CN115452362A - Fault diagnosis method for gear box - Google Patents

Fault diagnosis method for gear box Download PDF

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CN115452362A
CN115452362A CN202211299290.5A CN202211299290A CN115452362A CN 115452362 A CN115452362 A CN 115452362A CN 202211299290 A CN202211299290 A CN 202211299290A CN 115452362 A CN115452362 A CN 115452362A
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sparrow
value
fault diagnosis
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王梦姣
杜董生
刘雪梅
朱秀芳
季捷
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Huaiyin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/021—Gearings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention relates to a gearbox fault diagnosis method, which comprises the following steps: 1) Establishing a sample data set of the gearbox, and denoising signals by using wavelet threshold denoising; 2) Carrying out secondary noise reduction on the data by using Savitzky-Golay filtering; 3) And decomposing the denoised signal by improved adaptive noise complete set empirical mode decomposition (ICEEMDAN) to obtain a series of IMF components. Respectively calculating the contribution rate and the correlation value of each IMF component, and selecting the first six IMFs with the largest sum of the contribution rate and the correlation value to form a new IMF sequence; 4) Calculating time domain and frequency domain characteristics of the new IMF sequence, and constructing a sample characteristic set; 5) Selecting the characteristics of the sample by utilizing the mutual information; 5) Optimizing a sparrow optimization algorithm (SSA) using Tent mapping and gaussian variation; 6) And (3) optimizing the weight and the threshold of the extreme learning machine by using the optimized SSA (ICSSA), and establishing an extreme learning machine (ICSSA-ELM) model based on an improved sparrow optimization algorithm. The method is applied to the fault diagnosis process of the gearbox, has higher optimization precision, and ensures the accuracy of the fault diagnosis of the gearbox.

Description

Fault diagnosis method for gear box
Technical Field
The invention relates to the technical field of gearbox fault diagnosis, in particular to a gearbox fault diagnosis method.
Background
Gearboxes, which are key parts in mechanical equipment, play an irreplaceable role in modern industries and are often used in many large-scale machines. For example: the gear box is applied to aerospace, automobiles, automatic mechanical equipment and the like. The diagnosis of gearbox faults is especially important because large machines have a large amount of workload during operation and often work in a complex environment, which causes many faults of the gearbox and causes many losses.
At present, the types of faults of the gear box are more, signals generated by the faults are more complicated, and the fault diagnosis of the gear box is difficult due to the mixing of multiple fault modes. There are many methods for diagnosing faults of a gearbox, and the accuracy of diagnosis can be increased by a deep learning method, and a neural network is generally applied in the field. The Extreme Learning Machine (ELM) has the advantages of high algorithm speed, high training precision and the like, and plays an important role in the field of fault diagnosis. However, the ELM still has many disadvantages, such as poor nonlinear performance, unstable results, etc. Therefore, it is important to optimize the ELM.
The diagnosis accuracy can be greatly improved by processing the signals of the gearbox. Because of more noise in the vibration signal, denoising for solving the noise problem is a key step for fault diagnosis.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems pointed out in the background technology, the invention provides a gearbox fault diagnosis method, which combines a data multi-processing method and an improved sparrow optimization algorithm optimization limit learning machine and greatly improves the fault diagnosis capability of the gearbox.
The technical scheme is as follows: the invention discloses a fault diagnosis method for a gearbox, which comprises the following steps:
step 1: establishing a sample data set of the gearbox, and denoising the signal by using wavelet threshold denoising;
step 2: carrying out secondary noise reduction on the data by using Savitzky-Golay filtering to obtain more optimal noise-removed signal data;
and step 3: decomposing the denoised signal through an improved adaptive noise complete set empirical mode to obtain a series of IMF components; respectively calculating the variance contribution rate and the correlation value of each IMF component, and selecting the first six IMFs with the largest sum of the variance contribution rate and the correlation value to form a new IMF sequence;
and 4, step 4: calculating time domain and frequency domain characteristics of the new IMF sequence, and constructing a multi-dimensional sample characteristic set;
and 5: and selecting the characteristics of the sample by utilizing the mutual information, and dividing the training set and the test set.
