Adaptive mathematical form bearing fault feature extraction method based on multi-target genetic algorithm

Abstract

The invention relates to the technical field of bearing fault diagnosis, in particular to an adaptive mathematical form bearing fault feature extraction method based on a multi-target genetic algorithm, and provides an adaptive mathematical form operator. A multi-target genetic optimization algorithm is adopted to optimize an adaptive mathematical form operator so as to determine the optimal performance of structural element filtering, and proper structural element sizes and weight factor parameters are selected while the requirements of the maximum kurtosis and the minimum envelope entropy value are met; therefore, noise reduction and filtering are carried out on the bearing vibration signals under strong noise interference, details and morphological characteristics of the signals can be accurately captured in a time-frequency domain, and a more accurate and reliable basis is provided for fault diagnosis of the rolling bearing.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault diagnosis, and specifically to an adaptive mathematical morphology bearing fault feature extraction method based on a multi-objective genetic algorithm. Background Art

[0002] As a commonly used component in rotating machinery, rolling bearings often operate continuously under heavy loads, high temperatures, variable speeds and other working conditions, and are often required to be replaced during the maintenance of rotating machinery because they are vulnerable parts. In actual production, the applicant uses a centrifugal pump in which the normal operation of the bearing is crucial for the stable operation of the whole machine. Once a fault occurs and is not detected in time, it will cause equipment shutdown and even casualties, resulting in huge losses. Therefore, it is very important to carry out fault diagnosis on it.

[0003] Bearing vibration, as an important basis for judging mechanical damage and maintenance cycle, is an important performance parameter of bearings. How to accurately detect the fault information of bearings is the focus of research by many scholars at home and abroad. In actual use, the fault information of bearings is easily interfered and modulated and attenuated, becoming a weak signal under a strong noise background, and it is difficult to extract fault features. At present, the methods for extracting bearing fault information detection include spectrum analysis method, wavelet transform, empirical mode decomposition, mathematical morphology, etc. However, although the spectrum analysis method can intuitively present the frequency components of the signal, for non-stationary signals under complex working conditions, it cannot accurately capture the fault feature information that changes with time. Especially in equipment with variable loads and variable speeds, spectrum analysis is likely to miss key fault signs. Wavelet transform can handle non-stationary signals to a certain extent, but it is sensitive to the selection of wavelet basis functions. Different wavelet basis functions may lead to large differences in the analysis results, and the computational complexity is high during multi-scale analysis, which is not conducive to real-time fault diagnosis.

[0004] Traditional rolling bearing fault diagnosis methods often have limitations in dealing with complex vibration signals, are difficult to effectively extract weak fault feature information, and are sensitive to noise interference. At present, some scholars mainly focus on the design of mathematical morphology filters in aspects such as seismic detection, water or underwater target detection, etc. As a non-linear signal processing method, mathematical morphology has obtained good shape analysis and feature extraction capabilities in current application scenarios. However, there is less research on the optimization of structural elements in bearing vibration detection by mathematical morphology. In fault diagnosis based on mathematical morphology, the design of the size of structural elements and the type of morphological filters is easily affected by prior experience, and the accuracy of bearing fault diagnosis is low. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the purpose of the present invention is to provide an adaptive mathematical morphology bearing fault feature extraction method based on a multi-objective genetic algorithm.

[0006] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0007] An adaptive mathematical morphology bearing fault feature extraction method based on a multi-objective genetic algorithm, comprising:

[0008] S1. Construct an adaptive mathematical morphology operator:

[0009]

[0010] In the formula, y(n) is the signal after adaptive mathematical morphology processing, f(n) is the input signal, α and β are weighting factors, F oc is to perform opening and closing operations on the input signal, and F co is to perform closing and opening operations on the input signal;

[0011] S2. Collect the vibration signal during the operation of the bearing, and input the vibration signal as the input signal into the constructed adaptive mathematical morphology operator;

[0012] S3. For the adaptive mathematical morphology operator after inputting the vibration signal, with the maximization of kurtosis and the minimization of envelope entropy as the objectives, determine the optimal solution of the optimization parameters based on the multi-objective genetic algorithm, where the optimization parameters include: the weighting factor and the length of the structural element in the vibration signal;

[0013] S4. Use the signal y(n) corresponding to the optimal solution as the fault feature.

