CN101251445B - Fractal characteristic analysis method for rotary machinery rub-impact acoustic emission signal - Google Patents

Abstract

The invention relates to a fractal characteristic analysis method of a rubbing acoustic emission signal of a rotary machine. The technical scheme of the invention is that an AE signal is extracted from an AE sensor at a friction point, Gaussian white noise and non-stationary noise are superposed on the AE signal, sampling, quantization and framing are carried out, and data containing noise of each frame are equally divided into short-time frame data segments of m; and calculating the fractal dimension value of each short-time frame data segment by using a fractal dimension algorithm based on a waveform, and taking the data of the middle sequence number as the output of median filtering. The method solves the defects of very large calculated amount, low precision of Katz dimension and large fluctuation of short-time frame dimension dividing curve in the prior method. Under the strong noise environment, the log wavelength dimension is more than Katz and box dimension, so that the capability of distinguishing noise and AE signals is stronger, and the log wavelength dimension of an AE signal frame is more close to the fractal dimension of a pure AE signal than the Katz and box dimension, so that the occurrence of an rub-impact AE event can be effectively detected and reflected, the accuracy is high, and the calculated amount is reduced.

Description

Fractal Characteristic Analysis Method of Acoustic Emission Signal from Rotating Machinery

technical field

The invention relates to an analysis method for rubbing acoustic emission signals of rotating machines, in particular to a method for analyzing fractal characteristics of rubbing acoustic emission signals of rotating machines.

Background technique

Acoustic emission technology AE (Acoustic Emission) has shown its superiority in rubbing fault detection due to its high sensitivity, wide frequency response range, large amount of information, and dynamic detection. When rubbing occurs, it is accompanied by a strong AE signal. The occurrence and intensity of rubbing can be judged by the AE characteristic parameters and their changes, and the location of the rubbing point can be determined. However, due to the diversity of AE sources and the complexity of noise interference, the characteristic parameters of AE often cannot reflect the real state of the equipment, especially in strong noise environments, the identification and extraction of AE features has always been a problem. Using fractal theory to carry out theoretical calculation and experimental research on rubbing fault, and use it as a characteristic parameter to quantitatively describe AE signal. It can effectively identify the status and early warning of the equipment, and achieve good results. But in practical application, the calculation amount of fractal dimension algorithm is the bottleneck that limits its application.

Before the present invention, currently commonly used fractal dimension methods include box dimension, correlation dimension and Katz dimension methods. For the box dimension, as the dimension of the system increases, the number of boxes required increases exponentially, and the length of data required for calculation also increases accordingly, making the convergence of high-dimensional systems very difficult. Whereas the associative dimension heavily depends on two parameters: minimum latency and minimum embedding dimension. If the minimum delay time is too large to reach the size of the attractor, all vectors are correlated, and if it is too small, the calculated correlation dimension is the correlation dimension of noise. For the AE signal, since the minimum delay time of each frame is different, the minimum delay time must be calculated for each frame to calculate the accurate correlation dimension, and the amount of calculation is very large. Katz dimension does not require calculation limits, is not strongly dependent on parameters, and is superior to other algorithms in anti-noise ability, but Katz dimension has the disadvantage of low precision.

Contents of the invention

The purpose of the present invention is to solve the defects of the above-mentioned prior art. Starting from the definition of fractal dimension, with the purpose of reducing the amount of calculation and improving the accuracy, a fractal dimension calculation method based on the waveform length - wavelength logarithm method is designed. .

Technical scheme of the present invention is:

The fractal characteristic analysis method of the rubbing acoustic emission signal of rotating machinery, its steps are:

Firstly, the noise containing the AE signal after sampling and quantification is divided into frames, and then each frame signal is divided into short-time frame data segments of equal length, and the fractal dimension of each segment is calculated by using the waveform-based fractal dimension feature analysis algorithm. Finally, the Median filtering is performed on each frame.

(1) Extraction and preprocessing of AE signal:

(1-1) Extract the AE signal through the first AE sensor close to the friction point or the second AE sensor located at the other end of the coupling;

(1-2) Superimpose Gaussian white noise and non-stationary noise on the continuous rubbing AE signal;

(1-3) Sampling, quantization, and framing;

(1-4) Divide each frame of noise-containing data into m short-time frame data segments;

(2) Calculate the fractal value of each frame:

(2-1) Using the waveform-based fractal dimension algorithm, that is, the logarithmic wavelength dimension algorithm, to calculate the fractal dimension value of each short-time frame data segment:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; b\&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}$

in $a=1+\frac{{\mathrm{<figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout>}k}_1}{{\ln \mathrm{\&delta;}}_0},$ $b=r(\frac{\mathrm{\&delta;}}{{\mathrm{\&delta;}}_0}-1),$ δ is the scale of the box coverage curve, δ ₀ is the minimum sampling interval, δ is an integer multiple of the minimum sampling interval δ ₀ , that is, δ=kδ ₀ , and L(δ) is the corresponding curve length.

