A method for evaluating rolling bearing performance degradation

Abstract

The present invention discloses a method for evaluating the performance degradation of a rolling bearing, and belongs to the technical field of bearing health management. The method comprises the following steps: constructing an objective function using an estimated signal-to-noise ratio as a stopping criterion for the VMD algorithm decomposition process; performing VMD algorithm decomposition on the reconstructed signal according to the decomposition modal number K determined by the stopping criterion of step (1) to obtain K IMF components; respectively calculating the probability density function of each IMF component to form a characteristic vector group, respectively calculating the intra-class distance and inter-class distance of the IMF component, and obtaining a compensation distance evaluation index; performing false fluctuation repair on the compensation distance, and calculating the health threshold according to the Chebyshev inequality to evaluate the performance degradation state of the rolling bearing. The present invention adaptively determines the modal number K through the VMD algorithm decomposition method, solves the problem that the VMD decomposition method K is difficult to determine or needs to be manually set, and makes the VMD decomposition result more accurate and reliable.

Description

Technical Field

[0001] The present invention belongs to the technical field of bearing health management, and in particular relates to a rolling bearing performance degradation assessment method. Background Art

[0002] Complexity, precision, large-scale and intelligentization have become important development directions for rotating machinery and equipment in the future. As one of its important components, the health of rolling bearings is very important to mechanical equipment and is the key to ensuring the efficient and safe operation of rotating machinery and equipment. Unexpected bearing failure may cause equipment failure, resulting in equipment shutdown, downtime, major economic losses and casualties. Therefore, it is of great practical significance to evaluate the performance degradation of rolling bearings.

[0003] When a rolling bearing has a local defect, the fault information is often drowned out by strong background noise and interference, making it difficult to intuitively obtain key information from the vibration signal. At present, the signal preprocessing method mainly uses non-stationary vibration signal decomposition, which can effectively extract the amplitude modulation information of non-stationary and nonlinear vibration signals. The empirical mode decomposition (EMD) method is a widely used signal processing method. This method can adaptively decompose the vibration signal into multiple intrinsic mode functions (IMFs). However, when EMD uses the cubic spline method to construct the mean curve, problems such as over-envelope, under-envelope and poor envelope fitting accuracy will occur. Smith proposed the local mean decomposition (LMD) method, which retains more local information than the components obtained by EMD decomposition, improves the envelope fitting accuracy to a certain extent, and improves the over-envelope and under-envelope problems. However, the components obtained by the LMD decomposition method often have a large number of false frequencies, and will cause signal mutations and large computational complexity. In the LMD decomposition process, differential and integral operations are integrated to make the energy of the signal decrease from high to low frequency as much as possible, which can effectively distinguish different frequency components and effectively suppress modal aliasing. Variational Modal Decomposition (VMD) is a completely non-recursive decomposition method that can effectively avoid noise and sampling sensitivity, and can overcome the modal aliasing problem of EMD, LMD and other methods to a certain extent. However, the rationality of the preset decomposition mode number K determines the quality of VMD decomposition performance. An inappropriate preset decomposition mode number can lead to information loss or over-decomposition, affecting the decomposition accuracy of the signal.

[0004] Evaluating the performance degradation of bearings based on the correlation between normal vibration signals and fault vibration signals is one of the important research directions in the field of health management. Yin Aijun et al. proposed a new method for evaluating the performance degradation of rolling bearings based on synchronous extraction transformation and complex wavelet structure similarity index. Jiao Hanhui et al. optimized the dimension reduction of feature sets through the compensation distance evaluation method, and then constructed an intelligent fault identification model, which achieved a fault identification accuracy of more than 98%. However, the processing process increased the complexity of the algorithm and took a long time to run. Summary of the invention

[0005] In view of the shortcomings of the above-mentioned prior art, the present invention provides a rolling bearing performance degradation assessment method. Based on variational mode decomposition and compensation distance, the present invention proposes an accurate and effective method for completing the rolling bearing performance degradation state assessment, which improves the performance of VMD in signal decomposition, fault diagnosis and other aspects.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a rolling bearing performance degradation assessment method, comprising the following steps:

[0007] (1) Using the estimated signal-to-noise ratio to construct an objective function as the stopping criterion of the VMD algorithm decomposition process; the objective function is:

[0008]

[0009] Among them, x(n) is the original vibration signal, is the reconstructed signal, SNRe is the estimated signal-to-noise ratio, K is the number of decomposed modes, and n is the number of data points;

