A Nonlinear Noise Reduction Approach to Vibration Analysis for Bearing Health Diagnosis

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Ruqiang Yan ◽  
Robert X. Gao
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Noise Reduction ◽  
Nonlinear Filtering ◽  
Signal To Noise Ratio ◽  
Vibration Signal ◽  
One Dimensional ◽  
Synthetic Signal ◽  
Dimensional Phase Space ◽  
Vibration Signal Analysis

This paper presents a local geometric projection (LGP)-based noise reduction technique for vibration signal analysis in rolling bearings. LGP is a nonlinear filtering technique that reconstructs one dimensional time series in a high-dimensional phase space using time-delayed coordinates based on the Takens embedding theorem. From the neighborhood of each point in the phase space, where a neighbor is defined as a local subspace of the whole phase space, the best subspace to which the point will be orthogonally projected is identified. Since the signal subspace is formed by the most significant eigen-directions of the neighborhood, while the less significant ones define the noise subspace, the noise can be reduced by converting the points onto the subspace spanned by those significant eigen-directions back to a new, one-dimensional time series. Improvement on signal-to-noise ratio enabled by LGP is first evaluated using a chaotic system and an analytically formulated synthetic signal. Then, analysis of bearing vibration signals is carried out as a case study. The LGP-based technique is shown to be effective in reducing noise and enhancing extraction of weak, defect-related features, as manifested by both the multi-fractal and envelope spectra of the signal.

Local Geometric Projection-Based Noise Reduction for Vibration Signal Analysis in Rolling Bearings

2008 ◽  
Author(s):  
Ruqiang Yan ◽  
Robert X. Gao ◽  
Kang B. Lee ◽  
Steven E. Fick
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Noise Reduction ◽  
Signal Analysis ◽  
Signal To Noise Ratio ◽  
Multifractal Spectrum ◽  
Vibration Signal ◽  
Rolling Bearings ◽  
One Dimensional ◽  
Vibration Signal Analysis

This paper presents a noise reduction technique for vibration signal analysis in rolling bearings, based on local geometric projection (LGP). LGP is a non-linear filtering technique that reconstructs one dimensional time series in a high-dimensional phase space using time-delayed coordinates, based on the Takens embedding theorem. From the neighborhood of each point in the phase space, where a neighbor is defined as a local subspace of the whole phase space, the best subspace to which the point will be orthogonally projected is identified. Since the signal subspace is formed by the most significant eigen-directions of the neighborhood, while the less significant ones define the noise subspace, the noise can be reduced by converting the points onto the subspace spanned by those significant eigen-directions back to a new, one-dimensional time series. Improvement on signal-to-noise ratio enabled by LGP is first evaluated using a chaotic system and an analytically formulated synthetic signal. Then analysis of bearing vibration signals is carried out as a case study. The LGP-based technique is shown to be effective in reducing noise and enhancing extraction of weak, defect-related features, as manifested by the multifractal spectrum from the signal.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

KPCA Denoising and its Application in Machinery Fault Diagnosis

2011 ◽  
Vol 103 ◽  
pp. 274-278 ◽  
Author(s):  
Ling Li Jiang ◽  
Zong Qun Deng ◽  
Si Wen Tang
Keyword(s):  
Time Series ◽  
Principal Component ◽  
Vibration Signal ◽  
Rolling Bearing ◽  
Kernel Principal Component Analysis ◽  
Reconstruction Method ◽  
Denoising Method ◽  
One Dimensional ◽  
Multidimensional Time Series ◽  
Machinery Fault Diagnosis

This paper proposes a kernel principal component analysis (KPCA)-based denoising method for removing the noise from vibration signal. Firstly, one-dimensional time series is expanded to multidimensional time series by the phase space reconstruction method. Then, KPCA is performed on the multidimensional time series. The first kernel principal component is the denoised signal. A rolling bearing denoising example verify the effectiveness of the proposed method

Diagnosis for Engine Misfire Fault Based on Torsional Vibration and Neural-Network Analysis

2012 ◽  
Vol 433-440 ◽  
pp. 7240-7246
Author(s):  
Can Yi Du ◽  
Kang Ding ◽  
Zhi Jian Yang ◽  
Cui Li Yang
Keyword(s):  
Neural Network ◽  
Torsional Vibration ◽  
Bp Neural Network ◽  
Signal Analysis ◽  
Signal To Noise Ratio ◽  
Vibration Signal ◽  
Correction Method ◽  
Operating Conditions ◽  
Diagnostic Model ◽  
Vibration Signal Analysis

Misfire is a common fault which affects the engine performances. Because the signal-to-noise ratio of torsional vibration signal is high, torsional vibration test and analysis for the engine were performed in a variety of operating conditions, including healthy condition and single-cylinder misfire condition. In order to improve the accuracy of analysis, energy centrobaric correction method was used to correct the amplitude. Taking the corrected amplitude of main order as the fault feature, and then a BP neural-network diagnostic model can be established for misfire diagnosis. The result shows that the method of combining torsional vibration signal analysis and neural-network can diagnose engine misfire fault correctly.

