Fatigue Detection Using Phase-Space Warping

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Abdullatif Alwasel ◽  
Marcus Yung ◽  
Eihab M. Abdel-Rahman ◽  
Richard P. Wells ◽  
Carl T. Haas
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Musculoskeletal System ◽  
Physical State ◽  
Muscle Group ◽  
Physiological Signals ◽  
Laboratory Environment ◽  
Sharing Patterns ◽  
Fatigue Detection ◽  
Phase Space Warping

A novel application of phase-space warping (PSW) method to detect fatigue in the musculoskeletal system is presented. Experimental kinematic, force, and physiological signals are used to produce a fatigue metric. The metric is produced using time-delay embedding and PSW methods. The results showed that by using force and kinematic signals, an overall estimate of the muscle group state can be achieved. Further, when using electromyography (EMG) signals the fatigue metric can be used as a tool to evaluate muscles activation and load sharing patterns for individual muscles. The presented method will allow for fatigue evolution measurement outside a laboratory environment, which open doors to applications such as tracking the physical state of players during competition, workers in a plant, and patients undergoing in-home rehabilitation.

A Study On Methods for Determining Phase Space Reconstruction Parameters

2021 ◽  
Author(s):  
Shihui Lang ◽  
Zhu Hua ◽  
Guodong Sun ◽  
Yu Jiang ◽  
Chunling Wei
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Correlation Dimension ◽  
Nearest Neighbor ◽  
Correlation Method ◽  
Phase Space Reconstruction ◽  
Lorenz Attractor ◽  
Embedding Dimension ◽  
Phase Trajectories ◽  
Auto Correlation

Abstract Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chens attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex auto-correlation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex auto-correlation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified through combing the application of correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.

Invariant Manifold Detection From Phase Space Trajectories

2008 ◽  
Author(s):  
Joseph Kuehl ◽  
David Chelidze
Keyword(s):  
Phase Space ◽  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Basins Of Attraction ◽  
Detection Methods ◽  
Trajectory Data ◽  
Space Trajectories ◽  
Data Set ◽  
Phase Space Warping ◽  
Phase Space Trajectories

Invariant manifolds provide important information about the structure of flows. When basins of attraction are present, the stable invariant manifold serves as the boundary between these basins. Thus, in experimental applications such as vibrations problems, knowledge of these manifolds is essential to understanding the evolution of phase space trajectories. Most existing methods for identifying invariant manifolds of a flow rely on knowledge of the flow field. However, in experimental applications only knowledge of phase space trajectories is available. We provide modifications to several existing invariant manifold detection methods which enables them to deal with trajectory only data, as well as introduce a new method based on the concept of phase space warping. The method of Stochastic Interrogation applied to the damped, driven Duffing equation is used to generate our data set. The result is a set of trajectory data which randomly populates a phase space. Manifolds are detected from this data set using several different methods. First is a variation on manifold “growing,” and is based on distance of closest approach to a hyperbolic trajectory with “saddle like behavior.” Second, three stretching based schemes are considered. One considers the divergence of trajectory pairs, another quantifies the deformation of a nearest neighbor cloud, and the last uses flow fields calculated from the trajectory data. Finally, the new phase space warping method is introduced. This method takes advantage of the shifting (warping) experienced by a phase space as the parameters of the system are slightly varied. This results in a shift of the invariant manifolds. The region spanned by this shift, provides a means to identify the invariant manifolds. Results show that this method gives superior detection and is robust with respect to the amount of data.

scholarly journals Application of Phase Space Warping on Damage Tracking for Bearing Fault

2012 ◽  
Vol 364 ◽  
pp. 012025 ◽  
Author(s):  
Bin Fan ◽  
Niaoqing Hu ◽  
Lei Hu ◽  
Fengshou Gu
Keyword(s):  
Phase Space ◽  
Bearing Fault ◽  
Damage Tracking ◽  
Phase Space Warping

scholarly journals Chaotic Statistical Downscaling (CSD): Application and Comparison in the Bogotá River Basin

10.29007/wkcx ◽  
2018 ◽  
Author(s):  
Freddy Duarte ◽  
Gerald Corzo ◽  
Germán Santos ◽  
Oscar Hernández
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Predictive Model ◽  
River Basin ◽  
Statistical Downscaling ◽  
Climate Model ◽  
Global Climate ◽  
Global Climate Model ◽  
Deterministic Chaos ◽  
Climatic Information

This study presents a new statistical downscaling method called Chaotic Statistical Downscaling (CSD). The method is based on three main steps: Phase space reconstruction for different time steps, identification of deterministic chaos and a general synchronization predictive model. The Bogotá river basin was used to test the methodology. Two sources of climatic information are downscaled: the first corresponds to 47 rainfall gauges stations (1970-2016, daily) and the second is derived from the information of the global climate model MPI-ESM-MR with a resolution of 1,875° x 1,875° daily resolution. These time series were used to reconstruct the phase space using the Method of Time-Delay. The Time-Delay method allows us to find the appropriate values of the time delay and the embedding dimension to capture the dynamics of the attractor. This information was used to calculate the exponents of Lyapunov, which shows the existence of deterministic chaos. Subsequently, a predictive model is created based on the general synchronization of two dynamical systems. Finally, the results obtained are compared with other statistical downscaling models for the Bogota River basin using different measures of error which show that the proposed method is able to reproduce reliable rainfall values (RMSE=73.37).

scholarly journals Analysis of the optimal time delay for Reconstruction of Phase Space of VCG signals to identify anterior wall infarction

2021 ◽  
Author(s):  
Rafael Duarte de Sousa ◽  
José Barbosa ◽  
Ana Nogueira Rodrigues De Oliveira ◽  
Carlos Danilo Miranda Regis
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Anterior Wall ◽  
Optimal Time

An optimal global projection denoising algorithm and its application to shaft orbit purification

2011 ◽  
Vol 10 (6) ◽  
pp. 603-616 ◽  
Author(s):  
Shumin Hou ◽  
Ming Liang ◽  
Yourong Li
Keyword(s):  
Fault Diagnosis ◽  
Time Delay ◽  
Phase Space ◽  
Rotating Machinery ◽  
The Other ◽  
Optimal Time ◽  
Main Step ◽  
Signal Denoising ◽  
Embedding Dimension ◽  
Fault Features

Noise reduction is a main step in fault diagnosis of the rotating machinery. However, it is not effective enough to purify the nonlinear fault features from the vibration shaft orbits using the traditional signal denoising techniques. This article improved the global projection denoising algorithm via calculating the optimal time delay τ and embedding dimension m, which can be regarded as an extension of the global phase space reconstruction. The de-noising effects of Lorenz signal and the experiment cases illustrated the optimal global projection method is very effective and reliable in reducing the noise and reconstructing the signals. Consequently, it is heavily recommended for use in fault diagnosis of large rotating machinery as well as in the other kinds of machinery.

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