Step 6: and (4) optimizing a sparrow optimization algorithm by using Tent mapping and Gaussian variation, and updating the positions of different types of sparrows. Initializing a population of a sparrow optimization algorithm by using a Tent chaotic sequence, introducing a random variable into an original Tent mapping, and if the sparrow population has an aggregation phenomenon, carrying out Gaussian variation and selecting an optimal individual;
and 7: and (3) giving the optimal weight and the deviation of the improved sparrow optimization algorithm to an extreme learning machine to obtain an optimal extreme learning machine algorithm, establishing an extreme learning machine (ICSSA-ELM) model based on the improved sparrow optimization algorithm, and diagnosing faults by using the model.
Further, in the step 1, denoising is performed on the signal by using wavelet threshold denoising, and a fixed threshold denoising method is selected to denoise the signal;
a common expression for the fixed threshold is as follows:
λ＝σ 2 log(N)
where σ is the standard deviation of the noise, the noise level estimate
Figure BDA0003903062240000021
N is the rotor signal length; w is a λ Is the wavelet coefficient before denoising, and λ is the selected threshold.
Further, in step 2, the data is subjected to secondary noise reduction by using Savitzky-Golay filtering, and the Savitzky-Golay filtering smoothing formula is as follows:
Figure BDA0003903062240000022
wherein, Y * Is the time series data fitting value, h i Is a coefficient when filtering the ith time series data value, H is the number of convolutions,
Figure BDA0003903062240000023
is a smoothing coefficient.
Further, the step 3 decomposes the denoised signal through an improved adaptive noise complete set empirical mode decomposition, and the implementation process is as follows:
(41) Adding N controllable white noise signals into the original signal y:
Figure BDA0003903062240000024
wherein, y (i) Is the i-th structural signal, beta 0 Is the noise standard deviation of the signal at the first decomposition,
Figure BDA0003903062240000025
represents the i-th white noise added; e1 (. Is the first IMF operator of the computed signal;
(42) Calculating the local mean of each y (i) and taking the global mean to obtain the first residual component:
Figure BDA0003903062240000026
wherein M (-) is a local mean function;
(43) Calculating a first modal component IMF1
Figure BDA0003903062240000031
(44) Computing an nth modal component IMFn
Figure BDA0003903062240000032
Figure BDA0003903062240000033
(45) And (5) calculating n = n +1 modal components, and returning to the step (44) until an iteration condition is met.
Further, the calculating of the variance contribution rate and the correlation value of each IMF component in step 3 is specifically:
the variance contribution is expressed as:
Figure BDA0003903062240000034
the correlation coefficient expression is:
Figure BDA0003903062240000035
wherein, b ik The number of the ith IMF component is N, the number of the data of the signal is N, and the number of the IMF components is N; xk is the kth data point of the signal,
Figure BDA0003903062240000036
is the mean of the signals;
Figure BDA0003903062240000037
is the mean of the ith IMF component.
Further, the step 4 time domain and frequency domain features total 29 features. Wherein, the 16 time-domain characteristics are respectively mean value, root mean square value, square root amplitude, absolute mean value, skewness, kurtosis, variance, maximum value, minimum value, peak-peak value, waveform index, peak index, pulse index, margin index, skewness index and kurtosis index; the frequency domain characteristics are respectively the frequency value of the mth spectral line, the magnitude of frequency domain vibration energy, the dispersion or concentration degree of the frequency spectrum and the change of the position of the dominant frequency band.
Further, in the step 5, mutual information is used to perform feature selection on the sample features, and features with larger mutual information values are selected. The mutual information value ratio realization process is as follows:
setting variables X and Y, wherein X is an input characteristic parameter, Y is classification data, and the mutual information value between the variables X and Y is represented as I (X, Y), and the expression is as follows:
Figure BDA0003903062240000038
wherein p (X) is X = X i Probability of occurrence of time, p (Y) is Y = Y i The probability of occurrence is marginal probability, and p (X, y) is X = X i ，Y＝y i The probability of simultaneous occurrence is the joint probability density.
