An adaptive variational mode decomposition method for rolling bearing fault feature extraction

Abstract

The present invention discloses an adaptive variational mode decomposition method for rolling bearing fault feature extraction, including: (1) building a bearing data acquisition platform to collect the bearing fault vibration signal x(t), and initializing the number of intrinsic mode components IMF, that is, the parameter k = 1; (2) setting k = k + 1, performing variational mode decomposition on the collected vibration signal x(t), and respectively calculating the permutation entropy PE of the k-th and the (k-1)-th IMF components, and their values are respectively denoted as PE k and PE k‑1 , if |PE k - PE k‑1 | is greater than the threshold u1, then go to (2), otherwise, set k = k - 1, and perform VMD decomposition on the signal x(t); (3) if the value of k is less than 2, go to (5); (4) calculate the Pearson correlation coefficient e between adjacent components among the k IMF components, if there is an e value greater than the threshold u2, then set k = k - 1, perform VMD decomposition on the collected vibration signal x(t), and go to (3); (5) output k discrete IMF feature components. The present invention can adaptively determine the number of decomposition modes, effectively suppress the over-decomposition problem occurring in the decomposition process, and further improve the performance of bearing fault signal mode decomposition.

Description

Technical Field

[0001] The invention relates to an adaptive variational mode decomposition method, in particular to an adaptive variational mode decomposition method for rolling bearing fault feature extraction. Background Art

[0002] Rolling bearings play an important role in the transmission system of machinery and equipment. In actual situations, they usually operate under a certain pressure or load during use, which can easily lead to bearing failures and seriously affect the health of machinery and equipment. Therefore, it is crucial to judge their health status and fault type. In order to improve the reliability of physical assets during their service life, a condition monitoring method based on vibration signals is introduced in the area of ​​bearing fault diagnosis. This method is generally divided into three steps: (1) data acquisition of vibration signals; (2) processing of vibration signals and extraction of fault features; (3) identification and diagnosis of fault modes. The most critical of these are the processing of vibration signals and feature extraction.

[0003] The variational mode decomposition (VMD) method is a completely non-recursive decomposition method that can simultaneously estimate decomposition modes with sparsity in the frequency domain. Sparsity means that the obtained modes are very compact around their respective center frequencies, but the frequency components on both sides of these center frequencies are sparse. In most cases, the eigenfrequencies extracted by VMD are far away from the center frequencies, which is a good behavior for segmenting a real complex signal. Because of this advantage, many studies use the VMD method to extract eigenvectors of mechanical vibration signals.

[0004] However, the main limitation of VMD is that the number of modes k requires a proper definition, as it directly affects the performance of VMD. In practical applications, there are usually three methods to determine this parameter. The first method uses empirical knowledge, but lacks adaptability in complex situations. The second method uses optimization algorithms such as particle swarm and fish school optimization. Although they can obtain a suitable parameter, the efficiency is too low because it requires a large number of experiments. The last method is an adaptive method, that is, when VMD is performed using different numbers of modes, the time domain or multiple indicators are used to evaluate the changes in the amount of characteristic information in the decomposed mode, and then the number of modes is adaptively determined. However, the existing adaptive methods have the defects of over-decomposition and too many parameters introduced, making it difficult to determine the threshold. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide an adaptive variational mode decomposition method for rolling bearing fault feature extraction, which can not only adaptively determine the number of decomposition modes, but also effectively suppress the over-decomposition problem.

[0006] Technical solution: The present invention comprises the following steps:

[0007] Step 1: Build a bearing data acquisition platform, collect bearing fault vibration signal x(t), and initialize the intrinsic mode component IMF number, that is, parameter k=1;

[0008] Step 2: Set k = k + 1, perform variational mode decomposition on the collected vibration signal x(t), and calculate the permutation entropy PE of the kth and k-1th IMF components respectively, and their values ​​are recorded as PE k and PE k-1 , if |PE k -PE k-1 | is greater than the threshold u1, go to step 2; otherwise, set k = k-1 and perform VMD decomposition on the signal x(t);

[0009] Step 3: If the k value is less than 2, go to step 5;

[0010] Step 4: Calculate the Pearson correlation coefficient e between adjacent components in the k IMF components. If there is an e value greater than the threshold u2, set k=k-1, perform VMD decomposition on the collected vibration signal x(t), and go to step 3;

[0011] Step 5: Output k discrete IMF feature components.

