CN111693311B - Rotary machine fault diagnosis method based on independent component analysis and correlation criterion - Google Patents

Rotary machine fault diagnosis method based on independent component analysis and correlation criterion Download PDF

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CN111693311B
CN111693311B CN202010482741.3A CN202010482741A CN111693311B CN 111693311 B CN111693311 B CN 111693311B CN 202010482741 A CN202010482741 A CN 202010482741A CN 111693311 B CN111693311 B CN 111693311B
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汪抑非
黄志龙
付立
柴秋子
李创
吕巧玲
王绪康
沈新荣
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Hang Zhou Zeta Technology Co Lts
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Abstract

The invention relates to signal processing and artificial intelligence, and aims to provide a rotating machinery fault diagnosis method based on independent component analysis and correlation criteria. The method comprises the following steps: measuring a multi-channel vibration signal of the rotary machine, and converting by using an independent component analysis algorithm; selecting a separation signal based on a correlation criterion and a Bayesian information criterion, and extracting a fault feature vector; the rotary machine support vector machine diagnosis model training and diagnosis is carried out, fault diagnosis is carried out on the rotary machine through the input feature vector R input model, diagnosis results are classified according to preset judgment conditions, and an alarm is sent out. The method solves the problem that the prior independent component analysis is only applied to artificial diagnosis and is rarely applied to the aspect of artificial intelligent diagnosis, and improves the accuracy of fault diagnosis of the rotary machine to a greater extent, so the method has good use value.

Description

Rotary machine fault diagnosis method based on independent component analysis and correlation criterion
Technical Field
The invention relates to signal processing and application of artificial intelligence to mechanical fault diagnosis, in particular to an artificial intelligence fault diagnosis method for a rotating machine based on independent component analysis and correlation maximization criteria.
Background
Rotary machines are a very important and widely used class of mechanical devices in industrial fields, such as fans, water pumps, compressors, etc., and play an important role in various industrial fields. During the working process of the rotary machine, larger or smaller faults are inevitably generated, which cause economic loss and casualties, so that the fault diagnosis of the rotary machine is very important in the industrial field, and the research on the fault diagnosis method of the rotary machine is never stopped.
At present, fault diagnosis for rotary machines is mostly based on vibration signals, when the rotary machines are subjected to vibration testing, the measured signals are signals obtained by mixing a plurality of vibration sources in the rotary machines, and the difficulty is undoubtedly increased for fault feature extraction and fault diagnosis. And the independent component analysis is based on the independence assumption of the vibration source, and the vibration source signals are separated under the condition of no prior knowledge, so that the fault characteristics are more obvious. With the development of artificial intelligence, a plurality of rotary machine fault diagnosis algorithms based on artificial intelligence appear, and compared with the traditional artificial diagnosis, the artificial intelligence fault diagnosis method has the advantages of high accuracy, good timeliness and the like.
Because the independent component analysis has amplitude and sequence uncertainty and is difficult to be used as an input vector of an artificial intelligent diagnostic algorithm, the artificial intelligent diagnostic algorithm facing the rotating machinery based on the independent component analysis is not available at present. The invention designs an artificial intelligence fault diagnosis method based on independent component analysis and cross-correlation maximization criteria for rotary machinery, which adopts the measure criteria of cross-correlation coefficient maximization and combines the independent component analysis and support vector machine methods, and can greatly improve the accuracy of fault diagnosis.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects in the prior art and provides a rotary machine fault diagnosis method based on independent component analysis and cross-correlation maximization criteria.
In order to solve the technical problem, the solution of the invention is as follows:
a fault diagnosis method for a rotating machine based on independent component analysis and cross-correlation criteria is provided, which comprises the following steps:
(1) measuring a multi-channel vibration signal of a rotating machine:
arranging a vibration sensor on a bearing seat of a rotary machine, and acquiring vibration waveform data in three mutually perpendicular directions of a vertical radial direction, a horizontal radial direction and an axial direction; the collected vibration signals are transmitted to an upper computer in a wired or wireless mode, and data processing and calculation are carried out.