Further, the position updating formula of the sparrow optimization algorithm in the step 6 is as follows:
Figure BDA0003903062240000041
wherein t represents the current iteration number; a is the number of sparrow populations; b is the dimension of the optimization variable;
the finder location update formula is as follows:
Figure BDA0003903062240000042
wherein,
Figure BDA0003903062240000043
the position information of the mth sparrow in the nth dimension is shown; α (α ∈ (0, 1)) is a random number; t is a constant representing the maximum number of iterations; r2 (R2. Epsilon. [0,1 ]]) Is an early warning value; ST (ST ∈ [0.5,1)]) Is a security value; q is a random number following a normal distribution; l is a 1 × b matrix with all elements 1;
the follower position changes as the fitness value changes, which is updated according to the following equation:
Figure BDA0003903062240000044
wherein,
Figure BDA0003903062240000045
is the best position of the current area,
Figure BDA0003903062240000046
is the worst position of the current region, A is a 1 × b matrix randomly distributed as-1 or 1, and A + ＝A T (AA T ) -1 ；
When the temperature is higher than the set temperature
Figure BDA0003903062240000047
When the m-th sparrow is starved, a better place needs to be found again for foraging. When in use
Figure BDA0003903062240000048
When the sparrow m is going to forage in the current area;
when the danger is close to the warner, the warner carries out the anti-predation behavior, and the mathematical expression of the anti-predation behavior is as follows:
Figure BDA0003903062240000049
wherein,
Figure BDA00039030622400000410
is a global optimal solution, β is a random number that follows a normal distribution, K (K ∈ [ -1, 1)]) Is a random number; f. of m The fitness value of the mth sparrow is obtained; f. of g And f w Global optimal and worst fitness values of the current population are respectively obtained; epsilon is the smallest constant to avoid the occurrence of a denominator of 0; f. of m ＝f g Indicating that the risk exists, and adjusting a search strategy by the population; f. of m ＞f g Indicating that the sparrows are at the edge of the population, the area is at risk and vulnerable to predation.
Further, the Tent chaotic sequence is used in the step 6 to initialize the sparrow population, a random variable is introduced into the original Tent mapping for improvement, and the improved expression is as follows:
Figure BDA0003903062240000051
the improved Tent mapping is shown in the following expression after the bernoulli shift transformation, and then for z j+1 Performing multiple iterations to generate a chaotic variable z d ：
Figure BDA0003903062240000052
Wherein, N T The number of particles in the chaotic sequence; rand (0, 1) is [0,1 ]]A random number in between; mapping the chaotic variables to the solution of the problem to be solved as follows:
Figure BDA0003903062240000053
wherein, d max And d min Are respectively as
Figure BDA0003903062240000054
Maximum and minimum values of (a);
the expression of chaotic disturbance on sparrow individuals is as follows:
Figure BDA0003903062240000055
wherein M' is a sparrow individual needing chaotic disturbance; m new Is the amount of chaotic disturbance generated.
Further, the gaussian variation formula of the optimal individual selected by gaussian variation in step 6 is:
mutation(x)＝x(1+N(0，1))
where x is the parameter value, N (0, 1) represents a normally distributed random number expected to be 0 with a standard deviation of 1.
Advantageous effects
The invention discloses a method for diagnosing faults of a gearbox, which aims at the condition that signal data of the gearbox has a lot of noise signals, and provides a method for removing signal noise by combining wavelet threshold denoising and Savitzky-Golay filtering denoising; in order to increase the fault diagnosis precision, performing IMF decomposition on the denoised signal by using improved adaptive noise complete set empirical mode decomposition (ICEEMDAN), and screening out a more representative IMF component by combining variance contribution rate and correlation; in order to better optimize data, a method of combining time domain and frequency domain is used for carrying out feature extraction on the screened IMF components, and mutual information is utilized for carrying out feature selection. Optimizing a sparrow optimization algorithm by Tent mapping and Gaussian variation, optimizing an extreme learning machine by the improved sparrow optimization algorithm, and constructing an extreme learning machine (ICSSA-ELM) fault diagnosis model of the improved sparrow optimization algorithm. The fault diagnosis method used by the invention carries out secondary denoising on the vibration signal, and can reduce a plurality of noises. A series of operations such as decomposition and reconstruction, feature extraction and the like are carried out on the denoised data, the diagnosis result is greatly improved, and the fault diagnosis capability of the gearbox is greatly improved by combining a data multi-processing method and an improved sparrow optimization algorithm optimization extreme learning machine.
Drawings
FIG. 1 is a flow chart of a method for diagnosing model faults in accordance with the present invention;
FIG. 2 is a graph comparing various models of a sample data set according to the present invention;
FIG. 3 is a diagram showing comparison of two various models of a sample data set according to the present invention.
Detailed Description
The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and specific examples.
