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

Abstract

The invention discloses a method for extracting weak fault features of self-adaptive electromechanical equipment, which firstly collects vibration signals of electromechanical equipment; then performs two-scale similarity transformation on the selected initial multi-wavelet to improve the approximation order of the multi-wavelet scale function; The multi-wavelet lifting matrix of translation constraints is used to realize the multi-wavelet ensemble construction method. Finally, based on the vibration signal, the genetic algorithm is used to optimize the free parameters, and the adaptive multi-wavelet basis function matching the fault features is obtained, which provides a basis for the extraction of weak fault features. beneficial means. The invention solves the dynamic matching bottleneck in the weak fault feature extraction process in the actual monitoring and diagnosis application of electromechanical equipment.

Description

A method for extracting weak fault features of adaptive electromechanical equipment

technical field

The invention relates to the technical field of fault detection of electromechanical equipment, in particular to a method for extracting weak fault features of adaptive electromechanical equipment.

Background technique

Bearings, gears and rotors are the most common and important components of electromechanical equipment. The failure of any one of its components is likely to lead to major economic losses and serious safety accidents. In order to avoid accidents, signal processing methods based on vibration signals are widely used in health monitoring and fault diagnosis of electromechanical equipment, such as spectrum analysis, envelope spectrum analysis, etc. However, in the early stage of the fault, the signal features are very weak and non-stationary, and are overwhelmed by multiple interference sources and strong noises in the electromechanical system. The signal-to-noise ratio is low, which brings great difficulties to feature extraction and fault diagnosis.

According to the characteristics of non-stationary signals, many signal processing techniques have emerged, such as wavelet transform, sparse decomposition, empirical mode decomposition, spectral kurtosis and so on. The wavelet transform is widely used in the feature extraction of non-stationary signals due to its excellent time-frequency localization characteristics and rich selection of basis functions. tool. According to the study of wavelet theory, the symmetry, orthogonality, compactness and high-order vanishing moment of wavelet basis functions are very important properties in signal processing. However, it has been proved from the mathematical aspect that a single wavelet (except Haar wavelet) cannot have these properties at the same time, which affects the engineering application effect of wavelet and limits its practical application range. As a further development of wavelet theory, multi-wavelet has excellent characteristics such as orthogonality, symmetry, compact support and high-order vanishing moment, which are very important in signal processing, and overcomes the defects and shortcomings of single wavelet. The scale function and wavelet function with different time-frequency structures provide the premise for the accuracy, reliability and comprehensiveness of mechanical fault feature extraction, which makes multi-wavelet quite advantageous in early fault and multi-fault diagnosis.

The essence of multi-wavelet fault feature extraction is the same as wavelet, which is to search for the most similar or most relevant components to the "basis function" in the signal, and the dynamic response signals caused by different types of faults in the process of equipment operation have different characteristic waveforms. . Therefore, it is difficult to achieve the optimal extraction of fault characteristic signals when a fixed wavelet basis function is used for matching. However, if an inappropriate and inappropriate basis function is used for decomposition, it will dilute the fault feature information, but it will cause difficulties in fault feature extraction and diagnosis. , so that the multi-wavelet basis function has the ability to adapt to the dynamic signal.

SUMMARY OF THE INVENTION

The invention solves the problem of weak fault feature extraction of electromechanical equipment, and provides an adaptive weak fault feature extraction method for electromechanical equipment.

In order to solve the above-mentioned problems, the present invention is achieved through the following technical solutions:

A method for extracting weak fault features of adaptive electromechanical equipment, comprising the following steps:

Step 1. Collect the vibration signals that the electromechanical equipment needs to monitor;

Step 2: Constructing a two-scale similarity transformation matrix that satisfies the condition based on the two-scale similarity transformation theory, and using the constructed two-scale similarity transformation matrix to perform two-scale similarity transformation on the selected initial multi-wavelets to obtain an intermediate multi-wavelet;

Step 3. Based on the intermediate multi-wavelet, according to the given symmetry and translation constraints, construct a linear equation system in the process of symmetric lifting, and obtain the lifting coefficient by solving the linear equation system; bring the lifting coefficient into the lifting coefficient equation, And through transformation, the lifting matrix can be obtained; based on the lifting matrix, the integrated multi-wavelet can be obtained according to the lifting algorithm;

Step 4. Taking the kurtosis index of the signal as the objective function, the genetic algorithm is used to solve the multi-wavelet free parameter that maximizes the objective function. Adaptive multi-wavelet basis function matched to vibration signal;

Step 5. Redundant decomposition of the adaptive multi-wavelet basis function to achieve translation invariance of the decomposition results, obtain more intuitive periodic pulse fault information from the time domain, extract weak fault features, and restore the physical nature of the fault. characteristic.

