CN113188651B - Vibration signal feature extraction and tool wear value prediction method based on IMF-PSD spectral line - Google Patents
Vibration signal feature extraction and tool wear value prediction method based on IMF-PSD spectral line Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L3/00—Measuring torque, work, mechanical power, or mechanical efficiency, in general
- G01L3/24—Devices for determining the value of power, e.g. by measuring and simultaneously multiplying the values of torque and revolutions per unit of time, by multiplying the values of tractive or propulsive force and velocity
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M99/00—Subject matter not provided for in other groups of this subclass
- G01M99/005—Testing of complete machines, e.g. washing-machines or mobile phones
Abstract
The invention provides a vibration signal characteristic extraction and cutter wear value prediction method based on IMF-PSD spectral lines, which comprises the following steps: the method comprises the following steps: collecting an original signal, carrying out inherent modal decomposition on the original signal by utilizing ensemble empirical modal decomposition, adding white noise reduction, and simultaneously sequentially expanding the original signal according to the amplitude frequency from high to low to obtain a plurality of IMF components by decomposition; step two: obtaining a PSD spectral line of each IMF component obtained in the first step through power spectral density analysis, and averaging to obtain an IMF-PSD spectral line; step three: performing Pearson correlation analysis on the IMF-PSD spectral line obtained in the step two, and extracting an IMF-PSD component spectral line most relevant to the degradation amount; step four: establishing a prediction model for IMF-PSD component spectral lines extracted in the third step by using a regression analysis method; and step five: and predicting the tool wear value through the regression model established in the fourth step.
Description
Technical Field
The invention belongs to reliability evaluation and health management of mechanical equipment, and particularly relates to a vibration signal feature extraction and cutter wear amount prediction method based on EEMD (ensemble empirical mode decomposition) and power spectral density.
Background
With the development and progress of science and technology, mechanical equipment plays an important role in modern industrial application, and with the increasing complexity of equipment structures, the feature extraction and further diagnosis and evaluation of the operation process information of the mechanical equipment are also increasingly important. In order to ensure the long-term and efficient normal operation of the equipment, the maintenance is reasonably organized according to the health state of the electromechanical equipment, and the surplus maintenance and the insufficient maintenance can be avoided. The implementation of the 'predicted maintenance' can effectively reduce the maintenance cost of the equipment, prolong the service life of the equipment and shorten unnecessary downtime. Therefore, the monitoring and diagnosis of the current state of the mechanical equipment are of great significance.
However, when a fault is about to occur, the complexity of the natural oscillation of the mechanical system varies, which causes great trouble to the analysis process of the fault signal. To detect mechanical equipment failures, a number of methods have been developed. At present, most feature extraction technologies only rely on traditional root mean square and peak values to perform feature extraction, and a series of values are usually extracted through a fixed algorithm by the traditional feature extraction, without considering the actual operating environment and operating state of equipment. Furthermore, merely deriving a change in value is not sufficient to understand what kind of change has occurred in the device.
The state evaluation is one of indispensable key links of mechanical equipment reliability evaluation and health management, failure of the equipment needs to be observed based on a traditional life test or an accelerated life test, the test sample size is large, the period is long, the energy consumption is high, and in addition, the current monitoring technology is lack of connection between equipment load and equipment state and monitoring collection and monitoring of the self-state information of the equipment.
Disclosure of Invention
In order to solve the above problems, embodiments of the present invention provide a vibration signal feature extraction and tool wear prediction method based on an IMF-PSD spectrum, based on the definition of Ensemble Empirical Mode Decomposition (EEMD) and power spectral density analysis, based on the state data of the device operation process. According to the method, collected equipment operation process signals are decomposed by integrating empirical mode decomposition (EEMD), power Spectral Density (PSD) is used for calculating the power spectral density of the decomposed Intrinsic Mode Function (IMF), IMF-PSD component spectral lines with high correlation are extracted in a self-adaptive mode according to a correlation analysis method, a linear regression method is adopted to fit performance degradation quantity to predict a tool wear value, and corresponding technical basis is provided for subsequent state evaluation and the like.
The embodiment of the invention provides a vibration signal feature extraction and tool wear value prediction method based on an IMF-PSD spectral line, which comprises the following steps: the method comprises the following steps: collecting an original signal, carrying out inherent modal decomposition on the original signal by utilizing ensemble empirical modal decomposition, adding white noise reduction, and simultaneously sequentially expanding the original signal according to the amplitude frequency from high to low to obtain a plurality of IMF components by decomposition; step two: obtaining a PSD spectral line of each IMF component obtained in the first step through power spectral density analysis, and averaging to obtain an IMF-PSD spectral line; step three: performing Pearson correlation analysis on the IMF-PSD spectral line obtained in the second step, and extracting an IMF-PSD component spectral line most relevant to the degradation amount; step four: establishing a prediction model for IMF-PSD component spectral lines extracted in the third step by using a regression analysis method; and the fifth step: and predicting the tool wear value through the regression model established in the fourth step.
