scholarly journals Fault tracking of rotating machinery under variable operation based on phase space warping

2013 ◽  
Vol 62 (16) ◽  
pp. 160503
Author(s):  
Fan Bin ◽  
Hu Lei ◽  
Hu Niao-Qing
Keyword(s):  
Phase Space ◽  
Rotating Machinery ◽  
Phase Space Warping

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

Study on Fault Diagnosis of Rotating Machinery Based on Lyapunov Dimension

2011 ◽  
Vol 199-200 ◽  
pp. 905-908
Author(s):  
Bing Cheng Wang ◽  
Zhao Hui Ren ◽  
Bang Chun Wen
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Phase Space Reconstruction ◽  
Rotating Machinery ◽  
Effective Parameters ◽  
Lyapunov Dimension ◽  
Rotating Machine ◽  
Movement Characteristics ◽  
Nonlinear Dynamic Characteristics ◽  
Nonlinear Feature

Based on the study and analysis that Lyapunov exponent can be used to characterize the motion state of system, in connection with the nonlinear dynamic characteristics shown from the performance of fault rotating mechanical system, the authors proposed the analysis method of Lyapunov dimension on the signal feature of mechanical fault. Using theory of phase space reconstruction, simulating fault signal of rotating machine was reconstructed. In order to let the phase space reconstruction adequately reflect the movement characteristics of the system, the time delay and embedding dimension are discussed emphatically. Based on what mentioned above, the authors calculated the Lyapunov exponent and the Lyapunov dimension. From the analysis and calculation on simulation of different fault signals, it showed that under different rotating machinery fault conditions, its Lyapunov dimension were significantly different, which verified that this nonlinear feature quantities were effective parameters for fault information and they were excellent parameters in terms of extraction and recognition of fault features.

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.

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.

Phase space warping: nonlinear time-series analysis for slowly drifting systems

2006 ◽  
Vol 364 (1846) ◽  
pp. 2495-2513 ◽  
Author(s):  
D Chelidze ◽  
J.P Cusumano
Keyword(s):  
Phase Space ◽  
Damage Evolution ◽  
Systems Approach ◽  
Reference Model ◽  
Recursive Estimation ◽  
Time To Failure ◽  
Damage State ◽  
Beam Experiment ◽  
Vector Tracking ◽  
Phase Space Warping

A new general dynamical systems approach to data analysis is presented that allows one to track slowly evolving variables responsible for non-stationarity in a fast subsystem. The method is based on the idea of phase space warping , which refers to the small distortions in the fast subsystem's phase space that results from the slow drift, and uses short-time reference model prediction error as its primary measurement of this phenomenon. The basic theory is presented and the issues associated with its implementation in a practical algorithm are discussed. A vector-tracking version of the procedure, based on smooth orthogonal decomposition analysis, is applied to the study of a nonlinear vibrating beam experiment in which a crack propagates to complete fracture. Our method shows that the damage evolution is governed by a scalar process, and we are able to give real-time estimates of the current damage state and identify the governing damage evolution model. Using a final recursive estimation step based on this model, the time to failure is continuously and accurately predicted well in advance of actual failure.

Study on Fault Diagnosis of Rotating Machinery Based on Lyapunov Dimension and Exponent Energy Spectrum

2012 ◽  
Vol 591-593 ◽  
pp. 2042-2045
Author(s):  
Bing Cheng Wang ◽  
Zhao Hui Ren
Keyword(s):  
Energy Spectrum ◽  
Phase Space ◽  
Rotating Machinery ◽  
Effective Parameters ◽  
Lyapunov Dimension ◽  
Rotating Machine ◽  
Movement Characteristics ◽  
Nonlinear Dynamic Characteristics ◽  
Nonlinear Feature ◽  
Fault Information

In connection with the nonlinear dynamic characteristics shown from the performance of fault rotating mechanical system, the authors propose the analysis method of Lyapunov dimension and exponent energy Spectrum to the signal feature of mechanical fault. Using theory of phase space reconstruction, simulating fault signal of rotating machine is reconstructed. In order to reconstruct the phase space which can be adequately reflect the movement characteristics of the system, the time delay and embedding dimension are discussed emphatically, on this basis, calculated the Lyapunov dimension and exponential energy spectrum. From the analysis and calculation on simulation of different fault signals, it shows that under different rotating machinery fault conditions, its Lyapunov dimension and exponential energy are significantly different, which verifies that this two nonlinear feature quantities is effective parameters for fault information

Local Flow Variation Method for Damage Identification

2005 ◽  
Author(s):  
Ming Liu ◽  
David Chelidze
Keyword(s):  
Phase Space ◽  
Damage Identification ◽  
Computing Time ◽  
Variation Method ◽  
Fast Time ◽  
Slow Time ◽  
Local Flow ◽  
Flow Variation ◽  
Damage Process ◽  
Phase Space Warping

In this paper, a damage identification method called local flow variation is introduced. It is a practical implementation of a phase space warping concept. A hierarchical dynamical system is considered where a slow-time damage process causes drifts in the parameters of fast-time system describing measurable response of a structure. The method is based on the hypothesis that the probability distribution function of the fast-time trajectory in its phase space is a function of damage state. In this method, an ensemble of estimated expectations of trajectory in different locations of the reconstructed phase space is used as a damage feature vector. Using these feature vectors, damage identification is realized by a smooth orthogonal decomposition. An experiment is conducted to validate the method. A two dimensional slow-time damage process is identified from experimental fast-time data. Although damage identification through the local flow variation is not as accurate as trough phase space warping, the required computing time is about two-orders-of-magnitude shorter.

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