CN114861349A

CN114861349A - Rolling bearing RUL prediction method based on model migration and wiener process

Info

Publication number: CN114861349A
Application number: CN202210429223.4A
Authority: CN
Inventors: 王玉静; 李达; 康守强; 梁欣涛; 谢金宝; 王庆岩; 孙宇林
Original assignee: Harbin University of Science and Technology
Current assignee: Harbin University of Science and Technology
Priority date: 2022-04-22
Filing date: 2022-04-22
Publication date: 2022-08-05
Anticipated expiration: 2042-04-22
Also published as: CN114861349B

Abstract

A rolling bearing RUL prediction method based on model migration and a wiener process relates to the technical field of rolling bearing service life prediction and is used for solving the problems that the service life percentage is used as a label to difficultly and accurately describe the rolling bearing degradation process and the bearing service life prediction accuracy under different working conditions is low. The technical points of the invention comprise: extracting each vibration statistical characteristic of the whole-life rolling bearing under a certain working condition, constructing a health index model by utilizing a single-layer NCAE network and an SOM network, and marking a rolling bearing frequency domain amplitude sequence by using a health index; training a combined network combining a deep NCAE network and a feedforward neural network FNN by using source domain data to obtain a pre-training model; and (3) fine adjustment is carried out by utilizing the target domain data to obtain a rolling bearing performance degradation model, and a wiener process model is established by utilizing the increment of the performance degradation index quantization value to realize the RUL prediction of the rolling bearing under different working conditions. The method is suitable for the technology for predicting the residual service life of the rolling bearing.

Description

Rolling bearing RUL prediction method based on model migration and wiener process

Technical Field

The invention relates to the technical field of rolling bearing service life prediction, in particular to a rolling bearing RUL prediction method based on model migration and a wiener process.

Background

Rolling bearings are an important component of rotary machines, used in modern mechanical devices such as wind turbines, automotive transmissions, aeroengines and the like [ 1]. The performance of the bearing is degraded continuously due to continuous abrasion in work, the service life is reduced gradually, and once the bearing fails, the safe operation of mechanical equipment is directly influenced [ 2]. Therefore, prediction of the Remaining service Life (RUL) of the rolling bearing is becoming more and more important to the researchers.

Existing methods for predicting the remaining life of equipment can be divided into three categories, model-based, data-driven, and two-in-one methods [3 ]. In the model-based prediction method, document [4] updates the Paris-Erdogan model parameters using particle filtering, thereby better predicting the bearing RUL. Document [5] realizes RUL prediction of a rear bearing of a wind turbine generator based on an accumulated damage model and a rain flow counting method. In the literature [6], a prediction model is derived based on a reliability model of Weibull distribution, so that the rolling bearing RUL can be accurately predicted.

Data-driven methods have become mainstream prediction methods ^[7] There are a Machine Learning (ML) based method and a statistical data driven method. In recent years, depth science has been usedThe learning has strong deep feature extraction capability, so that the deep learning is gradually and widely applied to the aspect of life prediction. Document [8]The rolling bearing RUL prediction method combining the convolutional neural network and the long-time memory neural network is provided, and the method achieves a good prediction effect. Document [9]]Deep features of the rolling bearing frequency domain amplitude signal are extracted by using a full convolution variational self-coding network, and then a full convolution neural network is introduced to construct a prediction model, so that the overall prediction precision is improved. Document [10]]The rolling bearing RUL is predicted by using a full-parameter dynamic learning deep belief network, and experiments prove that compared with the traditional deep belief network, the convergence rate of the method is improved. Document [11]The improved sparse automatic encoder is used for extracting data characteristics, the characteristics are input into the Bi-LSTM network to predict the service life of the bearing, and experiments prove that compared with the traditional sparse automatic encoder, the model has higher convergence speed.

The service life percentages of the above documents are used as labels of the life cycle data of the rolling bearing, and the nonlinear degradation process of the bearing is difficult to accurately describe. Meanwhile, in actual work, the working condition of the rolling bearing is often changed, the performance degradation process of the bearing under different working conditions may be different, and a certain difference also exists in data distribution, and the above documents do not consider the situation of the change of the working condition. Therefore, there is a need for a more efficient method for predicting the remaining life of a rolling bearing under different operating conditions.

In recent years, there has been a rapid development of migration learning, which applies domain knowledge learned by a source domain to a target domain, thereby improving the ability to solve a target task. In the field of rolling bearing RUL prediction under different working conditions, a transfer learning method is also developed to a certain extent. Document [12] proposes a migratable convolutional neural network learning domain invariant feature to predict the RUL of a rolling bearing. Document [13] proposes a residual life prediction method based on depth model migration, which completes the life prediction of the rolling bearing under different working conditions. Document [14] uses a time convolution network to construct a health index of a rolling bearing under a certain working condition and uses the health index as degradation trend meta-information, and then uses depth time sequence characteristic migration to realize life prediction of the rolling bearing under other working conditions.