[0010] In the VMD decomposition process, the vibration signal is decomposed into a series of pure intrinsic mode functions IMF. In the decomposition process, there should be such a decomposition mode number K, that is, the sum of the first K IMF components constitutes the reconstructed signal to approximate the ideal noise-free signal f(t);

[0011] When the VMD algorithm is used to decompose the original vibration signal, when the energy ratio between the original vibration signal and the reconstructed signal satisfies formula (5), the optimal decomposition layer number is reached, and the decomposition mode number K is obtained:

[0012]

[0013] (2) According to the stopping criterion of step (1), the number of decomposition modes K is determined, and the reconstructed signal Perform VMD algorithm decomposition to obtain K IMF components;

[0014] (3) Calculate the probability density function of each IMF component to form a characteristic vector group, calculate the intra-class distance and inter-class distance of the IMF component, and obtain the compensation distance evaluation index;

[0015] (4) The false fluctuation of the compensation distance is repaired, and the health threshold is calculated according to the Chebyshev inequality to further evaluate the performance degradation state of the rolling bearing.

[0016] As a preferred embodiment of the present invention, the expression of the original vibration signal x(n) is:

[0017] x(n)=h(n)+w(n) (2)

[0018] Among them, h(n) represents the pure signal and w(n) represents the noise.

[0019] As a preferred embodiment of the present invention, the expression for estimating the signal-to-noise ratio is:

[0020]

[0021] As a preferred embodiment of the present invention, when formula (3) is satisfied, the energy relationship between the pure signal h(n) and the noise signal w(n) is:

[0022]

[0023] Ideally, the reconstructed signal will contain only pure signals, i.e. The energy of will be equal to the energy of the pure signal h(n). In the actual decomposition process, as the decomposition level increases, the reconstructed signal The energy of increases accordingly. Before reaching the optimal decomposition level, the energy ratio of the original vibration signal to the reconstructed signal is greater than the energy ratio in the ideal state.

[0024] When the VMD algorithm is used to decompose the signal, the number of decomposed modes is decomposed from 2 to K in sequence. The energy ratio of the vibration signal to the reconstructed signal decreases monotonically. When the condition of formula (5) is met, the decomposition process should be stopped, which is the optimal solution of formula (6). If the decomposition is continued, more noise will be decomposed into the reconstructed signal. If the decomposition is stopped before the condition of formula (4) is met, then More energy of the original signal will be lost.

[0025] As a preferred embodiment of the present invention, in step (2), the VMD algorithm decomposes the input signal into K ω k is the eigenmode component u of the center frequency k (t); The unconstrained problem expression of the VMD algorithm is:

[0026]

[0027] Where δ(t) is the impulse function, f(t) is the input signal, j is the imaginary unit, and uk is the mode function, ω k is the center frequency, λ is the Lagrange multiplier, is the regularization parameter, t is the time, α is the quadratic penalty factor, u k (t) is the mode function at time t, and λ(t) is the Lagrange multiplier at time t.

[0028] As a preferred embodiment of the present invention, the multiplier alternating direction method is used to solve the unconstrained problem of the VMD algorithm.

[0029] As a preferred embodiment of the present invention, the specific process of solving the problem by the multiplier alternating direction method includes:

[0030] Step 1: Initialization and n = 0; is the first modal function, is the first center frequency, is the Lagrange multiplier, n is the number of data points;

[0031] Step 2: m=m+1;

[0032] Step 3: k = 1: K, and for all ω ≥ 0 Update; ω is the center frequency;

[0033]

[0034] and u k and the Fourier transform of λ; is the mode function at point n+1, is the amplitude, is the modal function when the number of data points is n and the number of decomposition layers is i. is the Lagrange multiplier, α is the quadratic penalty factor, ω is the center frequency, is the center frequency of point n, is the center frequency when the data point is n+1.

[0035] Step 4: Update the Lagrangian operator λ:

[0036]

[0037] In the formula, τ is the noise tolerance parameter. In order to obtain a better denoising effect, τ = 0; is the Lagrange multiplier;

[0038] Step 5: Repeat steps 2-4 until equation (11) is satisfied, then stop the iteration and output K IMF components:

[0039]

[0040] Among them, the value of ε is 10 -6 , is the nth mode function.

[0041] The VMD algorithm consists of two parts: one is the constrained variation problem, and the other is solving the variation problem. The construction of the constrained variation problem can be described by equation (7):

[0042]

[0043] By introducing the Lagrangian multiplier λ and the quadratic penalty factor α, the constrained variational problem is transformed into an unconstrained variational problem for solution. Its augmented Lagrangian is shown in formula (8):

[0044]

[0045] As a preferred embodiment of the present invention, the probability density function of the IMF component is:

[0046]

[0047] In the formula, A 0 , B 0 is the mapping parameter, a i0 is the i+1th Lagrange multiplier of IMF, i=1, 2,…, I, I is the origin moment order, and x is the vibration signal.