(2-2) Arrange each segment, that is, D _iv ,..., D _i-1 , D _i , D _i+1 ,..., D _i+v according to the numerical value, and take the data with the middle serial number as the middle Value filtered output:

${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Med</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

In the fractal feature analysis method of the rotating mechanical rubbing acoustic emission signal, the sampling frequency is 5MHz, the A/D precision during quantization is 12 bits, and the frame length of each frame is 512 sampling points during frame division , 50% of frames overlap, and m must be odd.

In the method for analyzing the fractal characteristics of the rotating machinery rubbing acoustic emission signal, the AE signal extracted by the first AE sensor which is closer to the real sound source signal is usually analyzed.

Advantage and effect of the present invention are:

1. In a strong noise environment, the logarithmic wavelength dimension has a stronger ability to distinguish noise and AE signals than the Katz dimension and the box dimension, and the logarithmic wavelength dimension of the AE signal frame is closer to the pure AE signal than the Katz dimension and the box dimension. dimension, so as to effectively detect and reflect the occurrence of rubbing AE events.

2. In terms of computational complexity and stability of accuracy, the logarithmic wavelength dimension is also superior to the Katz dimension and the box dimension, thus effectively solving the problem of large amount of calculation for rubbing faults using fractal theory.

3. Using the median filter technology, the problem of large fluctuations in the short-time frame fractal dimension curve caused by noise is alleviated.

Other advantages and effects of the present invention will be described below.

Description of drawings

Figure 1—Schematic diagram of rubbing acoustic emission test bench.

Figure 2—Acoustic emission signal waveform diagram during continuous rubbing.

Figure 3——When δ is small, the AE waveform curve in the box.

Fig. 4—Comparison of fractal-dimensional means for logarithmic wavelength dimension, Katz dimension, and box dimension.

Fig. 5 - Computational complexity comparison of logarithmic wavelength dimension, Katz dimension and box dimension.

Fig. 6—Curves of three kinds of frame fractal dimension changes of continuous rubbing AE signals under white noise environment (0dB).

Figure 7——Curves of three kinds of frame fractal dimension changes of continuous rubbing AE signals in a colored noise environment (0dB).

Detailed ways

The technical solutions of the present invention will be further described below in conjunction with the drawings and embodiments.

1. Extraction and preprocessing of AE signal

1. Extraction of AE signal

This test uses a 3-support 2-span rotor system, as shown in Figure 1. The first bearing 2, the second bearing 6 and the third bearing 8 are all hydrodynamic lubricated sliding bearings, the friction point 4 is close to the motor 1, the first AE sensor 3 is close to the friction point, and the second AE sensor 7 is located on the other side of the coupling 5 one end. The AE signal waveform extracted by the first AE sensor or the second AE sensor. In this example, the AE signal waveform is extracted from the first AE sensor, which can be used to analyze the attenuation of acoustic signal propagation and signal distortion after coupling through a discontinuous medium. Here, we analyze the signal extracted by the first AE sensor 3 which is closer to the real sound source signal. In the experiment, the sampling frequency is set to 5MHz, and the waveform of the AE signal of continuous rubbing is shown in Figure 2.

2. Preprocessing of AE signal

Gaussian white noise and non-stationary noise were superimposed on the continuous rubbing AE signal (the noise source was provided by the Netherlands RSRE Research Center affiliated to the British TNO Perception Society). Sampling, quantization, and framing of noisy signals. When framing, the frame length of each frame is 512 sampling points, and 50% of the frames overlap.

Considering the influence of noise, the fractal curve of each frame may fluctuate greatly. After framing, each frame of noise-containing data is equally divided into m short-time frame data segments (m is an odd number), which is convenient for median value after calculating the fractal value of each short-time data frame filtering.