According to another alternative embodiment, the first step further comprises:
a) Setting the total iteration number of decomposition as NE, and initializing the added white noise amplitude;
b) Decomposing the original signal added with white noise at the mth time, wherein m =1,2 \8230, NE, the initial time order m =1, and adding white noise to the original signal X (t)
X m (t)＝X(t)+n m (t)
Wherein X m (t) represents the m-th denoised signal, n m (t) represents white noise added by the mth decomposition;
c) Decomposing the m-th noisy signal X by using an ensemble empirical mode method m (t) obtaining the mth IMF component IMF m M =1,2, \8230;, NE, if m < NE, return to step b), and m = m +1, repeating steps b) and c);
calculating NE IMF components and signal residual r (t) obtained after NE time decomposition
According to another optional embodiment, the second step further comprises:
let u (t) be a function in a spatial domain, and perform Fourier transform when u (t) satisfies the following three Dirichlet conditions, namely, having a finite number of discontinuities, having a finite number of extreme points, and having an absolute integrable; if u (t) does not satisfy the Dirichlet condition, then no Fourier transform is possible, but if there is a finite average power, then the formula is satisfied
The function can be truncated:
wherein u (t) is a function in the spatial domain, i.e. the IMF after the decomposition in step one m A function;
fourier transform the function to U T (v)
Wherein t is time, e is a natural constant which is a constant in mathematics, is an infinite acyclic decimal and is an transcendental number, the value of the transcendental number is about 2.7182818459045, i is an imaginary number unit, and v is the angular velocity of u (t) in a frequency domain;
according to the Parceval theorem, | U T (v)| 2 Is a truncated signal u T (t) energy distribution in the frequency domain, then u T Normalized spectral density of (t) is:
wherein T is the total frequency band of the signal u (T);
the above expression has a dimension of power per frequency band, and defines the power spectral density of u (t) as
The distribution situation of the energy of the multi-state signal under different frequencies, namely the distribution situation of the task load under different frequencies, is obtained through power spectral density analysis;
averaging the power spectral density values to obtain a power spectral density average value:
wherein k is the number of frequency points of PSD spectral lines;
the IMF-PSD spectrum is defined as follows: n groups of vibration signals are collected in the running process of the equipment, and the p group of vibration signals x are subjected to p (t) carrying out ensemble empirical mode decomposition to obtain NE IMF components, and carrying out IMF analysis on the p-th group of vibration signals m Obtaining IMF by averaging power spectral density m -PSD p M =1,2,. NE; p =1,2,3,. Ang, n; common NEThe IMF-PSD curve is shown, the m IMF of the p group of vibration signals m -PSD p Expressed as:
at the m-th IMF component, the vibration signal x 1 (t),x 2 (t),…,x NE (t) the IMF-PSD spectrum is represented as follows:
IMF-PSD m ＝[IMF-PSD 1m ,IMF-PSD 2m ,IMF-PSD 3m ,...,IMF-PSD nm ]。
according to another optional embodiment, the third step further comprises:
calculating to obtain NE IMF-PSD spectral lines through the n groups of vibration signals collected in the step two, carrying out Pearson correlation analysis on the NE IMF-PSD spectral lines obtained through decomposition and an actual performance degradation curve, and extracting h IMF-PSD component spectral lines with correlation coefficients larger than 0.8;
given a binary totality (X, Y)
Wherein E (XY), E (X), E (Y) represent expectation, cov represents covariance, σ X 、σ Y Representing the variance.
According to another optional embodiment, the fourth step further comprises:
performing linear regression analysis on the extracted h IMF-PSD spectral lines and the performance degradation curve;
given x = (x) 1 ；x 2 ；x 3 ；…x h ) Wherein x h Is the h-th IMF power spectral density curve, and the linear regression model is a function predicted by linear combination of a plurality of functions, wherein w is a coefficient before a variable, and b is a function intercept
f(x)＝w 1 x 1 +w 2 x 2 +w 3 x 3 +…+w h x h +b；
The function is expressed in the form of a vector
f(x)＝w T x+b
Wherein, w = (w) 1 ；w 2 ；w 3 ；…；w h ) And after w and b are determined, establishing a regression model of the composite model.
According to another optional embodiment, step five further comprises: and inputting a corresponding x value according to the established f (x) regression model, and predicting the tool wear value.