The above prediction literature regarding the transfer learning does not fully consider the characteristic that the degradation process of the rolling bearing has a random process, and if the probability distribution of the service life is obtained, it is convenient to quantify the uncertainty of the service life. In recent years, stochastic process models have become increasingly popular for use in life prediction. In the document [15], a performance degradation index of a bearing is established by using Root Mean Square (RMS) values of horizontal and vertical vibration signals of a rolling bearing, and a binary wiener process model is constructed according to the index, so that the RUL of the bearing is predicted. Document [16] proposes a bearing RUL prediction method based on a binary mixed random process, and a combined probability density function of the residual life is constructed by selecting a Gamma process and a wiener process to predict the residual life. Document [17] proposes the concept of a first prediction point by selecting RMS of an original vibration signal of a rolling bearing as a performance degradation index of the bearing, and calculates RUL using a wiener process method. Although the above documents use a random process model method to predict the bearing RUL and perform uncertainty expression on the prediction result of the rolling bearing RUL, the shallow layer characteristics obtained by statistical indexes are all used to construct performance degradation indexes, which reflect that the bearing degradation trend needs to be further improved.

Disclosure of Invention

In view of the above problems, the invention provides a rolling bearing RUL prediction method based on model migration and wiener processes, which is used for solving the problems that the service life percentage is used as a label to difficultly and accurately describe the rolling bearing degradation process and the bearing service life prediction accuracy under different working conditions is not high.

A rolling bearing RUL prediction method based on model migration and a wiener process comprises the following steps:

acquiring a time domain vibration signal of a full-life rolling bearing under a working condition A as source domain data, and acquiring a time domain vibration signal of a full-life rolling bearing under a working condition B as target domain data;

inputting the source domain data and the target domain data into a health index model based on a single-layer non-negative constraint self-encoder network and a self-organizing feature mapping network, and respectively obtaining a health index label of the source domain data and a health index label of the target domain data;

preprocessing the source domain data and the target domain data;

combining the preprocessed source domain data and the health index labels of the source domain data, inputting the source domain data and the health index labels of the source domain data into a source domain pre-training model based on a deep non-negative constraint self-encoder network and a feedforward neural network for training, and obtaining source domain pre-training model parameters; the source domain pre-training model parameters comprise weight parameters;

migrating the source domain pre-training model parameters to a target domain network based on a deep non-negative constraint self-encoder network and a feedforward neural network to serve as initial network parameters; combining the preprocessed target domain data and the health index label of the target domain data, inputting the target domain network based on a deep nonnegative constraint self-encoder network and a feedforward neural network for fine tuning training, and obtaining a rolling bearing performance degradation model;

inputting the preprocessed non-full-life label-free rolling bearing time domain vibration signal to be predicted into the rolling bearing performance degradation model to obtain a bearing performance degradation index;

calculating the increment of the bearing performance degradation index according to the wiener process, wherein the increment obeys normal distribution, so as to obtain the mean value and the standard deviation of the normal distribution;

and inputting the mean value and the standard deviation into a mathematical model constructed based on a wiener process to obtain the residual service life of the non-full-life label-free rolling bearing to be predicted.

Further, the working condition comprises load and rotating speed, and the working condition A is different from the working condition B.

Further, the preprocessing is to perform Fourier transform on the rolling bearing time domain vibration signal to obtain a frequency domain amplitude sequence.

Further, the obtaining process of the health index label of the source domain data and the health index label of the target domain data comprises:

extracting time domain characteristics, time-frequency domain characteristics and trigonometric function-based characteristics of a rolling bearing time domain vibration signal, inputting the time domain characteristics, the time-frequency domain characteristics and the trigonometric function-based characteristics into a single-layer non-negative constraint self-encoder network to obtain output characteristics, and calculating the correlation of the output characteristics;

the relevance of the output features is sorted in a descending order, the output features corresponding to the first N groups of relevance with the relevance sorted in the front order are input into a self-organizing feature mapping network for training, and an input vector is represented as x _k ＝{x _1k ,x _2k ,...,x _nk }，k＝1,2,…,q，x _k Is the n-dimensional feature of each time point, q is the number of time points, omega _c For the vector characterization of the best matching neuron, the health indicator H at each time point is calculated as follows:

H＝f{||x _k -ω _c ||}

wherein f represents normalization.

Further, the time domain features include RMS, standard deviation, maximum, minimum, peak-to-peak, kurtosis index, waveform index, mean, pulse index, and rectified mean; the time-frequency domain features include band energies and band energy ratios; the trigonometric function-based features include IHS standard deviation.