[0014] Preferably, a further technical solution of the present invention is: Specifically included in S1:

[0015] The most important in mathematical morphology is the design of the operator. In the mathematical morphology operator, it is assumed that there is a discrete signal f(n), the domain of definition is F(0, 1, 2... N - 1) and n ∈ [0, 1, 2... N - 1]; g(m) is the structural element, the domain of definition is G(0, 1, 2... M - 1), N ≥ M and m ∈ [0, 1, 2... M - 1], then the erosion and dilation operators of the signal f(n) with respect to g(m) are defined as follows:

[0016]

[0017] When filtering the signal f(n), due to the influence of noise factors on the signal, the effect of simply using the erosion and dilation operators for feature extraction of the noisy signal is not obvious. In order to improve the feature extraction performance, the concept of a cascaded operator is proposed, and the cascaded operator is defined as follows:

[0018]

[0019] Among them, · represents the closing operation, Denote the opening operation. In signal feature extraction, the closing operation has dilatation property, and the opening operation has contraction property. To control the dilatation and contraction of the operation, a combined operator strategy is proposed:

[0020]

[0021] where co is the closing-opening operator, and oc is the opening-closing operator. The combined operator takes into account all the filtering performances of the opening and closing operators;

[0022] Finally, since the fault vibration signal of the bearing will show periodic positive and negative pulses when bearing transient impact is endured, the adaptive mathematical morphology operator is proposed.

[0023] Preferably, the envelope entropy E in S3 p is calculated as follows:

[0024]

[0025] The kurtosis K is calculated as follows:

[0026]

[0027] In the formula, a(j) is the envelope signal obtained by the demodulation operation of the signal y(n) filtered by the adaptive mathematical morphology operator, and p j is the normalized form of a(j), that is, the probability distribution sequence. The smaller the value of the envelope entropy E p , the better the filtering performance of the adaptive mathematical morphology operator for the signal, and the stronger the extraction ability for the impact signal; F1 is the mean value of the signal, F2 is the standard deviation of the signal. Kurtosis is the feature of the signal in the time domain. The larger the kurtosis value, the more obvious the extracted fault information.

[0028] Preferably, the process of determining the optimal solution of the optimization parameters based on the multi-objective genetic algorithm in S3 includes:

[0029] S3-1. Define the population parameters, initialize the population to obtain the parental population of the optimization parameters. The population parameters include defining the population size, crossover probability, mutation probability, maximum iteration number, and the value range of the optimization parameters;

[0030] S3-2. Obtain the envelope entropy value corresponding to each individual in the parental population, and perform random crossover and mutation operations on the parental population to obtain the offspring population;

[0031] S3-3. Combine the offspring population with the parental population, and obtain the sorting of the individuals in the combined population through dominance sorting;

[0032] S3-4. Select the new population through elite strategy according to the sorting of the merged population. When it is determined that the maximum number of iterations is reached, obtain the non-dominated solution set of the optimized parameters in the new population according to the envelope entropy and kurtosis, and determine the optimal solution in the non-dominated solution set; when it is determined that the maximum number of iterations is not reached, use the new population as the parental population and return to S3-2.

[0033] Preferably, for the sorting of individuals at the same level in S3-3, the crowding degree needs to be calculated, and the individual with the smallest crowding degree is selected. The calculation of the crowding degree is as follows:

[0034]

[0035] In the formula, and are the objective function values of the (i-1)-th and (i+1)-th individuals at the selected j-th objective function respectively, and are the maximum and minimum values of the selected j-th objective function among all individuals respectively.

[0036] For the present invention adopting the above technical solution, compared with the prior art, its prominent features are:

[0037] An adaptive mathematical morphology operator is proposed, and the multi-objective genetic optimization algorithm is used to optimize the adaptive mathematical morphology operator to determine the optimal performance of the structural element filtering. While meeting the requirements of the maximum kurtosis and the minimum envelope entropy value, the appropriate structural element size and weight factor parameters are selected, so as to realize the noise reduction filtering of the bearing vibration signal under strong noise interference, and can accurately capture the details and morphological features of the signal in the time-frequency domain, providing a more accurate and reliable basis for the fault diagnosis of rolling bearings. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a schematic flowchart of the method for extracting the fault characteristics of an adaptive mathematical morphology bearing based on a multi-objective genetic algorithm in an embodiment of the present invention;