[0048] The probability density function f of IMF 0 (x) is expressed as:

[0049]

[0050] Where a i0 is the i+1th Lagrange multiplier of IMF, i=1, 2,…, I; I is the origin moment order.

[0051] In order to make the solution converge, the IMF data sequence is mapped to the interval [-e, e] based on the interval mapping method, e = 2.718282, so the IMF probability density function is transformed into:

[0052]

[0053] As a preferred embodiment of the present invention, the compensation distance evaluation method adds the inter-class distance on the basis of the intra-class distance, thereby compensating for the remaining signals that may be lost during the signal acquisition process, that is, calculating the compensation distance, which can avoid the loss of important information; in the step (3), the compensation distance evaluation specifically includes the following steps:

[0054] S1: Assume that the probability density function eigenvector obtained after VMD decomposition of the normal vibration signal is X = [PDF 11 PDF 12 ……PDF 1k ], the probability density function eigenvector of the vibration signal to be measured is Y = [PDF 11 PDF 12 ……PDF 1k ;PDF 21 PDF 22 ……PDF 2k ; ... ; PDF T1 PDF T2 ……PDF Tk ]; where PDF 11 is the first probability density of the first set of data, PDF 12 is the second probability density of the first set of data, PDF 1k is the kth probability density of the first set of data, PDF 21 is the first probability density of the second set of data, PDF 22 is the second probability density of the second set of data, PDF 2k is the kth probability density of the second set of data, PDF T1 is the first probability density of the Tth group of data, PDF T2 is the second probability density of the Tth group of data, PDF Tk is the kth probability density of the Tth group of data, T is the signal data group to be tested, and k is the number of decomposed modes;

[0055] S2: Calculate the average intra-class distance between the feature vectors of the normal vibration signal and the signal to be tested:

[0056]

[0057] Wherein, i = 1, 2, ..., T, T is the signal data group to be measured, j = 1, 2, ..., k, k is the VMD mode number;

[0058] S3: Calculate the inter-class distance of the feature vector of the signal to be tested:

[0059]

[0060] Among them, d b is the distance between classes, PDF (i+(i-1)k)1 is the first probability density of T group data, PDF ij is the jth probability density of the i-th group of data; j = 1, 2, …, k, k is the VMD mode number;

[0061] S4: Calculate d k and d bThe variance factor v k and v b :

[0062]

[0063]

[0064] S5: Calculate the compensation factor γ k :

[0065]

[0066] S6: In-class distance d k Increase the distance d between the upper classes b , and obtain the compensation distance evaluation index α k :

[0067]

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention utilizes the estimated signal-to-noise ratio to construct the objective function as the VMD algorithm decomposition process, which can adaptively determine the modal number K, thereby solving the problem that the VMD decomposition method K is difficult to determine or needs to be manually set, making the VMD decomposition result more accurate and reliable, and laying the foundation for the subsequent rolling bearing performance degradation assessment.

[0069] The invention constructs a method with probability density function as eigenvalue vector, calculates the compensation distance evaluation index combining the intra-class distance and the inter-class distance, performs bubble sorting on the index, optimizes the internal structure of data, effectively realizes the rolling bearing performance degradation evaluation, and provides a new method for bearing performance degradation evaluation extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flow chart based on the rolling bearing performance degradation assessment method.

[0071] Figure 2 It is a time domain waveform diagram of the entire life cycle of the rolling bearing of Example 1 of the present invention.

[0072] Figure 3 It is a time domain waveform diagram of some data of the rolling bearing in Example 1 of the present invention.

[0073] Figure 4 It is a curve showing the objective function of Example 1 of the present invention changing with the number of decomposition levels.

[0074] Figure 5 This is a diagram of the decomposition results of the improved VMD algorithm when K=5 in Example 1 of the present invention.

[0075] Figure 6 This is a distance value result diagram of Example 1 of the present invention.

[0076] Figure 7 This is a diagram showing the distance value results after the false fluctuations are repaired in Example 1 of the present invention.

[0077] Figure 8 This is the TKEO spectrum of the 532nd data set in Example 1 of the present invention.

[0078] Fig. 9 This is the TKEO spectrum of the 533rd data set in Example 1 of the present invention.

[0079] Fig.10 It is a time domain waveform diagram of the XJTU-SY bearing data of Example 2 of the present invention.

[0080] Fig.11 This is a distance value result diagram of Example 2 of the present invention.

