Digital Analysis of the Vibration Signals Amplitude Spectrum Based on Fourier Processing of the Binary-Sign Analog-Stochastic Quantization Result

2019 ◽  
Vol 20 (12) ◽  
pp. 723-731
Author(s):  
V. N. Yakimov ◽  
V. I. Batyschev ◽  
A. V. Mashkov
Keyword(s):  
Harmonic Analysis ◽  
Computational Efficiency ◽  
Amplitude Spectrum ◽  
Experimental Studies ◽  
Analytical Calculation ◽  
Frequency Resolution ◽  
Stochastic Quantization ◽  
Complex Signals ◽  
Workload Analysis ◽  
Vibration Signals

The article is devoted to the problem of developing a digital algorithm for operational harmonic analysis of complex vibration signals. The basis for solving this problem was the generalized equation of statistical measurements, which defines the measurement procedure as the sequential execution of interrelated measurement and computational transformations. During the development of the algorithm, special attention is paid to analog-to-digital conversion because it directly affects the computational efficiency of digital procedures for obtaining the final result. As such a conversion, the use of binarysign analog-stochastic quantization is justified, which allows performing two-level quantization without systematic error regardless of the statistical properties of the analyzed signals. The discrete-event model of the binary-sign analog-stochastic quantization result allowed for the analytical calculation of integration operations in the transition to estimating the amplitude spectrum in digital form. As a result, the developed algorithm of harmonic analysis does not require performing digital multiplication operations typical for classical algorithms, which are based on the calculation of the direct discrete Fourier transform. The execution of the algorithm is reduced to the implementation of the addition and subtraction arithmetic operations of the cosine-function values in the time moments determined by the result of the binary-sign analogue-stochastic quantization. The exclusion of digital multiplication operations provided an increase in the computational efficiency of amplitude spectrum estimation. Laboratory studies of the developed algorithm were carried out using simulation modeling. The simulation results showed that the algorithm allows calculating estimates of the amplitude spectrum of complex signals with high accuracy and frequency resolution in the presence of additive noise. In real conditions, the testing of the developed algorithm was carried out during bench studies of the operational status of the MAZ-206067 bus, designed for the transportation of passengers on urban and suburban routes of average workload. Analysis of the results of experimental studies confirmed the possibility of using the algorithm as part of the diagnosability provision for operational monitoring of vibration signals in a complex noise environment.

scholarly journals Damped CAPES 2D Spectral Estimation for Real-Valued Vibration Signals

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Danhui Dan ◽  
Jiongxin Gong ◽  
Yiming Zhao
Keyword(s):  
Spectral Estimation ◽  
Amplitude Spectrum ◽  
Vibration Signal ◽  
Angular Frequency ◽  
Frequency Resolution ◽  
Spectrum Estimation ◽  
Vibration Signals ◽  
Vibration Data ◽  
Decay Factor ◽  
Sine Term

We propose a 2D representation in the frequency-decay factor plane of an arbitrary real-world vibration signal. The signal is expressed as the sum of a decayed-attenuation sine term modulated by an amplitude function and a noise residue. We extend the combined approach of Capon estimation and amplitude and phase estimation (CAPES) to damped real vibration signals (DR-CAPES). In the proposed DR-CAPES method, the high-resolution amplitude and phase are estimated simultaneously for both angular frequency and decay factor grids. The performance of the proposed approach is tested numerically with noisy vibration data. Results show that the DR-CAPES method has an excellent frequency resolution, which helps to overcome difficulties in spectrum estimation when vibration modes are very close, and a small bias, which makes it suitable for obtaining accurate amplitude spectrums. The results also indicate that the proposed method can accurately estimate the amplitude spectrum with the use of averaging and denoising processes.

scholarly journals Periodogram estimating the spectral power density based upon signals’ binary-sign stochastic quantization using window functions

2021 ◽  
Vol 20 (2) ◽  
pp. 341-370
Author(s):  
Vladimir Yakimov
Keyword(s):  
Spectral Analysis ◽  
Discrete Event ◽  
Frequency Resolution ◽  
Dominant Factor ◽  
Stochastic Quantization ◽  
Digital Form ◽  
Complex Signals ◽  
Multiplicative Complexity ◽  
Event Modeling ◽  
Window Functions

