A gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy

Abstract

This invention discloses an improved method for extracting gear fault diagnosis features by combining Complete Empirical Mode Decomposition (CEEMDAN) with wavelet packet segmentation threshold denoising and energy entropy. The reconstructed signal after CEEMDAN threshold denoising is re-CEEMDAN decomposed to obtain the energy values ​​of each modal component, which are then used as fault features of the gear. The method includes the following steps: 1) acquiring vibration signals in the X, Y, and Z mutually perpendicular directions at the gear of a rotating device using a vibration sensor; 2) performing CEEMDAN decomposition on the data to obtain multiple intrinsic modal components; 3) using the Pearson correlation coefficient method to divide the modal components into noise-dominant components and signal-dominant components; 4) applying different wavelet denoising methods to different dominant components; 5) reconstructing the signal and re-CEEMDAN decomposing it to extract the energy values ​​of each mode, which are then used as features under different fault states.

Description

Technical Field

[0001] This invention belongs to the field of gear fault diagnosis and relates to a method for extracting gear fault features based on CEEMDAN threshold denoising and energy entropy. Background Technology

[0002] Gears, as key components in mechanical equipment, are widely used in various transmission systems. However, during operation, gears are often susceptible to failure due to special environmental influences, which in turn affects the performance and stability of the mechanical system. Vibration signals are typical non-stationary random signals, containing a wealth of crucial information that reflects the operating status of equipment. Due to the influence of complex environments, the acquired vibration signals often contain a significant amount of noise, masking the signal's inherent characteristics. Therefore, it is crucial that the acquired signals contain as much useful information as possible and as little noise as possible.

[0003] Traditional signal processing often focuses on time-frequency domain analysis, such as short-time Fourier transform, wavelet transform, and empirical mode decomposition. Complete Empirical Mode Decomposition (CEEMDAN) is a superior method for handling nonlinear and non-stationary signals. It is an improved version of EMD and EEMD algorithms. By incorporating adaptive noise to aid signal decomposition, it achieves a more complete decomposition. Furthermore, the decomposition of the signal into IMF components mitigates modal phenomena and reconstruction errors to some extent.

[0004] Wavelet thresholding denoising is also widely used in signal denoising. After wavelet decomposition of the original signal, wavelet coefficients with larger amplitudes are mostly effective components, while those with smaller amplitudes are generally noise components. By selecting a suitable threshold and a threshold function combined with it, wavelet coefficients are calculated using the threshold function, and the wavelet coefficients are automatically filtered. The threshold function and wavelet threshold are related to the selection of effective and noise components; setting them properly can achieve ideal denoising results. The threshold function is the core of wavelet denoising. Commonly used methods include hard thresholding and soft thresholding. Although both hard and soft thresholding methods are the most commonly used, they each have their own drawbacks. For hard thresholding, the discontinuity of the function will cause the reconstructed signal to exhibit oscillations and fluctuations, resulting in significant deviations. For soft thresholding, although the function is continuous, the reconstructed signal always deviates from the true effective signal. Therefore, it is necessary to improve the threshold function or the principle of threshold acquisition, selecting a suitable threshold and a threshold function combined with it to improve the denoising effect. Summary of the Invention

[0005] The purpose of this invention is to provide a gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy, thereby overcoming the shortcomings mentioned in the background art.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] Step 1: Collect vibration signals in the X, Y, and Z directions of the rotating device gear, which are perpendicular to each other. Measure the vibration signals y(t) of five states: normal, missing tooth, broken tooth, worn, and cracked, to form a dataset, which includes a normal sample set and a fault sample set.

[0008] Step 2: Perform CEEMDAN decomposition on the data to obtain different modal components;

[0009] Step 3: The modal components are re-screened and divided into noise-dominant components and useful signal-dominant components using the Pearson correlation coefficient method.

[0010] Step 4: Apply different wavelet denoising methods to the different dominant components identified in Step 3. Use soft threshold denoising for noise-dominant components and adaptive rule denoising for useful signal-dominant components.

[0011] Step 5: Reconstruct the signal after noise reduction in Step 4 and perform CEEMDAN decomposition again. Calculate the energy entropy value of each modal component after decomposition and use the energy spectrum to identify the fault type.

