Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

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A Novelty Detection Approach to Compressor Valve Fault Detection and Localization

Volume 14: Safety Engineering, Risk, and Reliability Analysis ◽

10.1115/imece2020-23314 ◽

2020 ◽

Author(s):

Colton M. Scott ◽

Jason R. Kolodziej

Keyword(s):

Frequency Analysis ◽

Learning Algorithm ◽

Novelty Detection ◽

Detection Algorithm ◽

Support Vector ◽

Flow Profile ◽

Shape Factors ◽

Time Frequency Analysis ◽

Time Frequency ◽

Vibration Data

Abstract Presented in this paper is the development of a vibration-based novelty detection algorithm for locating and identifying valve wear within industrial reciprocating compressors through the combined use of time-frequency analysis, image-based pattern recognition, and one-class support vector machines. A commonly reported cause of valve wear-related machine downtime is wear in the valve seat, causing a change in flow profile into and out of the compression chamber. Seeded faults are introduced into the valve manifolds of the ESH-1 industrial compressor and vibration data collected and separated into individual crank cycles before being analyzed using time-frequency analysis. The result is processed as an image and features used for classification are extracted using 1st and 2nd order images statistics and shape factors. A one-class support vector machine learning algorithm is then trained using data collected during healthy operation and then used to both detect and locate anomalous valve behavior with a greater than 82% success rate.

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Identification of Nonlinear Systems Through Time-frequency Filtering Technique

Journal of Vibration and Acoustics ◽

10.1115/1.1545769 ◽

2003 ◽

Vol 125 (2) ◽

pp. 199-204 ◽

Cited By ~ 4

Author(s):

Lili Wang ◽

Jinghui Zhang ◽

Chao Wang ◽

Shiyue Hu

Keyword(s):

Nonlinear System ◽

Nonlinear Systems ◽

Frequency Distribution ◽

Frequency Filtering ◽

Time Frequency ◽

Vibration Data ◽

Response Data ◽

Nonstationary Vibration ◽

Filtering Technique ◽

Time Frequency Distribution

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

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Application of Time-Frequency Analysis to Transient Data from Centrifuge Earthquake Testing

Shock and Vibration ◽

10.1155/2000/517193 ◽

2000 ◽

Vol 7 (4) ◽

pp. 195-202 ◽

Cited By ~ 4

Author(s):

David E. Newland ◽

Gary D. Butler

Keyword(s):

Frequency Analysis ◽

Good Method ◽

Centrifuge Modeling ◽

Transient Vibration ◽

Time Frequency Analysis ◽

Harmonic Wavelets ◽

Time Frequency ◽

Vibration Data ◽

Harmonic Wavelet ◽

Detailed Interpretation

Centrifuge model experiments have generated complex transient vibration data. New algorithms for time-frequency analysis using harmonic wavelets provide a good method of analyzing these data. We describe how the experimental data have been collected and show typical time-frequency maps obtained by the harmonic wavelet algorithm. Some preliminary comments on the interpretation of these maps are given in terms of the physics of the underlying model. Important features of the motion that are not otherwise apparent emerge from the analysis. Later papers will deal with their more detailed interpretation and their implications for centrifuge modeling.

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Experimental Wavelet Analysis of Rotor-Rub Vibration Signal

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.l3222.1081219 ◽

2019 ◽

Vol 8 (12) ◽

pp. 1756-1759

Keyword(s):

Frequency Analysis ◽

Mechanical Vibration ◽

Vibration Signal ◽

Time Frequency Analysis ◽

Signature Extraction ◽

Time Frequency ◽

Vibration Data ◽

Vibration Sensors ◽

Frequency Domains ◽

Frequency Components

A common defective phenomenon in rotating machinery is rotor-casing rub that generates impacts when the rotor rubs against the stator. Vibration sensors and data analysis techniques are commonly used for fault signature extraction and mechanical systems diagnosis. In this paper, an experimental characterization of rotor-rub is made by time-frequency analysis by means of the wavelet transform. A rotor kit, equipped with a variable speed DC motor, an accelerometer and a data acquisition system are used to acquire the mechanical vibration data. Vibration signal in frequency and time-frequency domains are shown for no-rubbing, light, and severe rubbing cases. Results show that FFT is unable to report where in time particular components of rubbing appear. However, the time-frequency analysis is able to give location information in time to differentiate light from severe rubbing, and extract the main spectral components showing a spectrum rich in high frequency components, characteristic of this phenomenon.

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