The invention discloses a gearbox fault diagnosis method based on WTD-SG-ICEEMDAN-MI and ICSSA-ELM, which mainly comprises the following steps as shown in figure 1:
step 1: and establishing a sample data set of the gearbox, and denoising the signal by using wavelet threshold denoising.
Denoising the signal by using wavelet threshold denoising, comparing denoising effects of a fixed threshold, a hard threshold and a soft threshold, and denoising the signal by comprehensively selecting a fixed threshold denoising method.
A common expression for the fixed threshold is as follows:
λ＝σ2log(N)
where σ is the standard deviation of the noise, the noise level estimate
Figure BDA0003903062240000061
N is the rotor signal length; w is a λ Is the wavelet coefficient before de-noising and λ is the selected threshold.
And 2, step: and carrying out secondary noise reduction on the data by using Savitzky-Golay filtering to obtain more excellent noise-removed signal data. The Savitzky-Golay filtering mathematical model is as follows:
Figure BDA0003903062240000062
where Y is the time series data fit, h i Is the coefficient at the time of filtering the ith time series data value, H is the number of convolutions,
Figure BDA0003903062240000063
is a smoothing factor.
And step 3: and decomposing the denoised signal by an improved adaptive noise complete set empirical mode to obtain a series of IMF components. And respectively calculating the variance contribution rate and the correlation value of each IMF component, and selecting the first six IMFs with the largest sum of the variance contribution rate and the correlation value to form a new IMF sequence.
The method comprises the following steps of decomposing a denoised signal through an improved adaptive noise complete set empirical mode, and realizing the following processes:
(31) Adding N controllable white noise signals into the original signal y:
Figure BDA0003903062240000071
wherein, y (i) Is the i-th structural signal, beta 0 Is the noise standard deviation of the signal at the first decomposition,
Figure BDA0003903062240000072
indicating the ith white noise added; e1 (. Is) the first IMF operator of the computed signal.
(32) Calculating the local mean of each y (i) and taking the global mean to obtain the first residual component:
Figure BDA0003903062240000073
where M (-) is a local mean function.
(33) Calculating a first modal component IMF1
Figure BDA0003903062240000074
(34) Computing an nth modal component IMFn
Figure BDA0003903062240000075
Figure BDA0003903062240000076
(35) And (5) calculating n = n +1 modal components, and returning to the step (34) until an iteration condition is met.
And calculating the variance contribution rate and the correlation value of each IMF component, and selecting the first six IMFs with the largest sum of the contribution rate and the correlation value to form a new IMF sequence.
The variance contribution expression is:
Figure BDA0003903062240000077
the correlation coefficient expression is:
Figure BDA0003903062240000078
wherein, b ik Is the ith IMF component, N is the data number of the signal, and N is the number of IMF components. x is the number of k For the k-th data point of the signal,
Figure BDA0003903062240000079
is the mean of the signals;
Figure BDA00039030622400000710
is the mean of the ith IMF component.
And 4, step 4: and calculating the time domain and frequency domain characteristics of the new IMF sequence to construct a multi-dimensional sample characteristic set.
The time and frequency domain features of the new IMF sequence amount to 29 features. The 16 time domain characteristics are respectively a mean value, a root mean square amplitude value, an absolute mean value, a skewness, a kurtosis, a variance, a maximum value, a minimum value, a peak-to-peak value, a waveform index, a peak index, a pulse index, a margin index, a skewness index and a kurtosis index; the frequency domain characteristics are respectively the frequency value of the mth spectral line, the magnitude of frequency domain vibration energy, the dispersion or concentration degree of the frequency spectrum and the change of the position of the dominant frequency band.
TABLE 1 time Domain characterization
Figure BDA0003903062240000081
TABLE 2 frequency domain characterization
Figure BDA0003903062240000082
And 5: and selecting the characteristics of the sample by utilizing the mutual information, and dividing the training set and the test set.
And selecting the characteristic with larger mutual information value. Setting variables X and Y, wherein X is an input characteristic parameter, Y is classification data, and the mutual information value between the variables X and Y is represented as I (X, Y), and the expression is as follows:
Figure BDA0003903062240000083
wherein p (X) is X = X i Probability of occurrence of time, p (Y) is Y = Y i The probability of occurrence is marginal probability, and p (X, y) is X = X i ，Y＝y i The probability of simultaneous occurrence is the joint probability density.