(2) An independent component analysis algorithm;
assuming that the acquired signal is a mixture of all the vibration source signals, which have mutually independent properties, the mixed signal (i.e. the observed signal) may be transformed such that the transformed signal can be represented as the aforementioned vibration source signal.
Assuming that the vibration source signal is S (t) and the mixed signal is X (t), the independent component analysis can be expressed by the following formula:
X(t)＝AS(t) (1)
wherein A is a mixing matrix.
The purpose of the independent components is to find a separation matrix W such that
Figure BDA0002517166510000021
Wherein W is referred to as a separation matrix; g is a global matrix, G ═ WA,
Figure BDA0002517166510000022
for the signals after the separation of the independent components, the adjustment of the separation matrix is carried out so that
Figure BDA0002517166510000026
Having the same generalized form as the source vibration signal.
(3) Selecting a separation signal based on a correlation criterion and a Bayesian information criterion;
after the independent component analysis, a plurality of separated vibration source signals contain information related to vibration faults, but a part of vibration source signals are noise input from the outside, and are irrelevant to mechanical vibration faults, and the vibration source signals related to the faults need to be separated out after the independent component analysis, the invention provides a correlation criterion, namely that the cross correlation coefficient calculation is carried out on the separated signals and the observed signals:
suppose that the split signal and the mixed signal are:
Figure BDA0002517166510000023
X(t)＝[X1(t)，X2(t)，...，Xm(t)]T
where n represents the number of separated signals, m represents the number of observed signals, and T represents the transposition;
the cross-correlation coefficient of the ith separated signal and the mixed signal is
Figure BDA0002517166510000024
In the formula (I), the compound is shown in the specification,
Figure BDA0002517166510000025
for the ith split signal, Xk(T) denotes the kth observed signal, T denotes transposition;
arranging the separation signals according to the cross-correlation coefficient from large to small, and arranging the separation signals according to the vibration source sequence, and recording as Y (t) ═ Y1(t)，Y2(t)，...，Yn(t)]TThe method solves the problem of order uncertainty in independent component analysis.
A Bayesian Information Criterion (BIC) is used to select the separate signals that were previously sorted according to a correlation Criterion. The BIC determines the number of effective vibration sources by finding a serial number which can maximize the cost function. Wherein the cost function is:
Figure BDA0002517166510000031
the effective vibration source number is estimated by calculating the maximum value k in equation (4).
In the formula, λjFor separating correlation matrices of signalsAnd (4) decomposing the j characteristic value after characteristic value decomposition, wherein N is the length of the data, and N is the number of the separation signals.
In the calculation process, k is respectively 1, 2, and n, the BIC value of each k value is respectively calculated, and if k is l, the BIC (l) reaches the maximum value, the former l separation signals are selected, namely
Figure BDA0002517166510000032
(4) Extracting a fault feature vector;
the wavelet packet decomposition can divide the frequency band according to the number j of decomposition layers, and the number of the decomposition layers is 2j-1And each node represents a waveform under a corresponding frequency band. And calculating the energy value of the waveform of each node of the j layer, so that the energy distribution of the j layer can be represented. The invention adopts a wavelet packet energy ratio mode to extract fault characteristics so as to select energy ratio distribution of a jth layer of wavelet packets for example, and the method specifically comprises the following steps:
step 1: signal to be extracted in step (3)
Figure BDA0002517166510000033
Each signal Y ink(t) carrying out wavelet packet decomposition, wherein the decomposition algorithm is shown as the formula (5):
Figure BDA0002517166510000034
wherein H is a low-pass filter, G is a high-pass filter,
Figure BDA0002517166510000035
is the ith wavelet packet node obtained by decomposing the jth layer of wavelet packet.
Step 2: and (4) calculating the energy proportion distribution of the j layer wavelet packet of the k separation signal, wherein the calculation formula is shown as the formula (6).