Spectral analysis of signals is used as one of the main methods for studying systems and objects of various physical natures. Under conditions of a priori statistical uncertainty, the signals are subject to random changes and noise. Spectral analysis of such signals involves the estimation of the power spectral density (PSD). One of the classical methods for estimating PSD is the periodogram method. The algorithms that implement this method in digital form are based on the discrete Fourier transform. Digital multiplication operations are mass operations in these algorithms. The use of window functions leads to an increase in the number of these operations. Multiplication operations are among the most time consuming operations. They are the dominant factor in determining the computational capabilities of an algorithm and determine its multiplicative complexity. The paper deals with the problem of reducing the multiplicative complexity of calculating the periodogram estimate of the PSD using window functions. The problem is solved based on the use of binary-sign stochastic quantization for converting a signal into digital form. This two-level signal quantization is carried out without systematic error. Based on the theory of discrete-event modeling, the result of a binary-sign stochastic quantization in time is considered as a chronological sequence of significant events determined by the change in its values. The use of a discrete-event model for the result of binary-sign stochastic quantization provided an analytical calculation of integration operations during the transition from the analog form of the periodogram estimation of the SPM to the mathematical procedures for calculating it in discrete form. These procedures became the basis for the development of a digital algorithm. The main computational operations of the algorithm are addition and subtraction arithmetic operations. Reducing the number of multiplication operations decreases the overall computational complexity of the PSD estimation. Numerical experiments were carried out to study the algorithm operation. They were carried out on the basis of simulation modeling of the discrete-event procedure of binary-sign stochastic quantization. The results of calculating the PSD estimates are presented using a number of the most famous window functions as an example. The results obtained indicate that the use of the developed algorithm allows calculating periodogram estimates of PSD with high accuracy and frequency resolution in the presence of additive white noise at a low signal-to-noise ratio. The practical implementation of the algorithm is carried out in the form of a functionally independent software module. This module can be used as a part of complex metrologically significant software for operational analysis of the frequency composition of complex signals.

Detection of Transients in Vibration Signals using Reverse Dispersion Entropy

2021 ◽  
pp. 1-33
Author(s):  
Jaafar Alsalaet
Keyword(s):  
Shannon Entropy ◽  
Vibration Signal ◽  
Fir Filter ◽  
Frequency Resolution ◽  
Frequency Bandwidth ◽  
Vibration Signals ◽  
Spectral Kurtosis ◽  
Ideal Filter ◽  
Envelope Signal ◽  
The Ideal

Abstract In this work, the reverse dispersion entropy (RDE) is used to process the squared envelope signal in order to detect nonstationarites. Based on the idea of spectral kurtosis (SK) and kurtogram, the squared envelope signal is first extracted by applying STFT to vibration signal. Then, as an alternative to negative Shannon entropy, the RDE is used to process the squared envelope to detect the range of frequencies at which the transients occur. The RDEgram color-coded map is used to represent the RDE values as a function of frequency and frequency resolution from which the ideal filter parameters can be inferred. Once, the best frequency and frequency bandwidth pair are found, an optimum FIR filter can be designed to filter the original vibration signal. The proposed method is tested against simulated and actual vibration signals and proved to be superior to existing methods.

Fault Detection of Broken Rotor Bar Using an Improved form of Hilbert–Huang Transform

2018 ◽  
Vol 17 (02) ◽  
pp. 1850012 ◽  
Author(s):  
F. Sabbaghian-Bidgoli ◽  
J. Poshtan
Keyword(s):  
Signal Processing ◽  
Fault Detection ◽  
Hilbert Transform ◽  
Wavelet Packet ◽  
Amplitude Spectrum ◽  
Vibration Signal ◽  
External Noise ◽  
Vibration Signals ◽  
Broken Rotor Bar ◽  
Hilbert Huang Transform

Signal processing is an integral part in signal-based fault diagnosis of rotary machinery. Signal processing converts the raw data into useful features to make the diagnostic operations. These features should be independent from the normal working conditions of the machine and the external noise. The extracted features should be sensitive only to faults in the machine. Therefore, applying more efficient processing techniques in order to achieve more useful features that bring faster and more accurate fault detection procedure has attracted the attention of researchers. This paper attempts to improve Hilbert–Huang transform (HHT) using wavelet packet transform (WPT) as a preprocessor instead of ensemble empirical mode decomposition (EEMD) to decompose the signal into narrow frequency bands and extract instantaneous frequency and compares the efficiency of the proposed method named “wavelet packet-based Hilbert transform (WPHT)” with the HHT in the extraction of broken rotor bar frequency components from vibration signals. These methods are tested on vibration signals of an electro-pump experimental setup. Moreover, this project applies wavelet packet de-noising to remove the noise of vibration signal before applying both methods mentioned and thereby achieves more useful features from vibration signals for the next stages of diagnosis procedure. The comparison of Hilbert transform amplitude spectrum and the values and numbers of detected instantaneous frequencies using HHT and WPHT techniques indicates the superiority of the WPHT technique to detect fault-related frequencies as an improved form of HHT.