In the above step 1, the vibration signal is collected by the vibration acceleration sensor.

Compared with the prior art, the present invention adopts the multi-wavelet integrated construction method to obtain a large-differentiated multi-wavelet basis function with symmetry and parameter control, and realizes the best matching between the wavelet basis function and the fault characteristic waveform through self-adaptive optimization, which is beneficial to The best extraction of fault features, the present invention has the following significant advantages:

1) The present invention constructs an integrated multi-wavelet base function with symmetric or anti-symmetric waveform, which ensures the linear phase of the filter, avoids phase distortion during decomposition and reconstruction, and can obtain an analysis result with zero phase shift in the analysis process . At the same time, it is beneficial to the boundary processing in the operation process and reduces the boundary distortion. Therefore, it has significant advantages in the process of fault feature extraction from the time domain;

2) The present invention adopts the kurtosis index as the optimization criterion in the adaptive matching process, and the kurtosis index has significant advantages for the early fault impact characteristics, and uses the genetic algorithm as the optimization method to avoid the mathematical expression between the objective function and the free variable. , making full use of the robustness and global parallel search advantages of the genetic algorithm, obtaining multi-wavelet basis functions suitable for the early fault features, and having corresponding advantages in the early fault feature extraction;

3) The present invention can improve the approximation order and vanishing moment to any order according to the actual needs of the project through the two-scale similarity transformation and the symmetric lifting framework, greatly improving the properties of the integrated multi-wavelet basis functions, and obtaining symmetric or anti-symmetric basis functions, Provide possibility for weak fault feature extraction;

4) The present invention can be used for fault feature extraction and fault diagnosis of large-scale electromechanical equipment based on vibration monitoring, so as to avoid sudden accidents and reduce economic losses.

Description of drawings

FIG. 1 is a flowchart of a method for extracting weak fault features of adaptive electromechanical equipment.

Figure 2 shows the original signal waveform of the faulty bearing.

Figure 3 shows the frequency spectrum of the faulty bearing.

Figure 4 shows the envelope spectrum of the faulty bearing.

Figure 5 is a graph of two basis functions after adaptation: (a) multi-wavelet wavelet function ψ ₁ , (b) multi-wavelet wavelet function ψ ₂ .

Figure 6 shows the adaptive multi-wavelet redundancy decomposition results: (a) the detail signal corresponding to ψ ₁ , (b) the detail signal corresponding to ψ ₂ .

Detailed ways

The invention is proposed based on the two-scale similarity transformation of multi-wavelets and the symmetric lifting framework. It first collects the vibration signal during the operation of the mechanical equipment through the vibration acceleration sensor; The approximation order of the function; then a multi-wavelet lifting matrix that satisfies the symmetry condition is designed to ensure the linear phase characteristics of the filter of the multi-wavelet basis function, to avoid the phase distortion during signal decomposition and reconstruction, and to improve the boundary processing capability; by studying the similarity of the two scales Transform and symmetric lifting framework multi-wavelet ensemble construction algorithm, design multi-parameter two-scale similarity transformation control matrix and multi-wavelet symmetric lifting matrix that meet the constraints, and realize multi-wavelet ensemble construction method; finally, based on vibration signal, genetic algorithm is used to carry out the calculation of free parameters. By optimization, an adaptive multi-wavelet basis function matching the fault features can be obtained, which provides a favorable means for the extraction of weak fault features. The invention solves the dynamic matching bottleneck in the weak fault feature extraction process in the actual monitoring and diagnosis application of electromechanical equipment, and proposes a novel multi-degree-of-freedom adaptive signal processing method.

Specifically, a method for extracting weak fault features of adaptive electromechanical equipment includes the following steps:

The first step is to collect the monitoring vibration signal of the electromechanical equipment system to provide the original information source for the subsequent selection of control parameters through the optimization method. For key rotating components such as bearings, gears and rotors in the electromechanical system, vibration sensors are used to obtain corresponding vibration signals.

