A PHM-based health state prediction method for rolling bearings

Abstract

The present invention discloses a method for predicting the health state of rolling bearings based on PHM, belonging to the technical field of fault prediction and health management, and comprising the following steps: acquiring vibration signals of the whole life of rolling bearings and extracting wavelet packet time-frequency features of the vibration signals; constructing an energy distribution map of the vibration signals in different frequency domains; obtaining vibration cumulative sequence values by using a deep stacked denoising autoencoder accumulator; normalizing the vibration cumulative sequence values to obtain a deep stacked denoising autoencoder cumulative health index; constructing a time-lagged window reconstruction sequence and continuously predicting the deep stacked denoising autoencoder cumulative health index by using a time-delay least squares support vector machine model; the present invention solves the problems of difficult acquisition of non-linear features and unreasonable selection of health prediction models during the prediction of the health state of rolling bearings in aviation and high-speed rail equipment.

Description

Technical Field

[0001] The present invention belongs to the technical field of fault prediction and health management, and particularly relates to a method for predicting the health state of rolling bearings based on PHM. Background Art

[0002] The PHM technology can predict the health state of equipment, improve the existing maintenance and management systems of large-scale equipment, and ensure the safe and reliable operation of equipment. In the health state prediction of equipment, features are extracted from the monitoring data of original sensors, reasonably transformed, health indicators of the equipment are established, and relevant models are constructed for prediction to obtain the health indicator values. According to the health indicator values, the changing trend of the health state of the equipment or its stage in the whole life cycle of the equipment can be judged, so as to carry out reasonable equipment management and maintenance. Accurate prediction is the basis and prerequisite of PHM health management.

[0003] The selection of health features is one of the keys to describing the health state of equipment. Usually, the extracted features are high-dimensional, which makes the calculation amount huge during data analysis and reduces the calculation efficiency. Therefore, a dimensionality reduction method is needed to process the data to improve the calculation efficiency. However, since the features of many aviation and high-speed rail equipment are non-linear, the data processing effects of linear dimensionality reduction methods such as PCA and linear discriminant method are not good. On the other hand, when the selection of the prediction model is unreasonable, the prediction accuracy will also be reduced. Rolling bearings in aviation and high-speed rail equipment are common and necessary. Therefore, a method that can accurately predict the changing trend of the health state of rolling bearings is urgently needed. Summary of the Invention

[0004] In view of the above deficiencies in the prior art, the present invention provides a method for predicting the health state of rolling bearings based on PHM, which is based on a deep stacked denoising autoencoder cumulative sum and time-delay least squares support vector machine. By predicting the health indicators of rolling bearings, the health state of the rolling bearings can be evaluated. The present invention solves the problems of difficult acquisition of non-linear features and unreasonable selection of health prediction models when predicting the health state of rolling bearings in aviation and high-speed rail equipment.

[0005] In order to achieve the above invention object, the technical solution adopted by the present invention is as follows:

[0006] The present invention provides a method for predicting the health state of rolling bearings based on PHM, including the following steps:

[0007] S1. Obtain the vibration signals of the rolling bearing during its whole life cycle, and extract the wavelet packet time-frequency features of the vibration signals;

[0008] S2. Normalize the wavelet packet time-frequency features and construct an energy distribution diagram of the vibration signals in different frequency domains;

[0009] S3. According to the energy distribution diagram, use the deep stacked denoising autoencoder to accumulate and obtain the vibration cumulative sequence value;

[0010] S4. Normalize the vibration cumulative sequence value to obtain the deep stacked denoising autoencoder cumulative health index;

[0011] S5. Construct a time-lagged window reconstruction sequence, and use the time-delay least squares support vector machine model to continuously predict the deep stacked denoising autoencoder cumulative health index.