2. Waveform-based fractal dimension method

According to the definition of fractal dimension:

$\mathrm{D.}=-\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }\frac{\ln N_{\mathrm{\&delta;}}\left(f\right)}{\ln \mathrm{\&delta;}}$ (Formula 1)

Among them, N _δ (F) is the minimum number of box-covering curves whose scale is δ, and l _i (δ) is the length of the curve inside the i-th box whose side length is δ.

make: $L\left(\mathrm{\&delta;}\right)=\underset{i=1}{\overset{N_{\mathrm{\&delta;}}\left(f\right)}{\mathrm{\&Sigma;}}}{l}_i\left(\mathrm{\&delta;}\right)$ (Formula 2)

Analyzing the AE signal waveform, when δ tends to 0, the curves inside the box can be mainly divided into several situations as shown in Figure 3. Among them, (a) and (b) are monotonic curves, (c) and (d) are curves containing one extreme point, and (e) and (f) are curves containing multiple extreme points. For the convenience of analysis, when δ tends to 0, the length of the curve inside the box is equivalent to:

(式3)

(Formula 3)

k ₁ and k ₂ are respectively the ratio of the equivalent length of the curve containing at most one extremum point and the curve containing multiple extremum points to the side length of the box.

but: $L_{\mathrm{the\; s}}=\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }L\left(\mathrm{\&delta;}\right)=\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }\underset{i=1}{\overset{N_{\mathrm{\&delta;}}\left(f\right)}{\mathrm{\&Sigma;}}}{l}_i\left(\mathrm{\&delta;}\right)=\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }(N_{\mathrm{\&delta;}}\left(f\right)-m){\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{\&delta;}+\mathrm{<figure-callout\; id="2"\; label="m\; k"\; filenames="S2008100238086E00011.png,S2008100238086E00012.png"\; state="\{\{state\}\}">m</figure-callout>}{k}_{}{}_2\mathrm{\&delta;}$

M is the number of boxes containing multiple poles, then $N_{\mathrm{\&delta;}}\left(f\right)=\frac{L\left(\mathrm{\&delta;}\right)+m(k_1-k_2)\mathrm{\&delta;}}{k_1\mathrm{\&delta;}}$

Then (Equation 1) can be rewritten as:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; lim</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout></span><figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">\; </figure-callout>}\mathrm{<span\; class="notranslate">\; </span>}\mathrm{<span\; class="notranslate">k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; )</span>$

Expand with Taylor series (δ ₀ is a very small value close to 0):

$\mathrm{D.}=(1+\frac{{\mathrm{<figure-callout\; id="1"\; label="ink"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ink</figure-callout>}}_1}{\ln {\mathrm{\&delta;}}_0}-\frac{\ln [L\left({\mathrm{\&delta;}}_0\right)+m(k_1-k_2){\mathrm{\&delta;}}_0]}{{\ln \mathrm{\&delta;}}_0})+\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }{(1+\frac{{\mathrm{<figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout>}k}_1}{\ln \mathrm{\&delta;}}-\frac{\ln [L\left(\mathrm{\&delta;}\right)+m(k_1-k_2)\mathrm{\&delta;}]}{\ln \mathrm{\&delta;}})}^{\&prime;}{|}_{\mathrm{\&delta;}={\mathrm{\&delta;}}_0}(\mathrm{\&delta;}-{\mathrm{\&delta;}}_0)$ (Formula 4)

Simplify the second item of (Formula 4):

$(\frac{{\mathrm{<figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout>}k}_1}{{\mathrm{\&delta;}}_0{\mathrm{<figure-callout\; id="2"\; label="ln"\; filenames="S2008100238086E00011.png,S2008100238086E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}}^2{\mathrm{\&delta;}}_0}+\frac{1}{{\mathrm{\&delta;}}_0\ln {\mathrm{\&delta;}}_0}-\frac{(L^{\&prime;}\left({\mathrm{\&delta;}}_0\right)+m(k_1-k_2))}{[L\left({\mathrm{\&delta;}}_0\right)+m(k_1-k_2){\mathrm{\&delta;}}_0]\ln [L\left({\mathrm{\&delta;}}_0\right)+m(k_1-k_2){\mathrm{\&delta;}}_0]})\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }(\mathrm{\&delta;}-{\mathrm{\&delta;}}_0)$ (Formula 5)

In item 3 of (Formula 5), when δ ₀ →0, the change of L(δ ₀ ) tends to be slow, let L′(δ ₀ )=r, when δ ₀ →0, the number of boxes containing multiple poles tends to at 0. but:

$(-\frac{r}{L\left({\mathrm{\&delta;}}_0\right)\ln L\left({\mathrm{\&delta;}}_0\right)})\underset{\mathrm{\&delta;}\&Right\; Arrow;0}{\lim }(\mathrm{\&delta;}-{\mathrm{\&delta;}}_0)$ (Formula 6)

According to (formula 4), (formula 5) and (formula 6) can get:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout></span><figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">\; </figure-callout>}\mathrm{<span\; class="notranslate">\; </span>}\mathrm{<span\; class="notranslate">k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; lim</span>}}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout></span><figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">\; </figure-callout>}\mathrm{<span\; class="notranslate">\; </span>}\mathrm{<span\; class="notranslate">k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="ln"\; filenames="S2008100238086E00011.png,S2008100238086E00012.png"\; state="\{\{state\}\}">ln</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

When δ ₀ →0, in the above formula $\frac{\ln {\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="2"\; label="ln"\; filenames="S2008100238086E00011.png,S2008100238086E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}}^2{\mathrm{\&delta;}}_0}$ and $\frac{1}{{\ln \mathrm{\&delta;}}_0}$ Both → 0, further simplified to get:

$\mathrm{D.}=a-\frac{\ln [L\left({\mathrm{\&delta;}}_0\right)+\mathrm{Mike}{\mathrm{\&delta;}}_0]}{\ln {\mathrm{\&delta;}}_0}-\frac{{\mathrm{b\&delta;}}_0}{L\left({\mathrm{\&delta;}}_0\right)\ln L\left({\mathrm{\&delta;}}_0\right)}$ (Formula 7)

In order to further reduce the amount of calculation, considering that when δ ₀ ≈δ→0, the number M of boxes containing multiple poles also tends to 0, it can be obtained:

$\mathrm{D.}=a-\frac{\ln L\left(\mathrm{\&delta;}\right)}{\ln {\mathrm{\&delta;}}_0}-\frac{{\mathrm{b\&delta;}}_0}{L\left(\mathrm{\&delta;}\right)\ln L\left(\mathrm{\&delta;}\right)}$ (Formula 8)

in: $a=1+\frac{\mathrm{<figure-callout\; id="1"\; label="ln\; k"\; filenames="S2008100238086E00013.png,S2008100238086E00021.png"\; state="\{\{state\}\}">ln</figure-callout>}{k}_{}{}_1}{\ln {\mathrm{\&delta;}}_0},$ $b=r(\frac{\mathrm{\&delta;}}{{\mathrm{\&delta;}}_0}-1)$

(Formula 8) is the waveform-based fractal dimension algorithm, which is called the logarithmic wavelength dimension. In the formula, δ ₀ can be an integer multiple of the minimum sampling interval δ, let δ ₀ =kδ, and L(δ ₀ ) is the corresponding curve length. The parameters a, b, and k are determined using fractal Brownian curves.

Calculate the fractal dimension value of each short-time frame data segment by (Formula 8), that is, D _iv ,..., D _i-1 , D _i , D _i+1 ,..., D _i+v , and press The numerical values are arranged, and the data with the middle serial number is taken as the output of the median filter:

$Y_i=\mathrm{Med}\{{\mathrm{D.}}_{i-v},...,{\mathrm{D.}}_{i-1,}{\mathrm{D.}}_i,{\mathrm{D.}}_{i+1},...,{\mathrm{D.}}_{i+v}\}v=\frac{m-1}{2}$ (Formula 9)

Since the median filter is a nonlinear filter and does not require the statistical characteristics of the signal, it can well reduce the influence of random interference and pulse interference, and has basically no effect on the spectrum.

3. Performance evaluation

In order to compare the performance of the logarithmic wavelength dimension, it is compared with the box dimension and Katz dimension. Figure 4 is the comparison result. The fractal Brownian curve in the comparison process is generated by the computer through 15 iterations, with a total of 2 ¹⁵ =32786 points, The program divides the curve into frames, each frame has 512 points, calculates the fractal dimension of each frame, and averages the fractal dimension values of each frame to obtain the final result. It can be seen from Figure 4 that the logarithmic wavelength dimension has the highest accuracy, followed by the box dimension, and finally the Katz algorithm.

Figure 5 shows the comparison results of the computational complexity of the logarithmic wavelength dimension, Katz dimension and box dimension. The minimum box length of is also 1, and a total of k points participate in box-dimensional curve fitting, and the box lengths are 1, l ₁ , l ₂ ,..., l _k . It can be seen from Figure 5 that the number of additions, multiplications, and nonlinear operations of the box dimension are significantly greater than those of the Katz dimension and the logarithmic wavelength dimension; while the logarithmic wavelength dimension has the best performance in terms of addition, multiplication, comparison, and nonlinear operations. are the smallest among them.