Step 2: Perform two-scale similarity transformation on the initial multi-wavelet. Based on the two-scale similarity transformation theory, a parameterized matrix that satisfies certain conditions (such as symmetry, large difference, reversibility, etc.) is designed, a multi-wavelet basis function library with greater degrees of freedom is obtained, and the approximation order is improved to improve the multi-wavelet properties.

Let H(ω) and G(ω) be the low-pass and high-pass filter symbols of the multiwavelet multiscale function, H ⁽ⁿ⁾ (ω) approximation order n, G ^(m) (ω) vanishing order m, and The spectral radius ρ(H ⁽ⁿ⁾ (0))<N, where N is a positive integer greater than 1. Further, let H ⁽ⁿ⁾ (0) have an eigenvalue of 1, corresponding to the right eigenvector rn, such that H ⁽ⁿ⁾ _{( 0} )rn= _rn .

都为对角矩阵，

为多尺度函数的对称点，T_j多小波函数的对称点，而diag(·)代表对角阵。(1) Select a two-scale matrix M(ω) that satisfies the conditions, and add symmetry constraints at the same time, so that the two-scale similarity matrix M(ω) satisfies: where E(ω),

are all diagonal matrices,

is the symmetry point of the multi-scale function, T _j is the symmetry point of the multi-wavelet function, and diag(·) represents the diagonal matrix.

(2) Structure

(3) Find a suitable r _n+1 corresponding to the eigenvalue of H ⁽ⁿ⁺¹⁾ (0) of 1;

(4) Repeat the first three steps until the desired approximation order H(ω) is obtained.

In the above algorithm, only the initial H ⁽ⁿ⁾ (ω) and M(ω) for each cycle need to be selected. After each cycle, the approximation order and regularity of the multi-scale function corresponding to H ⁽ⁿ⁾ (ω) are improved by one order, but unfortunately the vanishing moment of the multi-wavelet basis function corresponding to G ^(m) (ω) Lower one level. If M(ω) is a triangular polynomial, and |M(ω)| is linear at z=e ^{- iω} , then H ⁽ⁿ⁺¹⁾ (ω) constructed by this algorithm is a triangular polynomial and maintains a multi-scale function compactness and symmetry.

The multiwavelets after the above two-scale similarity transformation are called intermediate multiwavelets {Φ _p , Ψ _p }, and the corresponding low-pass and high-pass filter symbols are H _p (ω) and G _p (ω), respectively. The approximation order of the original multi-wavelet and the intermediate multi-wavelet is improved, its regularity is also enhanced, and the properties of multi-scale functions are also improved. However, at the cost of reducing the vanishing moment of the multi-wavelet basis function Ψ _p , it weakens the smoothness and local positioning ability of the multi-wavelet function, and has an adverse effect on the signal processing process.

The third step is to perform lifting frame transformation on the intermediate multiwavelets. Based on the symmetric lifting framework, adding symmetry constraints and translation constraints, according to the lifting coefficient equation, a multi-wavelet parameterized lifting matrix that satisfies the conditions is designed to ensure the linear phase characteristics of the multi-wavelet basis function filter.

The n-th order continuous moment of the intermediate multi-wavelet scaling function and the wavelet function {Φ _p ,Ψ _p } is M(Φ _p ,,n)=∫Φ _p (x)x ⁿ dx and M(Ψ _p ,n)=∫Ψ _p (x)x ⁿ dx. then there are

提升系数方程为：By means of the calculation formula of moment, the construction of multi-wavelet is realized for calculation. The process of constructing multi-wavelets by lifting method can be expressed as: first select the initial multi-wavelet ω ₀ (x), where ω ₀ (x)=ψ ₁ or ψ ₂ , and then select other basis functions ω ₁ for the modified multi-wavelet (x),...,ω _k (x) translation k, and finally can construct a new multi-wavelet through the "lifting coefficient equation"

The lift coefficient equation is:

对于显然，用于构造新的多小波函数的基本函数要多于单小波，为多小波的构造带来更大的自由度与灵活性，以满足更多、更具体的要求。Compared with single wavelet, multi-wavelet has more advantages in lifting structure. For example, in single-wavelet lifting, only the scale function can be used to modify the original wavelet function, while in multi-wavelet lifting, it is used to modify a certain multi-wavelet function. includes not only two multi-scale functions, but also another corresponding multi-wavelet function, that is, for ψ ₁ ,

for Obviously, there are more basic functions used to construct new multi-wavelet functions than single wavelet, which brings more freedom and flexibility to the construction of multi-wavelet to meet more and more specific requirements.

