CN107966287B - Weak fault feature extraction method for self-adaptive electromechanical equipment - Google Patents

Weak fault feature extraction method for self-adaptive electromechanical equipment Download PDF

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CN107966287B
CN107966287B CN201711174333.6A CN201711174333A CN107966287B CN 107966287 B CN107966287 B CN 107966287B CN 201711174333 A CN201711174333 A CN 201711174333A CN 107966287 B CN107966287 B CN 107966287B
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何水龙
李慧
王衍学
蒋占四
訾艳阳
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Guilin University of Electronic Technology
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Abstract

The invention discloses a weak fault feature extraction method for self-adaptive electromechanical equipment, which comprises the following steps of firstly, collecting vibration signals of the electromechanical equipment; then, performing two-scale similarity transformation on the selected initial multi-wavelet to improve the approximation order of the multi-wavelet scale function; then designing a multi-wavelet lifting matrix meeting symmetry and translation constraint conditions, and further realizing a multi-wavelet integrated construction method; and finally, optimizing the free parameters by adopting a genetic algorithm based on the vibration signals to obtain a self-adaptive multi-wavelet basis function matched with the fault characteristics, thereby providing a favorable means for extracting weak fault characteristics. The method solves the dynamic matching bottleneck in the weak fault feature extraction process in the actual monitoring and diagnosis application of the electromechanical equipment.

Description

Weak fault feature extraction method for self-adaptive electromechanical equipment
Technical Field
The invention relates to the technical field of electromechanical equipment fault detection, in particular to a method for extracting weak fault characteristics of self-adaptive electromechanical equipment.
Background
The bearings, gears and rotors are the most common important components of electromechanical equipment, and the failure of any one component of the electromechanical equipment is very likely to cause great economic loss and serious safety accidents. In order to avoid accidents, signal processing methods based on vibration signals are widely applied to health monitoring and fault diagnosis of electromechanical equipment, such as spectrum analysis, envelope spectrum analysis and the like. However, at the initial stage of a fault, the signal characteristics are very weak and non-stationary, and are submerged by multiple interference sources and strong noise of an electromechanical system, so that the signal-to-noise ratio is low, and great difficulty is brought to characteristic extraction and fault diagnosis.
For the characteristics of non-stationary signals, many signal processing techniques, such as wavelet transform, sparse decomposition, empirical mode decomposition, spectral kurtosis, etc., have emerged. The wavelet transform is widely applied to extraction of non-stationary signal characteristics by virtue of excellent time-frequency localization characteristics and rich basis function selection, and provides a powerful tool for non-stationary description of dynamic signals and extraction of fault information of mechanical parts. According to the research on wavelet theory, the symmetry, orthogonality, compactness and high-order vanishing moment of the wavelet basis function are very important properties in signal processing. However, it has been shown mathematically that a single wavelet (other than a Haar wavelet) cannot have these properties simultaneously, affecting the engineering application of the wavelet and limiting its practical application range. The multi-wavelet is used as the further development of the wavelet theory, has the excellent characteristics of orthogonality, symmetry, compactness, high-order vanishing moment and the like which are very important in signal processing, overcomes the defects and shortcomings of the single wavelet, has a plurality of scale functions and wavelet functions with different time-frequency structures, provides the premise for the accuracy, reliability and comprehensiveness of mechanical fault feature extraction, and has great advantages in early fault and multi-fault diagnosis.
The nature of the multi-wavelet fault feature extraction is that the search signal contains components most similar or related to the 'basis function' as well as the wavelets, and dynamic response signals caused by different types of faults in the operation process of equipment have different feature waveforms. Therefore, when matching is performed by using a certain fixed wavelet basis function, optimal extraction of fault characteristic signals is difficult to achieve. However, if an inappropriate and inappropriate basis function is adopted for decomposition, fault feature information is diluted, and difficulty is caused to fault feature extraction and diagnosis, so that in order to better extract the fault feature, the on-demand construction of the basis function needs to be realized, and the multi-wavelet basis function has the capability of adapting to a dynamic signal.
Disclosure of Invention
The invention aims to solve the problem of weak fault feature extraction of electromechanical equipment and provides a self-adaptive weak fault feature extraction method of the electromechanical equipment.