Figure 6 and Figure 7 respectively show the curves of three kinds of frame fractal dimension changes of continuous rubbing AE signals under white noise environment (0dB) and colored noise environment (0dB), as can be seen from the figure:

(1) In the noisy AE signal, the frame fractal dimension curve of the logarithmic wavelength method is relatively smooth. In Figure 6 and Figure 7, there are many places where the fractal dimension value is significantly smaller than the noise fractal dimension value, and it can be judged that there are AE in these places signal generation;

(2) Analyzing the noise segments of the three frame fractal dimension curves shows that the logarithmic wavelength method fluctuates the least, while the fluctuations of the Katz dimension and the box dimension are relatively large. It can be concluded that the logarithmic wavelength dimension is more stable than the Katz dimension and the box dimension ;

(3) The logarithmic wavelength dimension of the signal segment of the noisy AE signal is obviously smaller than that of the noise segment, while the box dimension has little difference between the two. In the colored noise environment, the box dimension and Katz are almost indistinguishable from the noise and the AE signal.

Figures 6 and 7 show that in the case of strong noise, the logarithmic wavelength method is more capable of distinguishing noise and rubbing AE signals, and the logarithmic wavelength dimension of the AE signal frame is closer to that of the pure AE signal than the Katz dimension and the box dimension fractal dimension.

The above results show that in a strong noise environment, the logarithmic wavelength dimension can reflect the occurrence of rubbing AE events; the logarithmic wavelength dimension has a stronger ability to distinguish noise and AE signals than the Katz dimension and the box dimension; in terms of computational complexity and accuracy The stability is also better than Katz dimension and box dimension. The good performance of the algorithm makes it provide a new way for the feature recognition and analysis of rubbing AE signals, and it is a better fractal dimension calculation and analysis method for dealing with rubbing AE signals.

The scope of protection claimed in the present invention is not limited only to the description of this specific embodiment.

Claims (3)

1. The fractal feature analysis method of the rubbing acoustic emission signal of rotating machinery, its steps are: First, the noise containing the AE signal after sampling and quantification is divided into frames, and then each frame signal is divided into short-time frame data segments of equal length, and the fractal dimension value of each segment is calculated by using the waveform-based fractal dimension feature analysis algorithm, and finally Perform median filtering on each segment; (1) Extraction and preprocessing of AE signal: (1-1) Extract the AE signal from the first AE sensor located at one end of the coupling or the second AE sensor located at the other end of the coupling by approaching the friction point of the friction acoustic emission test bench; (1-2) Superimpose Gaussian white noise and non-stationary noise on the continuous rubbing AE signal; (1-3) Sampling, quantization, and framing; (1-4) Divide each frame of noise-containing data into m short-time frame data segments; (2) Calculate the fractal value of each segment: (2-1) Using the waveform-based fractal dimension algorithm, that is, the logarithmic wavelength dimension algorithm, to calculate the fractal dimension value of each short-time frame data segment, ${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; b\&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}$ in $a=1+\frac{\ln k_1}{\ln {\mathrm{\&delta;}}_0},$ $b=r(\frac{\mathrm{\&delta;}}{{\mathrm{\&delta;}}_0}-1),$ δ is the scale of the box coverage curve, δ ₀ is the minimum sampling interval, δ is an integer multiple of the minimum sampling interval δ ₀ , that is, δ=kδ ₀ , and L(δ) is the length of the corresponding curve; k ₁ is that it contains at most one extremum The ratio of the equivalent length of the point curve to the side length of the box; r=L'(δ ₀ ); (2-2) Arrange each segment, that is, D _iv ,..., D _i-1 , D _i , D _i+1 ,..., D _i+v according to the numerical value, and take the data of the middle serial number as the The output of the segment's median filter: $\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Med</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; \}</span>& \mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}$ m is an odd number. 2. the fractal feature analysis method of rotating machinery rubbing acoustic emission signal according to claim 1, is characterized in that, the sampling frequency during sampling is 5MHz, and the A/D precision during quantization is 12, and each frame during subdivision The frame length of is 512 samples, 50% of the frames overlap, and m must be an odd number. 3. The method for analyzing fractal characteristics of rubbing acoustic emission signals of rotating machinery according to claim 1, characterized in that the AE signal extracted by the first AE sensor which is closer to the real sound source signal is usually analyzed.

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