Assuming that the vanishing moment of the multi-wavelet is lifted from p to p′, by integrating both sides of the “lifting coefficient equation”, the following system of lifting linear equations can be obtained:

The integral value in the above formula is calculated by the calculation formula of moment, and the solution {c _i } of the equation system is the coefficient of the multi-wavelet lifting function. The multi-wavelet lifting framework can be obtained by performing Z-transform on the lifting coefficient equation.

The above-mentioned multi-wavelet lifting process cannot guarantee the symmetry of the multi-wavelet function after lifting. In order to ensure the symmetry of the lifting process, the "symmetric selection" method is used to select the translation amount of other functions used to modify the multi-wavelet. Assuming an initial multiscale function It is symmetric or anti-symmetric with the multiwavelet functions ψ ₁ , ψ ₂ , and the center of symmetry is Then the symmetrical lifting method is expressed as follows. Taking the symmetrical lifting of ψ ₁ as an example, the translation of the lifting function must meet

In the formula: i=1,2; j=1,2,...; m=1,2.

与M(ψ_i,k,n)＝∫ψ_i(x+k)xⁿdx代入提升线性方程组，并将等号左边第一个矩阵表示M_B，其中M_B＝MB，M与B分别为make respectively represent the symmetry properties of the initial multiscale function and the initial multiwavelet function, where 1 represents symmetry and -1 represents antisymmetry. Will

and M(ψ _i ,k,n)=∫ψ _i (x+k)x ⁿ dx into the system of lifting linear equations, and the first matrix on the left of the equal sign represents M _B , where M _B =MB, M and B respectively

Let B be a symmetric matrix

且等式右边表示为M_ψ＝[M(ψ_i,0,p),M(ψ_i,0,p+1),…M(ψ_i,0,p'-1)]^T，则式变为下式The coefficient vector in the system of boosted linear equations is expressed as

And the right side of the equation is expressed as M _ψ =[M(ψ _i ,0,p),M(ψ _i ,0,p+1),…M(ψ _i ,0,p'-1)] ^T , then the formula becomes the following formula

M _B C = M _ψ

与

将提升系数代入式提升系数方程组，并进行Z变换获得提升矩阵T和S。因此，自适应集成多小波可以借助于提升矩阵T和S实现，具体如下：The solution C of the equation is the coefficient used to improve ψ ₁ , and the situation for ψ ₂ is similar, the only difference is that the function to improve ψ ₂ is

and

The lifting coefficients are substituted into the formula lifting coefficient equations, and Z-transformation is performed to obtain the lifting matrices T and S. Therefore, adaptive integrated multiwavelets can be realized with the help of lifting matrices T and S, as follows:

H _s (ω)=H _p (ω)

G _s (ω)=T(ω ² )(G _p (ω)+S(ω ² )H _p (ω))

In the formula: H _s and G _s are the symbols of the low-pass filter and the symbol of the high-pass filter of the integrated multi-wavelet, respectively.

Compared with the initial multi-wavelet, the multi-wavelet {Φ _s ,Ψ _s } after the ensemble construction has improved the approximation order and vanishing moment of the scale function and the wavelet function, the regularity, smoothness and local localization ability are enhanced, and the performance is improved. , and most importantly they guarantee the symmetry of multiwavelets, which is beneficial for their application in signal feature extraction, especially in time domain analysis.

The fourth step: realize the parametric multi-wavelet construction through the two-scale similarity transformation and the symmetric lifting framework integrated construction algorithm, and obtain the parametric control multi-wavelet basis function with excellent properties such as linear phase.

Free parameters will be introduced in the construction of the two-scale similarity transformation matrix and in solving the symmetric lift coefficient equation. These non-zero free parameters are the key to realize the adaptive construction. In view of the sensitivity of the kurtosis index to the early shock signal, the present invention takes the kurtosis index of the detail signal as the objective function, and solves the multi-wavelet free parameter that maximizes the objective function K _P , so as to optimize the adaptive multi-wavelet that matches the early fault characteristics. Wavelet basis function.

