The Fractal Dimension from the Experimental Pipe-vibration Signal

Author(s):  
Juanjuan Shi ◽  
Ming Liang

Vibration analysis has been extensively used as an effective tool for bearing condition monitoring. The vibration signal collected from a defective bearing is, however, a mixture of several signal components including the fault feature (i.e. fault-induced impulses), periodic interferences from other mechanical/electrical components, and background noise. The incipient impulses which excite as well as modulate the resonance frequency of the system are easily masked by compounded effects of periodic interferences and noise, making it challenging to do a reliable fault diagnosis. As such, this paper proposes an envelope demodulation method termed short time fractal dimension (STFD) transform for fault feature extraction from such vibration signal mixture. STFD transform calculation related issues are first addressed. Then, by STFD, the original signal can be quickly transformed into a STFD representation, where the envelope of fault-induced impulses becomes more pronounced whereas interferences are partly weakened due to their morphological appearance differences. It has been found that the lower the interference frequency, the less effect the interference has on STFD representations. When interference frequency keeps increasing, more effects on STFD representations will be resulted. Such effects can be reduced by the proposed kurtosis-based peak search algorithm (KPSA). Therefore, bearing fault signature is kept and interferences are further weakened in the STFD-KPSA representation. The proposed method has been favourably compared with two widely used enveloping methods, i.e. multi-morphological analysis and energy operator, in terms of extracting impulse envelopes from vibration signals obscured by multiple interferences. Its performance has also been examined using both simulated and experimental data.


Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050101
Author(s):  
MUHAMMAD OWAIS QADRI ◽  
HAMIDREZA NAMAZI

Tool wear is one of the unwanted phenomena in machining operations where tool has direct contact with the workpiece. Tool wear is an important issue in milling operation that is caused due to different parameters such as machine vibration. Tool wear shows complex structure, and machine vibration is a chaotic signal that also is complex. In this research, we analyze the correlation between tool wear and machine vibration using fractal theory. We run the experiments in which machining parameters, namely depth of cut, feed rate and spindle speed change, and accordingly analyze the variations of fractal dimension of tool wear versus the fractal dimension of machine vibration signal. Based on the obtained results, variations of complexity of tool wear are reversely correlated with the variations of complexity of vibration signal. Fractal analysis could potentially be applied to other machining operations in order to investigate the relation between tool wear and machine vibration.


Author(s):  
Zhao-Hui Wang ◽  
Lai-Bin Zhang ◽  
Wei Liang ◽  
Lixiang Duan

The compressor is dynamical equipment in pipeline station to deliver oil gas, it’s fault can result big accident such as stopping delivery and producing economic losing, and some fault of compressor are very complex due to the compressor’s complicated structure. Many compressor have carried simple diagnostic system, which can only diagnose normal fault, are not effective for diagnosing complex fault because these fault attributes are not obvious. This paper has researched the method to diagnose complex fault, by collecting the compressor’s vibration signals, using wavelet noise reduction technique and the fractal dimension method to process the vibration signal, which can abstract the non-obvious characteristics of complex fault effectively. The basic principle of fractal method applied in fault diagnosis is described. The result implies that the fractal dimension of good compressor is 4.4, and the fractal dimension of faulty compressor is 5.36, and fractal dimension of compressor with complex faults is 5.42. It is illustrated that this method is very effective for describing the fault features and diagnosing the complex fault of complex. This method can diagnose and predict the complex fault with a high correctness, and has been used in the Shanxi-Beijing pipeline station successfully, Which provide a good tool for pipeline’s Safety and Integrity Management.


2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740027 ◽  
Author(s):  
Ye Zhu ◽  
Shi-Cheng Wei ◽  
Yu-Cai Dong ◽  
Yi Liang ◽  
Yu-Jiang Wang

Concerning ultrasonic non-destructive testing of ceramic-lined composite steel pipes, a novel bonding flaw locating method based on fractal dimension is proposed. Ultrasonic A-scan method is used on different positions of the composite steel pipe test piece. The fractal dimension of each curve of ultrasonic vibration signal is calculated. The transformation of each fractal dimension is compared and abnormal positions where bonding defects potentially exist are detected. The result indicates that ultrasonic A-scan signal has an excellent fractal conduct characteristic. It is feasible to compare fractal dimension of signal with the normal range and find out abnormal positions, which can provide basis for follow-up inspections.