[0081] Fig.12 This is a diagram showing the distance value results after the false fluctuations are repaired in Example 2 of the present invention.

[0082] Fig.13 This is the TKEO spectrum of the 2348th data set in Example 2 of the present invention.

[0083] Fig.14 This is the TKEO spectrum of the 2349th data set in Example 2 of the present invention. DETAILED DESCRIPTION

[0084] In order to better illustrate the purpose, technical solutions and advantages of the present invention, the present invention will be further described below in conjunction with specific embodiments.

[0085] Example 1

[0086] The experimental data used in this embodiment comes from the Bearing Data Center of the University of Cincinnati, USA. The specific parameters are as follows: the AC motor rotates at a constant speed of 2000 rpm, a radial load of 6000 pounds is applied to the bearing through a spring mechanism, the sampling frequency is 20kHz, and the number of sampling points is 20480. In this embodiment, a total of 984 data groups are collected, each group contains 20480 data points, and the first group of data is selected as the normal signal, and the 984th group of data (full life cycle data) is selected as the signal to be tested.

[0087] Figure 2This is a time domain waveform diagram of the rolling bearing's entire life cycle. It can be seen from the figure that the bearing's amplitude suddenly increased at the 702th data set, the signal impact increased, and the bearing failed; the amplitude increased sharply from the 970th data set, and the bearing entered the complete failure period until the 984th data set completely failed, but it is impossible to observe whether there was a failure before the 702th data set. At the same time, during the operation of the bearing, transient impact information will be caused by noise and other reasons, and the amplitude cannot be completely used as the evaluation standard. Therefore, the vibration signal of the bearing needs to be further processed.

[0088] This embodiment takes one set of data as an example. The time domain waveform of the original vibration signal is as follows: Figure 3 The rolling bearing performance degradation assessment method described in this embodiment includes the following steps:

[0089] (1) First, construct the objective function as follows:

[0090]

[0091] Among them, x(n) is the original vibration signal, is the reconstructed signal, SNRe is the estimated signal-to-noise ratio, K is the number of decomposed modes, and n is the number of data points;

[0092] Initialize the parameter K = 1, the objective function value is ∞; secondly, Figure 3 The original vibration signal is decomposed by VMD, and the K IMF components are reconstructed to calculate the objective function value; secondly, the vibration signal is decomposed by VMD, and the K IMF components are reconstructed to calculate the objective function value; then, the objective function value is compared to see whether it reaches the minimum value. If the objective function is the minimum value, the iteration is stopped, otherwise the signal decomposition is continued. The curve of the objective function changing with the number of decomposition layers is as follows: Figure 4 As shown, according to the proposed VMD stopping criterion, it can be judged that the number of VMD decomposition layers is 3.

[0093] The estimated signal-to-noise ratio is used to construct the objective function as the stopping criterion of the VMD decomposition process. When the energy ratio of the original vibration signal and the reconstructed signal satisfies formula (5), the optimal decomposition level K is reached:

[0094]

[0095] (2) According to the stopping criterion of step (1), the number of decomposition modes K is determined, and the reconstructed signal Perform VMD decomposition to obtain K IMF components; use the number of valid IMF components as the modal number (K ​​= 5) and input it into the VMD algorithm, and use the VMD decomposition method to decompose the signal to obtain 5 IMF components, such as Figure 5 shown.

[0096] The specific steps include:

[0097] 1. VMD decomposition decomposes the input signal into K ω k is the eigenmode component u of the center frequency k (t); The unconstrained problem expression of the VMD algorithm is:

[0098]

[0099] Where δ(t) is the impulse function, f(t) is the input signal, j is the imaginary unit, and u k is the mode function, ω k is the center frequency, λ is the Lagrange multiplier, is the regularization parameter, t is the time, α is the quadratic penalty factor, u k (t) is the mode function at time t, and λ(t) is the Lagrange multiplier at time t.

[0100] 2. The multiplier alternating direction method is used to solve the unconstrained problem of the VMD algorithm. The specific process of the solution includes:

[0101] Step 1: Initialization and n = 0; is the first modal function, is the first center frequency, is the Lagrange multiplier, n is the number of data points;

[0102] Step 2: m=m+1;

[0103] Step 3: k = 1: K, and for all ω ≥ 0 Update; ω is the center frequency;

[0104]

[0105] and u k and the Fourier transform of λ; is the mode function at point n+1, is the amplitude, is the modal function when the number of data points is n and the number of decomposition layers is i. is the Lagrange multiplier, 2α is the quadratic penalty factor, ω is the center frequency, is the center frequency of point n, is the center frequency when the data point is n+1.