According to another alternative embodiment, the collecting of the raw signal in the first step includes collecting any one of the historical signals from the beginning of use to the complete failure from the processing equipment or the equipment of the same type and in the same working environment as the processing equipment.
According to another embodiment of the invention, an equipment signal feature extraction and tool wear value prediction method based on an IMF-PSD spectrum is provided, and comprises the following steps:
step 1: performing natural modal decomposition on the acquired original signal by using the EEMD, adding white noise for noise reduction, and simultaneously sequentially expanding the original signal from high frequency to low frequency to obtain a plurality of IMF components by decomposition;
and 2, step: calculating the power spectral density value of each IMF component obtained by decomposition in the step 1, and calculating an IMF-PSD spectral line of the IMF-PSD component;
and step 3: performing correlation analysis according to the IMF-PSD spectral line calculated in the step 2 and a performance degradation curve, and extracting a power spectral density curve with the correlation larger than 0.8;
and 4, step 4: establishing a linear regression model for the h IMF-PSD spectral lines extracted in the step 3;
and 5: and (4) using the linear regression model established in the step (4) for predicting the performance degradation amount.
According to another optional embodiment, in step 1, the original signal includes any section of historical signal from the beginning of use to complete failure of the current equipment or equipment of the same type and working environment as the current equipment.
The vibration signal feature extraction and tool wear value prediction method based on the IMF-PSD spectral line provided by the embodiment of the invention at least comprises the following advantages: 1) Decomposing signals to different frequency bands by fully utilizing the integral characteristic of the ensemble empirical mode decomposition, calculating the power spectral density of the signals of different frequency bands, and combining the characteristic that the ensemble empirical mode decomposes the signals from high to low and the characteristic that the power spectral density can have different task information, thereby adaptively selecting the optimal number of Intrinsic Mode Functions (IMF) of all the signals under different working conditions; 2) The invention provides the characteristic quantity of IMF-PSD spectral line, judges the change of specific frequency band segment, can also carry out characteristic extraction and service life prediction on signals, and has very important significance for carrying out efficient and effective self-adaptive characteristic extraction in the technical fields of signal processing, characteristic extraction and the like of mechanical equipment reliability evaluation and health monitoring.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. The invention may be better understood by reference to the following drawings.
FIG. 1 is a flow chart of a vibration signal feature extraction and tool wear value prediction method based on IMF-PSD according to an embodiment of the invention;
FIG. 2 is a diagram illustrating sensor signal acquisition and performance degradation in an exemplary embodiment of a method for IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction, according to an embodiment of the present invention;
FIG. 3 shows IMF5-10 after power spectral density computation of a first set of vibration signals using an exemplary embodiment of a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention;
FIG. 4 illustrates an embodiment of the present invention applied to IMF-PSD spectral line-based vibration signal feature extraction and extractionIMF-PSD with feature extraction in an exemplary embodiment of a tool wear value prediction method 1-5 Comparing the characteristics with the tool wear value;
FIG. 5 shows an IMF-PSD extracted in an exemplary embodiment applying a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention 1-5 A spectral line three-dimensional graph;
FIG. 6 shows a scatter plot and a regression line of a regression curve fitted in an exemplary embodiment applying the IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction method provided in accordance with an embodiment of the present invention;
FIG. 7 shows tool wear value life prediction results in an exemplary embodiment of a method for vibration signal feature extraction and tool wear value prediction based on IMF-PSD spectral lines provided by an embodiment of the invention.
FIG. 8 shows a flow chart of a method for IMF-PSD based vibration signal feature extraction and tool wear value prediction according to another embodiment of the invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It is to be noted that, unless otherwise specified, technical or scientific terms used herein shall have the ordinary meaning as understood by those skilled in the art to which the present invention belongs.
Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, the present embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It is to be noted that, unless otherwise specified, technical or scientific terms used herein shall have the ordinary meaning as understood by those skilled in the art to which the present invention belongs.
FIG. 1 shows a flow chart of a vibration signal feature extraction and tool wear value prediction method based on IMF-PSD according to an embodiment of the invention. Referring to fig. 1, according to an embodiment of the present invention, there is provided a vibration signal feature extraction and tool wear value prediction method based on an IMF-PSD spectral line, including the following steps: the method comprises the following steps: collecting an original signal, carrying out inherent modal decomposition on the original signal by utilizing ensemble empirical modal decomposition, adding white noise reduction, and simultaneously sequentially expanding the original signal according to the amplitude frequency from high to low to obtain a plurality of IMF components by decomposition; step two: obtaining PSD spectral lines of each IMF component obtained in the first step through power spectral density analysis, and averaging to obtain IMF-PSD spectral lines; step three: performing Pearson correlation analysis on the IMF-PSD spectral line obtained in the second step, and extracting an IMF-PSD component spectral line most relevant to the degradation amount; step four: establishing a prediction model for the IMF-PSD component spectral lines extracted in the third step by using a regression analysis method; and step five: and predicting the tool wear value through the regression model established in the fourth step.