Figure BDA0002517166510000036
In the formula, EjikRepresenting the energy, R, of the ith node in the jth layer wavelet packet of the kth split signaljikRepresenting the corresponding energy fraction.
And step 3: and (4) integrating the wavelet packet energy ratios of all the separated signals into a matrix form according to the sequence of the separated signals, as shown in the formula (7).
Figure BDA0002517166510000037
And taking R as an input feature vector of the support vector machine model so as to perform diagnosis.
(5) And (4) training and diagnosing a rotary machine support vector machine diagnosis model.
Adopting a directed acyclic graph DAG support vector machine to realize multiple classifiers, and if the number of fault types of equipment is k, calling k-1 two classifiers to classify the faults;
converting the multiple classifiers into a solution quadratic optimization problem, and solving the problem in the following way:
Figure BDA0002517166510000041
wherein m is the number of samples, αi，αjI, j groups of samples x respectivelyi，xjCorresponding Lagrange multiplier, yi，yjThe fault type values corresponding to the ith and jth groups of samples respectively; k (x)i，xj) Is a kernel function.
And obtaining the optimal Lagrange multiplication subset through solving, and completing the establishment and training of the model.
(6) And (5) taking the input feature vector R extracted in the step (4) as an input value of the model in the step (5) to perform fault diagnosis on the rotating machine, classifying diagnosis results according to preset judgment conditions and giving an alarm.
Compared with the prior art, the invention has the beneficial effects that:
the fault diagnosis method for the rotary machine comprises a series of steps from signal acquisition to fault diagnosis and the like. Based on an independent component analysis algorithm, mechanical fault vibration source signals are separated, and the separated fault vibration source signals can be input into a support vector machine model as feature vectors by combining a cross-correlation coefficient maximization criterion and a wavelet packet decomposition reconstruction technology. Therefore, the problem that the conventional independent component analysis is only applied to artificial diagnosis and is rarely applied to the aspect of artificial intelligent diagnosis is solved, and the accuracy of fault diagnosis of the rotary machine is improved to a greater extent, so that the method has a good use value.
Drawings
Fig. 1 is a detailed flowchart of a mechanical fault diagnosis method for a rotary machine according to the present invention.
FIG. 2 shows the installation of the vibration sensor (bearing seat 1, shaft 2, vibration sensor 3 in the figure).
Fig. 3 is a waveform diagram of a mix signal before independent component analysis.
Fig. 4 is a waveform diagram of the isolated signal after independent component analysis.
Fig. 5 is a waveform diagram sorted by the cross-correlation coefficient maximization criterion.
Fig. 6 shows entropy values of signals after bayesian information criterion calculation.
Fig. 7 is a structural diagram of wavelet packet decomposition.
FIG. 8 is a diagram of a multi-class support vector machine.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention relates to a signal processing and artificial intelligence technology, and is an application of a computer technology in the field of mechanical equipment operation. In the implementation process of the invention, the application of a plurality of software functional modules is involved. The applicant believes that it is fully possible for one skilled in the art to utilize the software programming skills in his or her own practice to implement the invention, as well as to properly understand the principles and objectives of the invention, in conjunction with the prior art, after a perusal of this application. All references made herein are to the extent that they do not constitute a complete listing of the applicants.
The main working flow of the fault diagnosis method for the rotary machine provided by the invention is shown in figure 1, and the fault diagnosis method specifically comprises the following steps:
(1) vibration signal testing and acquisition
The vibration sensor is fixedly arranged on a bearing seat of the rotary machine, so that vibration waveform data in three mutually perpendicular directions can be tested, and the three directions of vertical radial direction, horizontal radial direction and axial direction are usually selected. The vibration sensor transmits the collected vibration signals to a fault diagnosis module (software) installed in the upper computer in a wired or wireless mode. In this example, three sensors are mounted on the bearing seat, and the specific mounting position is shown in fig. 2. The three directions are vertical radial direction, horizontal radial direction and axial direction respectively, and the three collected observation signals are marked as x respectively1(t)，x2(t)，x3(t)。
(2) Performing independent component analysis
The observation signals collected in step (1) are collectively denoted as x (t) ═ x1(t)，x2(t)，x3(t)]TThe signals are formed by mixing vibration source signals inside the rotary machine. In the independent component analysis, the vibration source signals are assumed to be statistically independent from each other, and the vibration source signals in the mixed signal can be separated through certain transformation. Suppose that the vibration source signal of the rotary machine is S (t), and the separation signal is
Figure BDA0002517166510000051
Then
X(t)＝AS(t) (1)
Wherein A is a mixing matrix.
