A rolling bearing residual service life prediction method based on VMD-SSA-LSTM

Abstract

The application discloses a rolling bearing residual service life prediction method based on VMD-SSA-LSTM, and applies the method to bearing residual life prediction. ∞ Firstly, a fitness function based on L1 norm of fault feature is constructed. The fitness function utilizes the rolling bearing fault modeling knowledge; can effectively describe the fault pulse and cyclostationary characteristics, and improves the adaptability of VMD on the rolling bearing vibration signal. Secondly, the application proposes an IMF signal reconstruction method based on SES and HD, which improves the signal-to-noise ratio without losing the original signal. The reconstructed signal is used for rolling bearing RUL prediction, and the prediction accuracy is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of mechanical equipment fault prediction and health management, and relates to a rolling bearing residual service life prediction method based on VMD-SSA-LSTM. BACKGROUND

[0002] Rolling bearings are important mechanical components and are also one of the parts most prone to failure. Statistics show that in rotating equipment using rolling bearings, about 45%-55% of mechanical failures are caused by rolling bearings. Predicting the residual useful life (RUL) of rolling bearings can detect damage as early as possible and perform maintenance in advance, thereby avoiding machine failure. Therefore, the problem of predicting the residual useful life of rolling bearings has become a hot issue in the field of mechanical health management and fault prediction, and many prediction technologies have been developed.

[0003] RUL prediction is to predict the damage progression of a fault according to the current and future operating environment conditions and obtain the time when the expected function can no longer be performed within the expected range. At present, the RUL prediction of rolling bearings can be divided into model-based methods, data-driven methods and hybrid methods.

[0004] Model-based methods need to establish a series of mathematical or physical models to determine the degradation trend of the corresponding research object. Commonly used models for RUL prediction include Gaussian mixture model, Markov process model, proportional risk model and Wiener process model. However, the working conditions of rolling bearings are complex and diverse, and there are many factors affecting the service life of rolling bearings, so it is difficult to accurately establish a service life prediction mechanism model.

[0005] Data-driven is another RUL prediction method that does not need to consider the internal failure mechanism of rolling bearings, but directly maps the RUL value to the corresponding detection signal feature value for prediction. With the development of artificial intelligence and machine learning technologies, data-driven rolling bearing RUL prediction methods have been widely applied. Data-driven RUL methods mainly use machine learning techniques to explore the degradation of machinery from collected data, and then achieve RUL prediction through the construction of a neural network. Mainly artificial neural networks, Bayesian networks, support vector machines, etc. Among them, the long short-term memory neural network (LSTM) can effectively overcome the gradient vanishing or gradient explosion problem of RNN, so that the model has the ability to learn long-term dependencies and can effectively process sequence data. However, the application of neural networks to time series prediction needs to consider how to extract the features of historical sequences and combine them with neural networks. For rolling bearings, the running signal is noisy, and the signal is nonlinear and non-stationary. In addition, the characteristics of slight faults are not easy to detect and extract. Therefore, hybrid prediction methods have more advantages than the other two methods.

[0006] There are two types of methods for mixing. One is to use different prediction methods and obtain the final prediction result by weighting the RUL prediction results of different prediction methods, which is greatly affected by the weight. The other is to preprocess the original signal and model the processed signal to obtain the RUL prediction result. The preprocessing methods include wavelet analysis, empirical mode decomposition and VMD. VMD is an effective method for processing nonlinear and non-stationary signals. VMD obtains the center frequency and width of each decomposition component through iterative search of the variational mode, and finally adaptively realizes the frequency domain segmentation of the signal and the effective separation of each component, and eliminates the invalid noise in the signal. Existing researches have proved that VMD has fast calculation speed and strong anti-noise ability in signal processing. However, there are two key factors that determine the processing effect of VMD. First, the selection of decomposition mode number (k) and penalty factor (a) has a great influence on the stability of the algorithm. Second, the IMF obtained by decomposition has mode mixing, and it is necessary to evaluate and recombine the IMF to obtain the synthesized IMF signal as the input of the neural network. SUMMARY

[0007] The technical problem to be solved by the present application is to provide a method for predicting the remaining useful life of a rolling bearing, which can effectively solve the problems of incomplete feature extraction, poor robustness of the prediction model and low prediction accuracy in existing researches on the prediction of the remaining useful life of a rolling bearing.