According to another optional embodiment, the first step further comprises:
a) Setting the total iteration times of decomposition as NE, and initializing the amplitude of the added white noise;
b) The original signal added with white noise at the mth decomposition, m =1,2 \8230ne, the initial time order m =1, is added with white noise for the original signal X (t)
X m (t)＝X(t)+n m (t)
Wherein, X m (t) represents the m-th noisy signal, n m (t) represents white noise added by the mth decomposition;
c) Decomposing the m-th noisy signal X by using an ensemble empirical mode method m (t) obtaining the m-thIMF component IMF m M =1,2, \ 8230, NE, if m < NE, return to step b), and m = m +1, repeating steps b) and c);
calculating NE IMF components obtained after NE decomposition and signal residual r (t)
According to another optional embodiment, the second step further comprises:
let u (t) be a function in a spatial domain, and perform Fourier transform when u (t) satisfies the following three Dirichlet conditions, i.e., having a finite number of discontinuities, having a finite number of extreme points, and having an absolute integrable; if u (t) does not satisfy the Dirichlet condition, then no Fourier transform is possible, but if there is a finite average power, then the formula is satisfied
The function can be truncated:
where u (t) is a function in the spatial domain, i.e. IMF after decomposition in step one m A function;
fourier transform the function to U T (v)
Wherein t is time, e is a natural constant which is a constant in mathematics, is an infinite acyclic decimal and is an overtaking number, the value of the overtaking number is about 2.718281828459045, i is an imaginary number unit, and v is the angular velocity of u (t) in a frequency domain;
according to Parceval's theorem, | U T (v)| 2 Is a truncated signal u T (t) energy distribution in the frequency domain, then u T (t) ofThe normalized spectral density is:
wherein T is the total frequency band of the signal u (T);
the above expression has a dimension of power per frequency band, and defines the power spectral density of u (t) as
The distribution situation of the energy of the multi-state signal under different frequencies, namely the distribution situation of the task load under different frequencies, is obtained through power spectral density analysis;
averaging the power spectral density to obtain a power spectral density average value:
wherein k is the number of frequency points of PSD spectral lines;
the IMF-PSD spectrum is defined as follows: in the running process of the equipment, n groups of vibration signals are collected in common, and the p group of vibration signals x are p (t) carrying out ensemble empirical mode decomposition to obtain NE IMF components, and carrying out IMF analysis on the p-th group of vibration signals m Obtaining IMF by averaging power spectral density m -PSD p M =1,2,. NE; p =1,2,3,. N; the total NE pieces of IMF-PSD curves are obtained, and the mth IMF of the pth group of vibration signals m -PSD p Expressed as:
at the m-th IMF component, the vibration signal x 1 (t),x 2 (t),…,x NE The IMF-PSD spectrum constituted by (t) is expressed as follows:
IMF-PSD m ＝[IMF-PSD 1m ,IMF-PSD 2m ,IMF-PSD 3m ,...,IMF-PSD nm ]。
according to another optional embodiment, the third step further comprises:
calculating to obtain NE IMF-PSD spectral lines through the n groups of vibration signals collected in the second step, performing Pearson correlation analysis on the NE IMF-PSD spectral lines obtained through decomposition and an actual performance degradation curve, and extracting h IMF-PSD component spectral lines with correlation coefficients larger than 0.8;
given a binary population (X, Y)
Wherein E (XY), E (X), E (Y) represent expectation, cov represents covariance, σ X 、σ Y Representing the variance.
According to another optional embodiment, the fourth step further comprises:
performing linear regression analysis on the extracted h IMF-PSD spectral lines and the performance degradation curve;
given x = (x) 1 ；x 2 ；x 3 ；…x h ) Wherein x is h Is the h IMF power spectral density curve, and the linear regression model is a function predicted by linear combination of a plurality of functions, wherein w is a coefficient before a variable, and b is a function intercept
f(x)＝w 1 x 1 +w 2 x 2 +w 3 x 3 +…+w h x h +b；
The function is expressed in the form of a vector
f(x)＝w T x+b
Wherein, w = (w) 1 ；w 2 ；w 3 ；…；w h ) And after w and b are determined, establishing a regression model of the composite model.