The independent component analysis uses the maximum independence as the judgment criterion to search a separation matrix W so as to separate the signals
Figure BDA0002517166510000054
Has the same generalized form as the vibration source signal S (t), and the calculation formula is as follows
Figure BDA0002517166510000052
Many different algorithms exist in the independent component analysis according to different quantization standards for independence, and the quantization standards comprise high-order cumulant, negative entropy and the like. The invention uses an extended joint diagonalization algorithm (JADE), whose algorithm steps are described below in a simple example:
step 1: spheroidizing the mixed signals, calculating a proper spheroidizing matrix U, and eliminating the correlation of the signals, namely meeting the requirement
Figure BDA0002517166510000053
Wherein I represents an identity matrix, and X (t) represents an observed signal;
step 2: arbitrarily selecting a set of matrix vectors M ═ M1，M2，...，MP]Wherein M isiFor an arbitrary N matrix, then calculate each M bypThe fourth order cumulant matrix of (a).
Figure BDA0002517166510000061
In the formula, Kijkl(Z) is the fourth order cumulant of the ith, j, k, l 4 component in vector Z, mklIs a matrix MpThe k, l element of (1).
And step 3: initializing a matrix V, solving the V through an optimization step, and enabling Q to be achieved by adopting a Givens rotation methodZ(Mp) Joint diagonalization is achieved to minimize the size of equation (11).
Figure BDA0002517166510000062
In the formula, off [. cndot. ] represents the sum of squares of the off-diagonal elements.
And 4, step 4: calculating the separation matrix W and the separation signal by the formula (12)
Figure BDA0002517166510000063
Figure BDA0002517166510000064
Waveforms of the mixed signal and the split signal are shown in fig. 3 and 4. It can be seen that the separate signal is composed of three parts, a high-frequency component signal, a low-frequency component signal and a noise signal, and each part has more obvious fault characteristics compared with the mixed signal before independent component analysis. In the waveforms shown in fig. 3 and 4, the upper waveform is a low-frequency signal, the middle waveform is a noise signal, and the lower waveform is a high-frequency signal. In this example, the high and low frequencies correspond to vibration characteristics of bearing failure and rotor imbalance, respectively. Compared with the three signals in fig. 3, the signal in fig. 4 has more single frequency components, and the problem that the vibration characteristics of multiple faults are difficult to identify when appearing in one signal is avoided.
(3) Separation signal selection based on cross-correlation maximization criterion and Bayesian information criterion
Obtained in step (2)
Figure BDA0002517166510000065
However, the order of the separated signals is uncertain, and the separated signals cannot be directly used as input vectors of the artificial intelligence diagnostic method, so that the separated signals need to be sorted and selected. The invention provides a separation signal selection method based on a cross-correlation coefficient maximization criterion and a Bayesian information criterion, which comprises the following specific implementation steps of:
and performing cross-correlation coefficient calculation on the separation signal and the observation signal according to a correlation criterion: assuming separate signals
Figure BDA0002517166510000066
And the observed signals x (t) are:
Figure BDA0002517166510000067
X(t)＝[X1(t)，X2(t)，...，Xm(t)]T
where n represents the number of separate signals, m represents the number of observed signals, and T represents the transpose;
the cross-correlation coefficient of the ith separated signal with the mixed signal is:
Figure BDA0002517166510000068
in the formula (I), the compound is shown in the specification,
Figure BDA0002517166510000069
for the ith split signal, Xk(T) denotes the kth observed signal, T denotes transposition;
after the cross correlation coefficients of all the separated signals are calculated, the separated signals are arranged according to the cross correlation coefficients from large to small, and the separated signals are arranged according to the vibration source sequence, which is marked as Y (t) ([ Y) } Y1(t)，Y2(t)，...，Yn(t)]TReferring specifically to fig. 5, the method places the noise signal in the last position and the signal indicative of the mechanical fault in the front portion, solving the sequential uncertainty problem in the independent component analysis.