Further, the correlation calculation formula of the output characteristics of the single-layer non-negative constraint self-encoder network is as follows:

wherein, F _r Representing the characteristic value corresponding to the r sampling point;

represents the average of all characteristic values; l _r The number of the sampling points is represented,

an average value representing the number of sampling points; t represents the total number of sample points.

Further, the depth non-negative-restriction self-encoder network is formed by cascading a plurality of non-negative-restriction self-encoder networks.

Further, the mathematical model constructed based on the wiener process is as follows:

wherein t represents the remaining life; omega _W Represents a threshold value; μ represents a mean value; σ represents the standard deviation; x ₀ A quantized value representing an index of bearing performance degradation at the present time.

The beneficial technical effects of the invention are as follows:

the invention provides a method for predicting the residual life of a rolling bearing based on model migration and a wiener process, which utilizes fast Fourier transform to obtain frequency domain amplitude sequences of the bearing under different working conditions; extracting each vibration statistical characteristic of the full-life rolling bearing under a certain working condition, constructing a health index by utilizing a single-layer non-negative constraint self-encoder (NCAE) and a self-organizing feature mapping network (SOM), marking a frequency domain amplitude sequence by using the index, taking the marked frequency domain amplitude sequence as source domain data, and similarly, processing vibration signals of the full-life rolling bearing under other working conditions and taking the vibration signals as target domain data; training a combined network combining a deep NCAE network and a Feedforward Neural Network (FNN) by using source domain data to obtain a pre-training model; and (3) fine adjustment is carried out by utilizing the target domain data to obtain a rolling bearing performance degradation model, and a wiener process model is established by utilizing the increment of the performance degradation index quantization value to realize the RUL prediction of the rolling bearing under different working conditions. Through experimental verification, compared with a reference, the average error absolute value of the prediction of the residual life of the rolling bearing is reduced by at least 4.29%, and the average score is improved by at least 0.016.

Drawings

FIG. 1 is a diagram of a self-encoder structure;

FIG. 2 is a schematic diagram of a SOM network architecture;

FIG. 3 is a flow chart of a health index construction for a bearing according to an embodiment of the present invention;

FIG. 4 is a schematic structural view of a degradation model of the rolling bearing performance in the embodiment of the present invention;

FIG. 5 is a schematic diagram of model migration in an embodiment of the present invention;

FIG. 6 is a block flow diagram of a rolling bearing RUL prediction method based on model migration and wiener process according to an embodiment of the present invention;

FIG. 7 is an exemplary diagram of a time-domain signal of original data of an experimental bearing 1_1 according to an embodiment of the present invention;

FIG. 8 is an exemplary frequency domain amplitude signal diagram of the experimental bearing 1_1 according to an embodiment of the present invention;

FIG. 9 is an exemplary graph of a characteristic trend curve of the experimental bearing 1_1 according to the embodiment of the present invention;

FIG. 10 is an illustration of health indicators for an experimental bearing 1_1 in an embodiment of the present invention;

FIG. 11 is a loss function for an experimental first layer NCAE network in an embodiment of the present invention;

FIG. 12 is a loss function for an experimental second layer NCAE network in an embodiment of the present invention;

FIG. 13 is a loss function for an experimental third layer NCAE network in an embodiment of the present invention;

FIG. 14 is an illustration of performance degradation indicators for the experimental bearing 3_3 in an embodiment of the present invention;

FIG. 15 is a probability density function of the remaining service life of the experimental bearing 3_3 in the embodiment of the present invention;

FIG. 16 is a graph showing the simulation result of the degradation process of the experimental bearing 3_3 according to the embodiment of the present invention;

FIG. 17 shows the RUL predicted probability density function for different monitoring points in the example of the present invention.

Detailed Description

In order that those skilled in the art will better understand the disclosure, exemplary embodiments or examples of the disclosure are described below with reference to the accompanying drawings. It is obvious that the described embodiments or examples are only some, but not all embodiments or examples of the invention. All other embodiments or examples obtained by a person of ordinary skill in the art based on the embodiments or examples of the present invention without any creative effort shall fall within the protection scope of the present invention.

The invention provides a novel bearing service life prediction method, which aims at solving the problems that the service life percentage is used as a label to difficultly describe the degradation process of a rolling bearing accurately and the bearing service life prediction accuracy under different working conditions is low. In order to better describe the degradation process of a full-life bearing under a certain working condition, a bearing health index is constructed by utilizing a single-layer non-Negative Constrained Auto Encoder (NCAE) network and a Self-organizing feature mapping (SOM) network; acquiring a frequency domain amplitude sequence of the bearing through fast Fourier transform, taking the health index as a label corresponding to the frequency domain amplitude sequence, and then taking the frequency domain amplitude sequence as source domain data; constructing health indexes of the bearing under other working conditions, acquiring a frequency domain amplitude sequence of the bearing, and taking the frequency domain amplitude sequence as target domain data; a performance degradation index of the rolling bearing is constructed by introducing a combined Network based on a deep NCAE Network and a feed-Forward Neural Network (FNN). And establishing a wiener process model by utilizing the increment of the performance degradation index quantized value, and realizing the RUL prediction of the rolling bearing under different working conditions.