According to another optional embodiment, step five further comprises: and inputting a corresponding x value according to the established f (x) regression model, and predicting the tool wear value.
According to another alternative embodiment, the collecting of the raw signal in the first step includes collecting any one of the historical signals from the beginning of use to the complete failure from the processing equipment or the equipment of the same type and in the same working environment as the processing equipment.
FIG. 1 shows a flow chart of a vibration signal feature extraction and tool wear value prediction method based on IMF-PSD according to an embodiment of the invention. FIG. 2 is a diagram showing a sensor acquisition signal and a performance degradation amount in an exemplary embodiment of a vibration signal feature extraction and tool wear value prediction method based on IMF-PSD spectral lines according to an embodiment of the invention. FIG. 3 shows IMF5-10 of a first set of vibration signals subjected to power spectral density calculation in an exemplary embodiment applying the IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction method provided in accordance with an embodiment of the present invention. FIG. 4 shows IMF-PSD after feature extraction in an exemplary embodiment applying the IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction method provided in accordance with an embodiment of the present invention 1-5 The characteristics are compared to the tool wear value. FIG. 5 shows an IMF-PSD extracted in an exemplary embodiment applying a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention 1-5 And (4) a spectral line three-dimensional graph. FIG. 6 shows a scatter plot and a regression line of a regression curve fitted to an exemplary embodiment of a method for vibration signal feature extraction and tool wear value prediction based on IMF-PSD spectral lines provided in accordance with an embodiment of the present invention. FIG. 7 shows the tool wear value life prediction results in an exemplary embodiment using the IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction methods provided by embodiments of the present invention. FIG. 8 shows a flow chart of a vibration signal feature extraction and tool wear value prediction method based on IMF-PSD according to another embodiment of the invention.
Hereinafter, an exemplary embodiment to which the vibration signal feature extraction and tool wear value prediction method based on the IMF-PSD spectral line according to the embodiment of the present invention is applied will be described in detail with reference to the accompanying drawings. In the exemplary embodiment, to better ensure the accuracy of the test results, the present implementationThe method adopts the signals of the equipment operation historical signals (hereinafter referred to as original signals) as test bases to analyze, wherein the equipment operation process signals mainly refer to any section of historical signals from the beginning of use to complete failure collected from the current equipment or the equipment with the same type and the same working environment as the current equipment. The data to be decomposed employed in the present exemplary embodiment is externally disclosed in the big data game of the PHM association in 2010. The amount of wear, force signals, acoustic Emission (AE) signals and vibration signals of each tool are periodically detected during milling. Used in the present exemplary embodiment
The Tech RFM760 high-speed milling machine is characterized in that a cutter is a hard alloy three-edge ball-end milling cutter, the processing parameters such as the rotating speed of a main shaft, the feeding speed and the like are unchanged, and the specific model and the processing conditions of the cutter are as follows:
six full life cycle tests are carried out under the cutting condition, vibration signals of abrasion of six groups of cutters are measured, each group is cut for 315 times, and 315 abrasion values are measured, wherein the abrasion values are the performance degradation amount. FIG. 2 illustrates a first set of vibration signals and tool full life cycle wear values in an exemplary embodiment applying a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention.
Fig. 1 shows a flowchart of a vibration signal feature extraction and tool wear value prediction method based on IMF-PSD according to an embodiment of the present invention, which specifically includes the following steps:
step 1: natural mode decomposition of original signal by EEMD
Selecting a simulation superposition signal for research, wherein the added white noise signal-to-noise ratio Nstd is 0.2, the iteration total number NE is selected for 15 times, EEMD is carried out on the input original signal X (t), and the original signal is expanded from high frequency to low frequency. The specific process is as follows:
1) Firstly, initializing the amplitude of the white noise to be added, decomposing the signal to be decomposed added with the white noise for the mth time, initially setting m =1,
adding white noise to the original signal X (t)
X m (t)＝X(t)+n m (t)
Wherein n is m (t) represents white noise added by the mth decomposition, X m (t) represents the m-th time-denoised signal.
2) Decomposing the noisy signal by using an empirical mode method to obtain 15 IMF components;
if m < 15, return to step 1), and m = m +1; repeating steps 1) and 2),
each IMF component after m decompositions is computed to decompose the original signal into 15 IMF components and a signal residual component:
wherein, IMF m The mth IMF component obtained by the mth decomposition; r (t) is the signal residual component. Decomposing the tool cutting vibration signal by EEMD to obtain 315 groups of decomposed signals containing IMF 1-15 . FIG. 4 shows the first five sets of vibration signals IMF 1-5 Is shown in the figure of the time domain of (a),
step 2: calculating each IMF by power density analysis m The specific process of obtaining IMF-PSD spectral line is as follows:
in the implementation of calculating the power spectral density, the sampling frequency Fs is set to 50000.