Step 2: and (3) screening Y (t) by using a Bayesian information criterion, reserving a real vibration source signal part in r (t), and removing a noise signal stored in a separation signal, wherein a calculation formula is shown as a formula (4).
Figure BDA0002517166510000071
In the formula of lambdajFor separating lettersThe j-th eigenvalue of the correlation matrix of the number after eigenvalue decomposition, N is the length of the data, and N is the number of the separation signals.
In the calculation process, k is 1, 2, n, the BIC value of each k value is calculated, and if k is l, the BIC (l) reaches the maximum value, the former l separation signals are selected, namely
Figure BDA0002517166510000072
The BIC value in this example is shown in fig. 6, and according to the result, the first two signals are selected for fault feature extraction in this example.
(4) Extraction of fault feature vectors
The wavelet packet decomposition can divide the frequency band according to the number j of decomposition layers, and the number of the decomposition layers is 2j-1And each node represents the waveform under the corresponding frequency band. And calculating the energy value of the waveform of each node of the j layer, so that the energy distribution of the j layer can be expressed. The fault characteristics are extracted in a wavelet packet energy ratio mode, and the energy ratio distribution of the j-th layer of wavelet packets is selected for example. The method comprises the following specific steps:
step 1: signal to be extracted in step (3)
Figure BDA0002517166510000073
Each signal Y ink(t) performing wavelet packet decomposition, wherein the wavelet basis function is selected from daubechies (db) wavelets. The tree structure of the wavelet packet decomposition is shown in fig. 7. The decomposition algorithm is shown as formula (5):
Figure BDA0002517166510000074
wherein H is a low-pass filter, G is a high-pass filter,
Figure BDA0002517166510000075
is the ith wavelet packet node obtained by decomposing the jth layer of wavelet packet.
Step 2: and (3) calculating the energy ratio distribution of the j layer wavelet packet of the kth separation signal, wherein the calculation formula is shown as the formula (6).
Figure BDA0002517166510000076
In the formula, EjikRepresenting the energy, R, of the ith node in the jth layer wavelet packet of the kth split signaljikRepresenting the corresponding energy fraction.
And step 3: and integrating the wavelet packet energy ratios of all the separated signals into a matrix form according to the sequence of the separated signals, wherein the formula (7) is shown.
Figure BDA0002517166510000081
And taking R as an input feature vector of the support vector machine to diagnose.
(5) Training and diagnosing rotary machine support vector machine diagnostic model
The invention adopts a directed acyclic graph DAG support vector machine and a tree form multi-classification method to realize multi-classifiers, namely k-1 two-class classifiers are called to classify fault types, and k refers to the number of the fault types; the multi-class basic structure is shown in fig. 8.
And importing the data into a root node, dividing the input data into two subclasses by a support vector machine model in the root node, further dividing the two subclasses by using the support vector machine models on the child nodes, and circulating the steps until only one class is contained in the subclasses. The method has the advantages that the number of the support vector machines needing to be trained and the number of training samples of each support vector machine are small, all support vector machine classifiers do not need to be traversed during classification, the method has high training speed and classification speed, and the method has more obvious advantages for the classification problem with large number of classes.
Converting the multiple classifiers into a problem of solving the quadratic optimization, and solving according to the following formula:
Figure BDA0002517166510000082
wherein m is the number of samples, αi，αjI, j groups of samples x respectivelyi，xjCorresponding Lagrange multiplier, yi，yjThe fault type values corresponding to the ith and jth groups of samples respectively; k (x)i，xj) Is a kernel function;
in this example, the kernel function is chosen to be
Figure BDA0002517166510000083
Where σ is the bandwidth of the gaussian kernel.