In order to solve the problems, the invention is realized by the following technical scheme:
a weak fault feature extraction method for self-adaptive electromechanical equipment comprises the following steps:
step 1, collecting vibration signals needing to be monitored by electromechanical equipment;
step 2, constructing a two-scale similarity transformation matrix meeting the conditions based on a two-scale similarity transformation theory, and performing two-scale similarity transformation on the selected initial multi-wavelet by using the constructed two-scale similarity transformation matrix to obtain an intermediate multi-wavelet;
step 3, constructing a linear equation set in the symmetrical lifting process according to given symmetry and translation constraint conditions on the basis of the intermediate multi-wavelet, and obtaining a lifting coefficient by solving the linear equation set; the lifting coefficient is substituted into a lifting coefficient equation, and a lifting matrix can be obtained through transformation; based on the lifting matrix, obtaining integrated multi-wavelets according to a lifting algorithm;
step 4, taking the kurtosis index of the signal as an objective function, solving a multi-wavelet free parameter which enables the objective function to be maximum by adopting a genetic algorithm, wherein the free parameter is introduced into a two-scale similarity transformation matrix construction and a symmetric lifting coefficient equation solving so as to preferably select a self-adaptive multi-wavelet basis function matched with the vibration signal;
and step 5, performing redundancy decomposition on the self-adaptive multi-wavelet basis function to realize translation invariance of a decomposition result, acquiring more visual periodic pulse fault information from a time domain, realizing extraction of weak fault characteristics and restoring physical characteristics of faults.
In the step 1, the vibration signal is acquired by a vibration acceleration sensor.
Compared with the prior art, the method adopts a multi-wavelet integrated construction method to obtain the large-difference multi-wavelet basis function with symmetry and parameter regulation, realizes the optimal matching of the wavelet basis function and the fault characteristic waveform through self-adaptive optimization, is favorable for the optimal extraction of the fault characteristic, and has the following remarkable advantages:
1) the invention constructs an integrated multi-wavelet basis function with symmetrical or anti-symmetrical waveform, ensures the linear phase of the filter, avoids phase distortion during decomposition and reconstruction, and can obtain an analysis result of zero phase shift in the analysis process. Meanwhile, the method is beneficial to the boundary processing in the operation process and reduces the boundary distortion. Therefore, the method has significant advantages in the process of extracting the fault characteristics from the aspect of time domain;
2) the kurtosis index is adopted as an optimal rule in the self-adaptive matching process, the kurtosis index has obvious advantages on early fault impact characteristics, a genetic algorithm is used as an optimization means, mathematical expression between a target function and a free variable is avoided, the parallel search advantages of robustness and global property of genetic calculation are fully utilized, a multi-wavelet basis function adaptive to the early fault characteristics is obtained, and the method has corresponding advantages in early fault characteristic extraction;
3) according to the method, through two-scale similarity transformation and a symmetrical lifting frame, the approaching order and the vanishing moment can be lifted to any order according to the actual engineering requirements, the properties of the integrated multi-wavelet basis function are greatly improved, a symmetrical or anti-symmetrical basis function is obtained, and the possibility is provided for weak fault feature extraction;
4) the method can be used for fault feature extraction and fault diagnosis of large electromechanical equipment based on vibration monitoring, so that sudden accidents are avoided, and economic loss is reduced.
Drawings
Fig. 1 is a flowchart of a weak fault feature extraction method for an adaptive electromechanical device.
Fig. 2 is a waveform diagram of a failed bearing original signal.
FIG. 3 is a frequency spectrum diagram of a failed bearing.
Fig. 4 is a fault bearing envelope spectrum.
FIG. 5 is a graph of two adapted basis functions: (a) multi-waveletFunction psi1(b) multiple wavelet function ψ2。
Fig. 6 shows the result of adaptive multi-wavelet redundancy decomposition: (a) psi1Corresponding detail signal, (b) psi2Corresponding detail signals.