Step 6: and (4) optimizing a sparrow optimization algorithm by Tent mapping and Gaussian variation, and updating the positions of different types of sparrows.
The position updating formula of the sparrow optimization algorithm in the step 6 is as follows:
the position of the sparrow may be expressed as follows:
Figure BDA0003903062240000091
wherein t represents the current iteration number; a is the number of sparrow populations; b is the dimension of the optimization variable.
The finder location update formula is as follows:
Figure BDA0003903062240000092
wherein,
Figure BDA0003903062240000093
the position information of the mth sparrow in the nth dimension is shown; α (α ∈ (0, 1)) is a random number; t is a constant representing the maximum number of iterations; r2 (R2. Epsilon. [0,1 ]]) Is an early warning value; ST (ST ∈ [0.5,1 ]]) Is a security value; q is a random number following a normal distribution; l is a 1 × b matrix with all elements 1.
The follower position changes as the fitness value changes, which is position updated according to the following equation.
Figure BDA0003903062240000094
Wherein,
Figure BDA0003903062240000095
is the best position of the current area,
Figure BDA0003903062240000096
is the worst position of the current region, A is a 1 × b matrix randomly distributed as-1 or 1, and A + ＝A T (AA T ) -1 。
When in use
Figure BDA0003903062240000097
When the m-th sparrow is starved, a better place needs to be found again for feeding. When in use
Figure BDA0003903062240000098
When this happens, the mth sparrow will be foraging in the current area.
When the danger is close to the warner, the warner carries out the anti-predation behavior, and the mathematical expression of the anti-predation behavior is as follows:
Figure BDA0003903062240000099
wherein,
Figure BDA00039030622400000910
is a global optimal solution, β is a random number that follows a normal distribution, K (K ∈ [ -1, 1)]) Is a random number; f. of m The fitness value of the mth sparrow is shown. f. of g And f w The global best and worst fitness values of the current population are respectively. ε is the smallest constant used to avoid the denominator 0. f. of m ＝f g Indicates the existence of risk, speciesThe cluster needs to adjust the search strategy. f. of m ＞f g Indicating that the sparrows are at the edge of the population, the area is at risk and vulnerable to predation.
In step 6, a Tent chaotic sequence is used for initializing an SSA population, in order to increase stability, a random variable is introduced into an original Tent mapping for improvement, and an improved expression is as follows:
Figure BDA0003903062240000101
the improved Tent mapping is shown in the following expression after the bernoulli shift transformation, and then for z j+1 Performing multiple iterations to generate a chaotic variable z d 。
Figure BDA0003903062240000102
Wherein N is T The number of particles in the chaotic sequence; rand (0, 1) is [0,1 ]]A random number in between.
The solution mapping the chaotic variables to the problem to be solved is:
Figure BDA0003903062240000103
wherein d is max And d min Are respectively as
Figure BDA0003903062240000104
Maximum and minimum values of.
The expression of chaotic disturbance on sparrow individuals is as follows:
Figure BDA0003903062240000105
wherein M' is a sparrow individual needing chaotic disturbance; m new Is the amount of chaotic disturbance generated.
And 6, if the SSA population has the aggregation phenomenon, performing Gaussian variation and selecting the optimal individual, wherein the Gaussian variation formula is as follows:
mutation(x)＝x(1+N(0，1))
where x is the parameter value, N (0, 1) represents a normally distributed random number expected to be 0 with a standard deviation of 1.
And 7: endowing the optimal weight and the deviation calculated by the improved sparrow optimization algorithm to an extreme learning machine to obtain an optimal extreme learning machine algorithm, and establishing an extreme learning machine (ICSSA-ELM) model based on the improved sparrow optimization algorithm, which specifically comprises the following steps:
(71) Collecting gearbox signal data, and dividing training samples and testing samples.
(72) And establishing a classification model of the extreme learning machine.
The extreme learning machine body training process is as follows:
in the first stage, hidden layer parameters are initialized randomly, and hidden layer nodes generate random weight w and deviation b. Obtaining the output h of the ith hidden layer node by using the following formula i (x)。
h i (x)＝g(w i x+b i )
And mapping the input data to a new feature space by using an activation function g (x), wherein the expression is shown as the following formula.