[0012] Further, the calculation expression for normalizing the wavelet packet time-frequency feature in step S2 is as follows:

[0013]

[0014] where y represents the normalized energy feature value, y max represents the maximum value of the normalized energy feature value, y min represents the minimum value of the normalized energy feature value, x represents the energy feature value after wavelet packet transform, x min represents the minimum value of the energy feature values after wavelet packet transform, x max represents the maximum value of the energy feature values after wavelet packet transform.

[0015] Further, the deep stacked denoising encoder in step S3 includes several single-layer autoencoders stacked in sequence. Among them, the calculation expressions for the encoding mapping and decoding mapping of each single-layer autoencoder are as follows:

[0016]

[0017] where φ(·) represents the encoding mapping, c represents the output of the encoding, σ1 represents the activation function of the encoding, W1 represents the weight of the encoding, x′ represents the input of the encoding, b1 represents the bias of the encoding, represents the decoding mapping, y′ represents the output of the decoding, W2 represents the weight of the decoding, b2 represents the bias of the decoding.

[0018] Further, the loss function L(x′, y′) of each single-layer autoencoder is as follows:

[0019] L(x′, y′) = x′ - y′ 2

[0020] where represents the square root of the sum of the squares of each component after taking the difference between the input of the encoding and the output of the decoding.

[0021] Further, step S5 includes the following steps:

[0022] S51. Construct a time-lagged window reconstruction sequence, where the window size is m;

[0023] S52. Obtain a time-lagged matrix U and a prediction vector V respectively based on the time-lagged window reconstruction sequence:

[0024]

[0025]

[0026] where, u i represents the cumulative health index of the i-th deep stacked denoising autoencoder, and v i represents the prediction result of the cumulative health index of the i-th deep stacked denoising autoencoder, where i is a positive integer;

[0027] S53. Construct a time-delay least squares support vector machine model;

[0028] S54. Construct a Lagrange multiplier model based on the time-delay least squares support vector machine model;

[0029] S55. Take the partial derivative of the Lagrange multiplier model based on the Karush-Kuhn-Tucker conditions, and define the kernel function k(u k , v k ), to obtain the Lagrange multiplier coefficient matrix;

[0030] S56. Obtain the time-delay least squares support vector machine model according to the Lagrange multiplier coefficient matrix;

[0031] S57. Continuously predict the cumulative health index of the deep stacked denoising autoencoder based on the time-delay least squares support vector machine model.

[0032] Furthermore, the calculation expression of the time-delay least squares support vector machine model in step S53 is as follows:

[0033]

[0034]

[0035] where, min(·) represents finding the minimum value, J(w, e) represents the loss function of the time-delay least squares support vector machine model, w represents the weight coefficient vector, k represents the weight vector, e k represents the k-th error variable e, w T represents the transpose of the weight coefficient vector, γ represents the adjustable penalty coefficient, N represents the total number of weight vectors, v k represents the prediction result of the cumulative health index of the k-th deep stacked denoising autoencoder, and b represents the bias, Output of the decoder for the cumulative health index of the k-th deep stacked denoising autoencoder, where k = 1, 2, 3, …, N.

[0036] Furthermore, the calculation expression of the Lagrange multiplier model in step S54 is as follows:

[0037]

[0038] where L(w, b, e, a) represents the Lagrange multiplier result, and α k represents the k-th Lagrange multiplier coefficient.

[0039] Furthermore, the partial derivative result of the Lagrange multiplier model and the calculation expressions of the kernel function k(u k , v k ) in step S55 are as follows respectively:

[0040]

[0041]

[0042] where represents the transpose of the output of the decoder for the cumulative health index of the k-th deep stacked denoising autoencoder, represents the output of the decoder for the prediction result of the cumulative health index of k deep stacked denoising autoencoders.

[0043] Furthermore, the calculation expression of the time-delay least squares support vector machine model in step S56 is as follows:

[0044]

[0045] where f(u) represents the prediction result of the cumulative health index of the deep stacked denoising autoencoder, u represents the currently input cumulative health index of the deep stacked denoising autoencoder, and u k represents the cumulative health index of the k-th deep stacked denoising autoencoder.