The objective function K _P is defined as:

In the formula: x——detail signal; p(x)——probability density of signal amplitude.

In view of the robustness of the genetic algorithm and the advantages of global and parallel search, it does not require the mathematical expression between the objective function and the variables. The present invention adopts genetic algorithm and takes the objective function K _P as the fitness function to construct the multi-wavelet base function adaptively matching the signal characteristics, so as to complete the optimal construction of the self-adaptive multi-wavelet.

The adaptive matching of adaptive multi-wavelet ensemble construction is completed based on genetic optimization algorithm and kurtosis maximization optimization criterion.

Step 5: Use the adaptive optimal multi-wavelet basis function to perform redundant decomposition to achieve translation invariance of the decomposition result, obtain more intuitive periodic pulse fault information from the time domain, and realize the extraction of weak fault features , to restore the physical characteristics of the fault.

The invention combines the advantages of multi-wavelet two-scale similarity transformation and symmetrical lifting framework, and constructs a multi-wavelet multi-scale function with high approximation order and strong regularity, so that the energy of the signal in the frequency domain is more concentrated; The vanishing moment of the multi-wavelet function is improved, the localization ability of the basis function is improved, and the linear phase or generalized linear phase of the filter is also guaranteed. Describe and express higher-order complex signals. By designing the free parameters in the construction process and selecting specific basis function evaluation and optimization criteria, combined with optimization methods such as genetic algorithm, the free parameters in the construction process are optimally selected, and then the adaptive multi-wavelet basis function construction for the signal to be analyzed is realized. In order to realize the extraction of weak fault features.

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific examples.

Rolling bearings are one of the most common and important key components in electromechanical equipment. However, working for a long time in complex operating environments and operating conditions will lead to inevitable damage to rolling bearings, resulting in paralysis of electromechanical equipment, resulting in major economic losses or personnel. casualties. In order to prevent and avoid major accidents, it is necessary to find faults and hidden dangers in the process of equipment operation as early as possible, and eliminate the faults in the bud. In this embodiment, the GHM is used as the initial multi-wavelet, and the adaptive integrated multi-wavelet structure is performed to analyze the bearing monitoring vibration signal in the mechanical equipment, and the fault characteristics of the rollers in the rolling bearing are extracted from the time domain.

Based on the integrated multi-wavelet construction method and redundant decomposition embodiment of vibration signal feature extraction, this bearing designs a method for extracting weak fault features of adaptive electromechanical equipment, as shown in Figure 1, which mainly includes the following steps:

The first step: use the vibration acceleration sensor to collect the bearing vibration signal.

The acquisition system includes YE6267 dynamic data collector and CA-YD-117 piezoelectric acceleration sensor from Jiangsu Lianneng Electronic Technology Co., Ltd. The performance indicators of the acceleration sensor are shown in Table 1. The collector realizes 16-bit A/D parallel data acquisition based on the USB2.0 interface, and the signal acquisition and monitoring is completed by the lower computer (monitoring front-end computer).

Table 1 CA-YD-117 piezoelectric acceleration sensor characteristic parameter table

The bearing model used is 552732QT cylindrical roller bearing, which is installed on the input shaft of the gearbox. The bearing structure parameters are listed in Table 2. In this example, a slight fault on the outer ring of the rolling bearing is used to verify the effectiveness of the method. The damage size in the test is a slight scratch fault on the outer ring of 1*1mm.

Table 2 552732QT bearing structure parameter table

The fault characteristic frequency of the outer ring of the rolling bearing can be calculated by the following formula:

In the formula: z——the number of rolling elements; f _r ——rotation frequency/Hz; d——rolling element diameter/mm; D——the outer diameter of the bearing/mm; α——contact angle/°.

During the test, the vibration acceleration sensor is installed at the fault bearing seat, the input shaft speed is 673r/min, the sampling frequency is 12.8kHz, and the sampling length is 4096 points. The characteristic frequency of the bearing outer ring fault can be obtained from the fault formula (1) of the outer ring of the rolling bearing. 82.8Hz, that is, the time interval is 12.7ms.