Calculating 315 sets of vibration signals IMF 1-10 Wherein the IMF of each group m Denoted as u (t).
Where i is an imaginary unit, v is the angular velocity of u (t) in the frequency domain, and u (t) is the IMF of each group.
|U T (v)| 2 Is the original signal u T (t) energy distribution in the frequency domain, then u T The normalized spectral density of (t) is:
where T is the total frequency band of the signal u (T).
This expression has a dimension of power per unit frequency band, and therefore, it is logically possible to define the power spectral density of u (t) as
The distribution of the energy of the multi-state signal under different frequencies can be obtained through power spectral density analysis.
And taking the average value:
where k is the number of power spectrum points of the PSD (v).
Table 1 shows the calculation of the power spectral density average for each IMF1-10 of the first set for an exemplary embodiment of a method for vibration signal feature extraction and tool wear value prediction based on IMF-PSD spectral lines according to an embodiment of the present invention.
TABLE 1 power spectral density average of a first set of vibration signals IMF1-10
(a)
(b)
In the above table, the first and second sheets,
representing an average power spectral density of the mth IMF component of the decomposed first set of vibration signals; by analogy in the following way,
representing the mean value of the power spectral density of the 9 th IMF component of the vibration signal of the decomposed first group. There are 315 sets of data, and a total of 315 by 10 sets of power spectral density values are accumulated.
In the present invention, n groups of vibration signals u are subjected to n (t) performing EEMD decomposition to obtain NE IMFs, wherein the power spectral density PSD of the ith IMF is expressed as:
in the formula:
representing the power spectral density of the i-th IMF after decomposition of the vibration signal x (t). The IMF-PSD spectrum is defined by the present invention as follows: assuming that n groups of vibration signals are collected in the running process of the equipment, and the p-th group of vibration signals x p (t) EEMD decomposition is carried out to obtain NE IMF components, and the IMF in the p-th group of vibration signals is subjected to m Obtaining IMF by averaging power spectral density m -PSD p M =1,2,. NE; p =1,2,3,. N; the total NE pieces of IMF-PSD curves are obtained, and the mth IMF of the pth group of vibration signals m -PSD p Expressed as:
at the m-th IMF component, the vibration signal x 1 (t),x 2 (t),…,x NE The IMF-PSD spectrum constituted by (t) is expressed as follows:
IMF-PSD m ＝[IMF-PSD 1m ,IMF-PSD 2m ,IMF-PSD 3m ,...,IMF-PSD nm ]。
and step 3: and (3) extracting IMF components with most complex information by using a correlation analysis method according to the IMF-PSD spectral line obtained in the step (2).
And calculating to obtain NE IMF-PSD spectral lines, performing Pearson correlation analysis on the NE IMF-PSD spectral lines obtained by decomposition and an actual performance degradation curve, and extracting h IMF-PSD component spectral lines with the relation number larger than 0.8.
Given a binary population (X, Y):
wherein E (XY), E (X), E (Y) represent expectation, cov represents covariance, σ X 、σ Y Representing the variance.
Table 2 shows each IMF for calculating all vibration signals 1-10 Average power spectral density of (a).
(a)
(b)
As can be seen from Table 2 above, the IMF-PSD 1-5 The pearson correlation coefficient of the spectral line and the performance degradation curve is more than 0.8, and has high correlation with the performance degradation amount. Thus extracting the power spectral density average IMF-PSD 1-5 As key fitting parameters. FIG. 3 shows IMF of a first set of vibration signals applied with an exemplary embodiment of a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention 1-5 Work ofRate spectral density spectral lines.
And 4, step 4: and (5) performing a linear regression model on the extracted IMF-PSD spectral lines and the performance degradation value.
Given x = (x) 1 ；x 2 ；x 3 ；x 4 ；x 5 ) The linear regression model is a function in which a plurality of functions are predicted by linear combination
f(x)＝w 1 x 1 +w 2 x 2 +w 3 x 3 +…+w h x h +b
Written generally in the form of a vector:
f(x)＝w T x+b
wherein, w = (w) 1 ；w 2 ；w 3 ；…；w h ),x h Is the h-th IMF power spectral density curve, w is the coefficient before the variable, and b is the function intercept. After w and b are determined, a regression model of the composite model can be determined.
FIG. 4 illustrates an extracted IMF-PSD in an exemplary embodiment applying a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention 1-5 Graph comparing the wear value of the tool.