Detailed Description
The invention is provided based on a multi-wavelet two-scale similarity transformation and a symmetrical lifting frame, and firstly, a vibration acceleration sensor is used for collecting vibration signals in the operation process of mechanical equipment; then, performing two-scale similarity transformation on the selected initial multi-wavelet to improve the approximation order of the multi-wavelet scale function; then designing a multi-wavelet lifting matrix meeting the symmetric conditions, ensuring the linear phase characteristics of a filter of a multi-wavelet basis function, avoiding phase distortion during signal decomposition and reconstruction and improving the boundary processing capacity; by researching a two-scale similarity transformation and symmetrical lifting frame multi-wavelet integrated construction algorithm, a multi-parameter two-scale similarity transformation regulation matrix and a multi-wavelet symmetrical lifting matrix meeting constraint conditions are designed, and a multi-wavelet integrated construction method is realized; and finally, optimizing the free parameters by adopting a genetic algorithm based on the vibration signals to obtain a self-adaptive multi-wavelet basis function matched with the fault characteristics, thereby providing a favorable means for extracting weak fault characteristics. The invention solves the dynamic matching bottleneck in the weak fault feature extraction process in the actual monitoring and diagnosis application of the electromechanical equipment, and provides a novel multi-degree-of-freedom self-adaptive signal processing method.
Specifically, the method for extracting weak fault features of the self-adaptive electromechanical equipment specifically comprises the following steps:
the first step is as follows: and collecting a monitoring vibration signal of the electromechanical equipment system, and providing an original information source for selecting regulation and control parameters through an optimization method. Aiming at key rotating parts such as a bearing, a gear, a rotor and the like in an electromechanical system, a vibration sensor is adopted to obtain corresponding vibration signals.
The second step is that: and performing two-scale similarity transformation on the initial multi-wavelet. Based on a two-scale similarity transformation theory, a parameterized matrix meeting specific conditions (such as symmetry, large difference, reversibility and the like) is designed, a multi-wavelet basis function library with higher degree of freedom is obtained, and an approximation order is promoted to improve the multi-wavelet property.
Let H (omega) and G (omega) be the low-pass and high-pass filter symbols of the multi-wavelet multi-scale function, H(n)The (omega) approximation order being n, G(m)The (omega) extinction order is m and the spectral radius rho (H)(n)(0))<N and N are positive integers larger than 1. Further, let H(n)(0) Having a feature value of 1, corresponding to the right feature vector rnSo that H is(n)(0)rn＝rn。
(1) Selecting a two-scale matrix M (omega) meeting the conditions, and adding symmetry constraint to ensure that the two-scale similar matrix M (omega) meets the following requirements:wherein E (ω),
Figure BDA0001477887510000032
Are all a diagonal matrix and are,
Figure BDA0001477887510000034
being a point of symmetry of a multi-scale function, TjThe symmetry points of the multi-wavelet function, and diag (·) represents a diagonal matrix.
(2) Structure of the device
(3) Find a suitable rn+1Corresponds to H(n+1)(0) Has a characteristic value of 1;
(4) repeating the previous three steps until the H (omega) of the required approximation order is obtained.
In the above algorithm, only the starting H needs to be selected(n)(ω) and M (ω) per cycle. After each cycle, H(n)The multi-scale function approximation order and the regularity corresponding to (omega) are improved to the first order, but unfortunately G(m)The vanishing moment of the corresponding multi-wavelet basis function is reduced by a first order. If M (ω) is a triangular polynomial, and | M (ω) | is equal to e in z-iωIs linear, then H is constructed by the algorithm(n+1)And (omega) is a trigonometric polynomial, and the compactness and symmetry of the multi-scale function are kept.
The multi-wavelet after the two-scale similarity transformation is called as an intermediate multi-wavelet { phip,ΨpH for the corresponding low-pass and high-pass filter symbols, respectivelyp(omega) and Gp(omega), the approximation order of the intermediate multi-wavelet is improved relative to the original multi-wavelet, the regularity of the intermediate multi-wavelet is enhanced, and the property of the multi-scale function is improved. However, it does so by reducing the multi-wavelet basis function ΨpThe vanishing moment is the cost, the smoothness and the local positioning capability of the multi-wavelet function are weakened, and the adverse effect is generated on the signal processing process.
The third step: and performing lifting frame transformation on the intermediate multi-wavelet. Based on a symmetrical lifting frame, symmetry constraint and translation amount constraint are added, a multi-wavelet parameterized lifting matrix meeting conditions is designed according to a lifting coefficient equation, and the linear phase characteristics of the multi-wavelet basis function filter are guaranteed.