[0106] Step 4: Update the Lagrangian operator λ:

[0107]

[0108] In the formula, τ is the noise tolerance parameter. In order to obtain a better denoising effect, τ = 0; is the Lagrange multiplier;

[0109] Step 5: Repeat steps 2-4 until equation (11) is satisfied, then stop the iteration and output K IMF components:

[0110]

[0111] Among them, the value of ε is 10 -6 , is the nth mode function.

[0112] (6) According to the following formula, the probability density function of each IMF component is calculated to form a characteristic vector group, and the intra-class distance and inter-class distance of the IMF component are calculated respectively to obtain the compensation distance evaluation index;

[0113] First, the probability density function of the IMF component is:

[0114]

[0115] In the formula, A 0 , B 0 is the mapping parameter, a i0 is the i+1th Lagrange multiplier of IMF, i=1, 2,…, I, I is the origin moment order, and x is the vibration signal.

[0116] Secondly, the compensation distance evaluation method adds the inter-class distance on the basis of the intra-class distance, compensating for the remaining signals that may be lost during the signal acquisition process, that is, calculating the compensation distance, which can avoid the loss of important information; the compensation distance evaluation specifically includes the following steps:

[0117] S1: Assume that the probability density function eigenvector obtained after VMD decomposition of the normal vibration signal is X = [PDF 11 PDF 12 ……PDF 1k ], the probability density function eigenvector of the vibration signal to be measured is Y = [PDF 11 PDF 12 ……PDF 1k ;PDF 21 PDF 22 ……PDF 2k ; ...; PDF T1 PDF T2 ……PDF Tk ]; where PDF 11 is the first probability density of the first set of data, PDF 12 is the second probability density of the first set of data, PDF1k is the kth probability density of the first set of data, PDF 21 is the first probability density of the second set of data, PDF 22 is the second probability density of the second set of data, PDF 2k is the kth probability density of the second set of data, PDF T1 is the first probability density of the Tth group of data, PDF T2 is the second probability density of the Tth group of data, PDF Tk is the kth probability density of the Tth group of data, T is the signal data group to be tested, and k is the number of decomposed modes;

[0118] S2: Calculate the average intra-class distance between the feature vectors of the normal vibration signal and the signal to be tested:

[0119]

[0120] Wherein, i = 1, 2, ..., T, T is the signal data group to be measured, j = 1, 2, ..., k, k is the VMD mode number;

[0121] S3: Calculate the inter-class distance of the feature vector of the signal to be tested:

[0122]

[0123] Among them, d b is the distance between classes, PDF (i+(i-1)k)1 is the first probability density of T group data, PDF ij is the jth probability density of the i-th group of data; j = 1, 2, …, k, k is the VMD mode number;

[0124] S4: Calculate d k and d b The variance factor v k and v b :

[0125]

[0126]

[0127] S5: Calculate the compensation factor γ k :

[0128]

[0129] S6: In-class distance d k Increase the distance d between the upper classes b , and obtain the compensation distance evaluation index α k :

[0130]

[0131] After VMD decomposition in this embodiment, a total of 984×5 groups of IMF data are obtained. In order to avoid the influence of random factors, the probability density function of all IMF components is calculated to obtain 984×5 groups of data. The intra-class distance between the 984×5 groups of data and the first group of data is calculated according to the probability density function, and the average intra-class distance is obtained based on the 5 groups of data, a total of 984 groups of intra-class distances, the inter-class distance between each 5 groups of data and the first group of the current 5 groups of data is calculated, and the average value is calculated, a total of 984 groups of inter-class distances are obtained. According to formula (19), the compensation distance evaluation index can be calculated, as follows: Figure 6 As shown in the figure, the intra-class distance and the inter-class distance show similar trends, and the compensation distance has a relatively smaller fluctuation, which means that the compensation distance combines the advantages of the intra-class distance and the inter-class distance and has better statistical stability.

[0132] (4) Repair the false fluctuations of the compensation distance to make the logical relationship between the indicator data clearer; when the rolling bearing is in normal operation, the distance value remains stable for a long time, and begins to increase with the occurrence of early faults until the bearing fails completely. In order to optimize the internal structure of the distance value and make the logical relationship between the data clearer, the sliding window and 3σ principle are used to continue processing the data, and the results are as follows: Figure 7 As shown in the figure, it can be observed intuitively that the distance value gradually increases until the bearing fails completely.