The technical solution of the present invention will be explained in detail below.

The embodiment of the invention firstly explains the process of constructing the bearing health index by utilizing the single-layer NCAE network and the SOM network, firstly utilizes the NCAE network to extract the signal characteristics, and then obtains the health index through the SOM network.

An Auto Encoder (AE) is composed of an encoder and a decoder. For sample set x ═ x ₁ ,x ₂ ,...,x _i ,...,x _m }，x _i ＝{x ₁ ,x ₂ ,...,x _D }，x _i ∈[0,1] ^D M is the number of samples, D is the sample dimension, and the encoder reduces each input vector (high-dimensional feature) x to a low-dimensional feature S ═ S ₁ ,S ₂ ,...,S _i ,...,S _m }，S _i ∈[0,1] ^f . Reconstructing an original input x based on a reconstructed coding vector S of an f-dimensional feature space, and recording a reconstructed vector set as y ═ y ₁ ,y ₂ ,...,y _i ,...,y _D }，y _i ∈[0,1] ^D Wherein, the activation functions of the encoder and the decoder usually adopt sigmoid functions.

On the network structure, the NCAE network and the conventional self-codingThe same AE as shown in FIG. 1 has the structure of encoder and decoder ^[18] . The difference is that the cost function of the NCAE network training considers the non-negative sparse constraint limit. Model parameter set [ theta ] for minimizing reconstruction errors in encoder and decoder architectures ₁ ,θ ₂ }＝{W ₁ ,b ₁ ,W ₂ ,b ₂ The reconstruction error based on the squared error can be calculated by equation (1).

For a conventional AE, its cost function is typically:

wherein,

for the weight decay constraint term to avoid overfitting, λ is the coefficient of the equilibrium weight constraint term, s _l The number of layer l neuron nodes is,

is the weight parameter between the jth neuron at the l < th > layer and the ith neuron at the l +1 < th > layer.

Embedding non-negative constraint in the self-encoder, and considering decay constraint term of weight in formula (2) to reduce the number of non-negative weight in each layer as much as possible

Is defined as:

the non-negative constraint term is beneficial to improving the sparsity of the traditional self-encoder and reducing the reconstruction error of the self-encoder. Regarding sparseness, let μ _j (x _r ) Representing an input x _r If the activation degree of the hidden neuron j is small, the average activation degree of the neuron is defined as formula (4).

Setting average activation degree

p is a parameter close to zero. A divergence function based on Kullback-Leibler (KL) is used as a sparse penalty term, and the KL divergence is defined as shown in a formula (5).

In the formula,

the activation vector is averaged for the hidden neurons. The expression of the cost function of the self-encoder with embedded non-negative constraints is shown in formula (6).

The NCAE training objective is to make the cost function J _NCAE (W, b) minimizing, and adopting a gradient descent algorithm of an L-BFGS quasi-Newton method.

Effective feature extraction from the original vibration signal of the rolling bearing is the key for realizing RUL prediction, but the arbitrary single vibration statistical feature of the bearing can not well reflect the degradation condition of the bearing ^[19] . Therefore, on the basis of the extracted multiple features, the SOM network is used for feature reduction, and the health index is constructed. The SOM network consists of an input layer and an output layer, wherein the input layer is arranged in a form of a single-layer neuron; each neuron of the output layer is connected to other neurons in its vicinity, i.e., in a planar arrangement. The SOM network structure is shown in fig. 2.

To reduce the input redundancy characteristic of the SOM network, the output characteristic of the NCAE network is selected. The general flow of constructing the health index is shown in fig. 3. The detailed steps for constructing the bearing health index are as follows:

1) and extracting characteristics of a time domain, a time-frequency domain, a trigonometric function and the like of the original vibration signal of the bearing, inputting the characteristics into the NCAE network, and obtaining the output characteristics of the NCAE network.

2) The correlation of the NCAE output features is calculated and the features with higher correlation are selected as the input to the SOM network.

3) Training the SOM network, setting the number of neurons of the output layer as d, and setting the maximum training times T, omega _c For vector characterization of best-matching neurons, the input vector is x _k ＝{x _1k ,x _2k ,...,x _nk }，k＝1,2,…,q，x _k For the n-dimensional features at each time point, q is the number of time points.

4) Calculating the health index H of each time point after training, wherein the formula is shown as (7):

H＝f{||x _k -ω _c ||} (7)

wherein f represents normalization.