[0039] Figure 2 is a schematic block diagram of the principle for determining the optimal solution of the optimization parameters based on a multi-objective genetic algorithm in an embodiment of the present invention;

[0040] Figure 3 is a schematic diagram of the original simulation signal in an embodiment of the present invention, where Figure a is a time-domain waveform diagram and Figure b is a frequency-domain waveform diagram;

[0041] Figure 4 is a schematic diagram of the non-dominated solution set of the simulation signal in an embodiment of the present invention;

[0042] Figure 5It is the filtered time-domain waveform diagrams of two operators in the embodiments of the present invention. Among them, diagram a is the existing operator CMFH, and diagram b is the operator ACMFH of the present invention;

[0043] Figure 6 It is the envelope spectrum of two operators in the embodiments of the present invention. Among them, diagram c is the existing CMFH operator, and diagram d is the ACMFH operator of the present invention;

[0044] Figure 7 It is the non-dominated solution set of the outer bearing ring in the embodiments of the present invention. Among them, diagram a is the corresponding signal of 20-X-OUT, and diagram b is the corresponding signal of 20-Y-OUT;

[0045] Figure 8 It is the non-dominated solution set of the inner bearing ring in the embodiments of the present invention. Among them, diagram a is the corresponding signal of 10-Y-IN, and diagram b is the corresponding signal of 10-Z-IN;

[0046] Figure 9 It is the time-frequency diagram and envelope spectrum after filtering of each operator for the corresponding signal of the outer bearing ring 20-X-OUT in the embodiments of the present invention. Among them, a is the existing AEDH operator, b is the existing AVGH operator, c is the existing CMFH operator, and d is the ACMFH operator of the present invention;

[0047] Figure 10 It is the time-frequency diagram and envelope spectrum after filtering of each operator for the corresponding signal of the outer bearing ring 20-Y-OUT in the embodiments of the present invention. Among them, a is the existing AEDH operator, b is the existing AVGH operator, c is the existing CMFH operator, and d is the ACMFH operator of the present invention;

[0048] Figure 11 It is the time-frequency diagram and envelope spectrum after filtering of each operator for the corresponding signal of the inner bearing ring 10-Y-IN in the embodiments of the present invention. Among them, a is the existing AEDH operator, b is the existing AVGH operator, c is the existing CMFH operator, and d is the ACMFH operator of the present invention;

[0049] Figure 12 It is the time-frequency diagram and envelope spectrum after filtering of each operator for the corresponding signal of the inner bearing ring 10-Z-IN in the embodiments of the present invention. Among them, a is the existing AEDH operator, b is the existing AVGH operator, c is the existing CMFH operator, and d is the ACMFH operator of the present invention. Detailed implementation manners

[0050] The present invention will be further described below in conjunction with specific embodiments. The purpose is only to better understand the content of the present invention. Therefore, the examples given do not limit the protection scope of the present invention.

[0051] See Figure 1, this embodiment presents an adaptive mathematical morphology bearing fault feature extraction method based on a multi-objective genetic algorithm, including:

[0052] S1. Construct an adaptive mathematical morphology operator:

[0053]

[0054] In the formula, y(n) is the signal after adaptive mathematical morphology processing, f(n) is the input signal, α and β are weighting factors, and F oc is the opening and closing operation on the input signal, and F co is the closing and opening operation on the input signal;

[0055] S2. Collect the vibration signal during the operation of the bearing, and input the vibration signal as the input signal into the constructed adaptive mathematical morphology operator;

[0056] S3. For the adaptive mathematical morphology operator after inputting the vibration signal, with the maximization of kurtosis and the minimization of envelope entropy as the objectives, determine the optimal solution of the optimization parameters based on the multi-objective genetic algorithm, where the optimization parameters include: the weighting factor and the length of the structural element in the vibration signal;

[0057] S4. Use the signal y(n) corresponding to the optimal solution as the fault feature.