[0046] The beneficial effects of the present invention are as follows: A method for predicting the health state of rolling bearings based on PHM provided by the present invention realizes the prediction of the service life of rolling bearings in aviation and high-speed rail equipment through the cumulative deep stacked denoising autoencoder and the time-delay least squares support vector machine, and can more accurately predict the remaining service life of the rolling bearings of high-speed traction motors based on vibration signals. This method is also applicable to the health state prediction after obtaining the non-linear characteristics of other components in aviation and high-speed rail equipment. Description of the Drawings

[0047] Figure 1It is the flowchart of the steps of a rolling bearing health state prediction method based on PHM in an embodiment of the present invention.

[0048] Figure 2 It is the schematic diagram of the normalized wavelet packet time-frequency feature in an embodiment of the present invention. Specific embodiments

[0049] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0050] As Figure 1 shown, in an embodiment of the present invention, the present invention provides a rolling bearing health state prediction method based on PHM, including the following steps:

[0051] S1. Obtain the vibration signals of the rolling bearing throughout its life, and extract the wavelet packet time-frequency features of the vibration signals;

[0052] S2. Normalize the wavelet packet time-frequency features and construct an energy distribution diagram of the vibration signals in different frequency domains; the calculation expression for normalizing the wavelet packet time-frequency features in step S2 is as follows:

[0053]

[0054] where y represents the normalized energy eigenvalue, y max represents the maximum value of the normalized energy eigenvalue, y min represents the minimum value of the normalized energy eigenvalue, x represents the energy eigenvalue after wavelet packet transformation, x min represents the minimum value among the energy eigenvalues after wavelet packet transformation, x max represents the maximum value among the energy eigenvalues after wavelet packet transformation;

[0055] As Figure 2 shown, in the embodiment of the present invention, through normalizing the wavelet packet time-frequency features, the normalization after wavelet packet feature extraction is realized. As the rolling bearing is used, the frequency of the vibration signal will change. It is difficult to judge the detailed composition of its frequency only by time-domain feature analysis. The wavelet packet analysis and the normalization process after feature extraction can obtain the energy distribution diagram of the vibration signal in different frequency domains, can analyze the high-frequency part more finely, and can adaptively select the frequency band matching the vibration signal spectrum;

[0056] S3, according to the energy distribution diagram, using the deep stacked denoising autoencoder to accumulate and obtain the vibration accumulation sequence value;

[0057] An autoencoder can reduce the noise in a signal by training the network. In terms of neural structure, an autoencoder is a feedforward neural network that contains an input layer, a hidden layer, and an output layer. The transformation from the input layer to the hidden layer is called encoding, and the transformation from the hidden layer to the output layer is called decoding. By expanding the autoencoder, a deep autoencoder can be obtained. The difference between a deep autoencoder and an autoencoder is the number of hidden layers. A deep autoencoder has more hidden layers, which can avoid the problem that traditional neural network structures are prone to falling into local minima, thereby learning more robust feature representations.

[0058] The accumulation method amplifies data changes by continuously accumulating the difference between the measured value and the standard value, and can more sensitively detect small changes. It accumulates the encoded output of the deep stacking denoising autoencoder of the vibration data, and uses the accumulated sequence values to show the degradation of the health status of the rolling bearing.

[0059] The deep stacked denoising encoder in step S3 includes a plurality of single-layer autoencoders stacked in sequence, wherein the calculation expressions of the encoding mapping and the decoding mapping of each single-layer autoencoder are as follows:

[0060]

[0061] Among them, φ(·) represents the encoding mapping, c represents the encoding output, σ1 represents the encoding activation function, W1 represents the encoding weight, x′ represents the encoding input, and b1 represents the encoding bias. represents the decoding mapping, y′ represents the decoding output, W2 represents the decoding weight, and b2 represents the decoding bias;

[0062] The loss function L(x′, y′) of each single-layer autoencoder is as follows:

[0063] L(x′,y′)=x′-y′ 2

[0064] Where, represents the square root of the sum of the squares of the components after the difference between the encoded input and the decoded output;

[0065] S4, normalize the vibration cumulative sequence value to obtain the cumulative health index of the deep stacked denoising autoencoder;

[0066] S5, construct a time-lagged window reconstruction sequence, and use the time-lagged least squares support vector machine model to continuously predict the cumulative health indicators of the deep stacked denoising autoencoder;

[0067] The step S5 comprises the following steps:

[0068] S51. Construct a time-lagged window reconstruction sequence, where the window size is m;

[0069] S52. Obtain a time-lagged matrix U and a prediction vector V respectively based on the time-lagged window reconstruction sequence:

[0070]

[0071]

[0072] where, u i represents the cumulative health index of the i-th deep stacked denoising autoencoder, and v i represents the prediction result of the cumulative health index of the i-th deep stacked denoising autoencoder, where i is a positive integer;

[0073] S53. Construct a time-delay least squares support vector machine model;

[0074] The calculation expression of the time-delay least squares support vector machine model in step S53 is as follows:

[0075]

[0076]

[0077] where, min(·) represents finding the minimum value, J(w,e) represents the loss function of the time-delay least squares support vector machine model, w represents the weight coefficient vector, k represents the weight vector, and e k represents the k-th error variable e, w T represents the transpose of the weight coefficient vector, γ represents the adjustable penalty coefficient, N represents the total number of weight vectors, v k represents the prediction result of the cumulative health index of the k-th deep stacked denoising autoencoder, b represents the bias, represents the output of the decoding for the cumulative health index of the k-th deep stacked denoising autoencoder, where k = 1, 2, 3,..., N;

[0078] S54. Construct a Lagrange multiplier model based on the time-delay least squares support vector machine model;

[0079] The calculation expression of the Lagrange multiplier model in step S54 is as follows:

[0080]

[0081] where, L(w,b,e,a) represents the Lagrange multiplier result, and α k represents the k-th Lagrange multiplier coefficient;

[0082] S55. Take the partial derivative of the Lagrange multiplier model based on the Karush-Kuhn-Tucker conditions and define the kernel function k(u k , v k ) to obtain the Lagrange multiplier coefficient matrix;

[0083] The calculation expressions for the partial derivative result of the Lagrange multiplier model and the kernel function k(u k , v k ) in step S55 are as follows:

[0084]

[0085]

[0086] Among them, represents the transpose of the output of the decoding of the cumulative health index of the k-th deep stacked denoising autoencoder, represents the output of the decoding of the prediction result of the cumulative health index of the k deep stacked denoising autoencoders;

[0087] S56. Obtain the time-delay least squares support vector machine model according to the Lagrange multiplier coefficient matrix;

[0088] The calculation expression of the time-delay least squares support vector machine model in step S56 is as follows:

[0089]

[0090] Among them, f(u) represents the prediction result of the cumulative health index of the deep stacked denoising autoencoder, u represents the currently input cumulative health index of the deep stacked denoising autoencoder, and u k represents the cumulative health index of the k-th deep stacked denoising autoencoder;

[0091] S57. Continuously predict the cumulative health index of the deep stacked denoising autoencoder based on the time-delay least squares support vector machine model.