Intermediate multi-wavelet scale function and wavelet function [ phi ]p,ΨpThe n-th order continuous moment is M (phi)p,,n)＝∫Φp(x)xndx and M (Ψ)p,n)＝∫Ψp(x)xndx (x). Then there is
Figure BDA0001477887510000041
Figure BDA0001477887510000042
And the construction of the multi-wavelet is realized by means of a moment calculation formula for calculation. The process of constructing multiple wavelets using the lifting method can be expressed as: firstly, selecting initial multi-wavelet omega0(x) Wherein ω is0(x)＝ψ1Or psi2And further selecting other basis functions omega for correcting the multiple wavelets1(x),...,ωk(x) The translation amount k can finally construct a new multi-wavelet through a lifting coefficient equation
Figure BDA0001477887510000043
The lifting coefficient equation is:
Figure BDA0001477887510000044
multiple wavelets have more advantages in lifting construction than single wavelets, such as in single wavelet lifting where only the scale function is available for modifying the original wavelet function, while in multiple wavelet lifting where not only two multi-scale functions are included for modifying a certain multiple wavelet function, but also a corresponding further multiple wavelet function, i.e. for ψ1，
Figure BDA0001477887510000045
For theObviously, the basic functions used for constructing the new multi-wavelet function are more than those of a single wavelet, and the method brings more freedom and flexibility for constructing the multi-wavelet to meet more and more specific requirements.
Assuming that the vanishing moment of the multi-wavelet is lifted from p to p', the two sides of the "lifting coefficient equation" are integrated, the following lifting linear equation set can be obtained:
Figure BDA0001477887510000047
calculation of the formula Using moments the integral value in the equation, the solution of the equation set ciI.e. the coefficients of the multi-wavelet lifting function. Performing a Z-transform on the lifting coefficient equation may obtain a multi-wavelet lifting frame.
The above-mentioned multi-wavelet lifting process cannot guarantee the symmetry of the lifted multi-wavelet function, and in order to guarantee the symmetry of the lifting process, a 'symmetric selection' method is used to select the translation amount of other functions for correcting the multi-wavelet. Assuming an initial multiscale functionWith multiple wavelet functions psi1、ψ2Is symmetrical or antisymmetric, the centers of symmetry beingThe symmetric lifting method is expressed as follows, in psi1For example, the translation of the lifting functionMust satisfy
Figure BDA0001477887510000054
In the formula: i is 1, 2; j ═ 1,2, …; m is 1, 2.
Order toRespectively, the symmetry properties of the initial multi-scale function and the initial multi-wavelet function are represented, wherein 1 represents symmetry and-1 represents antisymmetry. Will be provided with
Figure BDA0001477887510000057
And M (psi)i,k,n)＝∫ψi(x+k)xndx is substituted into the lifting linear equation set, and the first matrix on the left of the equal sign is used to represent MBWherein M isBM and B are each MB
Figure BDA0001477887510000058
Let B be a symmetric matrix
The coefficient vector in the set of lifting linear equations is represented as
Figure BDA00014778875100000510
And the right of the equation is denoted as Mψ＝[M(ψi,0,p),M(ψi,0,p+1),…M(ψi,0,p'-1)]TThen the formula is changed to the following formula
MBC＝Mψ
The solution C of the equation is used to lift psi1Coefficient of (phi), phi2The situation is similar, the only difference being the hoisting ψ2A function of
Figure BDA00014778875100000511
And
Figure BDA00014778875100000512
and substituting the lifting coefficient into an equation set of the lifting coefficient, and performing Z transformation to obtain lifting matrixes T and S. Thus, an adaptively integrated multi-wavelet may be implemented by means of the lifting matrices T and S, as follows:
Hs(ω)＝Hp(ω)
Gs(ω)＝T(ω2)(Gp(ω)+S(ω2)Hp(ω))
in the formula: hs、GsRespectively a low-pass filter sign and a high-pass filter sign of the integrated multi-wavelet.
Multi-wavelet [ phi ] after integrated constructions,ΨsCompared with the initial multi-wavelet, the approximation order and vanishing moment of the scale function and the wavelet function are improved, the regularity, smoothness and local positioning capability are enhanced, the performance is improved, and most importantly, the symmetry of the multi-wavelet is ensured, so that the application of the multi-wavelet in signal feature extraction is facilitated, particularly in time domain analysis.