FIG. 5 shows an IMF-PSD in an exemplary embodiment applying a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention 1-5 Three-dimensional maps of the IMF set number, vibration set number, power spectral density values of (a).
From the linear regression model we derive:
y＝129.1246+2.8179x1+1.2333x2-0.4697x3-0.0314x4-0.0505x5。
FIG. 6 shows a scatter plot and a regression line of a predicted regression curve in an exemplary embodiment using a method for vibration signal feature extraction and tool wear value prediction based on IMF-PSD spectral lines provided in accordance with an embodiment of the present invention. It can be seen from the figure that the scatter diagram is uniformly distributed near the regression line, indicating that the fitting accuracy of the linear regression is high.
And 5: and (4) using the linear regression model established in the step (4) for predicting the performance degradation amount.
Table 3 predicts the relative error between the tool wear value and the actual tool wear value.
FIG. 7 shows a comparison of predicted and actual values of tool wear amount in an exemplary embodiment using a method for IMF-PSD spectral line based vibration signal feature extraction and tool wear value prediction provided in accordance with an embodiment of the present invention.
From the results shown in table 3, it can be seen that the method provided by the embodiment of the present invention can effectively solve the problem of predicting the tool wear value under the vibration signal when the known tool performs cutting, and as can be seen from table 3, the tool wear value prediction method provided by the embodiment of the present invention has small error between the theoretical value and the actual calculated value, has high accuracy, and verifies the effectiveness of the method.
In summary, through the above steps, the method for extracting the vibration signal feature and predicting the tool wear value based on the IMF-PSD spectral line according to the embodiment of the present invention can adaptively obtain the feature frequency band segments of the vibration signal under different conditions, so that not only the optimal number of the intrinsic mode functions can be adaptively extracted from the process signal, but also the performance degradation of the operation process can be predicted, and the method has a very important significance for efficiently and effectively performing adaptive feature extraction and life prediction.
Particularly, the vibration signal feature extraction and tool wear value prediction method based on the IMF-PSD spectral line provided by the embodiment of the invention can adaptively extract the optimal number of natural mode functions according to signals under different conditions, and provides certain reference guidance for selection of the natural mode functions under different conditions. The vibration signal feature extraction and tool wear value prediction method based on the IMF-PSD spectral line provided by the embodiment of the invention is not only suitable for PHM2010 public data set in a case, but also suitable for other mechanical equipment and key parts thereof, and provides reasonable reference for feature extraction. In addition, the vibration signal feature extraction and tool wear value prediction method based on the IMF-PSD spectral line provided by the embodiment of the invention has good expansion capability, and provides certain reference for other technical personnel in the technical field.
It is to be noted that the flowcharts and block diagrams in the figures of the present specification illustrate the architecture, functionality, and operation of possible implementations of systems and methods according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention, and all of the technical solutions are covered in the protective scope of the present invention.
In the several embodiments provided by the present invention, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
Furthermore, the foregoing describes only some embodiments and alterations, modifications, additions and/or changes may be made without departing from the scope and spirit of the disclosed embodiments, which are intended to be illustrative rather than limiting. Furthermore, the described embodiments are directed to embodiments presently contemplated to be the most practical and preferred, it being understood that the embodiments should not be limited to the disclosed embodiments, but on the contrary, are intended to cover various modifications and equivalent arrangements included within the spirit and scope of the embodiments. Moreover, the various embodiments described above can be used in conjunction with other embodiments, e.g., aspects of one embodiment can be combined with aspects of another embodiment to realize yet another embodiment. In addition, each individual feature or member of any given assembly may constitute an additional embodiment.
The above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being covered by the appended claims and their equivalents.
Claims (7)
1. A vibration signal feature extraction and tool wear value prediction method based on IMF-PSD spectral lines is characterized by comprising the following steps:
the method comprises the following steps: collecting an original signal, carrying out inherent modal decomposition on the original signal by using ensemble empirical modal decomposition, sequentially expanding the original signal from high to low according to amplitude frequency while adding white noise for noise reduction, and decomposing to obtain a plurality of IMF components;
step two: obtaining PSD spectral lines of each IMF component obtained in the first step through power spectral density analysis, and averaging to obtain IMF-PSD spectral lines;
step three: performing Pearson correlation analysis on the IMF-PSD spectral line obtained in the step two, and extracting an IMF-PSD component spectral line most relevant to the degradation amount;
step four: establishing a prediction model for the IMF-PSD component spectral lines extracted in the third step by using a regression analysis method; and
step five: and predicting the tool wear value through the regression model established in the fourth step.