[0058] In the implementation, S1 specifically includes:

[0059] The most important in mathematical morphology is the design of the operator. In the mathematical morphology operator, it is assumed that there is a discrete signal f(n) with the domain F(0, 1, 2... N - 1) and n ∈ [0, 1, 2... N - 1]; g(m) is the structural element with the domain G(0, 1, 2... M - 1), N ≥ M and m ∈ [0, 1, 2... M - 1]. Then the erosion and dilation operators of the signal f(n) with respect to g(m) are defined as follows:

[0060]

[0061] When filtering the signal f(n), due to the influence of noise factors on the signal, the effect of simply using the erosion and dilation operators on the feature extraction of the noisy signal is not obvious. In order to improve the feature extraction performance, the concept of cascaded operators is proposed, and the cascaded operators are defined as follows:

[0062]

[0063] Among them, · represents the closing operation, represents the opening operation. In signal feature extraction, the closing operation has expansibility, and the opening operation has contractility. In order to control the expansion and contraction of the operation, the combined operator strategy is proposed:

[0064]

[0065] Among them, co is a closing-opening operator, and oc is an opening-closing operator. The combined operator takes into account all the filtering performances of the opening and closing operators;

[0066] Finally, since the fault vibration signal will show periodic positive and negative pulses when the bearing bears transient impact, the adaptive mathematical morphology operator is proposed.

[0067] During implementation, the envelope entropy E in S3 p is calculated as follows:

[0068]

[0069] The kurtosis K is calculated as follows:

[0070]

[0071] In the formula, a(j) is the envelope signal obtained by demodulating the signal y(n) filtered by the adaptive mathematical morphology operator. p j is the normalized form of a(j), that is, the probability distribution sequence. The smaller the value of the envelope entropy E p , the better the filtering performance of the adaptive mathematical morphology operator for the signal, and the stronger the ability to extract the impact signal; F1 is the mean value of the signal, F2 is the standard deviation of the signal. Kurtosis is a feature of the signal in the time domain. The larger the kurtosis value, the more obvious the extracted fault information.

[0072] During implementation, at present, the optimal selection of the parameters of the mathematical morphology operator is mainly based on experience according to the collected vibration signals, which is bound to cause incomplete collection of fault information, especially when facing weak fault vibration signals. Therefore, the present invention proposes an adaptive filtering method for signals. The design of the adaptive mathematical morphology operator is mainly the adaptive design of the structural element scale. However, the filtering performance of the relatively single optimized parameter selection is insufficient. At present, there are few studies on the multi-objective adaptive filtering. Therefore, for the multi-objective problem that it is difficult to optimize the structural element scale and the weight coefficient in the operator of the present invention, the NSGA-II algorithm with fast processing speed is used to complete.

[0073] Specifically, referring to Figure 2 , the process of determining the optimal solution of the optimization parameters based on the multi-objective genetic algorithm includes:

[0074] S3-1. Define the population parameters, initialize the population to obtain the parental population regarding the optimization parameters. The population parameters include defining the population size, crossover probability, mutation probability, maximum iteration number, and the value range of the optimization parameters;

[0075] In implementation, considering the computational complexity and running time of the algorithm, the population size is defined as 50, the crossover probability is 0.8, the mutation probability is 0.5, the value range of the weighting factor in the optimization parameters is [0, 1], the length of the structural element is [3, 21], and the length of the structural element is an integer value.

[0076] S3-2. Obtain the envelope entropy value corresponding to each individual in the parent population, and perform random crossover and mutation operations on the parent population to obtain the offspring population;

[0077] S3-3. Merge the offspring population and the parent population, and obtain the ranking of individuals in the merged population through dominance sorting;

[0078] S3-4. Select the new population through the elite strategy for the merged population according to the ranking. When it is determined that the maximum number of iterations is reached, obtain the non-dominated solution set of the optimization parameters in the new population according to the envelope entropy and kurtosis, and determine the optimal solution in the non-dominated solution set; when it is determined that the maximum number of iterations is not reached, use the new population as the parent population and return to S3-2.

[0079] In implementation, for the ranking of individuals at the same level in S3-3, the crowding degree needs to be calculated, and the individual with the smallest crowding degree is selected. The calculation of the crowding degree is as follows:

[0080]

[0081] In the formula, and are the j-th objective function values of the (i - 1)-th and (i + 1)-th individuals respectively, and are the maximum and minimum values of the j-th objective function among all individuals respectively.