The fourth step: the parameterized multi-wavelet structure is realized through two-scale similarity transformation and a symmetrical lifting frame integrated structure algorithm, and a parameterized regulated multi-wavelet basis function with excellent properties such as linear phase and the like is obtained.
Free parameters are introduced in the construction of a two-scale similarity transformation matrix and the solution of a symmetric lifting coefficient equation. These non-zero free parameters are key to implementing adaptive construction. In view of the sensitivity of the kurtosis index to early-stage impact signals, the invention takes the kurtosis index of detail signals as an objective function, and solves the objective function KPThe largest multi-wavelet free parameter to optimize the adaptive multi-wavelet basis function matching the early failure signature.
Objective function KPDefining:
Figure BDA0001477887510000061
in the formula: x is a detail signal; p (x) -probability density of signal amplitude.
In view of the robustness and global, parallel search advantages of genetic algorithms, and without the need for mathematical expressions between objective functions and variables. The invention adopts genetic algorithm and uses an objective function KPAnd constructing a multi-wavelet basis function of the self-adaptive matching signal characteristics for the fitness function, and finishing the optimal construction of the self-adaptive multi-wavelet.
And completing the self-adaptive matching of the self-adaptive multi-wavelet integrated structure based on a genetic optimization algorithm and a kurtosis maximization optimization criterion.
The fifth step: and performing redundancy decomposition by using the self-adaptive optimal multi-wavelet basis function to realize translation invariance of a decomposition result, acquiring more visual periodic pulse fault information from a time domain, realizing extraction of weak fault characteristics and restoring physical characteristics of faults.
The method combines the advantages of multi-wavelet two-scale similarity transformation and a symmetrical lifting frame, constructs a multi-wavelet multi-scale function with high approximation order and strong regularity, and enables the energy of signals on a frequency domain to be more concentrated; the vanishing moment of the multi-wavelet function is improved through the symmetrical lifting process, the localization capability of the basis function is improved, the linear phase or the generalized linear phase of the filter is also ensured, errors generated by decomposition and reconstruction are avoided, and the boundary processing capability is improved, so that higher-order complex signals can be more accurately described and expressed. The method is characterized in that the free parameters in the construction process are optimally selected by designing the free parameters in the construction process and selecting specific basis function evaluation and optimization criteria and combining optimization methods such as genetic algorithm and the like, so that the self-adaptive multi-wavelet basis function construction aiming at the signals to be analyzed is realized, and the extraction of weak fault features is realized.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to specific examples below.
The rolling bearing is one of the most common and important key parts in electromechanical equipment, however, the rolling bearing is inevitably damaged after long-time operation under complex operation environment and operation condition, so that the electromechanical equipment is paralyzed, and great economic loss or casualties are caused. In order to avoid and avoid major accidents, faults and hidden dangers in the operation process of equipment must be discovered as early as possible, and the faults are eliminated in the sprouting state. In the embodiment, GHM is used as an initial multi-wavelet, a self-adaptive integrated multi-wavelet structure is performed to analyze a bearing monitoring vibration signal in mechanical equipment, and the fault characteristics of a roller in a rolling bearing are extracted from a time domain.
The integrated multi-wavelet construction method and the redundancy decomposition embodiment of the bearing based on vibration signal feature extraction are designed into a method for extracting weak fault features of self-adaptive electromechanical equipment, as shown in figure 1, and mainly comprise the following steps:
the first step is as follows: and a vibration acceleration sensor is adopted to acquire a bearing vibration signal.
The acquisition system comprises a dynamic data acquisition unit YE6267 and a CA-YD-117 type piezoelectric acceleration sensor of Jiangsu union electronic technology limited. The performance index of the acceleration sensor is shown in table 1. The collector realizes 16-bit A/D parallel data collection based on a USB2.0 interface, and signal collection and monitoring are completed by a lower computer (a monitoring front-end computer).
TABLE 1 CA-YD-117 piezoelectric acceleration transducer characteristic parameter table
Figure BDA0001477887510000071
The bearing model is 552732QT cylindrical roller bearing, installs on the gear box input shaft, and bearing structure parameter table 2. In the example, the effectiveness of the method is verified by adopting the slight fault of the outer ring of the rolling bearing, and the damage size in the test is 1 x 1mm, so that the outer ring has slight scratch fault.