And after the health indexes are obtained, constructing a performance degradation model based on the deep NCAE network. The rolling bearing performance degradation model consists of a deep NCAE network and a feedforward neural network, deep features are extracted by using the deep NCAE network, and then a quantitative value of a performance degradation index of the test bearing is obtained through the FNN network. The overall network structure is shown in fig. 4.

Since the NCAE network is a three-layer network and does not belong to a deep network, the characteristics of complex data are difficult to learn for evaluating the performance degradation of the bearing. Therefore, a plurality of NCAEs are cascaded to form a deep NCAE network, so that the deep characteristics of the rolling bearing frequency domain signal are extracted, and a foundation is laid for constructing a rolling bearing performance degradation model. The deep NCAE network has excellent performance in the aspect of extracting deep characteristics, but is an unsupervised learning network, and the FNN network is connected behind the deep NCAE network, so that a network model for measuring the performance degradation degree of a bearing is formed.

The FNN network training process comprises the following steps:

1) the number of neuronal nodes is determined.

The FNN network consists of a last hidden layer, a full connection layer and an output layer of the deep NCAE network. The FNN network is constructed by determining the number m of neuron nodes of the full connecting layer, but no unified standard is used for determining m. In a BP network, the number of hidden layer neuron nodes is generally determined using equations (8) to (10).

m＝log ₂ n (8)

Where α represents an integer between 1 and 10 and n represents the number of output layer neuron nodes. The invention uses the idea of BP network as reference, and adopts m as log ₂ n to determine the value of the FNN fully-connected layer neuron node number m.

2) And calculating hidden layer output.

According to input x _i Connection weight ω between input layer and hidden layer _ij And an offset value a _j Computing hidden layer output F _j 。

In the formula, l is the number of hidden layer nodes; f is the hidden layer activation function.

3) And outputting layer calculation.

Outputting F from hidden layer _j Connecting the weight ω _jk And an offset value b _k And obtaining the network output.

Wherein m is the number of samples, o _i Is output by the network.

4) And (4) error calculation.

In the formula, y _i To train the labels. And finding the most suitable w and b by using a random gradient descent method to minimize the cost function.

A combined network is constructed based on a deep NCAE network and an FNN network, and a foundation can be laid for predicting the residual service life of the bearing under different working conditions by subsequent model migration.

The method comprises the steps of training a combined network formed by a deep NCAE network and a FNN network by using source domain data to obtain a pre-trained model, transferring weight parameters of the pre-trained model network to a target domain network, freezing the deep NCAE of the target domain network, initializing the FNN network and carrying out fine adjustment by using the target domain data. A schematic diagram of the model migration process is shown in fig. 5.

And after obtaining the performance degradation model of the rolling bearing, predicting the service life of the rolling bearing to be predicted by using the model. First, the RUL prediction based on the wiener process is described.

The wiener process is also known as brownian motion process. A wiener process model is established by using the performance degradation index of the rolling bearing, and the expression of the wiener process is shown as a formula (15).

X(t)＝X(0)+μt+σB(t) (15)

Where μ denotes a drift coefficient, σ denotes a diffusion coefficient, and b (t) denotes a standard wiener process. X (t) represents a quantized value of a performance degradation indicator of the bearing at time t.

If the quantized value of the performance degradation index of the bearing is subjected to the wiener process, the increment of the performance degradation index of the bearing is subjected to normal distribution, as shown in formula (16).

ΔX _i ～N(μΔt _i ,σ ² Δt) (16)

According to the property of the wiener process, knowing the quantized value of the performance degradation index of the bearing at the current moment, the probability density function of the residual life t can be deduced, as shown in formula (17).

Wherein, ω is _W Is a threshold value, X ₀ The quantized value of the performance degradation index of the bearing at the current moment is obtained.

As can be seen from equation (17), the probability density function includes two unknown parameters (μ, σ), and can be solved by the maximum likelihood estimation method. From equation (16), a likelihood function of the model parameters (μ, σ) can be obtained, as shown in equation (18).

Based on equation (18), the partial derivatives are calculated for μ and σ, and the maximum likelihood estimates for μ and σ are expressed by equations (19) and (20), respectively.

And (4) calculating the increment of the FNN network output result (namely the performance degradation index of the tested bearing), and bringing the obtained maximum likelihood estimated values of mu and sigma into the formula (17), so as to obtain a probability density function of the residual service life of the tested bearing, wherein the peak point of the probability density function corresponds to the moment, namely the residual service life.

The flow of predicting the remaining service life of the rolling bearing based on the model migration and wiener process is shown in fig. 6. The method comprises the following specific steps:

1) data pre-processing

Extracting time domain characteristics, time-frequency domain characteristics and 27 groups of vibration statistical characteristics based on trigonometric functions and the like from the original vibration signals of the full-life bearing, wherein the time-frequency domain characteristics are 8 frequency band energies and frequency band energy ratios obtained by performing 3-layer wavelet packet decomposition on the original signals. The vibration statistics are shown in table 1.

