scholarly journals Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

2018 ◽  
Vol 5 (5) ◽  
pp. 180087 ◽  
Author(s):  
Xiang Chen ◽  
Jingchao Li ◽  
Hui Han ◽  
Yulong Ying
Keyword(s):  
Feature Extraction ◽  
Hilbert Transform ◽  
Radiation Source ◽  
Box Dimension ◽  
Instantaneous Amplitude ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Source Signal ◽  
The Hilbert Transform ◽  
Subtle Feature

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

scholarly journals Instantaneous Amplitude-Frequency Feature Extraction for Rotor Fault Based on BEMD and Hilbert Transform

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Chuanjin Huang ◽  
Haijun Song ◽  
Wenping Lei ◽  
Zhanya Niu ◽  
Yajun Meng
Keyword(s):  
Feature Extraction ◽  
Hilbert Transform ◽  
Vibration Signal ◽  
Three Dimensions ◽  
Intrinsic Mode Functions ◽  
Instantaneous Amplitude ◽  
Vibration Signals ◽  
Feature Extraction Method ◽  
Fault Features ◽  
The Hilbert Transform

The vibration signals propagating in different directions from rotating machines can contain a variety of characteristic information. A novel feature extraction method based on bivariate empirical mode decomposition (BEMD) for rotor is proposed to comprehensively extract the fault features. In this work, the number of signal projection directions is determined through simulation, and the energy end condition based on the energy threshold is increased using BEMD to enhance the decomposition quality. Mixed vibration signals are generated along two orthogonal directions. Then, the acquired vibration signal can be decomposed into several intrinsic mode functions (IMFs) at the rotational speed using the BEMD method. Furthermore, the instantaneous frequency and instantaneous amplitude of the real signals and the imaginary part of the IMF signals are obtained using the Hilbert transform. The fault features along two and three dimensions can be investigated, providing more comprehensive information to aid in the fault diagnosis of rotor. Experimental results on oil film oscillation, the oil whirl, the bistability of the rotor, and looseness and rotor rubbing composite fault indicate the effectiveness of the proposed method.

DIMENSION ANALYSIS OF CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (01) ◽  
pp. 1730001 ◽  
Author(s):  
JUN WANG ◽  
KUI YAO
Keyword(s):  
Hausdorff Dimension ◽  
Fractal Dimensions ◽  
Continuous Functions ◽  
Packing Dimension ◽  
Box Dimension ◽  
Box Counting ◽  
Dimension Analysis ◽  
Box Counting Dimension ◽  
Self Similar

In this paper, we mainly discuss fractal dimensions of continuous functions with unbounded variation. First, we prove that Hausdorff dimension, Packing dimension and Modified Box-counting dimension of continuous functions containing one UV point are [Formula: see text]. The above conclusion still holds for continuous functions containing finite UV points. More generally, we show the result that Hausdorff dimension of continuous functions containing countable UV points is [Formula: see text] also. Finally, Box dimension of continuous functions containing countable UV points has been proved to be [Formula: see text] when [Formula: see text] is self-similar.

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.

Box-Counting Dimension of Fractal Urban Form

2012 ◽  
Vol 3 (3) ◽  
pp. 41-63 ◽  
Author(s):  
Shiguo Jiang ◽  
Desheng Liu
Keyword(s):  
Fractal Dimension ◽  
Urban Form ◽  
Fractal Dimensions ◽  
Reliable Estimate ◽  
Box Dimension ◽  
Beijing City ◽  
Box Counting ◽  
Window Method ◽  
Box Counting Dimension ◽  
Data Points

The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead to unreliable estimates of fractal dimensions for urban forms, and thus cast doubt on further analysis. This paper presents a detailed discussion of these issues in the case of Beijing City. The authors propose corresponding improved techniques with modified measurement design to address these issues: 1) rectangular grids and boxes setting up a proper box cover of the object; 2) pseudo-geometric sequence of box sizes providing adequate data points to study the properties of the dimension profile; 3) generalized sliding window method helping to determine the scaling range. The authors’ method is tested on a fractal image (the Vicsek prefractal) with known fractal dimension and then applied to real city data. The results show that a reliable estimate of box dimension for urban form can be obtained using their method.

The Blemish Identify in Ultrasonic Testing of Friction Welded Joints Based on Fractal Theory

2015 ◽  
Vol 799-800 ◽  
pp. 942-946
Author(s):  
Yuan Peng Liu ◽  
Xin Yin ◽  
Min Wang
Keyword(s):  
Fractal Dimension ◽  
Welded Joints ◽  
Ultrasonic Testing ◽  
Fractal Theory ◽  
Metal Alloys ◽  
Box Dimension ◽  
Box Counting ◽  
Signal Characteristics ◽  
Box Counting Dimension ◽  
Dimension Number

The friction welded joints made by GH4169 heat metal alloys are detected by U1traPAC system of the ultrasonic wave explore instrument. Aimed at the blemish signal characteristics, a method is put forward to identify the blemish signal in ultrasonic testing of friction welded joints based on fractal theory., A new kind of fractal dimension number calculation method—normalized scale box-counting dimension method is used to calculate the box-dimension of the blemish signal, and statistic and analysis the scopes of the box-dimension of the blemish signal and the square differ of the result. The preliminary experimental results show that the blemish signal and have each fractal dimension zones, and don’t hand over to fold. So it can use to judge whether the blemish exist or not. The method is identified to have better covariance characteristics about the blemish identify of the friction welded joints.

scholarly journals Bypassing dynamical systems: a simple way to get the box-counting dimension of the graph of the Weierstrass function

2018 ◽  
Vol 11 (2) ◽  
Author(s):  
Claire David
Keyword(s):  
Dynamical Systems ◽  
Real Number ◽  
Box Dimension ◽  
Weierstrass Function ◽  
Real Numbers ◽  
Box Counting ◽  
Box Counting Dimension

In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by\[{\mathcal W}(x)= \sum_{n=0}^{+\infty} \lambda^n\,\cos \left ( 2\, \pi\,N_b^n\,x \right),\]where $\lambda$ and $N_b$ are two real numbers such that $0 <\lambda<1$, $N_b\,\in\,\N$ and $\lambda\,N_b >1$, using a sequence a graphs that approximate the studied one.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

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