TABLE 2552732 QT bearing structure parameter Table
The failure characteristic frequency of the outer ring of the rolling bearing can be calculated by the following formula:
in the formula: z is the number of rolling elements; f. ofr-frequency conversion/Hz; d-rolling body diameter/mm; d-the outer diameter/mm of the bearing; α -contact angle/°.
During testing, the vibration acceleration sensor is arranged at a fault bearing seat, the rotating speed of an input shaft is 673r/min, the sampling frequency is 12.8kHz, the sampling length is 4096 points, and the characteristic frequency of the bearing outer ring fault is 82.8Hz according to the fault formula (1) of the outer ring of the rolling bearing, namely the time interval is 12.7 ms.
Fig. 2 shows a vibration time domain signal of equipment when a bearing outer ring has a fault, fig. 3 shows a frequency spectrum of a fault bearing signal, and fig. 4 shows a hilbert envelope spectrogram of the fault bearing signal, it can be seen from the diagram that a weak impact signal generated by the fault is submerged in strong background noise, so that fault characteristics of periodic pulses are difficult to find, and spectral lines corresponding to fault characteristic frequencies in a frequency domain are also covered in noise spectral lines, so that it is difficult to judge whether the bearing has a fault.
The second step is that: GHM is one of the most common and most widely used engineering dual multi-wavelet basis functions, and has the advantages of compactness, orthogonality, symmetry, second order approximation order and vanishing moment. Here, the GHM multi-wavelet is used as the initial multi-wavelet. The symmetric point or the antisymmetric point of the GHM multi-wavelet multi-scale function and the multi-wavelet basis function is 1/2 or 1, and H (0) has a feature vector
Figure BDA0001477887510000081
Corresponding to the characteristic value 1. Therefore, according to the conditions that the two-scale similarity transformation matrix is required to meet, and the characteristics of the GHM multi-wavelet are combined, the two-scale similarity transformation matrix M (omega) based on the GHM multi-wavelet is constructed as follows:
in the formula: a, b-non-zero parameters.
Let HG(omega) and GG(ω) is the GHM multiple wavelet scale function and the low-pass and high-pass filter sign of the multiple wavelet function, according to the two-scale similarity transformation, there are:
after the transformation, a new intermediate function { phi ] is obtainedp,ΨpH, multi-scale function phipHaving an approximation order of 3, and a multi-wavelet basis function ΨpThe vanishing moment of the wavelet function is reduced to 1 order, and the smoothness and the local positioning capability of the wavelet function are weakened.
The third step: with intermediate multi-wavelets [ phi ]p,ΨpLet B be based on the assumption that the vanishing moment is raised from 1 st order to 5 th orderωi＝±1(ωi＝ψiOr
Figure BDA0001477887510000084
1 for symmetry, -1 for antisymmetry) for symmetry or antisymmetry of the initial multi-wavelet, the linear equation in the symmetric lifting process:
Figure BDA0001477887510000085
the solution of equation (4) is Ψ1Of the lifting coefficient of2Lifting is also analogous to Ψ1. After obtaining the lifting coefficient, the lifting coefficient equation is brought in, and the lifting matrixes T and S can be obtained through Z transformation. After the lifting matrices T and S are based, the following liftsThe lifting algorithm obtains a new multi-wavelet after integrated construction:
Figure BDA0001477887510000086
obtaining integrated constructed multi-wavelet [ phi ] through lifting frames,ΨsWith an approximation order of 3 and vanishing moments of 5.
The fourth step: in the former construction process, two-scale similarity transformation introduces two free parameters, and the linear equation M of the symmetrical lifting processBC＝MψWhen the system is an underdetermined linear equation system, N existsf＝4-Rank(MB) A free parameter. These free parameters will have an effect on the waveform of the multi-wavelet basis function. The kurtosis index is very sensitive to the impact response characteristics caused by early local faults, so that the kurtosis index of a detail signal is taken as an objective function in the self-adaptive construction process of the integrated multi-wavelet, and the objective function K is solvedPThe largest multi-wavelet free parameter to optimize the adaptive multi-wavelet basis function that matches the given signal.
An objective function:
Figure BDA0001477887510000091
in the formula: x is a detail signal; p (x) -probability density of signal amplitude.