2. The method of claim 1, wherein the step one further comprises:
a) Setting the total iteration times of decomposition as NE, and initializing the amplitude of the added white noise;
b) Decomposing the original signal added with white noise at the mth time, wherein m =1,2 \8230, NE, the initial time order m =1, and adding white noise to the original signal X (t)
X m (t)＝X(t)+n m (t)
Wherein, X m (t) represents the m-th noisy signal, n m (t) represents white noise added by the mth decomposition;
c) Decomposing the m-th noisy signal X by using an ensemble empirical mode method m (t) obtaining the mth IMF component IMF m M =1,2, \ 8230, NE, if m < NE, return to step b), and m = m +1, repeating steps b) and c);
calculating NE IMF components obtained after NE decomposition and signal residual r (t)
3. The method for vibration signal feature extraction and tool wear value prediction based on IMF-PSD spectral lines as claimed in claim 2, wherein said second step further comprises:
let u (t) be a function in a spatial domain, and perform Fourier transform when u (t) satisfies the following three Dirichlet conditions, i.e., having a finite number of discontinuities, having a finite number of extreme points, and having an absolute integrable; if u (t) does not satisfy the dirichlet condition, then no fourier transform is possible, but if there is a finite average power, then the formula is satisfied
The function can be truncated:
wherein u (t) is a function in the spatial domain, i.e. the IMF after the decomposition in step one m A function;
fourier transform the function to U T (v)
Wherein t is time, e is a natural constant which is a constant in mathematics, is an infinite acyclic decimal and is an overtaking number, the value of the overtaking number is about 2.718281828459045, i is an imaginary number unit, and v is the angular velocity of u (t) in a frequency domain;
according to Parceval's theorem, | U T (v)| 2 Is a truncated signal u T (t) energy distribution in the frequency domain, then u T The normalized spectral density of (t) is:
wherein T is the total frequency band of the signal u (T);
the above expression has a dimension of power per frequency band, and defines the power spectral density of u (t) as
The distribution situation of the energy of the multi-state signal under different frequencies, namely the distribution situation of the task load under different frequencies, is obtained through power spectral density analysis;
averaging the power spectral density to obtain a power spectral density average value:
wherein k is the number of frequency points of PSD spectral lines;
the IMF-PSD spectrum is defined as follows: n groups of vibration signals are collected in the running process of the equipment, and the p group of vibration signals x are subjected to p (t) carrying out ensemble empirical mode decomposition to obtain NE IMF components, and carrying out IMF analysis on the p-th group of vibration signals m Obtaining IMF by averaging power spectral density m -PSD p M =1,2,. NE; p =1,2,3,. N; the total NE pieces of IMF-PSD curves are obtained, and the mth IMF of the pth group of vibration signals m -PSD p Expressed as:
at the m-th IMF component, the vibration signal x 1 (t),x 2 (t),…,x NE The IMF-PSD spectrum constituted by (t) is expressed as follows:
IMF-PSD m ＝[IMF-PSD 1m ,IMF-PSD 2m ,IMF-PSD 3m ,...,IMF-PSD nm ]。
4. the IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction method according to claim 3, characterized in that said third step further comprises:
calculating to obtain NE IMF-PSD spectral lines through the n groups of vibration signals collected in the second step, performing Pearson correlation analysis on the NE IMF-PSD spectral lines obtained through decomposition and an actual performance degradation curve, and extracting h IMF-PSD component spectral lines with correlation coefficients larger than 0.8;
given a binary population (X, Y)
Wherein E (XY), E (X), E (Y) represent expectation, cov represents covariance, σ X 、σ Y Representing the variance.
5. The IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction method of claim 4, wherein said fourth step further comprises:
performing linear regression analysis on the extracted h IMF-PSD spectral lines and the performance degradation curve;
given x = (x) 1 ；x 2 ；x 3 ；…x h ) Wherein x is h Is the h IMF power spectral density curve, and the linear regression model is a function predicted by linear combination of a plurality of functions, wherein w is a coefficient before a variable, and b is a functionIntercept of a beam
f(x)＝w 1 x 1 +w 2 x 2 +w 3 x 3 +…+w h x h +b；
The function is expressed in the form of a vector
f(x)＝w T x+b
Wherein, w = (w) 1 ；w 2 ；w 3 ；…；w h ) And w and b are determined, the linear regression model is established.
6. The IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction method of claim 5, wherein said step five further comprises:
and inputting a corresponding x value according to the established f (x) regression model, and predicting the tool wear value.
7. The IMF-PSD spectral line-based vibration signal feature extraction and tool wear value prediction method of claim 1, wherein the step one of collecting raw signals comprises collecting any section of historical signals from the beginning of use to complete failure from a machining device or a device of the same type and working environment as the machining device.
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