Figure 2 shows the vibration time domain signal of the equipment when the outer ring of the bearing is faulty, Figure 3 is the signal spectrum of the faulty bearing, Figure 4 is the Hilbert envelope spectrum of the faulty bearing signal, and the weak shock signal generated by the fault can be seen from the figure. Submerged in the strong background noise, it is difficult to find the fault characteristics of periodic pulses, and the spectral lines corresponding to the fault characteristic frequencies in the frequency domain are also hidden in the noise spectral lines, making it difficult to judge whether the bearing is faulty.

相应于特征值1。因此，根据构造两尺度相似变换矩阵必须满足的条件，结合GHM多小波的特点，构造出基于GHM多小波的两尺度相似变换矩阵M(ω)如下所示：The second step: GHM is one of the most common and widely used double multi-wavelet basis functions in engineering. It has compact support, orthogonality, symmetry, second-order approximation order and vanishing moment. Here, the GHM multiwavelet is used as the initial multiwavelet. The symmetric point or anti-symmetric point of GHM multi-wavelet multi-scale function and multi-wavelet basis function is 1/2 or 1, at the same time, H(0) has an eigenvector

Corresponds to eigenvalue 1. Therefore, according to the conditions that must be satisfied to construct the two-scale similarity transformation matrix, combined with the characteristics of GHM multi-wavelets, the two-scale similarity transformation matrix M(ω) based on GHM multi-wavelets is constructed as follows:

Where: a, b—non-zero parameters.

Let H _G (ω) and G _G (ω) be the low-pass and high-pass filter symbols of the GHM multi-wavelet scaling function and multi-wavelet function, according to the two-scale similarity transformation:

After the above transformation, a new intermediate function {Φ _p ,Ψ _p } is obtained. The multi-scale function Φ _p has a third-order approximation order, while the vanishing moment of the multi-wavelet basis function Ψ _p is reduced to the first order, weakening the multi-wavelet Smoothness and local localization capabilities of functions.

1代表对称，-1代表反对称)代表初始多小波的对称性或反对称性，则对称提升过程中的线性方程：Step 3: Based on the intermediate multiwavelets {Φ _p ,Ψ _p }, assuming that the vanishing moment is raised from the first order to the fifth order, let B _ωi =±1(ω _i =ψ _i or

1 represents symmetry, -1 represents anti-symmetry) represents the symmetry or anti-symmetry of the initial multi-wavelet, then the linear equation in the process of symmetry lifting:

The solution of equation (4) is the boost coefficient of Ψ ₁ , and the boost of Ψ ₂ is also similar to Ψ ₁ . After the lifting coefficient is obtained, the lifting coefficient equation is brought into the equation, and the lifting matrix T and S can be obtained by Z transformation. Based on the lifting matrices T and S, a new multi-wavelet after ensemble construction is obtained according to the following lifting algorithm:

The multi-wavelet {Φ _s ,Ψ _s } obtained by the ensemble structure after the lifting framework has the third-order approximation order and the fifth-order vanishing moment.

Step 4: In the previous construction process, the two-scale similarity transformation introduced two free parameters, and when the linear equation M _B C = M _ψ group of the symmetric lifting process is an underdetermined linear equation system, there is N _f =4 _-Rank (MB) free parameters. These free parameters will affect the waveform of the multiwavelet basis function. The kurtosis index is very sensitive to the impulse response characteristics caused by early local faults. Therefore, the adaptive construction process of the integrated multi-wavelet takes the kurtosis index of the detail signal as the objective function to solve the multi-wavelet freedom that maximizes the objective function K _P parameters to optimize an adaptive multiwavelet basis function that matches the given signal.

Objective function:

In the formula: x——detail signal; p(x)——probability density of signal amplitude.

From the expression of the objective function K _P , it can be seen that there is no direct connection between the kurtosis maximization principle and these free parameters, and the relationship between them is very complex. Common optimization algorithms often require a complete relationship expression, which is difficult to achieve here. . In view of the strong robustness of genetic algorithm and the characteristics of global and parallel search, it does not require mathematical expression between objective functions and variables. In this section, the genetic algorithm is used, and the objective function K _P is used as the fitness function to construct a multi-wavelet adaptively matching the signal characteristics. The population size is 100, the number of initial populations is set to 50, the crossover probability is set to 0.6, and the mutation probability is set to 0.05.