Figure BDA0003903062240000111
The output H (x) of the hidden layer is calculated from the following equation by determining w and b.
H(x)＝[h 1 (x)，h 2 (x)，…，h m (x)]
Wherein m is the number of hidden layer nodes of the extreme learning machine.
In the second stage, the training error is required to be minimized in order to obtain a good output weight β. The least square difference obtained by the following equation and the sample label T is expressed as an objective function M (x) as follows.
M(x)＝min||Hβ-T|| 2
(73) Initializing sparrow population and extreme learning machine parameters, setting the number of the sparrow populations to be 50, and randomly allocating the number of discoverers and followers to the sparrows.
(74) Initializing a population by using Tent chaotic sequence to generate N D-dimensional vectors Z i 。
(75) And calculating the fitness value of each sparrow.
(76) And updating the positions of the sparrow finder, the follower and the alerter.
(77) And after one iteration is completed, recalculating the individual fitness value and the population fitness value. And judging whether the individual fitness value is larger than the average fitness value, if so, carrying out Tent chaotic disturbance on the individual, and selecting the individual with the optimal performance. Otherwise, indicating that "clustering" has occurred, gaussian mutation is performed and the best individual is selected.
(78) And updating the population position and the fitness value.
(79) And (4) judging whether the maximum iteration times is reached, if so, continuing, and otherwise, returning to the step 4.
(80) And (4) giving the optimal weight and the deviation calculated by the improved sparrow optimization algorithm to the extreme learning machine to obtain an optimal extreme learning machine model.
Index evaluation is carried out on the model according to five modes of RMSE, MAPE, MAE, R _2 and Accuracy, and the evaluation index results of the sample 1 and the sample 2 are shown in tables 3 and 4.
TABLE 3 sample 1 multiple model evaluation index results
Figure BDA0003903062240000112
Table 4 sample 2 multiple model evaluation index results
Figure BDA0003903062240000121
The WTD-SG-ICEEMDAN-MI-ICSSA-ELM model of the invention is compared with BP, SVM, ELM, SSA-ELM, ICSSA-ELM and ICEEMDAN-MI-ICSSA-ELM models. The results of the comparison in the different sample sets are shown in fig. 2 and 3. Taking fig. 2 as an example, it can be seen from the classification results in the figure that the classification results of SVM and icemdan-MI-ICSSA-ELM are the worst, and the coincidence degree of the real value and the predicted value data is small, resulting in large deviation of the results. This indicates that the SVM and ICEEMDAN-MI-ICSSA-ELM can not effectively diagnose the fault of the gearbox, and the diagnosis error of the ELM is relatively small, so that the selection of the ELM for diagnosis is correct. Also, it can be seen from the figure that SSA-ELM is a little better classification than GHO-ELM. Through data noise reduction processing and model optimization, the model provided by the invention has the best diagnosis effect. The true value and the predicted value can be observed to be completely coincided, and the diagnosis capability is completely superior to that of other models.
While the foregoing shows and describes the fundamental principles and principal features of the invention, together with the advantages thereof, it will be understood by those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (10)

1. A gearbox fault diagnosis method is characterized by comprising the following steps:
step 1: establishing a sample data set of the gearbox, and denoising the signal by using wavelet threshold denoising;
step 2: carrying out secondary noise reduction on the data by using Savitzky-Golay filtering to obtain more optimal noise-removed signal data;
and step 3: decomposing the denoised signal through an improved adaptive noise complete set empirical mode to obtain a series of IMF components; respectively calculating the variance contribution rate and the correlation value of each IMF component, and selecting the first six IMFs with the largest sum of the variance contribution rate and the correlation value to form a new IMF sequence;
and 4, step 4: calculating time domain and frequency domain characteristics of the new IMF sequence, and constructing a multi-dimensional sample characteristic set;
and 5: and selecting the characteristics of the sample by utilizing the mutual information, and dividing a training set and a testing set.
And 6: and (4) optimizing a sparrow optimization algorithm by Tent mapping and Gaussian variation, and updating the positions of different types of sparrows. Initializing a population of a sparrow optimization algorithm by using a Tent chaotic sequence, introducing a random variable into an original Tent mapping, and if the sparrow population has an aggregation phenomenon, carrying out Gaussian variation and selecting an optimal individual;
and 7: and (3) giving the optimal weight and the deviation of the improved sparrow optimization algorithm to an extreme learning machine to obtain an optimal extreme learning machine algorithm, establishing an extreme learning machine (ICSSA-ELM) model based on the improved sparrow optimization algorithm, and diagnosing faults by using the model.
