Application of the Energy Operator Separation Algorithm (EOSA) for the Instantaneous Amplitude and Frequency Calculation of Nonlinear Dynamic Systems Response

2009 ◽  
Author(s):  
Konstantinos Gryllias ◽  
Ioannis Antoniadis
Keyword(s):  
Energy Operator ◽  
Dynamic Responses ◽  
Van Der Pol Oscillator ◽  
Instantaneous Amplitude ◽  
Separation Algorithm ◽  
Estimation Errors ◽  
Time Frequency ◽  
Efficient Calculation ◽  
Frequency Calculation ◽  
The Hilbert Transform

A number of non-linear dynamic responses require analysis with an increased resolution in their time domain representation, especially the ones presenting abrupt changes, such as those caused by the introduction of cracks, gaps, and slip. Typical technological applications include bearings or gears with localized defects. Since the time resolution of well-known time-frequency analysis tools (such as Wavelet-Transform) presents limitations, the Energy Operator Separation Algorithm (EOSA) is considered. The algorithm is based on the Teager-Kaiser nonlinear differential energy operator and leads to the calculation of the instantaneous amplitude and frequency of the response. Compared to the Hilbert transform, it leads at least to the same estimation errors, but in addition presents smaller computational complexity and faster adaptation, due to its instantaneous nature. The EOSA is applied on responses of a nonlinear Van der-Pol oscillator, on signals simulating the dynamic response of defective rolling element bearings and on three signals measured at industrial installations, resulting from defective bearings. In all cases the algorithm leads to the efficient calculation, mainly of the instantaneous amplitude of the signals. However, certain improvements are necessary in order to increase the smoothness, mainly of the resulting instantaneous frequency time waveforms.

scholarly journals Hilbert Transform Analyzer for Mechanical Fault Detection of Vehicle Alternators

2020 ◽  
Vol 3 (3) ◽  
pp. 89-95
Author(s):  
Subekti Subekti ◽  
Muhammad Nurul Hidayat ◽  
Basuki Dwi Efendi ◽  
Abdul Hamid ◽  
Alim Murwanto
Keyword(s):  
Fault Detection ◽  
Hilbert Transform ◽  
Nonlinear Phenomena ◽  
Test Results ◽  
Instantaneous Amplitude ◽  
Backbone Curve ◽  
Time Frequency ◽  
Input Variables ◽  
Compact Design ◽  
The Hilbert Transform

Checking the alternator with mechanical measurements of moving parts takes sufficient time, especially in compact design engines. Therefore, this article presents a new method for alternator fault detection using the Hilbert transform application. The instantaneous amplitude and frequency are used as input variables for fault detection. Joint time-frequency analysis based on the wavelet analysis is also applied to identify the nonlinear characteristics. Various wavelet functions are examined, and some recommendations regarding the most suitable ones and the interpretation of the results are discussed. As a result, the backbone curve obtained from the instantaneous amplitude and frequency demonstrates the presence of the nonlinear phenomena, which can help make decisions about an alternator in normal conditions or indicate fault detection. From the test results, this method is very promising to be applied as part of vehicle's preventive maintenance.

ON INSTANTANEOUS FREQUENCY

2009 ◽  
Vol 01 (02) ◽  
pp. 177-229 ◽  
Author(s):  
NORDEN E. HUANG ◽  
ZHAOHUA WU ◽  
STEVEN R. LONG ◽  
KENNETH C. ARNOLD ◽  
XIANYAO CHEN ◽  
...  
Keyword(s):  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Energy Operator ◽  
Alternative Methods ◽  
Linear Processes ◽  
Zero Crossing ◽  
Time Frequency ◽  
Quarter Wavelength ◽  
True Time ◽  
The Hilbert Transform

Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90° shift of phase angle) directly. The second approach is designated as the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most localized, it is limited to data from linear processes, the GZC method is the most robust and accurate although limited to the mean frequency over a quarter wavelength of temporal resolution. With these results, we believe most of the problems associated with the IF determination are resolved, and a true time–frequency analysis is thus taking another step toward maturity.

DAMAGE DETECTION OF RC SLABS USING NONLINEAR VIBRATION FEATURES

2009 ◽  
Vol 09 (04) ◽  
pp. 687-709 ◽  
Author(s):  
XINQUN ZHU ◽  
HONG HAO
Keyword(s):  
Reinforced Concrete ◽  
Nonlinear Vibration ◽  
Structural Damage ◽  
Concrete Structures ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Reinforced Concrete Structures ◽  
Vibration Frequencies ◽  
Skeleton Curve ◽  
Time Frequency

Studied herein are the signatures of nonlinear vibration characteristics of damaged reinforced concrete structures using the wavelet transform (WT). A two-span RC slab built in 2003 was tested to failure in the laboratory. Vibration measurements were carried out at various stages of structural damage. The vibration frequencies, mode shapes, and damping ratios at each loading stage were extracted and analyzed. It is found that the vibration frequencies are not sensitive to small damages, but are good indicators when damage is severe. The dynamic responses are also analyzed in the time–frequency domain by WT and the skeleton curve is constructed to describe the nonlinear characteristics in the reinforced concrete structures. The results show that the skeleton curves are good indicators of damage in the reinforced concrete structures because they are more sensitive to small damages than vibration frequencies.