Turbulence Characteristics in a Rushton Stirring Vessel Measured via Time Resolved DPIV

2006 ◽  
Author(s):  
Michael R. Brady ◽  
Demetri P. Telionis ◽  
Pavlos P. Vlachos
Keyword(s):  
Experimental Studies ◽  
Turbulent Energy ◽  
Industrial Applications ◽  
Solid Particles ◽  
Analytical Models ◽  
Frequency Resolution ◽  
Time Resolved ◽  
Turbulence Characteristics ◽  
Stirred Vessels ◽  
Rushton Impeller

Stirred vessels are devices that find extensive industrial applications particularly in mineral and chemical industries. Interactions of solid particles and/or bubbles and particles depend on the characteristics of turbulent flow. In many analytical models, the rate of collision is a function of turbulence dissipation. It has been known that dissipation levels are much higher in the neighborhood of the agitating mechanism, in our case the Rushton impeller. In this paper we use time-resolved DPIV to measure the velocity field with a spatial resolution down to 100 μm, and a frequency resolution of 500 Hz. The range of Reynolds numbers investigated varied from 20,000 to 50,000, with the smallest Kolmogorov length scale of about 15 μm. The flow in the impeller stream of a Rushton impeller can be best summarized as a radial jet with a pair of convecting tip vortices. The turbulence quantities were found by removing the periodic component from the blade passing, which is the dominant part of the measured velocities. Dissipation was calculated from the velocity gradients, and assuming isotropy. We provide further evidence that larger dissipation values in the vicinity of the impeller are consistent with the dynamic motion generated by the blade passage. This is somewhat anti-intuitive, because energy is dissipated at the smallest eddy scales, and the immediate vicinity of the impeller contains large vortical structures and provides little space or time for such structures to break down. The maximum and mean normalized dissipation in the impeller stream showed decreasing trends with the Reynolds number. Other normalized turbulence quantities, namely Vrms and in plane vorticity are presented. Our experiments agree very well with other experimental studies. Estimates of turbulence characteristics and in particular distributions of turbulent energy dissipation determined in this study will be used in estimating rates of collisions of bubbles and particles in stirred vessels.

Application of entropy in identification of breathing cracks in a beam structure: Simulations and experimental studies

2017 ◽  
Vol 17 (3) ◽  
pp. 549-564 ◽  
Author(s):  
Buddhi Wimarshana ◽  
Nan Wu ◽  
Christine Wu
Keyword(s):  
Cantilever Beam ◽  
Time Domain ◽  
Fatigue Cracks ◽  
Unit Length ◽  
Crack Depth ◽  
Experimental Studies ◽  
Sample Entropy ◽  
Breathing Crack ◽  
Engineering Structures ◽  
Vibration Signals

A cantilever beam with a breathing crack is studied to detect the crack and evaluate the crack depth using entropy measures. During the vibration in engineering structures, fatigue cracks undergo the status from close-to-open (and open-to-close) repetitively leading to a crack breathing phenomenon. Entropy is a measure, which can quantify the complexity or irregularity in system dynamics, and hence employed to quantify the bi-linearity/irregularity of the vibration response, which is induced by the breathing phenomenon of a crack. A mathematical model of harmonically excited unit length steel cantilever beam with a breathing crack located near the fixed end is established, and an iterative numerical method is applied to generate accurate time domain vibration responses. The steady-state time domain vibration signals are pre-processed with wavelet transformation, and the bi-linearity/irregularity of the vibration signals due to breathing effect is then successfully quantified using both sample entropy and quantized approximation of sample entropy to detect and estimate the crack depth. It is observed that the method is capable of identifying crack depths even at very early stages of 3% of the beam thickness with significant increment in the entropy values (more than 200%) compared to the healthy beam. In addition, experimental studies are conducted, and the simulation results are in good agreement with the experimental results. The proposed technique can also be applied to damage identification in other types of structures, such as plates and shells.

Vibration measurement of a cantilever beam using root embedded piezoceramic sensor

2008 ◽  
Vol 222 (2) ◽  
pp. 147-161 ◽  
Author(s):  
M Sunar ◽  
B O Al-Bedoor
Keyword(s):  
Cantilever Beam ◽  
Experimental Studies ◽  
Finite Element Approximation ◽  
Vibration Measurement ◽  
Element Approximation ◽  
Structural Vibrations ◽  
Vibration Signals ◽  
Rotating Blade ◽  
Set Up ◽  
Transient And Steady State

Numerical and experimental studies are carried out to investigate the usability of a piezoceramic (PZT) sensor placed in the root of a stationary cantilever beam for measuring structural vibrations. The ability of the sensor for picking up the vibration signals during both the transient and steady-state phases is investigated. The piezoelectric equations obtained using the Hamilton's principle together with the finite-element approximation are utilized to extract the voltage outputs of the PZT sensor. An experimental set-up, to validate the theoretical results, is designed and manufactured. The experimentally measured sensor voltages are compared with the numerical ones. The results showed the excellent performance of the sensors in reading vibration signals of the beam. The root embedded PZT approach is an important step towards the application of measuring rotating blade vibrations.