Claims

1. A method for predicting the health state of a rolling bearing based on PHM, characterized in that, It includes the following steps: S1. Obtain the vibration signals of the full life of the rolling bearing, and extract the wavelet packet time-frequency characteristics of the vibration signals; S2. Normalize the wavelet packet time-frequency characteristics, and construct the energy distribution diagram of the vibration signals in different frequency domains; S3. According to the energy distribution diagram, use the deep stacked denoising autoencoder to accumulate and obtain the vibration cumulative sequence values; the deep stacked denoising encoder includes several single-layer autoencoders stacked in sequence. Among them, the calculation expressions of the encoding mapping and decoding mapping of each single-layer autoencoder are as follows: Among them, represents the encoding mapping, represents the output of the encoding, represents the activation function of the encoding, represents the weight of the encoding, represents the input of the encoding, represents the bias of the encoding, represents the decoding mapping, represents the output of the decoding, represents the weight of the decoding, represents the bias of the decoding; S4. Normalize the vibration cumulative sequence values to obtain the deep stacked denoising autoencoder cumulative health index; S5. Construct the time-lagged window reconstruction sequence, and use the time-delay least squares support vector machine model to continuously predict the deep stacked denoising autoencoder cumulative health index, which includes: S51. Construct a time-lag window reconstruction sequence, where the window size is m ; S52. Obtain a time-lag matrix and a prediction vector respectively based on the reconstructed sequences with time-lag windows and prediction vectors : Among them, represents the i th cumulative health index of the deep stacked denoising autoencoder, represents the prediction result of the i th cumulative health index of the deep stacked denoising autoencoder, where i is a positive integer; S53. Construct the time-delay least squares support vector machine model; S54. Construct the Lagrange multiplier model based on the time-delay least squares support vector machine model; S55. Take the partial derivative of the Lagrange multiplier model based on the Karush-Kuhn-Tucker conditions and define the kernel function , and obtain the Lagrange multiplier coefficient matrix; S56. Obtain the time-delay least squares support vector machine model according to the Lagrange multiplier coefficient matrix; S57. Continuously predict the deep stacked denoising autoencoder cumulative health index based on the time-delay least squares support vector machine model.

2. The PHM-based rolling bearing health state prediction method according to claim 1, wherein The calculation expression for normalizing the wavelet packet time-frequency characteristics in step S2 is as follows: Among them, represents the normalized energy eigenvalue, represents the maximum value of the normalized energy eigenvalue, represents the minimum value of the normalized energy eigenvalue, represents the energy eigenvalue after wavelet packet transform, represents the minimum value among the energy eigenvalues after wavelet packet transform, represents the maximum value among the energy eigenvalues after wavelet packet transform.

3. The PHM-based rolling bearing health state prediction method according to claim 2, wherein The loss function of each of the single-layer autoencoders is as follows: Among them, represents the square root of the sum of the squares of the components after taking the difference between the encoded input and the decoded output.

4. The PHM-based rolling bearing health state prediction method according to claim 1, wherein The calculation expression for the time-delay least squares support vector machine model in step S53 is as follows: Among them, represents finding the minimum value, represents the loss function of the time-delay least squares support vector machine model, represents the weight coefficient vector, k represents the weight vector, represents the k th error variable e , represents the transpose of the weight coefficient vector, represents the adjustable penalty coefficient, N represents the total number of weight vectors, represents the k th prediction result of the cumulative health index of the deep stacked denoising autoencoder, b represents the bias, represents the output of the decoding of the cumulative health index of the k th deep stacked denoising autoencoder, where, k = 1, 2, 3, …, N .

5. The PHM-based rolling bearing health state prediction method according to claim 4, characterized in that The calculation expression for the Lagrange multiplier model in step S54 is as follows: Among them, represents the Lagrange multiplier result, represents the k th Lagrange multiplier coefficient.

6. The PHM-based rolling bearing health state prediction method according to claim 5, wherein The partial derivative result of the Lagrange multiplier model and the kernel function in step S55 are calculated as follows: Among them, represents the transpose of the output of the decoding of the cumulative health index for the k th deep stacked denoising autoencoder, represents the output of the decoding of the prediction result of the cumulative health index for k deep stacked denoising autoencoders.

7. The PHM-based rolling bearing health state prediction method according to claim 6, wherein The calculation expression for the time-delay least squares support vector machine model in step S56 is as follows: Among them, represents the prediction result of the cumulative health index of the deep stacked denoising autoencoder, represents the cumulative health index of the current input deep stacked denoising autoencoder, represents the k th cumulative health index of the deep stacked denoising autoencoder.

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