scholarly journals Fault Diagnosis in the Slip–Frequency Plane of Induction Machines Working in Time-Varying Conditions

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3398 ◽  
Author(s):  
Ruben Puche-Panadero ◽  
Javier Martinez-Roman ◽  
Angel Sapena-Bano ◽  
Jordi Burriel-Valencia ◽  
Martin Riera-Guasp
Keyword(s):  
Fault Diagnosis ◽  
Single Point ◽  
General Scheme ◽  
Induction Machine ◽  
Induction Machines ◽  
Transient Conditions ◽  
Time Frequency ◽  
Bearing Defects ◽  
Motor Current Signature Analysis ◽  
The Hilbert Transform

Motor current signature analysis (MCSA) is a fault diagnosis method for induction machines (IMs) that has attracted wide industrial interest in recent years. It is based on the detection of the characteristic fault signatures that arise in the current spectrum of a faulty induction machine. Unfortunately, the MCSA method in its basic formulation can only be applied in steady state functioning. Nevertheless, every day increases the importance of inductions machines in applications such as wind generation, electric vehicles, or automated processes in which the machine works most of time under transient conditions. For these cases, new diagnostic methodologies have been proposed, based on the use of advanced time-frequency transforms—as, for example, the continuous wavelet transform, the Wigner Ville distribution, or the analytic function based on the Hilbert transform—which enables to track the fault components evolution along time. All these transforms have high computational costs and, furthermore, generate as results complex spectrograms, which require to be interpreted for qualified technical staff. This paper introduces a new methodology for the diagnosis of faults of IM working in transient conditions, which, unlike the methods developed up to today, analyzes the current signal in the slip-instantaneous frequency plane (s-IF), instead of the time-frequency (t-f) plane. It is shown that, in the s-IF plane, the fault components follow patterns that that are simple and unique for each type of fault, and thus does not depend on the way in which load and speed vary during the transient functioning; this characteristic makes the diagnostic task easier and more reliable. This work introduces a general scheme for the IMs diagnostic under transient conditions, through the analysis of the stator current in the s-IF plane. Another contribution of this paper is the introduction of the specific s-IF patterns associated with three different types of faults (rotor asymmetry fault, mixed eccentricity fault, and single-point bearing defects) that are theoretically justified and experimentally tested. As the calculation of the IF of the fault component is a key issue of the proposed diagnostic method, this paper also includes a comparative analysis of three different mathematical tools for calculating the IF, which are compared not only theoretically but also experimentally, comparing their performance when are applied to the tested diagnostic signals.

scholarly journals Dynamic Responses of a Metro Train-Bridge System under Train-Braking: Field Measurements and Data Analysis

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 735
Author(s):  
Xuhui He ◽  
Kehui Yu ◽  
Chenzhi Cai ◽  
Yunfeng Zou ◽  
Xiaojie Zhu
Keyword(s):  
Field Measurements ◽  
Dynamic Responses ◽  
Wavelet Coherence ◽  
Distribution Method ◽  
Bogie Frame ◽  
Time Frequency ◽  
Rigid Frame ◽  
Rigid Frame Bridge ◽  
Acceleration Signals ◽  
Bridge System

This paper focuses on the dynamic responses of a metro train–bridge system under train-braking. Experiments were performed on the elevated Metro Line 21 of Guangzhou (China). A continuous, three-span, rigid-frame bridge (42 m + 65 m + 42 m) and a standard B-type metro train were selected. The acceleration signals were measured at the center-points of the main span and one side-span, and the acceleration signals of the car body and the bogie frame were measured simultaneously. The train–bridge system’s vibration characteristics and any correlations with time and frequency were investigated. The Choi–Williams distribution method and wavelet coherence were introduced to analyze the obtained acceleration signals of the metro train–bridge system. The results showed that the Choi–Williams distribution provided a more explicit understanding of the time–frequency domain. The correlations between different parts of the bridge and the train–bridge system under braking conditions were revealed. The present study provides a series of measured dynamic responses of the metro train–bridge system under train-braking, which could be used as a reference in further investigations.

Crack Identification by Jointly Time-Frequency Analysis

2006 ◽  
Vol 324-325 ◽  
pp. 161-164
Author(s):  
Xin Feng ◽  
Jing Zhou
Keyword(s):  
Frequency Analysis ◽  
Crack Opening ◽  
Sampling Frequency ◽  
Dynamic Responses ◽  
Crack Identification ◽  
Crack Model ◽  
Breathing Crack ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Novel Approach

A novel approach for crack identification based on jointly time-frequency analysis is presented in the paper. A bilinear stiffness model for the breathing crack was introduced to represent the nonlinear dynamics of a cracked beam. The nonlinearity of the dynamic responses due to the crack opening-closing is used to identify the occurrence of the crack. The Wigner-Wille distribution technique is applied to analyze the response signals and the instantaneous frequency is extracted as damage-sensitive feature. The numerical simulations of a breathing crack model were carried out to validate the possibility and effectiveness of the proposed approach. The effects of crack severity and sampling frequency on crack identification were also studied in the simulations respectively. The results show that the proposed method can effectively identify the crack with slight severity without any baseline model or data, and the better the identification obtains as the larger the sampling frequency. The study demonstrates that the proposed approach by using of jointly time-frequency analysis is a promising technique for crack identification.

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