[0008] To solve the above technical problems, the technical solution adopted by the present application comprises the following steps:

[0009] Step 1, the value ranges of the decomposition mode number k and the penalty factor a of VMD (variational mode decomposition) are [k min , k max ] and [a min , a max ] respectively, and the original vibration signal is subjected to VMD to obtain k layers of IMF components.

[0010] Step 2, according to the fault characteristic frequency calculation formula table of various fault types of the rolling bearing, the fault characteristic frequencies of various faults of the rolling bearing are calculated.

[0011] The fault characteristic frequency calculation formula table of various fault types of the rolling bearing is as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] where f o represents the outer raceway damage characteristic frequency, f i represents the inner raceway damage characteristic frequency, f b1 represents the rolling element damage, impact one side raceway characteristic frequency, f b2 represents the rolling element damage, impact both sides raceway characteristic frequency, f z1 represents the cage and inner ring contact friction characteristic frequency, f z2 represents the cage and inner ring contact friction characteristic frequency; f R is the rotating frequency of the rotating shaft; Z is the number of bearing balls; D P is the diameter of the bearing pitch circle; D B is the diameter of the bearing ball; θ is the contact angle of the ball and raceway.

[0019] Step 3, calculate the Lp / Lq norm F(i) of the k-layer IMF component at the fault characteristic frequency domain according to the following formula L∞ / L1 , where p = ∞, q = 1;

[0020]

[0021] where SES is the square envelope spectrum, and the calculation formula is SES[n] = |x[n] + j*Hilbert{x[n]}| 2 , Hilbert{.} represents the Hilbert transform; N is the number of groups into which the fault signal in the characteristic frequency domain segment is uniformly divided; n represents the nth group of fault signals, x[n] is the time domain signal of the fault characteristic frequency estimate f(i) of the nth group of fault signals; the estimate f(i) of the fault characteristic frequency is the solution value of any formula of formula (1) to formula (6) in step 2.

[0022] Step 4, add the L ∞ / L1 norms of the M fault characteristic frequency estimates f(i) contained in the entire characteristic frequency domain segment to construct the L ∞ / L1 norm of the IMF component;

[0023]

[0024] where M ≤ N; since VMD is performed on the original vibration signal to obtain k-layer IMF components, the final fitness function ff is:

[0025]

[0026] where g represents the layer IMF component.

[0027] Step 5, compare [kmin ,k max ] and [a min , a max ] range, and record the corresponding k and a values of the maximum ff(k best , a best ).

[0028] Specific traversal description: The specific value mode is: k and a start from the minimum value k min and a min , the step size is 1, and each k in the range [k min , k max ] will be combined with all a in the range [a min , a max ].

[0029] Step 6, VMD is performed again on the original vibration signal, the values of k and a are taken as (k best , a best ), and k best IMF components are obtained;

[0030] Step 7, the square envelope spectrum (SES) and Hausdorff distance (HD) of the k best IMF components obtained by signal decomposition are calculated, and the HD matrix is obtained:

[0031]

[0032] The calculation method of SES has been given in step 3;

[0033] Step 8, the L ∞ / L1 norm FS L∞ / L1 of each IMF component calculated is constructed into an FS vector;

[0034]

[0035] Multiply the HD matrix with the FS vector:

[0036]

[0037] Calculate the sum of all elements in the vector HFS The reconstruction factor r of each IMF component is obtained by the following formula:

[0038]

[0039] Finally, multiply the components of the IMF by the reconstruction factor r and sum to obtain the reconstructed signal X(t);

[0040]

[0041] Step 9, input the reconstructed signal X(t) into the LSTM network to obtain the rolling bearing residual life prediction result.

[0042] The LSTM network is a mature network.

[0043] The beneficial effects of the present application are:

[0044] An optimized VMD algorithm is proposed, and it is applied to the bearing residual life prediction. First, the fitness function based on the L ∞ / L1 norm of the fault feature is constructed. The fitness function utilizes the rolling bearing fault modeling knowledge; it can effectively describe the fault pulse and cyclostationary characteristics, and improve the adaptability of VMD for rolling bearing vibration signals. Secondly, an IMF signal reconstruction method based on SES and HD is proposed, which improves the signal-to-noise ratio without losing the original signal. The reconstructed signal is used for rolling bearing RUL prediction, which improves the prediction accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The specific flowchart of the embodiment of the present application.