[0012] The steps of performing variational mode decomposition on the vibration signal in step 2 are as follows:

[0013] (1) Assume that the vibration signal acquired by the sensor is x(t), which is the original signal of variational mode decomposition. The parameter K is the number of decomposition modes, and a is the bandwidth parameter.

[0014] (2) Initialize the eigenmode function Center frequency Lagrange multiplier λ 1 and number of iterations n = 0;

[0015] (3) Set n = n + 1 and enter the loop;

[0016] (4) For all w>0, update u k , k∈{1,2,...,K}:

[0017]

[0018] Update w k :

[0019]

[0020] (5) Update λ:

[0021]

[0022] (6) Repeat steps (3) to (5) until the iteration stop condition is met:

[0023]

[0024] (7) Output K IMF components.

[0025] The calculation steps of the IMF component permutation entropy in step 2 are as follows:

[0026] (1) Considering a specific IMF component, the IMF can essentially be regarded as a time series {x(i), i = 1, 2, ..., N}, with a length of N. Reconstructing its phase space, we get the matrix:

[0027]

[0028] Where m is the embedding dimension and τ is the time delay;

[0029] (2) Each row in the matrix is ​​regarded as a reconstruction component, and each reconstruction component is sorted in ascending order. For example, the j-th reconstruction component:

[0030] X(j)={x(j),x(j+τ),...,x(j+(m-1)τ)}

[0031] After sorting in ascending order, we get:

[0032] x(j+(i1-1)τ)≤x(j+(i2-1)τ)≤...≤x(j+(i m -1)τ),

[0033] Among them, i1,i2,...,i m is the index of the column where each element in the reconstruction component is located. For any reconstruction component in the reconstruction matrix, a set of position index sequences can be obtained: L(j)=(i1,i2,...i m ),j=1,2,3,...,k,k≤m! ;

[0034] (3) Calculate the probability of each position index sequence appearing p1, p2, ..., p k , the permutation entropy of the IMF component can be defined as:

[0035]

[0036] The calculation steps of the Pearson correlation coefficient of adjacent IMF components in step 4 are as follows:

[0037] (1) Two adjacent IMF components are denoted by X = {x(i), i = 1, 2, ..., N}, Y = {y(i), i = 1, 2, ..., N}, where N is the data length;

[0038] (2) Calculate the Pearson correlation coefficient e between X and Y:

[0039]

[0040] in,

[0041] The bearing fault vibration signal in step 1 is collected by a torque sensor.

[0042] Beneficial effect: The present invention can effectively overcome the defect that the number of modes is difficult to determine in variational mode decomposition by analyzing the transformation law of the maximum value of the permutation entropy of the decomposition mode as the number of modes increases and the Pearson correlation of adjacent modes, so that it can be better used for feature extraction of rolling bearing fault signals. This method introduces few parameters and is easier to set the threshold. It can not only adaptively determine the number of decomposition modes, but also effectively suppress the over-decomposition problem occurring during the variational mode decomposition process, thereby improving the decomposition performance of the bearing fault signal mode and better serving the extraction of signal features. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flow chart of the present invention;

[0044] Figure 2 is the vibration signal collected by the present invention;

[0045] Figure 3 It is the spectrum of each IMF component decomposed by VMD when k=5;

[0046] Figure 4 It is the spectrum diagram of each IMF component decomposed by VMD when k=4. DETAILED DESCRIPTION

[0047] The present invention will be further described below in conjunction with the accompanying drawings.

[0048] like Figure 1 As shown, the present invention comprises the following steps:

[0049] Step 1: Build a mechanical bearing data acquisition platform, use a torque sensor to collect the bearing fault vibration signal x(t), and initialize the number of intrinsic mode components (IMF), that is, parameter k=1.