[0133] (5) The Chebyshev inequality is used to calculate the health threshold, identify the early failure point of the rolling bearing, and further evaluate the performance degradation state of the rolling bearing. Substituting the compensation distance evaluation index into the Chebyshev inequality, the threshold value is 0.0080. Figure 7 It can be seen that the 532nd group of data is less than the threshold, and the 533rd group of data is greater than the threshold. Therefore, the 533rd group of data is the time when the early fault point occurs. The Teager-Kaiser energy operator (TKEO) demodulation method is used to analyze the 532nd and 533rd group of data, and the TKEO spectra are as follows: Figure 8 , Fig. 9 As shown in the figure, no obvious fault frequency was found in the 532nd data, while the TKEO spectrum of the 533rd data set had a clear peak at fch (229.5Hz), which was close to the theoretical frequency value of the outer ring fault (236.4Hz), proving that the outer ring fault occurred at the 533rd data set, further indicating the accuracy of the starting failure point.

[0134] Example 2

[0135] The experimental data used in this embodiment comes from the XJTU-SY (Xi'an Jiaotong University-Changxing Shengyang Technology, XJTU-SY) bearing data test platform, and the test bearing is LDKUER204 rolling bearing. The sampling frequency is 25.6kHz, the drive motor speed is 2100r / min, the sampling points are 4096, the radial load is 12kN, the data is collected every 1min, and the sampling time is 1.28s each time, with a total of 2538 sets of data.

[0136] Fig.10 This is a time domain waveform diagram of the entire life cycle of a rolling bearing. During the operation of the bearing, transient impact information will be caused by noise and other reasons, and the amplitude cannot be used as the evaluation standard. Therefore, the vibration signal of the bearing needs to be further processed.

[0137] This embodiment Fig.10 The time domain waveform diagram of the rolling bearing throughout its life cycle is an original vibration signal. The rolling bearing performance degradation assessment method comprises the following steps:

[0138] (1) Using the estimated signal-to-noise ratio to construct an objective function as the stopping criterion of the VMD decomposition process; the objective function is:

[0139]

[0140] Among them, x(n) is the original vibration signal, is the reconstructed signal, SNRe is the estimated signal-to-noise ratio, K is the number of decomposed modes, and n is the number of data points;

[0141] When the energy ratio between the original vibration signal and the reconstructed signal satisfies formula (5), the optimal decomposition level K is reached:

[0142]

[0143] (2) According to the stopping criterion of step (1), the number of decomposition modes K is determined, and the reconstructed signal Perform VMD decomposition to obtain K IMF components, which specifically includes the following steps:

[0144] 1. VMD decomposition decomposes the input signal into K ω k is the eigenmode component u of the center frequency k (t); The unconstrained problem expression of the VMD algorithm is:

[0145]

[0146] Where δ(t) is the impulse function, f(t) is the input signal, j is the imaginary unit, and u kis the mode function, ω k is the center frequency, λ is the Lagrange multiplier, is the regularization parameter, t is the time, α is the quadratic penalty factor, u k (t) is the mode function at time t, and λ(t) is the Lagrange multiplier at time t.

[0147] 2. The multiplier alternating direction method is used to solve the unconstrained problem of the VMD algorithm. The specific process of the solution includes:

[0148] Step 1: Initialization and n = 0; is the first modal function, is the first center frequency, is the Lagrange multiplier, n is the number of data points;

[0149] Step 2: m=m+1;

[0150] Step 3: k = 1: K, and for all ω ≥ 0 Update; ω is the center frequency;

[0151]

[0152] and u k and the Fourier transform of λ; is the mode function at point n+1, is the amplitude, is the modal function when the number of data points is n and the number of decomposition layers is i. is the Lagrange multiplier, α is the quadratic penalty factor, ω is the center frequency, is the center frequency of point n, is the center frequency when the data point is n+1.

[0153] Step 4: Update the Lagrangian operator λ:

[0154]

[0155] In the formula, τ is the noise tolerance parameter. In order to obtain a better denoising effect, τ = 0; is the Lagrange multiplier;

[0156] Step 5: Repeat steps 2-4 until equation (11) is satisfied, then stop the iteration and output K IMF components:

[0157]

[0158] Among them, the value of ε is 10 -6 , is the nth mode function.

[0159] (7) Calculate the probability density function of each IMF component to form a characteristic vector group, calculate the intra-class distance and inter-class distance of the IMF component, and obtain the compensation distance evaluation index;

[0160] First, the probability density function of the IMF component is:

[0161]

[0162] In the formula, A 0 , B 0 is the mapping parameter, a i0 is the i+1th Lagrange multiplier of IMF, i=1, 2,…, I, I is the origin moment order, and x is the vibration signal.