[0012] The significant advantages of this invention compared to existing technologies are:

[0013] (1) The CEEMDAN decomposition method provided by the present invention can effectively eliminate the problem of mode aliasing and has better local features at the same time and frequency scale. Furthermore, it is combined with the wavelet packet thresholding method to improve the acquisition of the threshold, which not only has higher computational efficiency but also greatly improves the denoising effect.

[0014] (2) Based on the different signal characteristics of IMF components, the present invention adopts different noise reduction methods for high frequency and low frequency, which can achieve the goal of eliminating noise to the greatest extent while better preserving the useful features in the signal.

[0015] (3) This invention uses CEEMDAN decomposition on the preprocessed signal to obtain Intrinsic Mode Functions (IMFs) containing different frequency components. The energy of each IMF component is the energy of its corresponding frequency band. Compared with normal signals, fault signals have increased energy distribution in some frequency bands and decreased energy distribution in others. Different fault states will have different energy distributions, thus representing specific fault types. Compared with conventional judgment methods, the characteristics are more obvious and the accuracy is higher. Attached Figure Description

[0016] Figure 1 The flowchart shows the improved CEEMDAN-based gear fault diagnosis feature extraction method that combines wavelet packet segmentation thresholding denoising and energy entropy.

[0017] Figure 2 The flowchart shows the steps of the improved CEEMDAN-based gear fault diagnosis feature extraction method that combines wavelet packet segmentation thresholding denoising and energy entropy.

[0018] Figure 3 These are the IMF diagrams after the CEEMDAN decomposition in this invention;

[0019] Figure 4 This is a comparison image of the vibration signal before and after noise reduction according to the present invention;

[0020] Figure 5 This is an energy distribution diagram of each IMF component under the tooth-missing state of the gear in this invention; Detailed Implementation

[0021] Specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be noted that in the following description, detailed descriptions of known functions and designs that might obscure the main points of the invention will be omitted here. References Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 A gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy is described, with the following specific steps:

[0022] Step 1: Vibration signals y(t) in the X, Y, and Z directions of the rotating gear are collected at a sampling frequency of 20kHz. 1000 sets of vibration signals are measured for each of the five states: normal, missing tooth, broken tooth, worn, and cracked, forming a dataset including a normal sample set and a fault sample set. This paper uses a missing tooth fault as an example for detailed explanation.

[0023] Step 2: Perform CEEMDAN decomposition on the acquired data to obtain different modal components. The specific process of CEEMDAN acquiring the modal component set of the vibration signal and decomposing it into several intrinsic mode functions and a residual is as follows:

[0024] (1) Add M pairs of positive and negative Gaussian white noise to the original vibration signal y(t), resulting in a total of M new signals. The signal y0 after the j-th addition of Gaussian white noise is... j (t) is:

[0025] y0 j (t)=y(t)+ε0w j (t)

[0026] In the formula, ε0 is the standard deviation of the noise; w j Let j be the j-th Gaussian white noise that follows a standard normal distribution.

[0027] (2) Let E(·) be the EMD decomposition, then the j-th IMF1 component can be obtained through j decompositions:

[0028] E(y0 j (t))=IMF1 j (t)+r j (t)

[0029] Among them, IMF1 j (t) represents the j-th IMF1 component; r j (t) represents the j-th residual component.

[0030] (3) The M IMF1 components decomposed by equation (2) are weighted and averaged to obtain the final IMF1(t):

[0031]

[0032] (4) Calculate the first residual component r1(t):

[0033] r1(t) = y(t) - IMF1(t)

[0034] (5) Add the M pairs of positive and negative Gaussian white noise from step one to r1(t), and use the auxiliary noise decomposed by EMD. Let E i (·) represents the i-th modal component after EMD decomposition. Then, the new signal after the j-th addition of auxiliary noise is:

[0035] y1 j (t)=r1(t)+ε0E1(w j (t))

[0036] By analyzing y1 j (t) Performing j-th decompositions yields the j-th IMF2 component, with the following decomposition result:

[0037] E(x1 j (t))=IMF2 j (t)+r j (t)

[0038] Then, a weighted overall average is taken from the M decomposed IMF2 values ​​to obtain the final IMF2(t):

[0039]

[0040] Calculate the residual component r2(t):

[0041] r2(t) = r1(t) - IMF2(t)

[0042] (6) Repeat step 5 until the obtained residual components can no longer be used for EMD decomposition, then the algorithm ends. Let the order of the obtained IMF components at this point be k, then the original vibration signal y(t) is decomposed into k IMF components and a residual:

[0043]

[0044] (7) Figure 3 As shown, the original tooth-missing vibration signal can be decomposed into 13 intrinsic mode functions and one residual under the CEEMDAN algorithm.