[0050] Step 2: Set k = k + 1, perform variational mode decomposition on the collected vibration signal x(t), and calculate the permutation entropy PE of the kth and k-1th IMF components respectively, and their values ​​are recorded as PE k and PE k-1 If |PE k -PE k-1| is greater than the threshold u1, go to step 2; otherwise, set k=k-1 and perform VMD decomposition on the signal x(t).

[0051] Among them, the detailed steps of performing variational mode decomposition on the vibration signal are as follows:

[0052] (1) Assume that the vibration signal acquired by the sensor is x(t), which is the original signal of variational mode decomposition. The parameter K is the number of decomposition modes, and a is the bandwidth parameter.

[0053] (2) Initialize the eigenmode function Center frequency Lagrange multiplier λ 1 and number of iterations n = 0;

[0054] (3) Set n = n + 1 and enter the loop;

[0055] (4) For all w>0, update u k , k∈{1,2,...,K}:

[0056]

[0057] Update w k :

[0058]

[0059] (5) Update λ:

[0060]

[0061] (6) Repeat steps (3) to (5) until the iteration stop condition is met:

[0062]

[0063] (7) Output K IMF components.

[0064] The detailed steps for calculating the permutation entropy of the IMF components are as follows:

[0065] (1) Considering a specific IMF component, the IMF can essentially be regarded as a time series {x(i), i = 1, 2, ..., N}, with a length of N. Reconstructing its phase space, we get the matrix:

[0066]

[0067] Where m is the embedding dimension and τ is the time delay;

[0068] (2) Each row in the matrix is ​​regarded as a reconstruction component, and each reconstruction component is sorted in ascending order. For example, the j-th reconstruction component:

[0069] X(j)={x(j),x(j+τ),...,x(j+(m-1)τ)}

[0070] After sorting in ascending order, we get:

[0071] x(j+(i1-1)τ)≤x(j+(i2-1)τ)≤...≤x(j+(i m -1)τ),

[0072] Among them, i1,i2,...,i m is the index of the column where each element in the reconstruction component is located. For any reconstruction component in the reconstruction matrix, a set of position index sequences can be obtained: L(j)=(i1,i2,...i m ),j=1,2,3,...,k,k≤m! ;

[0073] (3) Calculate the probability of each position index sequence appearing p1, p2, ..., p k , the permutation entropy of the IMF component can be defined as:

[0074]

[0075] Step 3: If the k value is less than 2, go to step 5.

[0076] Step 4: Calculate the Pearson correlation coefficient e between adjacent components among the k IMF components. If there is an e value greater than the threshold u2, set k=k-1, perform VMD decomposition on the collected vibration signal x(t), and go to step 3. The calculation steps of the Pearson correlation coefficient of adjacent IMF components are as follows:

[0077] (1) Two adjacent IMF components are denoted as X = {x(i), i = 1, 2, ..., N}, Y = {y(i), i = 1, 2, ..., N}, where N is the data length;

[0078] (2) Calculate the Pearson correlation coefficient e between X and Y:

[0079]

[0080] in,

[0081] Step 5: Output k discrete IMF feature components.

[0082] Example:

[0083] Step 1: Build a bearing fault simulation test bench, use an acceleration sensor to collect the vibration signal x(t) of the rolling bearing fault, and initialize the number of intrinsic mode components (IMF), that is, parameter k=1.

[0084] The experimental bearing is a 6205-2RS deep groove ball bearing. The single-point fault processing is performed on the bearing surface using the electric spark technology. The fault diameter is 0.1778mm and the fault depth is 0.2794mm. The selected bearing is installed on the side of the motor shaft, and the acceleration sensor is arranged near the bearing position. The experimental setting is that the motor speed is 1797r / min, the load is 0, the sampling frequency is 12kHz, the sampling time length is 0.25s, and the bearing inner ring fault acquisition signal is x(t), such as Figure 2 shown.

[0085] Step 2: Set k = k + 1, perform variational mode decomposition (VMD) on the collected vibration signal x(t), and calculate the permutation entropy PE of the kth and k-1th IMF components respectively, and their values ​​are recorded as PE k and PE k-1 If |PE k -PE k-1 | is greater than the threshold u1, go to step 2; otherwise, set k=k-1 and perform VMD decomposition on the signal x(t).