scholarly journals Applying Harmonic Analysis in the Measurements of Geometrical Deviations of Crankshafts – Roundness Shapes Analysis

2018 ◽  
Vol 1 (1) ◽  
pp. 185-189 ◽  
Author(s):  
Krzysztof Nozdrzykowski
Keyword(s):  
Coordinate System ◽  
Harmonic Analysis ◽  
Amplitude Spectrum ◽  
Measuring System ◽  
Polar Coordinate System ◽  
Mathematical Methods ◽  
Graphic Form ◽  
Flexible Support ◽  
Analysis Theory ◽  
Polar Coordinate

Abstract The article presents measuring procedures and principles of determining deviations of shape and location of the crankshaft main necks assembly axis. We also described mathematical methods of roundness shapes description based on the harmonic analysis theory for the cases when the shaft is set with the external journals in prisms and for the case when the shaft is set on the external front faces in the claws. The results of sample calculations realized on the basis of the proposed mathematical methods have been presented in a form of diagrams of so called amplitude spectrum and in a graphic form of roundness shapes expressed in a polar coordinate system. The procedures described find a practical use during measurements of geometrical deviations of crankshafts realized on the basis of a measuring system with so called flexible support of the measured object.

scholarly journals Online frequency and amplitude tracking in structural vibrations under environment using APES spectrum postprocessing and Kalman filtering

2021 ◽  
Author(s):  
Xuewen Yu ◽  
Danhui Dan
Keyword(s):  
Structural Health Monitoring ◽  
Kalman Filtering ◽  
Health Monitoring ◽  
Time Window ◽  
Numerical Study ◽  
Amplitude Spectrum ◽  
Real Life ◽  
Structural Vibrations ◽  
Vibration Signals ◽  
Structural Health

Identifying time-varying frequency and amplitude online in real-life structural vibrations is an essential topic of data processing in structural health monitoring. This paper proposes a novel method for this task. We assume that structural vibration signals are stationary in a short time, thus a spectral analysis method called amplitude and phase estimation (APES) is conducted to obtain the amplitude spectrum at corresponding time window, and a postprocessing technique is proposed to extract the modal frequency and amplitude from the spectrum automatically. The extracted frequency and amplitude could be regarded as the average of the instantaneous frequency and instantaneous amplitude during the window. Due to the instability of measured structural vibrations and the uncertainty of spectral shapes under ambient excitation, Kalman ?filtering is introduced by taking the signal that reconstructed from the identi?fied frequencies and amplitudes as the prediction to enhance the reliability and quality (signal-to-noise ratio) of the next measured signals. Numerical study is performed to inspect the performance of the proposed method. It is also employed to analyze the vibration signals of actual structures, i.e., a cable of a cable-stayed bridge, a hanger of an arch bridge and the main girder of a suspension bridge. The results show its potential to track frequency and amplitude in structural vibrations under environmental measurements. The method is supposed to provide fundamental support for further information obtaining and high-level decision making for structural health monitoring systems.

scholarly journals High Resolution Order Tracking at Extreme Slew Rates Using Kalman Tracking Filters

1995 ◽  
Vol 2 (6) ◽  
pp. 507-515 ◽  
Author(s):  
Håvard Vold ◽  
Jan Leuridan
Keyword(s):  
Signal Amplitude ◽  
Accurate Estimate ◽  
Frequency Resolution ◽  
Vibration Signals ◽  
Noise And Vibration ◽  
Order Tracking ◽  
Precise Knowledge ◽  
Unknown Structure ◽  
Periodic Components ◽  
Amplitude Versus

The analysis of the periodic components in noise and vibration signals measured on rotating equipment such as car power trains, must be done more and more under rapid changes of an axle, or reference RPM. Normal tracking filters (analog or digital implementations) have limited resolution in such situations; wavelet methods, even when applied after resampling the data to be proportional to an axle RPM, must compromise between time and frequency resolution. The authors propose the application of nonstationary Kalman filters for the tracking of periodic components in such noise and vibration signals. These filters are designed to accurately track signals with a known structure among noise and signal components of different, “unknown,” structure. The tracking characteristics of these filters, i.e., the predicted signal amplitude versus time values versus exact signal amplitude versus time values, can be tailored to accurate tracking of harmonics buried in other signal components and noise, even at high rates of change of the reference RPM. A key to the successful construction is the precise knowledge of the structure of the signal to be tracked. For signals that vary with an axle RPM, an accurate estimate of the instantaneous RPM is essential, and procedures to this end will also be presented.

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