[0082] The solution provided in the embodiment of the present invention proposes an adaptive mathematical morphology operator, and uses a multi-objective genetic optimization algorithm to optimize the adaptive mathematical morphology operator to determine the optimal performance of the structural element filtering. While meeting the requirements of the maximum kurtosis and the minimum envelope entropy value, the appropriate structural element size and weight factor parameters are selected, so as to realize the noise reduction filtering of the bearing vibration signal under strong noise interference, and can accurately capture the details and morphological characteristics of the signal in the time-frequency domain, providing a more accurate and reliable basis for the fault diagnosis of rolling bearings.

[0083] To verify the recognition effect of the method designed by the present invention on periodic pulse signals, a simulation signal is constructed for verification. The constructed bearing outer ring signal model is as follows:

[0084]

[0085] Sampling frequency f s= 1024, the number of sampling points N is 1024, the fault frequency f m = 16, f1 is 200 Hz, f2 is 25 Hz, f3 is 30 Hz, r(t) is Gaussian white noise, and the signal-to-noise ratio is 2 db.

[0086] The time domain and frequency domain diagrams of the original simulation signal are as Figure 3 shown. It can be analyzed that the time domain waveform is affected by harmonic interference and Gaussian white noise, while the frequency domain can only identify the frequencies of harmonic interference; Figure 3 In b, the fault frequency of the original signal and its high-order harmonics in the simulation signal cannot be accurately identified.

[0087] The non-dominated solution set obtained based on the above bearing fault simulation and multi-optimization process is as Figure 4 shown. It can be concluded that: 1. In the operator AMCFH filtering of the present invention, there is a mutual restriction between the selected envelope entropy and kurtosis. The larger the envelope entropy value, the smaller the kurtosis. Since random functions are used to select the initialization, selection, and routing of the population, there are more similar parameters in the non-dominated solution set, improving the calculation efficiency; 2. When performing multi-objective optimization on the input signal, the changes in the envelope entropy value and kurtosis value are not greatly discontinuous in the non-dominated solution set, indicating that the selected parameters are relatively uniform; 3. According to the principle that the smaller the envelope entropy value and the larger the kurtosis, the better the filtering effect, select the point with a crowding degree of 0 in the non-dominated solution set, and the adaptive optimization parameters obtained are: 0.9292, 0.9948, 5. At the same time, use the traditional CMFH operator for filtering, and the obtained time domain and envelope spectra are as Figure 5 and 6 shown.

[0088] Compared with the traditional CMFH operator, the filtering effect of the ACMFH operator filtering of the present invention in the time domain and envelope spectrum is not much different from that of CMFH filtering, maintaining the filtering characteristics of the CMFH operator, which conforms to the design idea of the present invention as an improved operator of the CMFH operator. In the envelope spectrum, the traditional CMFH operator and the ACMFH operator can basically find the fault frequencies of 1-5 times the frequency. Therefore, the design of the adaptive scale operator of the present invention is relatively successful.

[0089] Further, a comprehensive comparative analysis is carried out on the filtering and noise reduction performance using the relatively traditional signal-to-noise ratio and mean square error indicators. The mean square error RMSE of CMFH is 0.6958, while the mean square error RMSE of ACMFH is 0.6415; the signal-to-noise ratio SNR of CMFH is -0.009 db; the signal-to-noise ratio SNR of ACMFH is 0.3844 db; therefore, it can be concluded that the filtering performance of the ACMFH operator designed by the present invention is better than that of the traditional CMFH operator.

[0090] In actual production, the vibration data of the bearing collected on-site is analyzed to verify whether the method designed by the present invention is applicable: First, the fault frequency of the bearing is calculated according to the given bearing parameters, and then the method of the present invention is used to process the bearing fault vibration signal to verify the superiority and innovation of the present invention.

[0091] 1. Calculation of Bearing Fault Frequency

[0092] According to the bearing size and structural parameters, the fault frequencies of the inner and outer rings of the bearing can be calculated:

[0093]

[0094] In the formula, f o is the fault frequency of the outer ring of the bearing, f r is the fault frequency of the inner ring of the bearing, f b is the fault frequency of the ball ring of the bearing, fr is the motor frequency of the bearing, d is the ball diameter, D is the bearing pitch diameter; α is the bearing contact angle; Z is the number of rolling elements in the bearing.

[0095] 2. Bearing Signal Acquisition

[0096] The vibration signals of the bearings in the centrifugal pump equipment in the workshop are collected for analysis and processing, and this data set is taken as an example for analysis and processing. The model of the bearing is ER-8K bearing, the number of its rolling elements is 8, the pitch diameter is 1.318 inches, the sampling frequency is 1024 Hz, and the selected structural element data length is 2048.