[0086] Obviously, step 2 is a loop process. Here, the threshold u1=0.01 is set. When k=6, the loop stops. As the value of k increases, the change of the permutation entropy PE value of the VMD decomposition mode IMF is shown in Table 1. It is not difficult to see from Table 1 that when the value of k is between 2 and 5, the difference in the PE values ​​of the last two IMF components under each value is greater than the threshold, while when k=6, the corresponding difference is less than the threshold. At this time, if the value of k continues to increase, the over-decomposition problem will occur. This can be seen from Figure 3 It's not hard to see. Figure 3 This is the spectrum of the five IMF components decomposed by VMD when k=5. It can be seen that the two components IMF4 and IMF5 are similar in the frequency domain, which also proves that when k is 6, the loop of step 2 should be stopped.

[0087] Table 1 Permutation entropy PE value of each IMF component decomposed by VMD under different k values

[0088] IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 k＝2 <![CDATA[ 0.5629 ]]> <![CDATA[ 0.7736 ]]> k＝3 0.5410 <![CDATA[ 0.7630 ]]> <![CDATA[ 0.7822 ]]> k＝4 0.4900 0.6402 <![CDATA[ 0.7611 ]]> <![CDATA[ 0.7793 ]]> k＝5 0.4865 0.6404 0.7537 <![CDATA[ 0.7615 ]]> <![CDATA[ 0.7512 ]]> k＝6 0.4830 0.6375 0.7614 0.7367 <![CDATA[ 0.7585 ]]> <![CDATA[ 0.7562 ]]>

[0089] Step 3: If the k value is less than 2, go to step 5.

[0090] Step 4: Calculate the Pearson correlation coefficient e between adjacent components in the k IMF components. If there is an e value greater than the threshold u2, set k=k-1, perform VMD decomposition on the collected vibration signal x(t), and go to step 3.

[0091] When running to this step, k takes the value of 5, and VMD decomposition obtains 5 IMF components, which are recorded as IMF1, IMF2, IMF3, IMF4, and IMF5, respectively. The threshold u2 = 0.1. The subscript represents the sequence number of the IMF component, and the Pearson correlation coefficient e between adjacent components is calculated in sequence: e 1,2 =0.0464, e 1,3 =0.0093, e 1,4 =0.0036, e 1,5 =0.002, e 2,3 =0.0181, e 2,4 =0.0076, e 2,5 =0.0037, e 3,4 =0.0849, e 3,5 =0.0249, e 4,5 =0.1308. Obviously, the Pearson correlation coefficient value of IMF4 and IMF5 is 4,5 = 0.1308, exceeding the threshold u2 = 0.1. Figure 3 It is not difficult to see that the components IMF4 and IMF5 have a high degree of similarity in the frequency domain, and over-decomposition has occurred, which also proves that it is effective to use the Pearson correlation between adjacent components to suppress the over-decomposition of the vibration signal. Therefore, according to step 4, set k = k-1, that is, k = 4, re-perform VMD decomposition on the fault vibration signal x(t), obtain four new IMF components, and calculate the Pearson correlation coefficient value between adjacent components: e 1,2 =0.047, e 1,3 =0.0102, e 1,4 =0.0038, e 2,3 =0.0192, e 2,4 =0.0059, e 3,4 =0.0416. Obviously, none of the correlation coefficient values ​​exceeds the threshold u2=0.1, so the final k value is 4. Figure 4 The spectra of the IMF components decomposed by VMD are given when k = 4. Figure 4 It is not difficult to see that the four IMF components finally generated have obvious feature distinction and reflect the intrinsic embedded characteristics of the fault vibration signal x(t) from different feature planes.

[0092] Step 5: Output k discrete IMF feature components. Directly generate the four feature components of the fault vibration signal x(t), such as Figure 4 shown.