2021 ◽  
pp. 107754632198952
Author(s):  
Xiaomin Yang ◽  
Yongbing Xiang ◽  
Bingzhen Jiang

Bearing multi-fault detection from stochastic vibration signal is still a thorny task to dispose of because of the complex interplay between different fault components under severe noise interference. In such case, conventional techniques such as filter processing and envelope demodulation may cause undesired results. To overcome the limitation, this article explores a filtering-free technique combined probabilistic principal component analysis denoising with the Higuchi fractal dimension transformation to diagnose the bearing multi-faults. Fractal theory is used to optimize the model parameters and stabilize the random vibrational signal for fast Fourier transform spectrum analysis. Noise interference in the Higuchi transformation is capped using a probabilistic principal component analysis model whose parameters are optimized through embedding dimension Cao algorithm and correlation dimension Grassberger and Procaccia algorithm. The fault diagnostic scheme mainly falls into three steps. First, the original vibration signal is truncated into a series of sub-signal segments by moving window whose length is determined as twice the value of maximum time delay that is provided by examining the steady Higuchi fractal dimension value of a raw signal in a process of plotting the fractal dimension over a range of time delay. Then, the Higuchi approach is used to estimate the average fractal dimension for each segment to create a quasi-stationary Higuchi fractal dimension sequence on which, finally, the fault features are straightforwardly extracted by the fast Fourier transform algorithm. The effectiveness of the proposed method is validated using simulated and experimental compound bearing fault vibration signals. Some fault components may be clouded if applied Higuchi fractal dimension alone because of the noise interference, but using the probabilistic principal component analysis–Higuchi fractal dimension method leads to clear diagnostic results. It indicates that the proposed approach can be incorporated into bearing multi-fault extraction from raw vibration signals.


2011 ◽  
Vol 301-303 ◽  
pp. 139-142
Author(s):  
Ya Feng Li ◽  
Yu Xiu Xu ◽  
Xin Hua Ma

According to characteristic of wind turbine vibration signal, base on the length fractal dimension principle, carry out quantitative description of length fractal characteristics to nonlinear signals on the fault generated by the wind turbine blades. The test and calculation results show that when the different wind turbine blades failures occur, the length fractal dimension value appear clear rules. Therefore, we can use the length fractal dimension effectively extract the fault character parameters of wind turbine blade.


2014 ◽  
Vol 926-930 ◽  
pp. 1712-1715
Author(s):  
Zhen Shu Ma ◽  
Chao Liu ◽  
Hua Gang Sun ◽  
Zhi Chuan Liu

As a result of the presence of noise in the measured vibration signal has a great influence on the results of calculation of fractal dimension, Therefore the empirical mode decomposition method for noise reduction of gear vibration signal is used, calculation fractal dimension, extraction fault feature of Gear in different conditions. The measured results show that: Different fault states have different fractal dimension, we can judge the fault type of gear effectively by the fractal dimension.


2010 ◽  
Vol 34-35 ◽  
pp. 1269-1273
Author(s):  
Bing Cheng Wang ◽  
Zhao Hui Ren

Four different fault signals are simulated and collected which are oil whip fault signal, rub-impact fault signal, rub- oil whip coupling fault signal and rub - loose coupling fault signal in the lab. According to the Restructuring the theory of phase space, in foundation of the optimal delay time τ and the embedding dimension d, phase space is restructured to the time sequence of different fault. Simultaneously in connection with the general fractal theory and its algorithm, author has conducted the analysis and study, and the correlation integral is used to the concrete calculation of general fractal dimension, fractal dimensions of four kind of fault are calculated separately by this calculation method. The research goal is attempting to explore one new calculation method of general fractal dimension to improve accuracy and increase the degree of differentiation, to provide the basis for the analysis of the fault signal.


2021 ◽  
pp. 107754632110418
Author(s):  
Mingyue Yu ◽  
Minghe Fang ◽  
Wangying Chen ◽  
Haonan Cong

To effectively extract the information of compound faults of inter-shaft bearing of an aero-engine based on casing vibration signals, the paper has introduced the concept of weighted Katz fractal dimension and proposed the method combining information fusion, wavelet transform (WT), singular value decomposition (SVD), and Katz fractal dimension, the cross-correlation function (CCF-WT-SVD-Katz algorithm). The method includes homologous information fusion achieved by the CCF of horizontal and vertical vibration signals of the rotor from the same section; signal separation and denoising of blended signals through WT and SVD; reinforcement of fault characteristics of signals according to weighted Katz fractal dimension; and extraction of characteristic frequencies of compound faults of inter-shaft bearing by frequency spectrum of weighted and reconstructed signals. The result indicates that the proposed CCF-WT-SVD-Katz algorithm is capable of effectively extracting compound fault characteristics of inter-shaft bearing and precisely identifying a fault type based on whole casing vibration signals and will be of very good application value in engineering.


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