Embedding Dimension Of Time Series Research Articles

Reconstruction of Phase Space and Eigenvalue Decomposition from a Biological Time Series: A Malayalam Speech Signal Case Study

Our objective is to describe the speech production system from a non-linear physiological system perspective and reconstruct the attractor from the experimental speech data. Mutual information method is utilized to find out the time delay for embedding. The False Nearest Neighbour (FNN) method and Principal Component Analysis (PCA) method are used for optimizing the embedding dimension of time series. The time series obtained from the typical non-linear systems, Lorenz system and Rössler system, is used to standardize the methods and the Malayalam speech vowel time series of both genders of different age groups, sampled at three sampling frequencies (16[Formula: see text]kHz, 32[Formula: see text]kHz, 44.1[Formula: see text]kHz), are taken for analysis. It was observed that time delay varies from sample to sample and, it ought to be better to figure out the time delay with the embedding dimension analysis. The embedding dimension is shown to be independent of gender, age and sampling frequency and can be projected as five. Hence a five-dimensional hyperspace will probably be adequate for reconstructing attractor of speech time series.

Fault classification of rolling bearing based on reconstructed phase space and Gaussian mixture model

Rolling bearings are common and vital elements in rotating machinery and vibration signal is a kind of effective mean to characterize the status of rolling bearing fault and its severity. In this paper, a novel method is introduced to realize classification of fault signal without extracting feature vector preliminarily. By estimating the time delay and embedding dimension of time series, vibration signal is reconstructed into phase space and Gaussian mixture model (GMM) is established for every kind of fault signal in the reconstructed phase space. After these models are built, classification of fault signal is accomplished by computing the conditional likelihoods of the signal under each learned GMM model and selecting the model with the highest likelihood. By testifying of vibration signal under different kinds of bearing status, it is proved that this method is effective for classifying not only fault types but also fault severity. Moreover, all parameters needed in this method could be obtained by analyzing the time series directly so it is very suitable for industry application.

EFFECT OF NOISE ON THE AVERAGED FALSE NEIGHBORS METHOD APPLIED TO SIMULATED AND EXPERIMENTAL CHAOTIC TIMES SERIES

We examine the influence of noise on the averaged false neighbors method (AFN), which was proposed by L. Cao to identify the deterministic nature and estimate the minimum embedding dimension of time series. In a numerical experiment, we add a raising amount of noise to time series from numerical simulation of well known chaotic models and to experimentally recorded time series. We find that the AFN method acknowledges the deterministic nature of the underlying process of these noisy times series. For the assessment of the embedding, sensitivity to noise generally decreases when the dimension of the underlying dynamical process increased.