A framework for assessing frequency domain causality in physiological time series with instantaneous effects

We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the known directed coherence (DC) and partial DC measures. The new measures are illustrated in theoretical examples showing that they reduce to the known measures in the absence of instantaneous causality, and describe peculiar aspects of directional interaction among multiple series when instantaneous causality is non-negligible. Then, the issue of estimating eMVAR models from time-series data is faced, proposing two approaches for model identification and discussing problems related to the underlying model assumptions. Finally, applications of the framework on cardiovascular variability series and multichannel EEG recordings are presented, showing how it allows one to highlight patterns of frequency domain causality consistent with well-interpretable physiological interaction mechanisms.

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EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408022640 ◽

2008 ◽

Vol 18 (12) ◽

pp. 3679-3687 ◽

Cited By ~ 6

Author(s):

AYDIN A. CECEN ◽

CAHIT ERKAL

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Lyapunov Exponents ◽

Correlation Dimension ◽

Time Series Data ◽

Logistic Map ◽

Model Identification ◽

Series Data ◽

Largest Lyapunov Exponent ◽

The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

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Remaining Useful Life Prediction Using Temporal Convolution with Attention

AI ◽

10.3390/ai2010005 ◽

2021 ◽

Vol 2 (1) ◽

pp. 48-70

Author(s):

Wei Ming Tan ◽

T. Hui Teo

Keyword(s):

Neural Network ◽

Time Series ◽

Time Series Data ◽

Remaining Useful Life ◽

Sensor Data ◽

Series Data ◽

Multiple Time ◽

Data Set ◽

Form Complex ◽

Useful Life

Prognostic techniques attempt to predict the Remaining Useful Life (RUL) of a subsystem or a component. Such techniques often use sensor data which are periodically measured and recorded into a time series data set. Such multivariate data sets form complex and non-linear inter-dependencies through recorded time steps and between sensors. Many current existing algorithms for prognostic purposes starts to explore Deep Neural Network (DNN) and its effectiveness in the field. Although Deep Learning (DL) techniques outperform the traditional prognostic algorithms, the networks are generally complex to deploy or train. This paper proposes a Multi-variable Time Series (MTS) focused approach to prognostics that implements a lightweight Convolutional Neural Network (CNN) with attention mechanism. The convolution filters work to extract the abstract temporal patterns from the multiple time series, while the attention mechanisms review the information across the time axis and select the relevant information. The results suggest that the proposed method not only produces a superior accuracy of RUL estimation but it also trains many folds faster than the reported works. The superiority of deploying the network is also demonstrated on a lightweight hardware platform by not just being much compact, but also more efficient for the resource restricted environment.

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Assessment of Occupational Exposure Patterns by Frequency-Domain Analysis of Time Series Data

Applied Occupational and Environmental Hygiene ◽

10.1080/104732200301944 ◽

2000 ◽

Vol 15 (1) ◽

pp. 120-130 ◽

Cited By ~ 3

Author(s):

Gary J. Mihlan ◽

Lori A. Todd ◽

Kinh N. Truong

Keyword(s):

Time Series ◽

Occupational Exposure ◽

Frequency Domain ◽

Time Series Data ◽

Domain Analysis ◽

Frequency Domain Analysis ◽

Series Data ◽

Exposure Patterns ◽

Analysis Of Time Series

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Stochastic Subspace Model Identification and One-step Prediction on Time Series Data

Advanced Design and Manufacture to Gain a Competitive Edge ◽

10.1007/978-1-84800-241-8_38 ◽

2008 ◽

pp. 367-376

Author(s):

Na Meng ◽

Yi-qi Zhou

Keyword(s):

Time Series ◽

Time Series Data ◽

Model Identification ◽

Series Data ◽

One Step

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Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Vibration ◽

10.3390/vibration2010002 ◽

2019 ◽

Vol 2 (1) ◽

pp. 25-46 ◽

Cited By ~ 3

Author(s):

Merten Stender ◽

Sebastian Oberst ◽

Norbert Hoffmann

Keyword(s):

Time Series ◽

Differential Equations ◽

Time Series Data ◽

Model Identification ◽

Transient Behavior ◽

Series Data ◽

Special Focus ◽

Suitable Model ◽

Reconstruction Method ◽

Minimal Models

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

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