2. The gearbox fault diagnosis method as claimed in claim 1, wherein in the step 1, denoising is performed on the signal by using wavelet threshold denoising, and a fixed threshold denoising method is selected for denoising the signal;
the common expression for the fixed threshold is as follows:
λ＝σ 2 log(N)
where σ is the standard deviation of the noise, the noise level estimate
Figure FDA0003903062230000011
N is the rotor signal length; w is a λ Is the wavelet coefficient before de-noising and λ is the selected threshold.
3. The gearbox fault diagnosis method of claim 1, wherein in step 2, the data is subjected to secondary noise reduction by using Savitzky-Golay filtering, and the Savitzky-Golay filtering smoothing formula is as follows:
Figure FDA0003903062230000012
wherein, Y * Is the time series data fitting value, h i Is the coefficient at the time of filtering the ith time series data value, H is the number of convolutions,
Figure FDA0003903062230000013
is a smoothing factor.
4. The gearbox fault diagnosis method according to claim 1, wherein the step 3 is implemented by decomposing the denoised signal through an improved adaptive noise complete set empirical mode decomposition, and the process is as follows:
(41) Adding N controllable white noise signals into the original signal y:
Figure FDA0003903062230000021
wherein, y (i) Is the ith structural signal, beta 0 Is the noise standard deviation of the signal at the first decomposition,
Figure FDA0003903062230000022
indicating the ith white noise added; e 1 (. Is the first IMF operator of the computed signal;
(42) Calculating the local mean of each y (i) and taking the global mean to obtain the first residual component:
Figure FDA0003903062230000023
wherein M (-) is a local mean function;
(43) Calculating a first modal component IMF1
Figure FDA0003903062230000024
(44) Computing an nth modal component IMFn
Figure FDA0003903062230000025
Figure FDA0003903062230000026
(45) And (5) calculating n = n +1 modal components, and returning to the step (44) until an iteration condition is met.
5. A gearbox fault diagnosis method according to claim 4, characterized in that the values of variance contribution and correlation for each IMF component calculated in step 3 are in particular:
the variance contribution expression is:
Figure FDA0003903062230000027
the correlation coefficient expression is:
Figure FDA0003903062230000028
wherein, b ik The number of the ith IMF component is N, the number of the data of the signal is N, and the number of the IMF components is N; x is the number of k For the k-th data point of the signal,
Figure FDA0003903062230000029
is the mean of the signals;
Figure FDA00039030622300000210
is the mean of the ith IMF component.
6. The gearbox fault diagnosis method according to claim 1, characterized in that said step 4 time and frequency domain signatures amount to 29 signatures. Wherein, the 16 time-domain characteristics are respectively mean value, root mean square value, square root amplitude, absolute mean value, skewness, kurtosis, variance, maximum value, minimum value, peak-peak value, waveform index, peak index, pulse index, margin index, skewness index and kurtosis index; the frequency domain characteristics are respectively the frequency value of the mth spectral line, the magnitude of frequency domain vibration energy, the dispersion or concentration degree of the frequency spectrum and the change of the position of the dominant frequency band.
7. A gearbox fault diagnosis method according to claim 1, characterized in that in step 5, mutual information is used to perform feature selection on sample features, and features with larger mutual information values are selected. The mutual information value ratio realization process is as follows:
setting variables X and Y, wherein X is an input characteristic parameter, Y is classification data, and the mutual information value between the variables X and Y is represented as I (X, Y), and the expression is as follows:
Figure FDA0003903062230000031
wherein p (X) is X = X i Probability of occurrence of time, p (Y) is Y = Y i The probability of occurrence is marginal probability, and p (X, y) is X = X i ，Y＝y i The probability of simultaneous occurrence is the joint probability density.