[0045] Step 3: The modal components are re-screened and divided into noise-dominant components and useful signal-dominant components using the Pearson correlation coefficient method. Specifically, this includes:

[0046] (1) The Pearson correlation coefficient is a linear correlation coefficient used to measure the linear relationship between two random variables. The correlation coefficient is represented by r, which describes the strength of the linear correlation between the two variables. The larger the absolute value of r, the stronger the correlation.

[0047] Let m be the number of original vibration signal y(x) data sequences, n = 1, 2, ..., m, then the formula for calculating the correlation coefficient is:

[0048]

[0049] Where k represents the order of the intrinsic mode function; y n This represents the nth data point of the original vibration signal. This represents the average value of each data point in the original vibration signal. This represents the nth data point of the kth-th intrinsic mode function component; is the average value of each data point of the k-th order intrinsic mode function component.

[0050] Generally, the degree of correlation is divided into five categories: a correlation coefficient between 0.8 and 1.0 is considered highly correlated; a correlation coefficient between 0.6 and 0.8 is considered strongly correlated; a correlation coefficient between 0.4 and 0.6 is considered moderately correlated; a correlation coefficient between 0.2 and 0.4 is considered weakly correlated; and a correlation coefficient between 0.0 and 0.2 is considered very weakly correlated or uncorrelated.

[0051] (2) Calculate the Pearson correlation coefficient r between each natural mode function and the original vibration signal. k As the frequency decreases, the correlation between each component and the original signal decreases, and there will be a specific critical component 'a', from which the critical mode IMF can be determined. a When k = a, r a ≥0.4, r a+1<0.4 means the first a-order modal components (IMF1, IMF2, ..., IMF) a-1 The modal components (IMFs) are grouped into one group, characterized by high-frequency noise dominating, while the remaining modal components (IMFs) are separated. a IMF a+1 ,...,IMF k They are grouped together, characterized by the dominance of useful signals at low frequencies.

[0052] (3) Based on the Pearson correlation coefficient formula in (1), the Pearson correlation coefficients between each modal component and the original vibration signal under the tooth-missing state of the gear are calculated as shown in the table below:

[0053] IMF order 1 2 3 4 5 6 7 Correlation coefficient 0.8710 0.5305 0.4915 0.4050 0.1136 0.0875 0.0769 IMF order 8 9 10 11 12 13 14 Correlation coefficient 0.0513 0.0211 0.0347 0.0179 0.0267 0.0198 0.0009

[0054] As shown in the table above, the correlation coefficients of the first four IMFs are above 0.4, indicating that the first four IMF components are strongly correlated with the original signal. Therefore, we take a = 4, which is the critical mode IMF. a =IMF4. Therefore, the first four modal components are classified into a group dominated by high-frequency noise, while the 5th to 14th modal components are classified into another group dominated by useful signals.

[0055] Step 4: Different wavelet denoising methods are applied to the different dominant components. Soft threshold denoising is used for noise-dominant components, while adaptive rule-based denoising is used for useful signal-dominant components. Specifically, this includes:

[0056] Wavelet thresholding denoising is the process of suppressing useless components and enhancing useful components in a signal. The wavelet thresholding denoising process involves: selecting an appropriate wavelet function and decomposition scale to perform wavelet decomposition on the IMF components to obtain the corresponding wavelet coefficients; and then selecting an appropriate threshold function to perform threshold quantization on the decomposed wavelet coefficients, thereby achieving the purpose of denoising. The key is the selection of the threshold and the determination of the threshold function to meet different needs. This paper uses the db4 wavelet to perform a three-level decomposition on the noisy signal to extract coefficients.