The training data is mainly selected from faults commonly seen in rotary machines, including: rotor unbalance, rotor misalignment, bearing failure, base looseness, dynamic and static part friction and bearing crack 6 types.
Solving the formula (8) to obtain an optimal Lagrange multiplication subset, and completing the establishment and training of a support vector machine model;
(6) and (5) taking the input feature vector R extracted in the step (4) as an input value of the model in the step (5) to perform fault diagnosis on the rotating machine, classifying diagnosis results according to preset judgment conditions and giving an alarm.

Claims (4)

1. A rotary machine fault diagnosis method based on independent component analysis and correlation criteria is characterized by comprising the following steps:
(1) collecting multi-channel vibration signals of a rotating machine
Arranging a vibration sensor on a bearing seat of a rotary machine, collecting vibration signals to acquire vibration waveform data in three directions which are vertical to each other, and taking the vibration waveform data as an observation signal;
(2) performing independent component analysis
Transforming the acquired observation signals through independent component analysis, and transforming mixed signals formed by mixing all vibration source signals into independent vibration source signals;
assuming that the vibration source signal is S (t) and the observation signal is X (t), the independent component analysis is represented by the following formula:
X(t)＝AS(t) (1)
wherein A is a mixing matrix;
finding a separation matrix W by independent component analysis such that
Figure FDA0003495961730000011
In the formula (I), the compound is shown in the specification,
Figure FDA0003495961730000012
w is a separation matrix for separating signals; g is a global matrix, and G is WA;
by adjustment of the separation matrix W such that
Figure FDA0003495961730000013
Has the same generalized form as the source vibration signal;
(3) selecting a separation signal based on a correlation criterion and a Bayesian information criterion
Firstly, according to a correlation criterion, performing cross-correlation coefficient calculation on a separation signal and an observation signal; assuming separate signals
Figure FDA0003495961730000018
And the observed signals x (t) are:
Figure FDA0003495961730000014
X(t)＝[X1(t)，X2(t)，...，Xm(t)]T
where n represents the number of separate signals, m represents the number of observed signals, and T represents the transpose;
the cross-correlation coefficient of the ith separated signal with the mixed signal is:
Figure FDA0003495961730000015
in the formula (I), the compound is shown in the specification,
Figure FDA0003495961730000016
for the ith split signal, Xk(T) denotes the kth observed signal, T denotes transposition; e () means averaging the inside of the brackets;
arranging the separation signals according to the cross-correlation coefficient from large to small, and arranging the separation signals according to the vibration source sequence, and recording as Y (t) ═ Y1(t)，Y2(t)，...，Yn(t)]T；
Secondly, selecting the sorted separation signals Y (t) according to a Bayesian information criterion, and determining the number of effective vibration sources by searching a serial number which can enable the cost function to be maximum; wherein the cost function is:
Figure FDA0003495961730000017
estimating the number of effective vibration sources through a maximum value k in an equation (4);
in the formula, λjThe j-th eigenvalue of the correlation matrix of the separation signals after eigenvalue decomposition, wherein N is the length of data, and N is the number of the separation signals;
in the calculation process, k is 1, 2, n, the BIC value at each k value is calculated, and if k is l, BIC (l) reaches the maximum value, the former l separation signals are selected, namely
Figure FDA0003495961730000021
(4) Extracting fault feature vectors
Extracting fault characteristics by adopting a wavelet packet energy ratio mode: the frequency bands are divided according to the number j of the layers of decomposition, and the number j of the layers is 2j-1Each node represents a waveform under a corresponding frequency band; calculating the energy value of the waveform of each node of the jth layer, and expressing the energy distribution of the jth layer; to selectThe energy ratio distribution of the j-th layer wavelet packet is taken as an example, and the specific steps are as follows:
step 1: signal to be extracted in step (3)