From the objective function KPThe expression of (2) shows that the kurtosis maximization principle is not directly connected with the free parameters, the relation between the kurtosis maximization principle and the free parameters is very complex, and a common optimization algorithm usually needs a complete relational expression and is difficult to implement. The genetic algorithm has strong robustness and global and parallel searching characteristics, and mathematical expression between an objective function and a variable is not required. The section adopts genetic algorithm and uses an objective function KPConstructing multiple wavelets of the adaptive matching signal characteristics for the fitness function, wherein the range of the free parameters is selected as [ -50,0) U (0, 50)]Selecting arithmetic crossover operator and non-uniform mutation operator, the population scale is 100, the number of initial population is respectivelyThe set is 50, the crossover probability is set to 0.6, and the mutation probability is set to 0.05.
Through the optimization of the above process, the multi-wavelet basis function after the adaptive multi-wavelet integrated construction is shown in fig. 5.
The fifth step: after the integrated multi-wavelet self-adaptive construction is completed, multi-wavelet redundant decomposition is carried out on the signal, and translation invariance of a decomposition result is realized, wherein the specific realization process is as follows:
the decomposition process of the redundant multi-wavelet transform is the result of carrying out matrix interpolation zero filling on a low-pass filter and a high-pass filter of a later decomposition layer to a former decomposition layer, and the matrix interpolation zero filling means that a zero matrix with the size of r multiplied by r is inserted. Let T denote the interpolation zero-padding operator, then for any integer i,
(Tx)2i＝xi,(Tx)2i+1＝0
then the coefficients { H, G } of the low-pass and high-pass filters at the decomposition level of l in the redundant multi-wavelet transform process are calculated by the following equation:
(1) when k is not 2lAt an integer multiple of the number of the first to the second,
Figure BDA0001477887510000092
(2) in the case of the other cases, the case,
Figure BDA0001477887510000093
the adoption of redundant multi-wavelet transform is beneficial to improving the accuracy of feature extraction and the spectral precision of a decomposition result, thereby realizing more accurate mechanical equipment fault feature extraction and fault interruption.
After the 3-level redundancy decomposition, the branch with the highest kurtosis is selected, and the result is shown in fig. 6. As can be seen from fig. 6, the method can successfully extract the periodic pulse signal of the outer ring fault with the period of 12.7ms, so that the method has an obvious effect on enhancing the weak fault characteristic, and can extract the fault characteristic of the outer ring of the rolling bearing from the strong background noise.
The invention provides an integrated construction method of a self-adaptive multi-wavelet basis function on the basis of deep research of a two-scale similarity transformation and a symmetrical lifting frame, adopts a kurtosis index which is most sensitive to an impact pulse occurring in an early fault as an optimal rule in a self-adaptive process, optimizes through a genetic algorithm, analyzes a vibration signal acquired by a sensor, obtains the self-adaptive integrated multi-wavelet basis function which is matched with fault features and has excellent properties, and further realizes weak fault feature extraction. The invention improves the approximation order of a multi-scale function and the vanishing moment of a multi-wavelet basis function, simultaneously restrains the symmetry of the basis function, ensures the linear phase and the generalized linear phase of a filter, improves the performance of the original multi-wavelet, avoids phase distortion in the decomposition process, improves the boundary processing capability, constructs a self-adaptive multi-wavelet basis function adaptive to a dynamic signal, maintains the excellent characteristics of the initial multi-wavelet such as compactness, symmetry and the like, and provides a new method for extracting weak fault characteristics of electromechanical equipment.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.