[0057] (1) Selection of threshold λ:

[0058] a. An improvement on the general threshold (sqtwolog principle) method, with a threshold λ. o The specific calculation process is as follows:

[0059] ① After performing three-stage decomposition on the original vibration signal using wavelets, the low-frequency approximation coefficients ca3 of the third layer and the high-frequency detail coefficients cd of each layer are extracted. o o = 1, 2, 3;

[0060] ②Average calculation is performed for the detail coefficients of each layer: n represents the length of each detail coefficient at each level;

[0061] ③At this time, the threshold λ o for: Where N is the length of the vibration signal.

[0062] b. Stein's unbiased likelihood estimation threshold (rigor principle), the threshold is obtained as follows:

[0063]

[0064] Where σ is the noise standard deviation, the estimation formula is: median(w) is the median of the wavelet packet multi-resolution decomposition coefficients; w b It is a risk function.

[0065] (2) Selection of threshold function:

[0066] a. The soft thresholding function noise processing method is as follows:

[0067]

[0068] In the formula, sgn(·) is the sign function, and λ o The threshold obtained in (1)a is w, where w is the wavelet coefficient. λo These are the processed wavelet coefficients. Calculated using a threshold function, wavelet coefficients are set to zero when their absolute value is less than or equal to the threshold; when a wavelet coefficient is greater than the threshold, the threshold value is subtracted from the wavelet coefficient.

[0069] b. The principle of the improved soft threshold function noise processing method is as follows:

[0070]

[0071] In the formula, sgn(·) is the sign function, and λ o The threshold obtained in (1)b is w, where w is the wavelet coefficient. λo These are the processed wavelet coefficients. This function is an improvement on the soft thresholding function, eliminating the discontinuities of the thresholding function while making the function closer to the hard thresholding function, resulting in a smoother function curve.

[0072] (3) Wavelet coefficients are obtained by performing wavelet decomposition on each target component, and wavelet coefficients within the preset amplitude range are selected using the target wavelet threshold function. After signal reconstruction, the denoised signal is obtained. As can be seen from step 3, the tooth-missing vibration signal should be processed by the soft threshold denoising method for the first 4 IMFs. After the first 4 IMFs are decomposed, the corresponding wavelet coefficients are obtained, and the thresholds of each layer are obtained under principle a. Each layer is denoised using the soft threshold function; while the 5th to 14th IMFs are all processed by the improved soft threshold denoising method under principle b.

[0073] Step 5: The signal reconstruction after threshold denoising above yields the final denoised signal, such as... Figure 4 As shown, a comparison is presented between the reconstructed signal after denoising and the original signal. After re-performing CEEMDAN decomposition on the signal, the corresponding IMF components are obtained, the energy values ​​of each component are calculated, and an energy spectrum diagram of this state is plotted, specifically including:

[0074] (1) Formula for calculating energy entropy:

[0075]

[0076] In the formula, p i =E i / E represents the energy E of the i-th intrinsic mode function (IMF). i In total energy The proportion of [something].

[0077] (2) Based on the energy entropy solution formula in (1), the energy table of each IMF component under the tooth-missing state of the gear is calculated as follows, and the energy spectrum is plotted as follows. Figure 5 As shown.

[0078] IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 Energy value 0.1543 0.1786 0.0572 0.0560 0.1239 0.0846 0.0531 IMF8 IMF9 IMF10 IMF11 IMF12 IMF13 IMF14 Energy value 0.0156 0.0086 0.0055 0.0044 0.0019 0.0009 0.0007

[0079] Similarly, the above experimental process can obtain energy spectra under normal, broken tooth, cracked, and worn conditions, respectively, as characteristics representing the fault state. As can be seen from the above experimental process, this invention can effectively eliminate noise in gear vibration signals and achieve clear extraction of gear fault characteristics. It has broad application prospects in the field of simulated mechanical fault diagnosis.