[0163] Secondly, the compensation distance evaluation method adds the inter-class distance on the basis of the intra-class distance, compensating for the remaining signals that may be lost during the signal acquisition process, that is, calculating the compensation distance, which can avoid the loss of important information; the compensation distance evaluation specifically includes the following steps:

[0164] S1: Assume that the probability density function eigenvector obtained after VMD decomposition of the normal vibration signal is X = [PDF 11 PDF 12 ……PDF 1k ], the probability density function eigenvector of the vibration signal to be measured is Y = [PDF 11 PDF 12 ……PDF 1k ;PDF 21 PDF 22 ……PDF 2k ; ...; PDF T1 PDF T2 ……PDF Tk ]; where PDF 11 is the first probability density of the first set of data, PDF 12 is the second probability density of the first set of data, PDF 1k is the kth probability density of the first set of data, PDF 21 is the first probability density of the second set of data, PDF 22 is the second probability density of the second set of data, PDF 2k is the kth probability density of the second set of data, PDF T1 is the first probability density of the Tth group of data, PDF T2 is the second probability density of the Tth group of data, PDF Tkis the kth probability density of the Tth group of data, T is the signal data group to be tested, and k is the number of decomposed modes;

[0165] S2: Calculate the average intra-class distance between the feature vectors of the normal vibration signal and the signal to be tested:

[0166]

[0167] Wherein, i = 1, 2, ..., T, T is the signal data group to be measured, j = 1, 2, ..., k, k is the VMD mode number;

[0168] S3: Calculate the inter-class distance of the feature vector of the signal to be tested:

[0169]

[0170] Among them, d b is the distance between classes, PDF (i+(i-1)k)1 is the first probability density of T group data, PDF ij is the jth probability density of the i-th group of data; j = 1, 2, …, k, k is the VMD mode number;

[0171] S4: Calculate d k and d b The variance factor v k and v b :

[0172]

[0173]

[0174] S5: Calculate the compensation factor γ k :

[0175]

[0176] S6: In-class distance d k Increase the distance d between the upper classes b , and obtain the compensation distance evaluation index α k :

[0177]

[0178] from Fig.11 It can be seen that after the compensation distance is combined with the inter-class distance and the intra-class distance, the distance value is larger, the intra-class distance and the inter-class distance show similar trends, and the compensation distance has a relatively smaller fluctuation, indicating that the compensation distance combines the advantages of the intra-class distance and the inter-class distance, has better statistical stability, and further demonstrates the effectiveness of the compensation distance.

[0179] (4) Repair the false fluctuations of the compensation distance evaluation index to make the logical relationship between the index data clearer; when the rolling bearing is in normal operation, the distance value remains stable for a long time, and begins to increase with the occurrence of early faults until the bearing fails completely. In order to optimize the internal structure of the distance value and make the logical relationship between the data clearer, the sliding window and 3σ principle are used to continue processing the data, and the results are as follows: Fig.12 As shown in the figure, it can be observed intuitively that the distance value gradually increases until the bearing fails completely.

[0180] (5) The health threshold is calculated using the Chebyshev inequality to identify the early failure point of the rolling bearing and further evaluate the performance degradation of the rolling bearing. The compensation distance evaluation index is combined with the Chebyshev inequality to obtain a threshold of 0.0347. Fig.12 It can be seen that the 2348th group of data is less than the threshold, and the 2349th group of data is greater than the threshold. The 2349th group of data is the time when the early fault point occurs. The 2348th and 2349th groups of data are analyzed by TKEO demodulation, and the spectrum is as follows Fig.13 , Fig.14 As shown, it can be seen that no obvious fault frequency was found in the 2348th group of data, and a relatively obvious fault frequency was found in the 2349th group of data, proving that the fault began to occur in the 2349th group of data, further indicating the accuracy of the starting failure point.

[0181] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A rolling bearing performance degradation assessment method, characterized in that: The steps include: (1) Using the estimated signal-to-noise ratio to construct an objective function as the stopping criterion of the VMD algorithm decomposition process; the objective function is: Among them, x(n) is the original vibration signal, is the reconstructed signal, SNRe is the estimated signal-to-noise ratio, K is the number of decomposed modes, and n is the number of data points; When the VMD algorithm is used to decompose the original vibration signal, when the energy ratio between the original vibration signal and the reconstructed signal satisfies formula (5), the optimal decomposition layer number is reached, and the decomposition mode number K is obtained: (2) According to the stopping criterion of step (1), the number of decomposition modes K is determined, and the reconstructed signal Perform VMD algorithm decomposition to obtain K IMF components; (3) respectively calculating the probability density function of each IMF component in step (2) to form a characteristic vector group, respectively calculating the intra-class distance and inter-class distance of the IMF component, and obtaining the compensation distance evaluation index; (4) The false fluctuation of the compensation distance is repaired, and the health threshold is calculated according to the Chebyshev inequality to further evaluate the performance degradation state of the rolling bearing.