[0046] Figure 2 It is the time domain graph of the original vibration signal of the rolling bearing.

[0047] Figure 3 It is the L ∞ / L1 norm fitness function optimized VMD method flowchart.

[0048] Figure 4 It is the IMF component time domain graph of the L ∞ / L1 norm fitness function optimized VMD.

[0049] Figure 5 IMF signal reconstruction flowchart.

[0050] Figure 6 It is the result of RUL estimation using the method in this paper.

[0051] Figure 7 It is the result of RUL estimation without using the method in this paper.

[0052] Figure 8 The above is the original signal and the below is the reconstructed signal. DETAILED DESCRIPTION

[0053] The present application will be further described below in conjunction with the drawings and examples.

[0054] Step 1, initialize the value range of VMD parameters k and alpha [k min ,k max] and [α min ,α max ] to the original vibration signal as shown in Figure 2

[0055] Step 2, according to the fault characteristic frequency calculation formula table of various fault types of the rolling bearing, the fault characteristic frequency of the rolling bearing is calculated.

[0056] In step 2, according to the fault characteristic frequency calculation formula table of various fault types of the rolling bearing, the table is as follows:

[0057] Table 1 fault characteristic frequency calculation formula table of various fault types of the rolling bearing

[0058]

[0059] Wherein, is the rotating frequency of the rotating shaft; Z is the number of bearing balls; D P is the diameter of the bearing pitch circle; D B is the diameter of the bearing ball; θ is the contact angle of the ball and the raceway.

[0060] Step 3, according to the following formula, the Lp / Lq norm F(i) of the k-layer IMF component fault characteristic frequency domain is calculated L∞ / L1 , wherein p=∞, q=1;

[0061]

[0062] Wherein, SES is the square envelope spectrum, the calculation formula is SES[n]=|x[n]+j*Hilbert{x[n]}| 2 , Hilbert{.} represents Hilbert transform; N is the number of groups of the fault signal in the characteristic frequency domain segment which is uniformly divided; n represents the nth group of fault signal, x[n] is the time domain signal of the fault characteristic frequency estimation value f(i) of the nth group of fault signal; the estimation value f(i) of the fault characteristic frequency is the solution value of any formula of formula (1)-formula (6) in step 2.

[0063] Step 4, according to the flow of Figure 3 , the L ∞ / L1 norm of the M fault characteristic frequency estimation values f(i) contained in the whole characteristic frequency domain segment is added to construct the L ∞ / L1 norm of the IMF component;

[0064]

[0065] Wherein, M≤N; since the original vibration signal is subjected to VMD to obtain k-layer IMF component, the finally obtained fitness function ff is: ​

[0066]

[0067] where g denotes the gth IMF component.

[0068] Step 5, compare the size of ff obtained by different k and a in the range of [k min ,k max ] and [a min ,a max ], and record the corresponding k and a values (k best ,a best ) of the largest ff.

[0069] Specific traversal description: the specific value mode is: k and a start from the minimum value k min and a min , and the step is 1. Each k in the range of [k min ,k max ] will be combined with all a in the range of [a min ,a max ].

[0070] Step 6, VMD is performed again on the original vibration signal, and the values of k and a are taken as (k best ,a best ), k best IMF components are obtained;

[0071] Step 7, reconstruct the IMF signal as shown in the flow Figure 5 Step 7, calculate the square envelope spectrum (SES) and Hausdorff distance (HD) of the k best IMF components obtained by signal decomposition, and obtain the HD matrix:

[0072]

[0073] The calculation method of SES has been given in step 3;

[0074] Step 8, construct the FS vector of the L ∞ / L1 norm FS L∞ / L1 of each IMF component calculated;

[0075]

[0076] Multiply the HD matrix with the FS vector:

[0077]

[0078] Calculate the sum of all elements in the vector HFS The reconstruction factor r of each IMF is obtained by:

[0079]

[0080] Finally, the components of the IMF are multiplied by the reconstruction factor r and summed to obtain the reconstructed signal X(t);

[0081]

[0082] Step 9, input the reconstructed signal X(t) into the LSTM network to obtain the rolling bearing residual life prediction result. As shown in Figure 6 .