Figure FDA0003495961730000027
Each signal Y ink(t) carrying out wavelet packet decomposition, wherein the decomposition algorithm is shown as the formula (5):
Figure FDA0003495961730000022
wherein H is a low-pass filter, G is a high-pass filter,
Figure FDA0003495961730000023
is the ith wavelet packet node obtained by decomposing the jth layer of wavelet packet;
step 2: calculating the energy ratio distribution of the j layer wavelet packet of the kth separation signal, wherein the calculation formula is shown as a formula (6);
Figure FDA0003495961730000024
in the formula, EjikRepresenting the energy, R, of the ith node in the jth layer wavelet packet of the kth split signaljikRepresenting the corresponding energy fraction;
Figure FDA0003495961730000025
an ith wavelet packet node in a jth layer wavelet packet representing a kth observed signal;
and step 3: integrating the wavelet packet energy ratios of all the separated signals into a matrix form according to the sequence of the separated signals, wherein the formula is shown as a formula (7);
Figure FDA0003495961730000028
taking R as an input feature vector of a support vector machine for diagnosis;
(5) training and diagnosing rotary machine support vector machine diagnostic model
Adopting a directed acyclic graph DAG support vector machine to realize multiple classifiers, and calling k-1 two classifiers to classify the faults if the number of the fault types of the equipment is k;
converting the multiple classifiers into a solution quadratic optimization problem, and solving according to the following formula:
Figure FDA0003495961730000026
wherein m is the number of samples, αi，αjI, j groups of samples x respectivelyi，xjCorresponding Lagrange multiplier, yi，yjThe fault type values corresponding to the ith and jth groups of samples respectively; k (x)i，xj) Is a kernel function; maxαMeans that the parameter alpha is adjusted to make the following expression reach the maximum value, and the parameter alpha means alphaiAnd alphaj；
Obtaining an optimal Lagrange multiplication subset through solving, and completing the establishment and training of a support vector machine model;
(6) and (5) taking the input feature vector R extracted in the step (4) as an input value of the model in the step (5) to perform fault diagnosis on the rotating machine, classifying diagnosis results according to preset judgment conditions and giving an alarm.
2. The method according to claim 1, wherein in step (1), the three mutually perpendicular directions are vertical radial direction, horizontal radial direction and axial direction.
3. The method according to claim 1, wherein in the step (1), the vibration sensor transmits the collected vibration signal to the host computer in a wired or wireless manner, and performs data processing and calculation.
4. The method according to claim 1, wherein in the step (2), the independent component analysis is performed by using an extended joint diagonalization algorithm, and specifically comprises the following steps:
(4.1) spheroidizing the mixed signals, calculating a proper spheroidizing matrix U, and eliminating the correlation of the signals, namely, meeting the requirement
Figure FDA0003495961730000031
Wherein I represents an identity matrix, and X (t) represents an observed signal;
(4.2) arbitrarily selecting a set of matrix vectors M ═ M1，M2，...，Mp]Definition of MiIs M1～MpAny one of the nxn matrices, and then each M is calculated bypThe fourth order cumulant matrix of (a);
Figure FDA0003495961730000032
in the formula, Kijkl(Z) is the fourth order cumulant of the 4 components i, j, k, l in the vector Z, mklpIs a matrix MpThe kth, l element of (1);
(4.3) initializing a matrix V, solving the V through an optimization step, and enabling Q to be in a Givens rotation methodZ(Mp) Joint diagonalization, thereby achieving the goal of minimizing equation (11);
Figure FDA0003495961730000035
in the formula, off [. ]]Represents the sum of the squares of the off-diagonal elements; dM(V) is a process of solving for a matrix V by jointly diagonalizing qz (mp) by Givens rotation, where matrix V refers to the matrix used to compute the separation matrix W;
(4.4) calculating the separation matrix W and the separation signal by the equation (12)
Figure FDA0003495961730000033
Figure FDA0003495961730000034
The finally obtained separation signal consists of three parts, namely a high-frequency component signal, a low-frequency component signal and a noise signal.
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