After the optimization of the above process, the multi-wavelet basis function constructed by the adaptive multi-wavelet ensemble is shown in Figure 5.

Step 5: After completing the integrated multi-wavelet adaptive construction, perform multi-wavelet redundancy decomposition on the signal to realize the translation invariance of the decomposition result. The specific implementation process is as follows:

The decomposition process of redundant multi-wavelet transform is the result of matrix interpolation and zero-filling performed by the low-pass and high-pass filters of the subsequent decomposition layer on its previous decomposition layer, and the matrix interpolation zero-filling refers to the insertion of zeros of size r×r. matrix. Let T denote the interpolation zero-filling operator, then for any integer i,

(Tx) _2i =x _i , (Tx) _2i+1 =0

Then the low-pass and high-pass filter coefficients {H, G} are calculated by the following equations when the decomposition layer is l in the redundant multi-wavelet transform process:

(1) When k is not an integer multiple of 2 ^l ,

(2) In other cases,

The use of redundant multi-wavelet transform is beneficial to improve the accuracy of feature extraction and the spectral accuracy of decomposition results, thereby achieving more accurate feature extraction and fault detection of mechanical equipment faults.

After 3-level redundancy decomposition, the branch with the largest kurtosis is selected, and the result is shown in Figure 6. It can be seen from Figure 6 that the method can successfully extract the periodic pulse signal of the outer ring fault with a period of 12.7ms, so it can be seen that this method has a significant effect on enhancing the weak fault characteristics, and it can effectively improve the weak fault characteristics from the strong background. The fault features of the outer ring of the rolling bearing are extracted from the noise.

On the basis of in-depth research on two-scale similarity transformation and symmetric lifting framework, the invention proposes an integrated construction method of adaptive multi-wavelet basis functions, and adopts the kurtosis index that is most sensitive to the shock pulse of early faults as a parameter in the adaptive process. The optimal criterion is optimized by genetic algorithm, and the vibration signal collected by the sensor is analyzed to obtain an adaptive integrated multi-wavelet basis function with excellent properties that matches the fault characteristics, so as to realize the weak fault feature extraction. The invention improves the approximation order of the multi-scale function and the vanishing moment of the multi-wavelet base function, constrains the symmetry of the base function, ensures the linear phase and the generalized linear phase of the filter, improves the performance of the original multi-wavelet, and avoids decomposition The phase distortion occurred in the process and the boundary processing ability were improved, an adaptive multi-wavelet basis function adapted to the dynamic signal was constructed, and the compact support and symmetry of the initial multi-wavelet were maintained. Weak fault feature extraction provides a new method.

It should be noted that, although the embodiments of the present invention described above are illustrative, they are not intended to limit the present invention, so the present invention is not limited to the above-mentioned specific embodiments. Without departing from the principles of the present invention, all other embodiments obtained by those skilled in the art under the inspiration of the present invention are deemed to be within the protection of the present invention.

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),...,ω_k(x) K; finally, a new multi-wavelet can be constructed through a lifting coefficient equation

The lifting coefficient equation is:

for psi₁，

For psi₂，

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:

the integral value in equation ② is calculated using a formula for moment calculation, the solution of the equation set c_iThe 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

a_ψ1,a_ψ2(ii) a The symmetric lifting method is then expressed as follows:

for psi₁Symmetric lifting of (2), translation of lifting function

Must satisfy

In the formula: i is 1, 2; j ═ 1,2, …; m is 1, 2;

order to

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

And M (psi)_i,k,n)＝∫ψ_i(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 M_BWherein M is_BM and B are each MB

Let B be a symmetric matrix

In lifting linear equationsThe coefficient vector is represented as

And the right of the equation is denoted as M_ψ＝[M(ψ_i,0,p),M(ψ_i,0,p+1),…M(ψ_i,0,p'-1)]^TThen formula M_BMB is changed to the following formula

M_BC＝M_ψ⑥

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

And

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:

H_s(ω)＝H_p(ω)

G_s(ω)＝T(ω²)(G_p(ω)+S(ω²)H_p(ω))

in the formula: h_p(omega) and G_p(omega) is an intermediate multi-wavelet [ phi ]_p,Ψ_pThe low-pass and high-pass filter symbols of { C }; h_s(omega) and G_s(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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