[0093] In view of the problem that the number of decomposition modes in the variational mode decomposition method is difficult to determine, which in turn affects the mode decomposition performance, the present invention proposes an adaptive variational mode decomposition method that can be used for mechanical bearing fault signal feature extraction. The method comprehensively analyzes the change law of the permutation entropy value of the decomposition mode as the number of modes increases, as well as the Pearson correlation between adjacent modes in the decomposition mode. It can not only adaptively determine the number of decomposition modes, but also effectively suppress the over-decomposition problem occurring during the variational mode decomposition process, thereby improving the bearing fault signal mode decomposition performance and better serving the extraction of signal features. The present invention only introduces two technical indicators, the permutation entropy and the Pearson correlation coefficient, introduces fewer parameters and is easier to set the threshold. In addition, it can effectively suppress the over-decomposition problem.

Claims

1. An adaptive variational mode decomposition method for rolling bearing fault feature extraction, characterized in that: The following steps are involved: Step 1: Build a bearing data acquisition platform, collect bearing fault vibration signal x(t), and initialize the intrinsic mode component IMF number, that is, parameter k=1; Step 2: Set k = k + 1, perform variational mode decomposition on the collected vibration signal x(t), and calculate the permutation entropy PE of the kth and k-1th IMF components respectively, and their values ​​are recorded as PE k and PE k-1 , if |PE k -PE k-1 | is greater than the threshold u1, go to step 2; otherwise, set k = k-1 and perform VMD decomposition on the signal x(t); the steps of performing variational mode decomposition on the vibration signal are as follows: (1) Assume that the vibration signal acquired by the sensor is x(t), which is the original signal of variational mode decomposition. The parameter K is the number of decomposition modes, and a is the bandwidth parameter. (2) Initialize the eigenmode function Center frequency Lagrange multiplier λ 1 and number of iterations n = 0; (3) Set n = n + 1 and enter the loop; (4) For all w>0, update u k , k∈{1,2,...,K}: Update w k : (5) Update λ: (6) Repeat steps (3) to (5) until the iteration stop condition is met: (7) Output K IMF components; Step 3: If the k value is less than 2, go to step 5; Step 4: Calculate the Pearson correlation coefficient e between adjacent components in the k IMF components. If there is an e value greater than the threshold u2, set k=k-1, perform VMD decomposition on the collected vibration signal x(t), and go to step 3; Step 5: Output k discrete IMF feature components.

2. The adaptive variational mode decomposition method for rolling bearing fault feature extraction according to claim 1 is characterized in that: The calculation steps of the IMF component permutation entropy in step 2 are as follows: (1) Considering a specific IMF component, the IMF can essentially be regarded as a time series {x(i), i = 1, 2, ..., N}, with a length of N. Reconstructing its phase space, we get the matrix: Where m is the embedding dimension and τ is the time delay; (2) Each row in the matrix is ​​regarded as a reconstruction component, and each reconstruction component is sorted in ascending order. For example, the j-th reconstruction component: X(j)={x(j),x(j+τ),...,x(j+(m-1)τ)} After sorting in ascending order, we get: x(j+(i1-1)τ)≤x(j+(i2-1)τ)≤...≤x(j+(i m -1)t), Among them, i1,i2,...,i m is the index of the column where each element in the reconstruction component is located. For any reconstruction component in the reconstruction matrix, a set of position index sequences can be obtained: L(j) = (i1, i2, ... i m ),j=1,2,3,...,k,k≤m! ; (3) Calculate the probability of each position index sequence appearing p1, p2, ..., p k , the permutation entropy of the IMF component can be defined as:

3. The adaptive variational mode decomposition method for rolling bearing fault feature extraction according to claim 1, characterized in that: The calculation steps of the Pearson correlation coefficient of adjacent IMF components in step 4 are as follows: (1) Two adjacent IMF components are denoted by X = {x(i), i = 1, 2, ..., N}, Y = {y(i), i = 1, 2, ..., N}, where N is the data length; (2) Calculate the Pearson correlation coefficient e between X and Y: in, 4. The adaptive variational mode decomposition method for rolling bearing fault feature extraction according to claim 1, characterized in that: The bearing fault vibration signal in step 1 is collected by an acceleration sensor.

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