8. The gearbox fault diagnosis method according to claim 1, characterized in that the position update formula of the sparrow optimization algorithm in step 6 is as follows:
Figure FDA0003903062230000032
wherein t represents the current iteration number; a is the number of sparrow populations; b is the dimension of the optimization variable;
the finder location update formula is as follows:
Figure FDA0003903062230000033
wherein,
Figure FDA0003903062230000034
the position information of the mth sparrow in the nth dimension is shown; α (α ∈ (0, 1)) is a random number; t is a constant representing the maximum number of iterations; r2 (R2. Epsilon. [0,1 ]]) Is an early warning value; ST (ST ∈ [0.5,1)]) Is a security value; q is a random number following a normal distribution; l is a 1 × b matrix with all elements 1;
the follower position changes as the fitness value changes, which is updated according to the following equation:
Figure FDA0003903062230000035
wherein,
Figure FDA0003903062230000041
is the best position of the current area,
Figure FDA0003903062230000042
is the worst position of the current region, A is a 1 × b matrix randomly distributed as-1 or 1, and A + ＝A T (AA T ) -1 ；
When in use
Figure FDA0003903062230000043
When the m-th sparrow is starved, a better place needs to be found again for feeding. When in use
Figure FDA0003903062230000044
When the m-th sparrow forages in the current area;
when the danger is detected to approach, the alertor carries out anti-predation behavior, and the mathematical expression of the anti-predation behavior is as follows:
Figure FDA0003903062230000045
wherein,
Figure FDA0003903062230000046
is a global optimal solution, β is a random number that follows a normal distribution, K (K ∈ [ -1, 1)]) Is a random number; f. of m The fitness value of the mth sparrow is obtained; f. of g And f w Global optimal and worst fitness values of the current population are respectively obtained; epsilon is the smallest constant to avoid the occurrence of a denominator of 0; f. of m ＝f g Indicating that the risk exists, and adjusting a search strategy by the population; f. of m ＞f g Indicating that the sparrows are at the edge of the population, the area is at risk and vulnerable to predation.
9. The gearbox fault diagnosis method according to claim 1, wherein a Ten chaotic sequence is used in the step 6 to initialize a sparrow population, a random variable is introduced into an original Ten mapping for improvement, and the improved expression is as follows:
Figure FDA0003903062230000047
the improved Tent mapping is shown in the following expression after the bernoulli shift transformation, and then for z j+1 Performing multiple iterations to generate a chaotic variable z d ：
Figure FDA0003903062230000048
Wherein N is T The number of particles in the chaotic sequence; rand (0, 1) is [0,1 ]]A random number in between; mapping the chaotic variables to the solution of the problem to be solved as follows:
Figure FDA0003903062230000049
wherein d is max And d min Are respectively as
Figure FDA00039030622300000410
Maximum and minimum values of;
the expression of chaotic disturbance on sparrow individuals is as follows:
Figure FDA00039030622300000411
wherein M' is a sparrow individual needing chaotic disturbance; m new Is the amount of chaotic disturbance produced.
10. The gearbox fault diagnosis method according to claim 1, characterized in that the gaussian variation in step 6 selects the gaussian variation formula of the optimal individual as:
mutation(x)＝x(1+N(0，1))
where x is the parameter value, N (0, 1) represents a normally distributed random number expected to be 0 with a standard deviation of 1.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116226619A (en) * 2023-02-09 2023-06-06 淮阴工学院 Gearbox fault diagnosis method based on INGO optimization HKELM
CN116465624A (en) * 2023-05-12 2023-07-21 淮阴工学院 HNGO-optimized KELM-based gearbox fault diagnosis method
CN116595449A (en) * 2023-06-06 2023-08-15 西安科技大学 Asynchronous motor fault diagnosis method based on improved SSA optimization support vector machine

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116226619A (en) * 2023-02-09 2023-06-06 淮阴工学院 Gearbox fault diagnosis method based on INGO optimization HKELM
CN116226619B (en) * 2023-02-09 2024-06-11 淮阴工学院 Gearbox fault diagnosis method based on INGO optimization HKELM
CN116465624A (en) * 2023-05-12 2023-07-21 淮阴工学院 HNGO-optimized KELM-based gearbox fault diagnosis method
CN116465624B (en) * 2023-05-12 2024-06-11 淮阴工学院 Gearbox fault diagnosis method based on HNGO optimization KELM
CN116595449A (en) * 2023-06-06 2023-08-15 西安科技大学 Asynchronous motor fault diagnosis method based on improved SSA optimization support vector machine
CN116595449B (en) * 2023-06-06 2023-12-12 西安科技大学 Asynchronous motor fault diagnosis method based on improved SSA optimization support vector machine

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