scholarly journals A ‘metric’ semi-Lagrangian Vlasov–Poisson solver

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
Stéphane Colombi ◽  
Christophe Alard
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Second Order ◽  
Space Distribution ◽  
Third Order ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Poisson Solver ◽  
Dimensional Phase Space ◽  
Speed Up

We propose a new semi-Lagrangian Vlasov–Poisson solver. It employs metric elements to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $\boldsymbol{Q}(\boldsymbol{P})$ of any test particle $\boldsymbol{P}$, by expanding at second order the geometry of the motion in the vicinity of the closest element. It is thus possible to reconstruct accurately the phase-space distribution function at any time $t$ and position $\boldsymbol{P}$ by proper interpolation of initial conditions, following Liouville theorem. When distortion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling. To speed up the process, interpolation of the phase-space distribution is performed at second order during the transport phase, while third-order splines are used at the moments of remapping. We also show how to compute accurately the region of influence of each element of metric with the proper percolation scheme. The algorithm is tested here in the framework of one-dimensional gravitational dynamics but is implemented in such a way that it can be extended easily to four- or six-dimensional phase space. It can also be trivially generalised to plasmas.

THE 2-D SEXTIC HAMILTONIAN OSCILLATOR

2013 ◽  
Vol 23 (06) ◽  
pp. 1330019
Author(s):  
F. J. MOLERO ◽  
J. C. VAN DER MEER ◽  
S. FERRER ◽  
F. J. CÉSPEDES
Keyword(s):  
Phase Space ◽  
Elliptic Functions ◽  
Singular Values ◽  
Nonlinear Oscillators ◽  
Momentum Mapping ◽  
Dimensional Model ◽  
Integrable Hamiltonian Systems ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

scholarly journals Multistage noise reduction processing for vibration signal of hydropower units

2021 ◽  
Vol 2108 (1) ◽  
pp. 012008
Author(s):  
Yousong Shi ◽  
Jianzhong Zhou
Keyword(s):  
Noise Reduction ◽  
Signal To Noise Ratio ◽  
Vibration Signal ◽  
Field Testing ◽  
Signal To Noise ◽  
Vibration Signals ◽  
Multi Stage ◽  
Actual Field ◽  
Stationary Vibration ◽  
Testing Environments

Abstract In actual field testing environments of hydropower units, unit vibration signals are often contaminated with noise. In order to obtain the real vibration signal, a multi-stage vibration signal denoise method SG-SVD-VMD is proposed for the guide bearing nonlinear and non-stationary vibration signals. And the root mean square error (RMSE) and signal to noise ratio (SNR) are used to evaluate the noise reduction ability of eight methods. The results show that the noise-canceling ability of this proposed method has improved to some extent. It can effectively suppress the noise of the hydropower units vibration signals. This method can effectively identify the shaft track and the running state of hydropower units.

Embedded Sensing Design of Gearboxes for Vibration Monitoring

2010 ◽  
Vol 29-32 ◽  
pp. 264-268
Author(s):  
Z.S. Chen ◽  
Yong Min Yang ◽  
Z.X. Ge ◽  
C. Li
Keyword(s):  
Signal Analysis ◽  
Signal To Noise Ratio ◽  
Vibration Signal ◽  
Vibration Monitoring ◽  
Embedded Sensors ◽  
Analysis Method ◽  
Signal To Noise ◽  
Normal Functions ◽  
Embedded Sensing ◽  
Vibration Signal Analysis

Vibration signal analysis is one of the most effective ways for condition monitoring of gearboxes. Traditional way is often to mount additional accelerometer sensors on their cases, which has two unavoidable defects: signal-to-noise ratio is often low due to long signal travel paths and it may be not allowable due to space limitations. While embedded diagnostics (ED) can solve these two problems well by embedding sensors close to fault sources. However, embedded sensing design is a great challenge of ED because embedded sensors must have effects on the structure integrity of a gearbox. So it is necessary to determine how to embed sensors in order to ensure normal functions of a gearbox. In this paper, a finite element-based structure analysis method was proposed to perform embedded sensing design of bearings and gears to determine the optimal modified structure size.

scholarly journals Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Liyun Su ◽  
Chenlong Li
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaos Theory ◽  
Nearest Neighbor ◽  
Simulated Data ◽  
Real Data ◽  
Chaotic Time Series ◽  
Dimensional Phase Space ◽  
Local Functional ◽  
Functional Coefficient

A new methodology, which combines nonparametric method based on local functional coefficient autoregressive (LFAR) form with chaos theory and regional method, is proposed for multistep prediction of chaotic time series. The objective of this research study is to improve the performance of long-term forecasting of chaotic time series. To obtain the prediction values of chaotic time series, three steps are involved. Firstly, the original time series is reconstructed inm-dimensional phase space with a time delayτby using chaos theory. Secondly, select the nearest neighbor points by using local method in them-dimensional phase space. Thirdly, we use the nearest neighbor points to get a LFAR model. The proposed model’s parameters are selected by modified generalized cross validation (GCV) criterion. Both simulated data (Lorenz and Mackey-Glass systems) and real data (Sunspot time series) are used to illustrate the performance of the proposed methodology. By detailed investigation and comparing our results with published researches, we find that the LFAR model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting.

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