[0083] Embodiment:

[0084] Figure 6 The prediction result graph obtained by using the method is shown in Figure 7 , and the prediction result graph obtained without using the method is shown in Figure 8 . It can be found that the prediction accuracy is improved by using the method.

Claims

1. A method for predicting the remaining service life of rolling bearings based on VMD-SSA-LSTM, characterized in that The following steps are involved: Step 1: Initialize the VMD decomposition mode number k and the penalty factor α to be in the range of [k min ,k max ] and [α min ,α max ], perform VMD on the original vibration signal to obtain the k-layer IMF components; Step 2: Calculate the characteristic frequencies of various rolling bearing faults according to the calculation formula table of the characteristic frequencies of various rolling bearing fault types; Step 3: Calculate the Lp / Lq norm F(i) of the k-layer IMF component fault characteristic frequency domain. L∞ / L1 ; Step 4: L of the M fault characteristic frequency estimation values ​​f(i) contained in the entire characteristic frequency domain segment ∞ / L1 norm is added to construct the L of IMF component ∞ / L1 norm; Step 5: Compare [k min ,k max ] and [α min ,α max ] range, and record the values ​​of k and α corresponding to the maximum ff (k best ,α best ); Step 6: Perform VMD on the original vibration signal again, and the values ​​of k and α are taken as (k best ,α best ), get k best IMF components; Step 7: Reconstruct the IMF signal and calculate the k obtained by signal decomposition best The square envelope spectrum and Hausdorff distance of the IMF components are used to obtain the HD matrix: Step 8: The L of each IMF component calculated ∞ / L1 norm FS L∞ / L1 Construct a FS vector, multiply the HD matrix by the FS vector, calculate the sum of all elements in the vector HFS, calculate the reconstruction factor r of each IMF quantity, and finally multiply the components of the IMF by the reconstruction factor r and sum them to obtain the reconstructed signal X(t); Step 9: Input the reconstructed signal X(t) into the LSTM network to obtain the remaining life prediction result of the rolling bearing; Lp / Lq norm F(i) of step 3 L∞ / L1 , where p = ∞, q = 1; Where SES is the square envelope spectrum, and the calculation formula is SES[n]=|x[n]+j*Hilbert{x[n]}| 2 , Hilbert{.} represents Hilbert transform; N is the number of groups into which the fault signal of the characteristic frequency domain segment is evenly divided; n represents the nth group of fault signals, and x[n] is the time domain signal of the fault characteristic frequency estimation value f(i) of the nth group of fault signals; L of the IMF component described in step 4 ∞ / L1 norm; Where M≤N; since VMD is performed on the original vibration signal to obtain k layers of IMF components, the final fitness function ff is: Among them, g represents the layer-th IMF component.

2. The method for predicting the remaining service life of a rolling bearing based on VMD-SSA-LSTM according to claim 1 is characterized in that Step 5: Compare [k min ,k max ] and [α min ,α max The size of ff obtained by taking different values ​​of k and α within the range of ] is specifically implemented as follows: k and α start from the minimum value k min and α min Start taking, step size is 1, [k min ,k max Each k in the range [α min ,α max ] all α in the range are combined.

3. The method for predicting the remaining service life of a rolling bearing based on VMD-SSA-LSTM according to claim 2 is characterized in that Perform VMD again on the original vibration signal, and the values ​​of k and α are taken as (k best ,α best ), get k best IMF components.

4. The method for predicting the remaining service life of a rolling bearing based on VMD-SSA-LSTM according to claim 3 is characterized in that The k obtained by calculating the signal decomposition in step 7 best The square envelope spectrum and Hausdorff distance of the IMF components are used to obtain the HD matrix:

5. The method for predicting the remaining service life of a rolling bearing based on VMD-SSA-LSTM according to claim 4 is characterized in that Step 8: The L of each IMF component calculated ∞ / L1 norm FS L∞ / L1 Construct into FS vector; Multiply the HD matrix by the FS vector: Calculate the sum of all elements in the vector HFS The reconstruction factor r of each IMF quantity is obtained by the following formula: Finally, the reconstructed signal X(t) is obtained by multiplying the IMF components by the reconstruction factor r and summing them up.

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