Analysis

TL;DR: Two issues are addressed: the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and the Hilbert transform methodology for chao...
References
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Journal ArticleDOI

Deterministic nonperiodic flow

TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Book

Linear and Nonlinear Waves

G. B. Whitham
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Book

RANDOM DATA Analysis and Measurement Procedures

TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.

Theory of communication

Dennis Gabor
Journal ArticleDOI

Mathematical analysis of random noise

TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
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