2. The rolling bearing performance degradation assessment method according to claim 1, characterized in that: The expression of the original vibration signal x(n) is: x(n)=h(n)+w(n) (2) Among them, h(n) represents the pure signal and w(n) represents the noise.

3. The rolling bearing performance degradation assessment method according to claim 1, characterized in that: The expression for estimating the signal-to-noise ratio is: Among them, h(n) represents the pure signal and w(n) represents the noise.

4. The rolling bearing performance degradation assessment method according to claim 1, characterized in that: In step (2), the VMD algorithm decomposes the input signal into K ω k is the eigenmode component u of the center frequency k (t); The unconstrained problem expression of the VMD algorithm is: Where δ(t) is the impulse function, f(t) is the input signal, j is the imaginary unit, and u k is the mode function, ω k is the center frequency, λ is the Lagrange multiplier, is the regularization parameter, t is the time, α is the quadratic penalty factor, u k (t) is the mode function at time t, and λ(t) is the Lagrange multiplier at time t.

5. The rolling bearing performance degradation assessment method according to claim 4, characterized in that: The alternating direction method of multipliers is used to solve the unconstrained problem of the VMD algorithm.

6. The rolling bearing performance degradation assessment method according to claim 5, characterized in that: The specific process of solving the problem by the multiplier alternating direction method includes: Step 1: Initialization and n = 0; is the first modal function, is the first center frequency, is the Lagrange multiplier, n is the number of data points; Step 2: m=m+1; Step 3: k = 1: K, and for all ω ≥ 0 Update; ω is the center frequency; and u k and the Fourier transform of λ; is the mode function at point n+1, is the amplitude, is the modal function when the number of data points is n and the number of decomposition layers is i. is the Lagrange multiplier, 2α is the quadratic penalty factor, ω is the center frequency, is the center frequency of point n, is the center frequency when the data point is n+1; Step 4: Update the Lagrangian operator λ: In the formula, τ is the noise tolerance parameter. In order to obtain a better denoising effect, τ = 0; is the Lagrange multiplier; Step 5: Repeat steps 2-4 until equation (11) is satisfied, then stop the iteration and output K IMF components: Among them, the value of ε is 10 -6 , is the nth mode function.

7. The rolling bearing performance degradation assessment method according to claim 1, characterized in that: The probability density function of the IMF component is: In the formula, A0 and B0 are mapping parameters, a i0 is the i+1th Lagrange multiplier of IMF, i=1, 2,…, I is the origin moment order, and x is the vibration signal.

8. The rolling bearing performance degradation assessment method according to claim 1, characterized in that: In step (3), the compensation distance evaluation specifically includes the following steps: S1: Assume that the probability density function eigenvector obtained after VMD decomposition of the normal vibration signal is X = [PDF 11 PDF 12 ……PDF 1k ], the probability density function eigenvector of the vibration signal to be measured is Y = [PDF 11 PDF 12 ……PDF 1k ;PDF 21 PDF 22 ……PDF 2k ; ...; PDF T1 PDF T2 ……PDF Tk ]; where PDF 11 is the first probability density of the first set of data, PDF 12 is the second probability density of the first set of data, PDF 1k is the kth probability density of the first set of data, PDF 21 is the first probability density of the second set of data, PDF 22 is the second probability density of the second set of data, PDF 2k is the kth probability density of the second set of data, PDF T1 is the first probability density of the Tth group of data, PDF T2 is the second probability density of the Tth group of data, PDF Tk is the kth probability density of the Tth group of data, T is the signal data group to be tested, and k is the number of decomposed modes; S2: Calculate the average intra-class distance between the feature vectors of the normal vibration signal and the signal to be tested: Wherein, i = 1, 2, ..., T, T is the signal data group to be measured, j = 1, 2, ..., k, k is the VMD decomposition mode number; S3: Calculate the inter-class distance of the feature vector of the signal to be tested: Among them, d b is the distance between classes, PDF (i+(i-1)k)1 is the first probability density of T group data, PDF ij is the jth probability density of the i-th group of data; j = 1, 2, …, k, k is the number of VMD decomposition modes; S4: Calculate d k and d b The variance factor v k and v b : S5: Calculate the compensation factor γ k : S6: In-class distance d k Increase the distance d between the upper classes b , and obtain the compensation distance evaluation index α k :

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