Claims

1. A method for extracting gear fault features based on CEEMDAN threshold denoising and energy entropy, characterized in that, Includes the following steps: Step 1: Collect vibration signals from the gears of the rotary device in the three mutually perpendicular directions of X, Y, and Z. Vibration signals under normal and fault conditions are measured separately to form a dataset, which includes a normal sample set and a fault sample set. Step 2: Perform CEEMDAN decomposition on the data to obtain different modal components; Step 3: The modal components are re-screened and divided into noise-dominant components and useful signal-dominant components using the Pearson correlation coefficient method. Step 4: Apply different wavelet denoising methods to the different dominant components identified in Step 3. For the noise-dominant component, use an improved soft-threshold denoising method. ； In the formula, Here, w is the sign function, and w is the wavelet coefficient. These are the processed wavelet coefficients; The threshold is selected as follows: ； Where N is the length of the vibration signal, This is the average value of the detail coefficient for each layer; The component dominated by the useful signal is processed using an adaptive rule-based noise reduction method: ； In the formula, These are the processed wavelet coefficients; The threshold is selected as follows: ； in It is the standard deviation of noise. It is a risk function; Noise Standard Deviation The estimation formula is as follows ; in The median of the wavelet packet multi-resolution decomposition coefficients; By performing wavelet decomposition on each target component to obtain its corresponding wavelet coefficients, and using the target wavelet threshold function to filter out wavelet coefficients within a preset amplitude range, the denoised signal is obtained after signal reconstruction. Step 5: Reconstruct the signal after noise reduction in Step 4 and perform CEEMDAN decomposition again. Calculate the energy value of each modal component after decomposition and use the energy spectrum to identify the fault type.

2. The gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy according to claim 1, characterized in that, The data described in step 2 is decomposed using CEEMDAN, that is, the original vibration signal is decomposed into several intrinsic mode functions and a residual using CEEMDAN, specifically as follows: (1) Add M pairs of positive and negative Gaussian white noise to the original vibration signal. There are a total of M new signals; The signal after adding Gaussian white noise for the jth time for: ； In the formula The standard deviation of the noise; Let j be the j-th Gaussian white noise that follows a standard normal distribution; (2) Let For EMD decomposition, the j-th element is obtained through j decompositions. Quantity: ； in, Indicates the j-th Quantity; This represents the j-th residual component; (3) The M elements decomposed by equation (2) The components are weighted and averaged to obtain the final result. : ； (4) Calculate the first residual component : ； (5) In Add the M pairs of positive and negative Gaussian white noise from the first step, and use EMD decomposition as auxiliary noise. Let i be the i-th modal component after EMD decomposition. Then, the new signal after adding auxiliary noise for the j-th time is: ； Through the Perform j decompositions to obtain the j-th element. The components, decomposed into the following results: ； Then decompose the M into Perform a weighted overall average to obtain the final result. : ； Calculate the residual components : ； 6) Repeat step 5 until the obtained residual components can no longer be used for EMD decomposition, then the algorithm ends; let the order of the obtained IMF components at this time be k, then the original vibration signal It is decomposed into k IMF components and a residual: 。 3. The gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy according to claim 1, characterized in that, As described in step 3, the modal components are re-screened and divided using the Pearson correlation coefficient method into noise-dominant components and useful signal-dominant components, specifically including: (1) Assume the original vibration signal The number of data sequences is m. The formula for calculating the correlation coefficient is: ； Where k represents the order of the intrinsic mode function; This represents the nth data point of the original vibration signal. This represents the average value of each data point in the original vibration signal. This represents the nth data point of the kth-th intrinsic mode function component; This represents the average value of each data point of the k-th order intrinsic mode function component; (2) Calculate the Pearson correlation coefficient between each natural mode function and the original vibration signal. As the frequency decreases, the correlation between each component and the original signal decreases, and a critical component 'a' will appear, allowing the identification of the critical mode. .

4. The gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy according to claim 1, characterized in that, a. Based on improvements to the general thresholding method, the threshold... The calculation process is as follows: ① After performing three decompositions on the original vibration signal using wavelets, the low-frequency approximation coefficients ca3 of the third layer and the high-frequency detail coefficients of each layer are extracted respectively. ; ②Average calculation is performed for the detail coefficients of each layer: , where n represents the length of each detail coefficient at each level; At this time, the threshold for: .

5. The gear fault feature extraction method based on CEEMDAN threshold denoising and energy entropy according to claim 1, characterized in that, The energy entropy mentioned in step 5 is: ； In the formula, p i This represents the proportion of the energy of the i-th intrinsic mode function (IMF) in the total energy E.

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