Claims (2)

1. A weak fault feature extraction method for self-adaptive electromechanical equipment is characterized by comprising the following steps:
step 1, collecting vibration signals needing to be monitored by electromechanical equipment;
step 2, constructing a two-scale similarity transformation matrix meeting the conditions based on a two-scale similarity transformation theory, and performing two-scale similarity transformation on the selected initial multi-wavelet by using the constructed two-scale similarity transformation matrix to obtain an intermediate multi-wavelet;
step 3, constructing a linear equation set in the symmetrical lifting process according to given symmetry and translation constraint conditions on the basis of the intermediate multi-wavelet, and obtaining a lifting coefficient by solving the linear equation set; the lifting coefficient is substituted into a lifting coefficient equation, and a lifting matrix can be obtained through transformation; based on the lifting matrix, obtaining integrated multi-wavelets according to a lifting algorithm;
the process of constructing the multi-wavelet by using the lifting method can be expressed as follows: firstly, selecting initial multi-wavelet omega0(x) Wherein ω is0(x)＝ψ1Or psi2(ii) a Further selecting other basis functions omega for correcting the multiple wavelets1(x),...,ωk(x) K; finally, a new multi-wavelet can be constructed through a lifting coefficient equation
Figure FDA0002273239970000011
The lifting coefficient equation is:
Figure FDA0002273239970000012
for psi1，
Figure FDA0002273239970000013
For psi2，
Figure FDA0002273239970000014
Assuming that the vanishing moment of the multi-wavelet is lifted from p to p', the two sides of the lifting coefficient equation are integrated, so that the following lifting linear equation set can be obtained:
Figure FDA0002273239970000015
the integral value in equation ② is calculated using a formula for moment calculation, the solution of the equation set ciThe coefficient of the multi-wavelet lifting function in the formula ① is obtained, and the multi-wavelet lifting frame can be obtained by performing Z transformation on the lifting coefficient equation;
assuming an initial multiscale functionWith multiple wavelet functions psi1、ψ2Is symmetrical or antisymmetric, the centers of symmetry being
Figure FDA0002273239970000017
aψ1,aψ2(ii) a The symmetric lifting method is then expressed as follows:
for psi1Symmetric lifting of (2), translation of lifting function
Figure FDA0002273239970000018
Must satisfy
Figure FDA0002273239970000019
In the formula: i is 1, 2; j ═ 1,2, …; m is 1, 2;
order to
Figure FDA00022732399700000111
Respectively representing the symmetry properties of the initial multi-scale function and the initial multi-wavelet function, wherein 1 represents symmetry, and-1 represents antisymmetry; will be provided with
Figure FDA00022732399700000112
And M (psi)i,k,n)＝∫ψi(x+k)xndx is substituted into the lifting linear equation set, n is an approximation order, and the first matrix on the left of the equal sign represents MBWherein M isBM and B are each MB
Figure FDA0002273239970000021
Let B be a symmetric matrix
Figure FDA0002273239970000022
In lifting linear equationsThe coefficient vector is represented as
Figure FDA0002273239970000023
And the right of the equation is denoted as Mψ＝[M(ψi,0,p),M(ψi,0,p+1),…M(ψi,0,p'-1)]TThen formula MBMB is changed to the following formula
MBC＝Mψ⑥
The solution C of the equation is used to lift psi1The coefficient of (a);
for psi2Symmetrical lifting of (a) with psi1The only difference of the symmetric lifting is the lifting psi2A function of
Figure FDA0002273239970000024
And
Figure FDA0002273239970000025
substituting the lifting coefficient into an equation set of lifting coefficients, and performing Z transformation to obtain lifting matrixes T and S; thus, an adaptively integrated multi-wavelet may be implemented by means of the lifting matrices T and S, as follows:
Hs(ω)＝Hp(ω)
Gs(ω)＝T(ω2)(Gp(ω)+S(ω2)Hp(ω))
in the formula: hp(omega) and Gp(omega) is an intermediate multi-wavelet [ phi ]p,ΨpThe low-pass and high-pass filter symbols of { C }; hs(omega) and Gs(ω) a low-pass filter sign and a high-pass filter sign of the integrated multi-wavelet, respectively;
step 4, taking the kurtosis index of the signal as an objective function, solving a multi-wavelet free parameter which enables the objective function to be maximum by adopting a genetic algorithm, wherein the free parameter is introduced into a two-scale similarity transformation matrix construction and a symmetric lifting coefficient equation solving so as to preferably select a self-adaptive multi-wavelet basis function matched with the vibration signal;
and step 5, performing redundancy decomposition on the self-adaptive multi-wavelet basis function to realize translation invariance of a decomposition result, acquiring more visual periodic pulse fault information from a time domain, realizing extraction of weak fault characteristics and restoring physical characteristics of faults.
2. The method for extracting weak fault features of adaptive electromechanical equipment according to claim 1, wherein in the step 1, vibration signals are acquired through a vibration acceleration sensor.
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