[0097] Considering the influence of the motor speed on the acquisition of bearing fault information, when the rotation frequencies are 10 and 20 Hz respectively, the fault information outside and inside the faulty bearing is measured. The present invention mainly collects from the three directions of X, Y, and Z of the bearing in space. For example, 20-X-OUT represents the data obtained by measuring the outer raceway of the measured bearing in the X direction when the motor frequency is 20, and 10-Y-IN represents the data obtained by measuring the inner raceway of the measured bearing in the Y direction when the motor frequency is 10.

[0098] 3. Result Analysis

[0099] Table 1 calculates the bearing fault frequencies at different input speeds. In order to better observe the weak fault information of the bearing in the envelope spectrum, based on the bearing fault frequencies in Table 1, the fault frequencies of each part of the bearing in the signal envelope spectrum are marked multiple times at a single frequency in the signal envelope spectrum.

[0100] Table 1 Bearing Fault Test Frequencies

[0101] Motor frequency (r / min) <![CDATA[f o > <![CDATA[f i > <![CDATA[f b > 10 30 50 20 20 60 100 40

[0102] The design of the ACMFH operator in the present invention mainly adopts the ideas of CMF and top-hat transformation. Therefore, this type of operator is selected for vertical comparison, and mainly the AEDH, AVGH, and CMFH operators are selected. The non-dominated solution sets of the outer and inner rings of the bearing are set as shown in Figure 7 , 8 respectively. The abscissa represents the envelope entropy value, and the ordinate represents the kurtosis.

[0103] The adaptive optimization parameters are as follows:

[0104] Table 2 Adaptive Optimal Parameters of the Outer Ring Frequency of the Bearing

[0105] Number α β L 20 - X - OUT 0.7620 0.2561 17 20 - Y - OUT 0.1609 0.0259 20

[0106] Table 3 Adaptive Optimal Parameters of the Inner Ring Frequency of the Bearing

[0107] Number α β L 10 - Y - IN 0.8868 0.6240 3 10 - Z - IN 0.0214 0.9711 3

[0108] After determining the structural element scale through ACMFH filtering, the time-frequency diagrams and envelope spectra after filtering obtained by each operator are as shown in Figure 9 , 10 , 11, and 12.

[0109] The SNR and RMSE of the four operators in different situations are calculated as shown in Tables 4 and 5:

[0110] Table 4 Signal-to-Noise Ratio and Root Mean Square Error of the Outer Ring of the Bearing

[0111]

[0112]

[0113] Table 5 Signal-to-Noise Ratio and Root Mean Square Error of the Inner Ring of the Bearing

[0114]

[0115] By collecting the fault detection signals of the outer ring, ball, and inner ring of the bearing at different motor speeds, and filtering them using 4 operators, it is analyzed that:

[0116] 1. ACMFH performs well in terms of the SNR and RMSE evaluation indicators. The filtering effect and accuracy of the adaptive operator of the present invention are higher than those of the existing AEDH, AVGH, and CMFH. The NSGA-II algorithm designed in the present invention is applicable to the selection of the structural scale of other operators.

[0117] 2. When processing the fault information of the outer ring, inner ring, and ball ring of the bearing, the distribution of the non-dominated solution set is relatively uniform.

[0118] 3. From the time domain perspective, the filtering effects of the four operators are basically the same. From the frequency domain analysis, it can be seen that there is more outer ring fault information during filtering. At the 20 - Y - OUT signal in Figure 10 d, the motor rotation frequency of ACMFH is better identified.

[0119] 4. The ACMFH and filtering method proposed by the present invention can effectively extract the fault frequencies of each component of the bearing, especially the multi - frequency extraction of each component of the bearing. For example, in the 10 - Y - IN experiment, ACMFH can extract 5f more clearly than other operators i .

[0120] The above are only the preferred embodiments of the present invention that can be implemented, and do not limit the scope of the rights of the present invention. Any equivalent changes made by using the content of the specification and drawings of the present invention are included in the scope of the rights of the present invention.