TABLE 1 statistical characteristics of vibrations

2) Construction of Rolling bearing health index

And normalizing each initial characteristic to be used as the input of the single-layer NCAE network to obtain the output characteristic, and calculating the correlation C of the output characteristic. In order to reduce redundant features, the first groups of features with the highest correlation are selected to be input into the SOM network and trained. The correlation C is represented by equation (21).

And (4) calculating the health index of the bearing according to the formula (7), and using the index as a label of the frequency domain amplitude sequence of the original vibration signal of the rolling bearing after FFT.

3) Source domain model training

Acquiring a frequency domain amplitude sequence of a full-life rolling bearing with a label under a certain working condition, and taking the frequency domain amplitude sequence as source domain data; this data is used as input to a deep NCAE and FNN combination network, which is pre-trained.

4) Construction of rolling bearing performance degradation model

And acquiring a frequency domain amplitude sequence with a label of the full-life rolling bearing under other working conditions, taking the frequency domain amplitude sequence as target domain data, transferring weight parameters of a pre-training model network to the target domain network, freezing target domain depth NCAE network parameters, and carrying out fine adjustment by using the target domain data so as to construct a rolling bearing performance degradation model.

5) Testing phase

And taking the data of the non-full-life bearing as a test set, inputting the data into the rolling bearing performance degradation model, and acquiring the performance degradation index of the rolling bearing in the test set.

6) Remaining life prediction

And (3) calculating the increment of the quantized value of the performance degradation index by using the performance degradation index obtained in the step 5), carrying in the formula (19) and the formula (20) to obtain the maximum likelihood estimated values of mu and sigma, and carrying in a mathematical model constructed in the wiener process, namely the formula (17), so as to obtain the residual service life of the rolling bearing. In order to check the performance of the prediction, the measurement error E and the prediction scoring standard are used, and the calculation formulas are respectively shown in formulas (22), (23) and (24).

Where ActRIL represents the true value of the remaining life, preRUL represents the predicted value of the remaining life, E _J Representing the prediction error of a bearing, A _J Represents the score for that bearing and n represents the number of bearings tested.

The technical effect of the invention is further verified through experiments.

Bearing Data using IEEE PHM2012 Data Challenge ^[21] Experimental tests are carried out on the extracted residual life prediction methodAnd (4) syndrome differentiation. The experiment was performed on a PRONOSTIA experimental platform while collecting online health monitoring data. The experimental data comprises 3 working conditions, wherein the working condition 1 is load 4000N and rotating speed 1800 rpm; working condition 2 is load 4200N, and rotating speed 1650 rpm; working condition 3 is load 5000N and rotating speed 1500 rpm. The vibration signal comprises vibration information in the horizontal direction and the vertical direction, the sampling frequency of the sensor is 25.6kHz, the time interval for collecting the vibration signal is 10s, and the time for collecting each vibration signal is 0.1s, namely, the number of data points for sampling each vibration signal is 2560. When the amplitude of the vibration signal exceeds 20g, the data collection is stopped. The database had 17 sets of bearing vibration data, of which 6 were life cycle data and the remaining 11 were non-life cycle data. The detailed data are shown in table 2.

TABLE 2 PHM2012 challenge data description

And (3) carrying out fast Fourier transform on the original vibration data of the full-life bearing, and simultaneously extracting each vibration statistical characteristic (shown in table 1) of the data and carrying out normalization processing. Taking the bearing 1_1 as an example, fig. 7 is a time-domain vibration signal diagram of the bearing 1_1, and fig. 8 is a frequency-domain amplitude diagram after FFT. And (3) normalizing each characteristic, inputting the characteristic into the single-layer NCAE network, and determining that the input layer of the single-layer NCAE network is 27 and the output layer is 13 through experiments. Taking the bearing 1_1 as an example, 27 sets of signal characteristics are input, and 13 sets of characteristics are output, and the output characteristics are shown in fig. 9. And respectively selecting the first few characteristics in the 1-13 groups from the 13 groups of characteristics output to be input into the SOM network for training. Experiments prove that the correlation degree of the obtained result is highest by selecting the first 5 features with higher correlation degree as the input of the SOM network. The number of neuron nodes of the output layer is taken as

M is the number of input samples, that is, a planar array with 5 × 2 output layers, and the obtained degradation curve is subjected to sliding smoothing with a window size of 11 and normalized, thereby obtaining the health index of the bearing 1_ 1. The results are shown in FIG. 10.