Claims

1. An adaptive mathematical morphology bearing fault feature extraction method based on multi-objective genetic algorithm, characterized in that: include: S1. Constructing adaptive mathematical morphological operators: Where y(n) is the signal after adaptive mathematical morphology processing, f(n) is the input signal, α and β are weighting factors, and F oc To perform on / off operation on the input signal, F co To perform a closing and opening operation on the input signal; S2, collecting vibration signals during the operation of the bearing, and using the vibration signals as input signals to construct an adaptive mathematical morphology operator; S3, for the adaptive mathematical morphological operator after the vibration signal is input, with the goal of maximizing the kurtosis and minimizing the envelope entropy, the optimal solution of the optimization parameters is determined based on the multi-objective genetic algorithm, wherein the optimization parameters include: a weighting factor and the length of the structural element in the vibration signal; S4. Use the signal y(n) corresponding to the optimal solution as the fault feature.

2. The method for extracting bearing fault features based on adaptive mathematical morphology based on multi-objective genetic algorithm according to claim 1 is characterized in that: S1 specifically includes: The most important thing in mathematical morphology is the design of operators. In mathematical morphology operators, it is assumed that there is a discrete signal f(n), the domain is F(0, 1, 2…N-1) and n∈[0, 1, 2…N-1]; g(m) is a structural element, the domain is G(0, 1, 2…M-1), N≥M and m∈[0, 1, 2…M-1], then the erosion and expansion operators of the signal f(n) with respect to g(m) are defined as follows: When filtering the signal f(n), since the signal is affected by noise factors, the simple use of corrosion and expansion operators is not effective in extracting features from noisy signals. In order to improve the feature extraction performance, the concept of cascade operators is proposed. The definition of cascade operators is as follows: Among them, · represents the closing operation, Represents the open operation. In signal feature extraction, the closed operation is expansive and the open operation is contractive. In order to control the expansion and contraction of the operation, a combination operator strategy is proposed: Among them, co is the close-open operator, oc is the open-close operator, and the combined operator takes into account all the filtering performance of the open and close operators; Finally, because the fault vibration signal of the bearing will show periodic positive and negative pulses when it is subjected to transient impact, the adaptive mathematical morphology operator is proposed.

3. The method for extracting bearing fault features based on adaptive mathematical morphology using a multi-objective genetic algorithm according to claim 2 is characterized in that: Envelope entropy E in S3 p The calculation is as follows: The kurtosis K is calculated as follows: Where a(j) is the envelope signal obtained by demodulating the signal y(n) after filtering by the adaptive mathematical morphology operator, and p j is the normalized form of a(j), i.e., the probability distribution sequence, and the envelope entropy E p The smaller the value is, the better the filtering performance of the adaptive mathematical morphology operator is for the signal, and the stronger the ability to extract the impact signal is. F1 is the mean of the signal, F2 is the standard deviation of the signal, and the kurtosis is the characteristic of the signal in the time domain. The larger the kurtosis value is, the more obvious the fault information extracted is.

4. The method for extracting bearing fault features based on adaptive mathematical morphology using a multi-objective genetic algorithm according to claim 3 is characterized in that: The process of determining the optimal solution of optimization parameters based on the multi-objective genetic algorithm in S3 includes: S3-1, define population parameters, initialize the population to obtain the parent population of the optimization parameters, the population parameters include defining the population size, crossover probability, mutation probability, maximum number of iterations and the value range of the optimization parameters; S3-2, obtain the envelope entropy value corresponding to each individual in the parent population, and perform random crossover and mutation operations on the parent population to obtain the offspring population; S3-3, merge the offspring population with the parent population, and obtain the order of individuals in the merged population through dominance ordering; S3-4. Perform elite strategy selection on the merged population according to the sorting to obtain a new population. When it is determined that the maximum number of iterations has been reached, obtain the non-dominated solution set of the optimization parameters in the new population according to the envelope entropy and kurtosis, and determine the optimal solution in the sub-dominated solution set. When it is determined that the maximum number of iterations has not been reached, use the new population as the parent population and return to S3-2.

5. The method for extracting bearing fault features based on adaptive mathematical morphology using a multi-objective genetic algorithm according to claim 4 is characterized in that: In S3-3, the ranking of individuals of the same level requires crowding calculation, and the individual with the smallest crowding is selected. The crowding calculation is as follows: In the formula, and are the values ​​of the jth objective function selected by the i-1th and i+1th individuals, respectively. and are respectively the maximum and minimum values ​​of the j-th objective function selected among all individuals.

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