Aiming at the problem of predicting the residual life of the bearing under variable working conditions, the effectiveness of the method is verified by adopting the migration tasks of working condition 1 → working condition 2, working condition 1 → working condition 3 and the like. Wherein, working condition 1 → working condition 2 represents to migrate the knowledge of the rolling bearing data set under working condition 1 to the data set under working condition 2, and so on. And inputting the frequency domain amplitude sequences of the bearing 1_1 and the bearing 1_2 into a rolling bearing performance degradation network to obtain a pre-training model. Because the deep NCAE network is obtained by cascading a plurality of NCAE networks, when the number of the neuron nodes is determined, loss functions of different neuron numbers of each layer of the NCAE network are calculated, and the number of the neuron nodes is further determined. The layer loss functions are shown in fig. 11, 12, and 13, respectively. As can be seen from fig. 11, 12 and 13, the parameter settings of the deep NCAE network are shown in table 3.

TABLE 3 deep NCAE network parameter settings

The input layer is set to 2048, and the full connection layer of the FNN network is determined to be 12 according to the formula (8); setting parameters in formula (6) according to multiple experimental results and experiences, wherein p is 0.05, α is 3, and β is 0.1; in each hidden layer of the deep NCAE network, an activation function selects a sigmoid function; in the FNN network, the activation function selects the tansig function.

Taking predicting the RUL of the bearing 3_3 as an example, the source domain data is the frequency domain amplitude sequence of the bearing 1_1 and the bearing 1_2 under the working condition 1, the frequency domain amplitude sequence of the bearing 3_1 is subjected to fine tuning pre-training, and fig. 14 is a performance degradation index of the bearing 3_ 3. The increment of the performance degradation index in fig. 14, that is, the difference between the quantization value of the performance degradation index at the current time and the quantization value of the performance degradation index at the previous time, is calculated, and whether the increment of the performance degradation index conforms to normal distribution is determined by using a Jarque-bera (jb) test method. The detection result of the Jarqe-Bera test method is called JB statistic, and the smaller the value of the JB statistic is, the more the test data conform to the normal distribution, and the definition of the JB statistic is shown as a formula (25).

Wherein, the skewness coefficient S and the skewness coefficient K are respectively shown in formulas (26) and (27).

And (5) according to the formula (25), JB statistics of the increment of the performance degradation index quantized value at the last 200, 150, 100 and 50 monitoring time points are respectively obtained. Experiments prove that the JB statistical value of the increment of the performance degradation index quantitative values of the last 50 monitoring points is the smallest, namely the JB statistical value is the most consistent with normal distribution; the quantized values of the 50 monitoring point performance degradation indexes are incrementally brought into formulas (19) and (20), maximum likelihood estimated values of mu and sigma are obtained, and the maximum likelihood values are then brought into formula (17). Wherein the threshold is set to 1 because the health indicator H ∈ [0, 1]. And finally obtaining a calculation result, and taking the time corresponding to the peak point as the predicted RUL. The calculation results are shown in fig. 15. The quantized value increment of the performance degradation index of the bearing 3_3 is carried into the formulas (19) and (20), the result is calculated, and the degradation process of the bearing 3_3 after the current time is simulated by using a wiener process, and the process is shown in the graph 16.

Similarly, the rolling bearing under the working condition 2 is processed, the pre-training network is finely adjusted by using the data of the bearing 2_1, the performance degradation index of the non-full-life bearing (namely, test data, bearings 2_3, 2_4, 2_5, 2_6 and 2_7) is obtained, and then the RUL result of the non-full-life bearing under the working condition 2 is obtained by using the wiener process model. And inputting the data of the non-full-life bearing under the working condition 1 into a pre-training model for testing, wherein the rest steps are the same as the steps for predicting the RUL of the bearing under the working condition 2. The results are shown in tables 4 and 5, respectively. As can be seen from Table 4, under the same working condition, the prediction error of most of the tested bearings is small, which indicates that the pre-training model is good, and also indicates that the health index label is helpful for constructing the rolling bearing performance degradation model; as can be seen from table 5, the prediction errors of the bearings 2_3 and 3_3 are small, and the prediction errors of the bearings 2_6 and 2_7 are large, which indicates that even though the fine adjustment is performed by using the bearing data under the same working condition, the prediction results still have a deviation because the performance degradation processes of the bearings under the same working condition are different, and the proposed method still has an improved space. The error in tables 3 and 4 is positive, indicating that the predicted value is less than the value of the true remaining life, and the error is negative indicating that the predicted value is greater than the value of the true remaining life.

TABLE 4 bearing Life prediction results under Condition 1

TABLE 5 bearing Life prediction results under Condition 2 and Condition 3

In order to prove the superiority of the wiener process model, the frequency domain amplitude sequence of the non-life bearing under the working condition 1 is used as test data, and a linear function is used for fitting the degradation trend of the non-life bearing in a contrast experiment ^[22] . According to the formula (22) and the formula (24), the prediction effect is measured according to the prediction error and the score, and the comparison result is shown in table 6.

TABLE 6 comparison of RUL prediction results for bearings under working conditions 1

As seen from the comparison results in Table 6, the error of the wiener process model provided by the invention in the aspect of prediction is smaller, and the fact that the wiener process model is more suitable for processing the nonlinear performance degradation index compared with the linear function fitting is verified, so that the residual service life of the bearing is more accurately predicted.

In order to prove that the model migration method has a better prediction effect, the method carries out experiment comparison before and after migration, namely, the comparison experiment takes the frequency domain amplitude sequence of the non-full-life bearing as the input of a pre-training model to obtain the performance degradation index of the model, the residual life is predicted by using the wiener process, and the comparison experiment result is shown in table 7.

TABLE 7 comparison of RUL prediction results for bearings under working

conditions

2 and 3

As can be seen from table 7, the prediction error of the method provided by the present invention is lower than that of the comparative experiment, so that the residual life prediction method based on the model migration and wiener process provided by the present invention can predict the residual life of the rolling bearing more accurately.

In order to better prove the effectiveness of the method, the prediction results of the method are compared with those of other literature methods. Document [23] uses the life percentage as a training label, and uses a ConvLSTM network to construct a prediction model to predict the remaining service life; document [24] predicts the remaining useful life using a gaussian process regression algorithm. The results of the comparative experiments of the method of the present invention and other documents are shown in Table 8, together with the results of Table 5.

TABLE 8 comparison of the experimental results of the process of the present invention with other literature methods

As can be seen from the results of the experiment shown in Table 8, the average error of the residual service life predicted by the method of the present invention was-17.05%, the average score was 0.279, the average error of the document [23] was-21.68%, the average score was 0.263, the average error of the document [24] was 55.77%, and the average score was 0.197. In contrast, the method provided by the invention has a low absolute value of the average error and a high average score. In conclusion, the effectiveness of the method provided by the invention is proved through experiments.

Still with bearing 3_3 predicted resultsFor example, the probability density function of the RUL predicted value is obtained by predicting different time monitoring points ^[25] As shown in fig. 17. As can be seen from fig. 17, as the number of monitoring points increases, the probability density function curve of the wiener process is narrower and sharper, which indicates that the uncertainty of prediction is smaller and smaller, i.e., the method provided by the present invention can obtain a good prediction result in the aspect of life prediction.

In conclusion, aiming at the problem that the service life percentage is used as a label of the life cycle data of the rolling bearing, the nonlinear degradation process of the bearing is difficult to accurately describe, the NCAE network and the SOM network are introduced to construct a bearing health index, the index is used as the label, and an effective pre-training model is established; aiming at the problem of bearing working condition change, a model migration method is introduced to realize the construction of the performance degradation index of the non-full-life rolling bearing under different working conditions, and a foundation is laid for the subsequent life prediction work; the rolling bearing degradation process has the characteristic of a random process, and a method combining deep learning and a wiener process is provided for predicting the residual service life aiming at the problem that the traditional method for fitting a degradation curve cannot accurately describe the rolling bearing degradation process, so that the problem of low prediction precision is solved. Compared with the reference, the absolute value of the average error is reduced by at least 4.29%, and the average score is improved by at least 0.016.

While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.

The documents cited in the present invention are as follows:

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Claims

1. A rolling bearing RUL prediction method based on model migration and a wiener process is characterized by comprising the following steps:

preprocessing the source domain data and the target domain data;

2. The rolling bearing RUL prediction method based on model migration and wiener process as claimed in claim 1, wherein the operating condition comprises load and rotation speed, and the operating condition A is different from the operating condition B.

3. The rolling bearing RUL prediction method based on model migration and wiener process as claimed in claim 2, wherein the preprocessing is to perform Fourier transform on rolling bearing time domain vibration signals to obtain frequency domain amplitude sequence.

4. The rolling bearing RUL prediction method based on model migration and wiener process as claimed in claim 3, wherein the obtaining process of the health index label of the source domain data and the health index label of the target domain data comprises:

H＝f{||x _k -ω _c ||}

wherein f represents normalization.

5. The rolling bearing RUL prediction method based on model migration and wiener process of claim 4, wherein the time domain features include RMS, standard deviation, maximum, minimum, peak-to-peak, kurtosis index, waveform index, mean, pulse index and rectified mean; the time-frequency domain features include band energies and band energy ratios; the trigonometric function-based features include IHS standard deviation.

6. The rolling bearing RUL prediction method based on model migration and wiener process as claimed in claim 5, wherein the correlation calculation formula of the output characteristics of single-layer non-negative constraint self-encoder network is:

7. The rolling bearing RUL prediction method based on model migration and wiener process as claimed in claim 6, wherein the deep non-negatively constrained auto-encoder network is formed by cascading a plurality of non-negatively constrained auto-encoder networks.

8. The rolling bearing RUL prediction method based on model migration and wiener process as claimed in claim 7, wherein the mathematical model constructed based on the wiener process is: