A method for predicting the remaining life of rolling bearings

Abstract

The present invention discloses a method for predicting the remaining life of a rolling bearing, comprising the following steps: S1, constructing fuzzy entropy as a rolling bearing performance degradation feature for the original vibration acceleration data of the rolling bearing in the source domain and the target domain; S2, inputting the training fuzzy entropy sample sets of multiple different source domains and the training fuzzy entropy sample sets of the target domain into the AAET-Crossformer model for training the parameters of the AAET-Crossformer model at the same time; S3, using the trained AAET-Crossformer model to hierarchically decode and predict the performance degradation characteristic trend of the rolling bearing in the target domain in the future; S4, establishing a three-parameter Weibull distribution reliability model to predict the failure threshold time point and RUL of the rolling bearing in the target domain. The prediction method of the present invention can achieve higher RUL prediction accuracy, better generalization performance and higher computational efficiency.

Description

Technical Field

[0001] The invention relates to a method for predicting the remaining life of a rolling bearing. Background Art

[0002] As one of the key components of rotating machinery (such as aircraft engines, high-speed rail wheels, and generator sets), rolling bearings play an important role in supporting the high-precision rotation of rotating machinery. Since rolling bearings usually operate for a long time under variable speed and variable load environments, they are prone to wear and degradation, and failure forms such as fatigue wear, cracks, and surface peeling occur. Once failure occurs, it may cause mechanical failure, economic losses, or even casualties. Therefore, accurate and early prediction of the remaining useful life (RUL) of rolling bearings is very important for ensuring the safe and stable operation of mechanical equipment, preventing the occurrence of mechanical equipment safety accidents, reducing economic losses caused by accidental downtime, and avoiding casualties.

[0003] At present, the RUL prediction methods of rolling bearings can be divided into three categories: physical model-based, prior knowledge-based, and artificial intelligence-based methods. However, the simulation of the nonlinear, random, and dynamically changing rolling bearing degradation process will introduce a large number of uncertain parameters into the physical model, which makes it difficult to estimate the parameters of the physical model. Therefore, it is difficult to establish a definite physical model for the simulation of the rolling bearing degradation process; and the RUL prediction method based on prior knowledge relies on expert knowledge and experience for logical reasoning, which is restricted by various rules and is therefore difficult to apply to the RUL prediction of rolling bearings. Different from the first two methods, the artificial intelligence RUL prediction method represented by machine learning and deep learning extracts features from the historical monitoring data of rolling bearings, and then establishes a prediction model based on feature data and feature degradation process to achieve RUL prediction. This type of method has become a new research hotspot for the RUL prediction of rolling bearings due to its powerful feature extraction capabilities. For example, Yizhe Shen et al. used a multi-head attention bidirectional long short-term memory neural network (multi-head attention BiLSTM, MHA-BiLSTM) to predict the RUL of rolling bearings; Juan Xu et al. used a self-attention augmented convolution GRU network (SACGNet) model with an attention mechanism to predict the RUL of rolling bearings; Jianghong Zhou et al. used a reinforced memory gated recurrent unit neural network (reinforced memory gated recurrent unit, RMGRU) to predict the RUL of rolling bearings; Yajun Shang et al. proposed a network model CNN-BGRU that combines a convolution neural network (CNN) and a bidirectional gate recurrent unit (BGRU) to predict the RUL of rolling bearings. However, the above-mentioned rolling bearing RUL prediction methods based on artificial intelligence all have certain defects. Specifically, the ability of MHA-BiLSTM, SACGNet, RMGRU and CNN-BGRU to capture the spatial local information and temporal interdependence of time series data will decay rapidly under long sequence conditions, that is, memory degradation will occur, and they cannot migrate historical time series data. Therefore, their generalization capabilities are insufficient, and there are certain limitations in using them for rolling bearing RUL prediction. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a rolling bearing remaining life prediction method which has more obvious advantages in parameter training speed, nonlinear approximation ability, MTS trend prediction accuracy and generalization performance, and can achieve higher RUL prediction accuracy, better generalization performance and higher computational efficiency.

[0005] The object of the present invention is achieved through the following technical solution: A method for predicting the remaining life of a rolling bearing comprises the following steps:

[0006] S1, constructing fuzzy entropy as the rolling bearing performance degradation feature for the original vibration acceleration data of the rolling bearing in the source domain and the target domain;

[0007] S2, inputting a plurality of fuzzy entropy sample sets for training in different source domains and a fuzzy entropy sample set for training in the target domain into the AAET-Crossformer model at the same time for training the parameters of the AAET-Crossformer model; the AAET-Crossformer model constructs an adversarial autoencoder denoising mechanism on the Crossformer model, and constructs a dynamic domain adaptation network DDAN in the encoding layer of the Crossformer model; the data processing of the AAET-Crossformer model includes the following sub-steps:

[0008] S21. De-noising the rolling bearing performance degradation feature sequence using an adversarial autoencoder denoising mechanism, where the adversarial autoencoder denoising mechanism consists of an adversarial autoencoder AAE and a self-organizing map network;

[0009] S22, inputting the rolling bearing performance degradation depth feature F into the Crossformer model for processing;

[0010] S23. Use the policy gradient learning algorithm to train the AAET-Crossformer model.

[0011] S3, using the trained AAET-Crossformer model to hierarchically decode and predict the future performance degradation characteristics of the target domain rolling bearing;

[0012] S4. Combine the performance degradation feature sequence used for target domain training and the predicted performance degradation feature trend value to establish a three-parameter Weibull distribution reliability model to predict the failure threshold time point and remaining service life RUL of rolling bearings in the target domain.

[0013] The beneficial effects of the present invention are:

[0014] 1) In the AAET-Crossformer model, an adversarial autoencoder denoising mechanism is constructed for the Crossformer model to adaptively extract deep features reflecting the performance degradation of rolling bearings to improve the nonlinear approximation ability of the Crossformer. This mechanism can adapt to the form of the Crossformer model input and enable the Crossformer model to more effectively capture the cross-temporal and cross-dimensional dependencies of multivariate time series (MTS), thereby further improving the Crossformer model's prediction accuracy for MTS trends.

[0015] 2) A dynamic domain adaptation network (DDAN) was constructed in the Crossformer model encoding layer of the AAET-Crossformer model to utilize the historical performance degradation characteristic data of different rolling bearings under different working conditions (i.e., the historical performance degradation characteristic data of rolling bearings in different source domains) to generalize the Crossformer model to perform a new task of predicting the performance degradation characteristic trend of the current rolling bearing (i.e., the rolling bearing in the target domain) under the current working conditions.

[0016] 3) A policy gradient learning algorithm was designed for the AAET-Crossformer model to improve the training speed of the AAET-Crossformer model parameters.

[0017] 4) The invented AAET-Crossformer model also inherits the advantages of the Crossformer model with smaller time and space complexity.

[0018] 5) Due to the reasons pointed out in 1) to 4) above, the AAET-Crossformer model of the present invention has more obvious advantages in parameter training speed, nonlinear approximation ability, MTS trend prediction accuracy and generalization performance. Therefore, the invented rolling bearing RUL prediction method based on the AAET-Crossformer model can achieve higher RUL prediction accuracy, better generalization performance and higher computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The theoretical framework diagram of the AAET-Crossformer model of the present invention;

[0020] Figure 2 It is the structural diagram of AAE;

[0021] Figure 3 Physical diagram of the bearing test bench and sensor placement;

[0022] Figure 4 It is the fuzzy entropy curve of the No. 1 rolling bearing in the whole life cycle under working condition 2;

[0023] Figure 5 It is the fuzzy entropy curve of the No. 2 rolling bearing in the whole life cycle under working condition 2;

[0024] Figure 6 It is the fuzzy entropy curve of the No. 5 rolling bearing in the whole life cycle under working condition 2;

[0025] Figure 7 It is the fuzzy entropy curve of No. 1 rolling bearing in the whole life cycle under working condition 1;

[0026] Figure 8 The performance degradation trend prediction results of bearing No. 1 under working condition 1;

[0027] Fig. 9 The reliability prediction curve of rolling bearing No. 1 under working condition 1 is obtained by the three-parameter Weibull distribution reliability model;

[0028] Fig.10 The figure is a comparison between the RUL predicted by the method based on the AAET-Crossformer model and the actual RUL;

[0029] Fig.11 Learning curves for five machine learning methods;

[0030] Fig.12 The fuzzy entropy trend, RUL and actual RUL predicted by the method based on the T-Crossformer model;

[0031] Fig.13 Fuzzy entropy trend, RUL and actual RUL predicted by the Crossformer model-based method;

[0032] Fig.14 The fuzzy entropy trend, RUL and actual RUL predicted by the Transformer model-based method;

[0033] Fig.15 Fuzzy entropy trend, RUL and actual RUL predicted by LSTM-based method;

[0034] Fig.16 Average prediction time for 50 RUL predictions performed for the six methods. DETAILED DESCRIPTION

[0035] Crossformer is a new type of codec with low time and space complexity. In addition, it has a certain ability to explore the cross-time and cross-dimensional dependencies of multivariate time series (MTS), which helps to improve the prediction accuracy of time series. This performance is not available in existing advanced codecs such as Transformer model and Informer model, as well as typical recurrent neural networks (RNNs) such as long short-term memory neural network (LSTM) and gated recurrent unit (GRU). However, the Crossformer model still has defects such as poor noise resistance, weak generalization performance, and slow network parameter training speed, which can lead to problems such as low RUL prediction accuracy and high model training cost.

[0036] In view of the above shortcomings of Crossformer, the present invention provides a new codec - adversarial autoencoding crossformer model with transferlearning, AAET-Crossformer, and introduces it into the application field of rolling bearing RUL prediction for the first time. Compared with Crossformer, AAET-Crossformer model improves nonlinear approximation ability, enhances the prediction accuracy and generalization performance of time series, and further improves the training speed of network parameters. In view of the above advantages of the AAET-Crossformer model, the present invention applies it to the RUL prediction of rolling bearings: first, fuzzy entropy is constructed for the vibration acceleration data of rolling bearings in different source domains and target domains as the performance degradation characteristics of rolling bearings; then, the fuzzy entropy sample sets used for training in different source domains and the fuzzy entropy sample sets used for training in the target domain are input into the AAET-Crossformer model for training the parameters of the AAET-Crossformer model; next, the trained AAET-Crossformer model is used to hierarchically decode and predict the future performance degradation characteristics (i.e., fuzzy entropy) trend of rolling bearings in the target domain; finally, a three-parameter Weibull distribution reliability model is established by combining the performance degradation characteristic sequence (i.e., fuzzy entropy sample set) used for training in the target domain and the predicted performance degradation characteristic trend value to predict the failure threshold time point and RUL of rolling bearings in the target domain. Since the AAET-Crossformer model has a faster parameter training speed, better nonlinear approximation ability, higher MTS trend prediction accuracy and better generalization performance, the rolling bearing RUL prediction method based on the AAET-Crossformer model has higher RUL prediction accuracy, better generalization performance and higher computational efficiency. The application example of RUL prediction of rolling bearings on the experimental platform of the Joint Laboratory for Health Monitoring of Mechanical Equipment of Xi'an Jiaotong University in this embodiment also verifies the effectiveness and superiority of this method.

[0037] The adversarial autoencoder migration Crossformer model of the present invention first inherits the advantages of the Crossformer model with small time and space complexity, and on this basis constructs an adversarial autoencoder denoising mechanism for the Crossformer model to adaptively extract deep features reflecting the performance degradation of rolling bearings to improve the nonlinear approximation ability of the Crossformer, and the mechanism can adapt to the form of Crossformer model input, and enable the Crossformer model to more effectively capture the cross-time and cross-dimensional dependencies of multivariate time series (MTS), thereby further improving the prediction accuracy of the Crossformer model for the MTS trend; then, a dynamic domain adaptation network (Dynamic Domain Adaptation The Crossformer model is designed to train the parameters of the AAET-Crossformer model using the historical performance degradation feature data of different rolling bearings under different working conditions (i.e., the historical performance degradation feature data of rolling bearings in different source domains) to generalize the Crossformer model to predict the performance degradation feature trend of the current rolling bearing (i.e., the rolling bearing in the target domain) under the current working conditions, thus achieving the purpose of transfer learning. Finally, a policy gradient learning algorithm is designed to improve the training speed of the AAET-Crossformer model parameters.

[0038] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0039] like Figure 1 As shown, a method for predicting the remaining life of a rolling bearing of the present invention comprises the following steps:

[0040] S1. Construct (1-dimensional) fuzzy entropy as the rolling bearing performance degradation feature for the original vibration acceleration data of the rolling bearing in the source domain and the target domain; Under normal conditions, the vibration time domain signal of the rolling bearing is approximately Gaussian distributed, and the signal frequency component is relatively simple, and the fuzzy entropy of the signal is very small; With the appearance of the most subtle performance degradation of the rolling bearing, a weak fault frequency appears in the signal, and the signal energy distribution and frequency components begin to disperse, and the fuzzy entropy begins to increase; When obvious performance degradation occurs, the proportion of the noise signal frequency component increases sharply, and the energy dispersion intensifies, resulting in a significant increase in the fuzzy entropy. Therefore, the fuzzy entropy can quantitatively describe the changes in the rolling bearing vibration time and frequency domain characteristics over time, that is, it can better reflect the changes in the performance degradation characteristics of the rolling bearing.

[0041] S2, inputting a plurality of fuzzy entropy sample sets for training in different source domains and a fuzzy entropy sample set for training in the target domain into the AAET-Crossformer model at the same time for training the parameters of the AAET-Crossformer model; the AAET-Crossformer model constructs an adversarial autoencoder denoising mechanism on the Crossformer model, and constructs a dynamic domain adaptation network DDAN in the encoding layer of the Crossformer model;

[0042] Rolling bearings often operate under variable working conditions (variable load, variable speed), and their monitoring data are often interfered by strong environmental noise, which leads to the extracted performance degradation features often having low signal-to-noise ratio, non-stationary and nonlinear. Therefore, an adversarial autoencoder (AAE) denoising mechanism is constructed in the AAET-Crossformer model to extract the deep features of rolling bearing performance degradation, so as to reduce the interference of environmental noise and enhance the nonlinear approximation ability of the Crossformer model for non-stationary and nonlinear performance degradation features.

[0043] The data processing of the AAET-Crossformer model includes the following sub-steps:

[0044] S21. Before the rolling bearing performance degradation feature sequence is input into the Crossformer model, the rolling bearing performance degradation feature sequence is denoised using the adversarial autoencoder denoising mechanism. The adversarial autoencoder denoising mechanism consists of an adversarial autoencoder AAE and a self-organizing mapping (SOM) network. The structure of AAE is as follows: Figure 2 shown.

[0045] The input sequence is denoted by X 1:Τ ={x 1 ,x 2 ,...,x t ,x t+1 ,...,x Τ-1 ,x Τ}, where x t ∈R D Represents the time series X 1:Τ At time t, the D-dimensional data, X 1:Τ is the performance degradation characteristic data of the rolling bearing; the time series predicted by the AAET-Crossformer model is recorded as X T+1:T+τ , where τ and T are the future and past time steps respectively;

[0046] Assume that Z is the latent encoding vector of the autoencoder in AAE; Assume that p(Z) is the vector of X 1:Τ The prior distribution imposed on the encoding vector Z, q(Z|X 1:T ) is Z about X1:Τ The coding distribution; assuming that p d (X 1:T ) is X 1:Τ The prior distribution of q(Z|X 1:T ) is defined as the posterior distribution q(Z) on the encoding vector Z in the autoencoder, namely:

[0047]

[0048] Since q(Z|X 1:T ) is about X 1:Τ is a deterministic function of , so the only source of randomness in q(Z) is the data distribution p d (X 1:T ); therefore, the regularization of the autoencoder can be achieved by matching the aggregated posterior distribution q(Z) with an arbitrary prior distribution p(Z); thus, the following two stages are alternately trained using the Adaptive Moment Estimation (Adam) algorithm to optimize the generator of the Generative Adversarial Networks (GAN) (i.e. q(Z|X 1:T )) corresponds to the encoder function, which ensures that the posterior distribution q(Z) can deceive the GAN discriminator Make GAN ensure that the posterior distribution q(Z) comes from the true prior distribution p(Z)) and optimize the discriminator of GAN (a) Fixed The discriminator is trained on the premise of To distinguish between real samples and generators Generated fake samples; (b) in fixed The generator is trained on the premise of In order to deceive the discriminator with the fake samples it generates Then, from The angle is used to maximize the following loss function L AAEN :

[0049]

[0050] In the formula, Indicates that Z passes Generated fake samples; express The result of judging the false sample is express For the real sample X 1:T The result of the judgment, and and are the probabilities that the samples are judged to be true; Indicates that all samples are true samples X 1:T hour expectations, Indicates that all samples are generated fake samples expectations;

[0051] Then from The angle of the loss function L shown in formula (2) AAEN Minimize, let and In the shared loss function L AAEN Under the condition of , adversarial training between them is realized; the above AAE training process is specifically expressed as follows:

[0052]

[0053] The purpose of training AAE is to use GAN to guide the posterior distribution q(Z) to match the prior distribution p(Z), while enabling the autoencoder to minimize X 1:T Once the above training process is completed, the decoder of AAE will define a generative model, which maps the prior distribution p(Z) applied to the encoding vector Z to the prior distribution p of the rolling bearing performance degradation feature sequence data. d (X 1:T ), thereby obtaining a high-dimensional rolling bearing performance degradation feature sequence denoised by the AAE denoising mechanism. Next, the denoised high-dimensional rolling bearing performance degradation feature sequence is input into the SOM network trained by the Stochastic Gradient Descent (SGD) algorithm to reduce the feature dimension, and finally obtain the rolling bearing performance degradation deep feature F; the above AAE denoising mechanism can improve the anti-interference ability of environmental noise, avoid serious information loss of rolling bearing performance degradation feature data, and then enhance the nonlinear approximation ability of the Crossformer model to the performance degradation characteristics, and the low-dimensional performance degradation deep feature output by this mechanism can adapt to the form of Crossformer model input.

[0054] S22. Input the rolling bearing performance degradation deep feature F into the Crossformer model for processing: define the total set of training samples from multiple different source domains as The target domain training sample set is in, represents a labeled training sample in the source domain, for The training goal is represents an unlabeled training sample in the target domain, for The training goal is n S represents the number of labeled training samples in the source domain, n T represents the number of unlabeled training samples in the target domain; D S and D T The label values ​​of D are in the same range, but S and D T The marginal probability distribution and conditional probability distribution of are different, that is, p S (F S )≠p T (F T ) and p S (y S |F S )≠p T (y T |F T ); In order to align D S and D T The marginal probability distribution and conditional probability distribution of the rolling bearing are learned and domain-invariant features are obtained to improve the generalization effect of the Crossformer model on the new task of predicting the performance degradation characteristic trend of the current rolling bearing under the current working condition (i.e., the new task of predicting the performance degradation characteristic trend of the rolling bearing in the target domain). DDAN is constructed at the encoding layer of the Crossformer model; DDAN uses the historical performance degradation characteristic data of different rolling bearings under different working conditions (i.e., D S and D T ) is used to learn the parameters of the encoding layer of the Crossformer model and obtain the rolling bearing domain invariant performance degradation features that help improve the cross-domain migration capability and generalization performance of the Crossformer model.

[0055] First, design the label classifier f in DDAN y To utilize the source domain D S The supervised information in the source domain is used to distinguish the source domain training samples F k S The label, f y The training objective is defined as the cross entropy loss function as follows:

[0056]

[0057] In the formula, C is the number of categories (i.e. labels), Indicates F k S The probability of belonging to the cth class, f enc It is the feature extractor of the encoding layer of the Crossformer model;

[0058] Then, the global domain discriminator f is constructed in DDAN gTo align the source domain D S and the target domain D T The marginal probability distribution between g The construction idea of ​​​​the domain classification method follows the domain-adversarial neural network (DANN) to reduce the difference in data distribution between the source domain and the target domain. g The loss function is defined as follows:

[0059]

[0060] Where, L d is the cross entropy loss function of the domain discriminator;

[0061] Next, construct the local domain discriminator f in DDAN l To align the source domain D S and the target domain D T The conditional probability distribution between the global domain discriminator f g In contrast, the local domain discriminator f l It can achieve more fine-grained domain adaptation. Specifically, the local domain discriminator f l The global domain discriminator f in formula (5) g The domain discriminator is divided into C categories, each of which is responsible for matching the source domain training samples and the target domain training samples of each category. Therefore, the local domain discriminator f l The loss function is defined as follows:

[0062]

[0063] In the formula, and They represent the cross entropy loss function corresponding to the c-th domain discriminator and the c-th domain discriminator respectively; is a source domain sample Probability distribution over category c; c∈{1,2,…,C};

[0064] Therefore, the overall loss function of DAAN is expressed as follows:

[0065]

[0066] In the formula, θ enc is the parameter of the feature extractor of the encoding layer of the Crossformer model; θ y ,θ g , Respectively represent the label classifier f y , global domain discriminator f g and local domain discriminator f lParameters in; μ and λ are the parameters that balance f g and f l The hyperparameters of the loss function. Define the parameter set According to the overall loss function of DAAN shown in formula (7), the parameter set θ can be derived DDAN The gradient expression is as follows:

[0067]

[0068] According to the parameter set θ shown in formula (8) DDAN The gradient expression of , using the Stochastic Gradient Descent (SGD) algorithm to efficiently train the parameter set θ of DAAN DDAN ; When the overall loss function value of DAAN converges to the expected value, the rolling bearing domain invariant performance degradation features that help improve the domain adaptation (i.e., cross-domain migration) ability and generalization performance of the Crossformer model are learned l represents the number of layers of the encoder of the Crossformer model;

[0069] In order to preserve the time and dimension information of the time series in MTS prediction, the Crossformer model uses the Dimension-Segment-Wise (DSW) mechanism to train the performance degradation deep feature sequence of the target domain rolling bearings. Divide into length L seg The process is expressed as follows:

[0070]

[0071] In the formula, is the kth segment of dimension d and length L seg ; For convenience, assume that T and τ can be represented by L seg Then, for each segment, linear projection and position embedding are used to obtain the corresponding embedding vector (i.e., univariate time series segment) h k,d ,Right now:

[0072]

[0073] In the formula, represents the linear projection matrix to be learned, d model is the number of rows of the linear projection matrix; Represents the learnable position embedding at position (k, d); after the above operation, a two-dimensional vector is obtained The above DSW mechanism is used to preserve the temporal and dimensional information of MTS, so that the two-stage attention (TSA) layer in the Crossformer model can more effectively capture the cross-temporal and cross-dimensional dependencies of MTS, thereby further improving the prediction accuracy of the Crossformer model for MTS trends.

[0074] Then, the domain-invariant performance degradation characteristics of the rolling bearing are Input the TSA layer to get the output matrix F of the encoding layer of the Crossformer model enc,l , the process is expressed as follows:

[0075]

[0076] Where, TSA(·) represents the encoding function of the TSA layer;

[0077] Using F enc,0 ,F enc,1 ,...,F enc,N To represent the N+1 output matrix of the encoder of the Crossformer model,

[0078] F enc,0 =H; after obtaining the N+1 feature matrices output by the encoder, the decoder of the Crossformer model uses a decoding layer with N+1 layers for output prediction; the lth (l=0,...,N)th decoding layer uses the output matrix of the lth encoding layer as its input to obtain the decoded output of the decoding layer. The process is expressed as:

[0079] F dec,l =Decoder(F dec,l-1 ,F enc,l ) (12)

[0080] When l = 0 in formula (12), F dec,l =Decoder(E dec ,F enc,l ),in Represents the learnable position embedding of the decoder;

[0081] Next, linear projection is applied to the output of each layer of the decoder to obtain the prediction matrix of the decoding layer. The process is shown in the following equations (13) to (14):

[0082]

[0083]

[0084] In formula (13), represents the kth segment in the d-dimensional time series output by the l-th decoding layer; is a learnable weight matrix used to project a vector into a time series segment; in formula (14), Represents the prediction matrix after all segments output by the l-th decoding layer are rearranged;

[0085] Finally, the prediction matrices of each decoding layer are summed to obtain the final prediction value of the AAET-Crossformer model. The process is expressed as follows:

[0086]

[0087] S23. Use the policy gradient learning algorithm to train the AAET-Crossformer model; for the remaining parameters of the AAET-Crossformer model, that is, the generator in the AAE denoising mechanism Parameters and the discriminator Parameters And the parameters θ of the decoder in the Crossformer model dec , design a policy gradient learning algorithm to train them.

[0088] The specific implementation method is: for the remaining parameters of the AAET-Crossformer model, that is, the generator in the AAE denoising mechanism Parameters and the discriminator Parameters And the parameters θ of the decoder in the Crossformer model dec , design a policy gradient learning algorithm to train them; including the following sub-steps:

[0089] S231, will and θ dec Combined into parameter sets Initialization parameter set

[0090] S232, training sample sets of multiple source domains and the target domain training sample set At the same time, the AAET-Crossformer model is input to obtain the performance degradation characteristic trend prediction value and T ;

[0091] Assume that the input rolling bearing performance degradation feature (i.e. fuzzy entropy) sequence of a source domain is (S i represents the i-th source domain), reconstructing the time series into a training sample set and the training target set The process is represented as follows:

[0092]

[0093] The training sample set Each row of is a T-dimensional training sample, and the training target of the training sample is the training target set The elements on the corresponding rows in The construction methods of training sample sets and training target sets of other source domains can refer to the above methods.

[0094] At the same time, it is assumed that the input target domain rolling bearing performance degradation feature sequence is Reconstruct the time series into a training sample set and the training target set The process is represented as follows:

[0095]

[0096] The training sample set Each row of is a T-dimensional training sample, and the training target of the training sample is the training target set The elements on the corresponding rows in the T =K T -T training samples.

[0097] S232, use the policy gradient learning algorithm to adjust the parameter set of the AAET-Crossformer model Update the updated parameter set As the initial value of the parameter set for the next training; the specific update method is: define the loss function of the AAET-Crossformer model as the mean square error (MSE) between its predicted value and the true value in is the predicted value at time t', is the true value at time t'; to update the parameter set The AAET-Crossformer model is used as an intelligent agent that can interact with the environment, and the parameter set of the AAET-Crossformer model is As the state value of the environment; when the agent updates the parameter set In the process of Maximize the cumulative return from the initial state to the terminal state; the cumulative return expression is as follows:

[0098]

[0099] In the formula, Is based on strategy The distribution of the generated Markov chain with respect to the state s; Indicates that in a given state s and parameter set The probability of taking any possible action a under represents the immediate reward obtained by taking action a at time t'; according to the policy gradient theorem, equation (16) is converted into a state distribution that does not involve For policy parameter sets The expression form of the derivative is:

[0100]

[0101] Following the strategy And produce a complete trajectory (i.e., a set of states, actions, and rewards: s 0 ,a 0 ,r 1 ,...,s t'-1 ,a t'-1 ,r t' ,...,s T'-1 ,a T'-1 ,r T' )(r t' is the reward of the agent at time t', T' is the total time required to obtain the complete trajectory), the objective function Gradient Relative to the proportional constant (i.e., trajectory length) on the right side of equation (17), the updated parameter set When , it can be absorbed by the step length β, so equation (17) is further derived as follows:

[0102]

[0103] In the formula, Q π (s, a) represents the state action value function; in order not to change the policy gradient To further reduce the variance of the policy gradient in the case of Subtract a baseline function B(s) from the state; in order to ensure that the baseline function is only related to the state s and has nothing to do with the action a, set For strategy The value of the current state s, then Further expressed as:

[0104]

[0105]

[0106] In the formula, express right The derivative of Q π (s,a), The product of the differences is about To simplify formula (19), Defined as advantage function Rewrite formula (19) into the following form:

[0107]

[0108] Using temporal-difference (TD) Instead of advantage function To calculate the policy gradient, because is the advantage function An unbiased estimate of The definition is as follows:

[0109]

[0110] In the formula, r is the return of environmental feedback, γ is the discount coefficient, For strategy The value of the next state s- (i.e. the state of environmental feedback); thus, the policy gradient The calculation formula becomes:

[0111]

[0112] Therefore, the parameter set The update process is expressed as:

[0113]

[0114] The policy gradient Instantiated as the gradient of the inverse of the mean squared error function, so the parameter set The update process is expressed as:

[0115]

[0116] Comparing equation (23) and equation (24), to make the two equations consistent, let r = 0, Represents the state value function The weight at time t', After the agent interacts with the environment The subsequent update of ; so formula (23) is further derived as:

[0117]

[0118] Formula (25) completes the AAET-Crossformer model parameter set The update process;

[0119] S234, repeat steps S232 and S233 until the training target set and Performance degradation characteristic trend prediction value and T The mean square error function Less than the training threshold, or the number of training steps reaches the maximum number of training steps, then the parameter set No longer updated, that is, the policy gradient learning algorithm is considered to be trained to convergence. From formula (25), we can see that the policy gradient learning algorithm can track the parameter set Historical update information and quickly find Updated optimal strategy This speeds up the convergence of the AAET-Crossformer model parameters, that is, improves the accuracy of the AAET-Crossformer model parameter set. training speed.

[0120] S3, using the trained AAET-Crossformer model to hierarchically decode and predict the performance degradation characteristics (i.e., fuzzy entropy) trend of the target domain rolling bearing; Input the trained AAET-Crossformer model, and the hierarchical decoder of the AAET-Crossformer model can output the performance degradation characteristic trend prediction values ​​of τ target domain rolling bearings at one time, that is,

[0121] S4. Combine the performance degradation feature sequence (i.e., fuzzy entropy sample set) used for target domain training and the predicted performance degradation feature trend value to establish a three-parameter Weibull distribution reliability model to predict the failure threshold time point and remaining service life RUL of rolling bearings in the target domain.

[0122] The specific implementation method of step S4 is: combining the performance degradation feature sequence used for target domain training And the predicted target domain performance degradation characteristic trend value Establish a reliability model for RUL prediction of rolling bearings in the target domain;

[0123] First, the failure rate function λ(t,s) of the rolling bearing is considered to obey the three-parameter Weibull distribution, so the failure rate function is calculated as follows:

[0124]

[0125] In the formula, represents the performance degradation feature set, α is the scale parameter, η is the shape parameter, τ' represents the covariate regression parameter, and t represents the time variable;

[0126] Then, since the three-parameter Weibull distribution reliability function R(t,s) and the failure rate function λ(t,s) satisfy Then, combined with formula (26), the reliability at time t is expressed as:

[0127]

[0128] At this point, the establishment of the three-parameter Weibull distribution reliability model is completed;

[0129] Assume that the starting prediction time is t s , the predicted time corresponding to the failure threshold of the target domain rolling bearing (i.e., the predicted reliability is R fp =10% corresponding to the time) is t fp , then the predicted RUL of the rolling bearing in the target domain is calculated as:

[0130] T P =t fp -t s +1×ΔT=R -1 (R fp )-N s ×ΔT+1×ΔT=(N fp -N s +1)×ΔT (28)

[0131] Where ΔT represents the time interval between two adjacent points in the performance degradation characteristic curve of the target rolling bearing, R fp Represents the reliability value corresponding to the predicted failure threshold point, N s Indicates the starting prediction time point, N fp Represents the predicted failure threshold time point.

[0132] The effectiveness and superiority of the present invention are further verified by specific examples below.

[0133] (1) Experimental platform: The full life cycle vibration signal data of rolling bearings obtained using the experimental platform designed by the Joint Laboratory for Mechanical Equipment Health Monitoring of Xi'an Jiaotong University was used to verify the effectiveness and superiority of the proposed rolling bearing remaining life prediction method based on the AAET-Crossformer model. The bearing experimental platform and sensor layout are as follows: Figure 3As shown in the figure, it mainly consists of an AC motor, a motor speed controller, a rotating shaft, a support bearing, a hydraulic loading system and a test bearing. A rolling bearing of model LDK UER204 is installed on the rotating shaft as a test bearing. The adjustable working conditions of the experimental platform mainly include radial force and speed. The radial force is generated by the hydraulic loading system and acts on the bearing seat of the test bearing. The speed is set and adjusted by the speed controller of the AC motor. Three types of working conditions are designed for the experiment, as shown in Table 1. Five bearings are used for full life cycle test experiments under each type of working condition. Two PCB 352C33 accelerometers are fixed to the horizontal and vertical directions of the bearing seat through magnetic bases to measure the horizontal and vertical vibration signals of the test bearing. The vibration signal of the bearing is collected using the DT9837 portable dynamic signal collector, with a sampling frequency of 25.6KHz, a sampling period of 1min, a sampling time of 1.28s, and 32 768 sample points are collected each time. The data set collected through the above experiments includes the full life cycle vibration signals of 15 test rolling bearings. The detailed information of the data set is shown in Table 2.

[0134] Table 1 Bearing test conditions

[0135] Condition No. 1 2 3 Speed / (r / min) 2100 2250 2400 Radial force / kN 12 11 10

[0136] Table 2 Description of XJTU-SY bearing dataset

[0137]

[0138]

[0139] (2) Prediction of the remaining life of rolling bearings: The full life cycle vibration acceleration data of rolling bearing No. 1, rolling bearing No. 2 and rolling bearing No. 5 collected by the Joint Laboratory for Mechanical Equipment Health Monitoring under working condition 2 are randomly used as source domain data, and the running vibration acceleration data of rolling bearing No. 1 under working condition 1 is used as the target domain test data. The performance degradation characteristics (i.e., fuzzy entropy) are extracted from the full life cycle vibration acceleration data collected under the above two working conditions respectively. Figure 4 to Figure 7 As shown. Among them, Figure 4 is the fuzzy entropy curve of the No. 1 rolling bearing in the whole life cycle under working condition 2. Figure 5 is the fuzzy entropy curve of the No. 2 rolling bearing in the whole life cycle under working condition 2. Figure 6 This is the fuzzy entropy curve of the No. 5 rolling bearing in the whole life cycle under working condition 2. Figure 7This is the fuzzy entropy curve of the No. 1 rolling bearing in the whole life cycle under working condition 1. For the four rolling bearings under the above two working conditions, their fuzzy entropy has a stable period from the starting point, which indicates that these four bearings are in the normal operation stage; then, the fuzzy entropy of the No. 1 bearing under working condition 2 gradually increases from the 441st point to the 451st point; the fuzzy entropy of the No. 2 bearing under working condition 2 also gradually increases from the 46th point to the 135th point; the fuzzy entropy of the No. 5 bearing under working condition 2 also gradually increases from the 120th point to the 264th point; the fuzzy entropy of the No. 1 bearing under working condition 1 also begins to rise continuously from the 57th point to the 88th point, which indicates that these four bearings are experiencing the initial degradation stage; finally, these four bearings respectively increase from their failure threshold points N f =452 (i.e., using the method in Section 2.4, according to the reliability R fp =10% of the failure threshold point, the same below), N f =136, N f =265 and N f =89, and their fuzzy entropies all rise sharply to their last points, which indicates that the four bearings are in a severe degradation stage until the inner ring failure, outer ring failure, outer ring failure, and outer ring failure occur respectively.

[0140] For rolling bearings, the initial degradation stage and its subsequent severe degradation stage are the most critical time periods for observing the performance degradation trend and predicting RUL. Therefore, the fuzzy entropies of points 442 to 491 of bearing No. 1 under working condition 2 are randomly selected as the training samples of the first source domain of the AAET-Crossformer model; the fuzzy entropies of points 62 to 161 of bearing No. 2 under working condition 2 are randomly selected as the training samples of the second source domain of the AAET-Crossformer model; the fuzzy entropies of points 151 to 300 of bearing No. 5 under working condition 2 are randomly selected as the training samples of the third source domain of the AAET-Crossformer model; then, the fuzzy entropies of points 57 to 69 of bearing No. 1 under working condition 1 are used as the training samples of the target domain of the AAET-Crossformer model; finally, the fuzzy entropies of points N to N of bearing No. 1 under working condition 1 are randomly selected as the training samples of the target domain of the AAET-Crossformer model. s = 70 points and their subsequent data (i.e., the remaining τ = 54 fuzzy entropies) are used as the target domain test samples. The parameters in the AAET-Crossformer model are set as follows: the dimension of the training sample D = 1, the length of the training sample T = 5; in the AAE denoising mechanism, the learning rate l used to train the AAE AAEN = 0.001, the maximum number of training steps for AAE The learning rate l used to train the SOM network SOM =0.1, the maximum number of training steps for the SOM network The segment length L of the Crossformer model seg =3, the number of rows of its linear projection matrix is ​​d model =512; in the policy gradient learning algorithm, the discount factor γ = 0.9, the learning rate α = 0.001, and the maximum number of training steps n max =500, MSE training threshold MSE min =5×10 -4 After completing the parameter setting of the AAET-Crossformer model, the training samples of the above three source domains and the target domain training samples are simultaneously input into the AAET-Crossformer model. Then, according to the AAET-Crossformer model training and prediction process, the performance degradation characteristic trend prediction results of bearing No. 1 under working condition 1 can be obtained, such as Figure 8 Obviously, within the predicted time point interval [70,123] of bearing No. 1 under working condition 1, the performance degradation characteristic trend value predicted by the AAET-Crossformer model is very close to the actual value, and the change trends of the two are relatively consistent.

[0141] Then, the fuzzy entropy sequence as the target domain training sample and the fuzzy entropy trend sequence predicted by the AAET-Crossformer model are input into the three-parameter Weibull distribution reliability model to obtain the reliability prediction curve of the No. 1 rolling bearing under working condition 1, as shown in Fig. 9 As shown, the scale parameter α, shape parameter η and covariate regression parameter τ' of the three-parameter Weibull distribution reliability model can be obtained based on the maximum likelihood estimation of the product of the failure rate function (i.e., formula (26)) and the reliability function (i.e., formula (27)) as follows: α = -3.97, η = -6.06, τ' = 12.89. Fig. 9 It can be seen that the time point corresponding to the reliability of 10%, that is, the predicted value of the failure threshold time point is N fp =88.

[0142] Therefore, the RUL of rolling bearing No. 1 under working condition 1 to be predicted is the predicted failure threshold time point N fp =88 and the starting prediction time point N s = The time difference between 70, that is, T P =(N fp -N s +1)×ΔT=19min; meanwhile, the actual RUL of the bearing is T Pa =(N f -N s +1)×ΔT=20min. Fig.10 This is a comparison chart of the RUL predicted by the AAET-Crossformer model and the actual RUL, where ΔT = 1min. Fig.10 The time interval between two adjacent points in the fuzzy entropy curve shown in Figure 1 is the time interval between two adjacent points in the fuzzy entropy curve shown in Figure 1. Therefore, the prediction error of the AAET-Crossformer model is only

[0143] (3) Comparative analysis:

[0144] 1) In order to verify the advantages of the rolling bearing RUL prediction method based on the AAET-Crossformer model, first, the training speed and nonlinear approximation ability of the AAET-Crossformer model are compared with those of the AAET-Crossformer (T-Crossformer) model without the AAE denoising mechanism, the Crossformer model, the Transformer model, and the LSTM. In order to compare the five machine learning methods under conditions as similar as possible, the performance degradation characteristics of the latter four methods are also expressed by fuzzy entropy; at the same time, the maximum number of training steps and the MSE training threshold of the latter four methods are set to the same values ​​as the AAET-Crossformer model; in addition, the learning rates of the T-Crossformer model, the Crossformer model, the Transformer model, and the LSTM are all set to η'=0.001. It should be noted that since the Crossformer model, the Transformer model, and the LSTM do not have transfer learning capabilities, the training samples used by these three methods can only be the above-mentioned target domain training samples. The learning curves of the five machine learning methods are shown in the figure below. Fig.11 As shown in the figure, it can be seen that the parameters of the AAET-Crossformer model are trained to convergence when the training steps reach the 294th step, while the T-Crossformer model, Crossformer model, Transformer model and LSTM are trained to convergence at the 430th, 480th, 410th and 342th steps respectively. In the subsequent training process, the MSE value of the AAET-Crossformer model is always smaller than that of the other four methods. Therefore, the AAET-Crossformer model has a faster network parameter training speed and better nonlinear approximation ability than the T-Crossformer model, Crossformer model, Transformer model and LSTM.

[0145] In order to further quantitatively evaluate the nonlinear approximation capabilities of the five machine learning methods, namely, AAET-Crossformer model, T-Crossformer model, Crossformer model, Transformer model and LSTM, the mean square error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and goodness of fit (R) were used to evaluate the nonlinear approximation capabilities of the five machine learning methods, namely, AAET-Crossformer model, T-Crossformer model, Crossformer model, Transformer model and LSTM. 2As an evaluation index of nonlinear approximation ability, that is:

[0146]

[0147]

[0148]

[0149]

[0150] In equations (29) to (32), τ is the number of samples to be predicted, x i and They are the predicted fuzzy entropy trend value and its corresponding actual value, and VAR are the mean and variance of the predicted τ actual fuzzy entropies, respectively. In order to reduce random accidental errors, the nonlinear approximation ability evaluation indicators of the above five machine learning methods were statistically analyzed, and the average value of the nonlinear approximation ability evaluation indicators in 50 repeated RUL predictions was obtained, that is, and As shown in Table 3.

[0151] Table 3 Comparison of nonlinear approximation capabilities of five machine learning methods

[0152]

[0153] As shown in Table 3, compared with the other four methods, the AAET-Crossformer model The value is the smallest, and its The value is closest to 1, which indicates that the AAET-Crossformer model has better nonlinear approximation ability and stability in multiple repeated experiments.

[0154] 2) Compare the denoising effect and prediction accuracy of the RUL prediction method based on the AAET-Crossformer model with the RUL prediction methods based on the T-Crossformer model, Crossformer model, Transformer model and LSTM. To ensure the same conditions, the latter four methods use the same reliability model as the AAET-Crossformer model, namely the three-parameter Weibull distribution reliability model. The fuzzy entropy trend and RUL of the No. 1 rolling bearing under working condition 1 predicted by the latter four methods are shown as follows: Figure 12-15 As shown. Among them, Fig.12 The fuzzy entropy trend, RUL and actual RUL predicted by the method based on the T-Crossformer model are shown in Figure 2. Fig.13 The fuzzy entropy trend, RUL and actual RUL predicted by the Crossformer model method. Fig.14 The fuzzy entropy trend, RUL and actual RUL predicted by the Transformer model-based method. Fig.15 Fuzzy entropy trend, RUL and actual RUL predicted by LSTM-based method.

[0155] Depend on Fig.10 , Figures 12 to 15 It can be seen that the fuzzy entropy trend predicted by the RUL prediction method based on the AAET-Crossformer model is closer to the actual trend of the fuzzy entropy than the latter four methods without denoising mechanism; at the same time, the RUL prediction method based on the AAET-Crossformer model and the latter four methods predict RUL of 19min, 23min, 22min, 26min and 25min respectively, and the prediction error δ P They are 5%, 15%, 10%, 30% and 25% respectively. Obviously, the RUL prediction error of the method based on the AAET-Crossformer model is the smallest compared with the latter four methods. The above fuzzy entropy trend prediction results and RUL prediction results show that the method based on the AAET-Crossformer model has better nonlinear approximation ability and higher RUL prediction accuracy than the latter four methods without denoising mechanism because of its ability to resist environmental noise interference given by the AAE denoising mechanism.

[0156] 3) In order to compare the generalization performance of the RUL prediction method based on the AAET-Crossformer model with the prediction methods based on the AAET-Crossformer (AAE-Crosformer) model without DDAN, the Crossformer model, the Transformer model and the LSTM, these five methods are forced to use only the training samples of the first source domain, the second source domain and the third source domain to train themselves, so as to predict the fuzzy entropy trend of the target domain samples to be tested. The five methods use only the training samples of the first source domain, the second source domain and the third source domain to train themselves, and the predicted fuzzy entropy trend values ​​of the target domain are and (i.e., MSE, MAE, MAPE, and R in 50 repeated RUL predictions) 2 The average values ​​are shown in Table 4.

[0157] Table 4 Comparison of generalization performance of five machine learning methods

[0158]

[0159]

[0160] As can be seen from Table 4, even when the training samples and the test samples come from different working conditions (i.e., different data domains), the AAET-Crossformer model has a higher accuracy than the following four methods. The value is still the smallest. The value is still the closest to 1; the following four methods do not have the ability to migrate across domains, so when the training samples and the test samples come from different fields, the values ​​they obtain are and The value is much worse than the corresponding value in Table 3. The comparison between Table 3 and Table 4 above confirms that the cross-domain migration performance of DDAN in the AAET-Crossformer model can promote the improvement of the generalization ability of the AAET-Crossformer model, that is, the AAET-Crossformer model has better adaptability to the new task of predicting the trend of performance degradation characteristics in the target domain than the latter four methods.

[0161] 4) Compare the RUL prediction time of the RUL prediction method based on the AAET-Crossformer model (i.e., the sum of the time for extracting fuzzy entropy, the time for training the AAET-Crossformer model, the time for predicting fuzzy entropy trends, and the time for calculating RUL) with the RUL prediction time of the methods based on the T-Crossformer model, the AAE-Crossformer model, the Crossformer model, the Transformer model, and the LSTM. The prediction time was measured using Pycharm 2022.1 under the following hardware configuration: 16GRAM and 2.6GHz Intel CPU. The average prediction time of 50 RUL predictions performed by the six methods was recorded, as follows: Fig.16 As shown. It can be seen that the prediction time of the RUL prediction method based on the AAET-Crossformer model is 159.4s, while the prediction times of the method based on the T-Crossformer model, the method based on the AAE-Crossformer model, the method based on the Crossformer model, the method based on the Transformer model, and the method based on the LSTM are 126.4s, 141.8s, 133.5s, 200.6s, and 27.8s, respectively. Obviously, the prediction time of the method based on the AAET-Crossformer model is only slightly longer than that of the methods based on the T-Crossformer model, the AAE-Crossformer model, and the Crossformer model, but is significantly shorter than that of the method based on the Transformer model, which indicates that it has a faster training speed and higher computational efficiency.

[0162] 5) Compare the differences in time and space complexity of the AAET-Crossformer model with the T-Crossformer model, AAE-Crossformer model, Crossformer model, Transformer model and LSTM when used for RUL prediction of No. 1 rolling bearing under working condition 1, and the comparison results are shown in Table 5. As can be seen from Table 5, the time and space complexity of the AAET-Crossformer model is basically at the same order of magnitude as that of the T-Crossformer model, AAE-Crossformer model, Crossformer model and LSTM, that is, it is not much different from the Crossformer model whose time and space complexity is originally small; but the time and space complexity of the AAET-Crossformer model is significantly smaller than that of the Transformer model. The above comparison results show that the AAET-Crossformer model is similar to the Crossformer model and also has the advantage of smaller time and space complexity.

[0163] Table 5 Comparison of time and space complexity of six machine learning methods

[0164]

[0165] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of a rolling bearing, characterized in that: The following steps are involved: S1, constructing fuzzy entropy as the rolling bearing performance degradation feature for the original vibration acceleration data of the rolling bearing in the source domain and the target domain; S2, inputting a plurality of fuzzy entropy sample sets for training in different source domains and a fuzzy entropy sample set for training in the target domain into the AAET-Crossformer model at the same time for training the parameters of the AAET-Crossformer model; the AAET-Crossformer model constructs an adversarial autoencoder denoising mechanism on the Crossformer model, and constructs a dynamic domain adaptation network DDAN in the encoding layer of the Crossformer model; the data processing and model training of the AAET-Crossformer model include the following sub-steps: S21. De-noising the rolling bearing performance degradation feature sequence using an adversarial autoencoder denoising mechanism, where the adversarial autoencoder denoising mechanism consists of an adversarial autoencoder AAE and a self-organizing map network; The input sequence is denoted by X 1:Τ ={x1,x2,...,x t ,x t+1 ,...,x Τ-1 ,x Τ }, where x t ∈R D Represents the time series X 1:Τ At time t, the D-dimensional data, X 1:Τ is the performance degradation characteristic data of the rolling bearing; the time series predicted by the AAET-Crossformer model is recorded as X T+1:T+τ , where τ and T are the future and past time steps respectively; Assume that Z is the latent encoding vector of the autoencoder in AAE; Assume that p(Z) is the vector of X 1:Τ The prior distribution imposed on the encoding vector Z, q(Z|X 1:T ) is Z about X 1:Τ The coding distribution; assuming that p d (X 1:T ) is X 1:Τ The prior distribution of q(Z|X 1:T ) is defined as the posterior distribution q(Z) on the encoding vector Z in the autoencoder, namely: Since q(Z|X 1:T ) is about X 1:Τ is a deterministic function of , so the only source of randomness in q(Z) is the data distribution p d (X 1:T ); therefore, the autoencoder is regularized by matching the aggregated posterior distribution q(Z) with an arbitrary prior distribution p(Z); then, the following two stages are alternately trained using an adaptive motion estimation optimization algorithm to optimize the generator of the generative adversarial network The encoder corresponding to the encoding function is: (a) at a fixed The discriminator is trained on the premise of To distinguish between real samples and generators Generated fake samples; (b) in fixed The generator is trained on the premise of In order to deceive the discriminator with the fake samples it generates Then, from The angle is used to maximize the following loss function L AAEN : In the formula, Indicates that Z passes Generated fake samples; express The result of judging the false sample is express For the real sample X 1:T The result of the judgment, and and are the probabilities that the samples are judged to be true; Indicates that all samples are true samples X 1:T hour expectations, Indicates that all samples are generated fake samples expectations; Then from The angle of the loss function L shown in formula (2) AAEN Minimize, let and In the shared loss function L AAEN Under the condition of , adversarial training between them is realized; the above AAE training process is specifically expressed as follows: Next, the denoised high-dimensional rolling bearing performance degradation feature sequence is input into the self-organizing mapping network trained by the stochastic gradient descent algorithm to reduce the feature dimension, and finally the rolling bearing performance degradation deep feature F is obtained; S22. Input the rolling bearing performance degradation deep feature F into the Crossformer model for processing: define the total set of training samples from multiple different source domains as The target domain training sample set is Among them, F k S represents a labeled training sample in the source domain, for The training goal is represents an unlabeled training sample in the target domain, for The training goal is n S represents the number of labeled training samples in the source domain, n T represents the number of unlabeled training samples in the target domain; D S and D T The label values ​​of D are in the same range, but S and D T The marginal probability distribution and conditional probability distribution of are different; in order to align D S and D T The marginal probability distribution and conditional probability distribution of the model are used to learn the domain invariant features, and DDAN is constructed in the encoding layer of the Crossformer model. DDAN learns the parameters of the encoding layer of the Crossformer model by using the historical performance degradation feature data of different rolling bearings under different working conditions. First, design the label classifier f in DDAN y To utilize the source domain D S The supervised information in the source domain is used to distinguish the source domain training samples The label, f y The training objective is defined as the cross entropy loss function as follows: In the formula, C is the number of categories, express The probability of belonging to the cth class, f enc It is the feature extractor of the encoding layer of the Crossformer model; Then, the global domain discriminator f is constructed in DDAN g To align the source domain D S and the target domain D T The marginal probability distribution between g The loss function is defined as follows: Where, L d is the cross entropy loss function of the domain discriminator; Next, construct the local domain discriminator f in DDAN l To align the source domain D S and the target domain D T The conditional probability distribution between local domain discriminator f l The global domain discriminator f in formula (5) g The domain discriminator is divided into C categories, each of which is responsible for matching the source domain training samples and the target domain training samples of each category. Therefore, the local domain discriminator f l The loss function is defined as follows: In the formula, and They represent the cross entropy loss function corresponding to the c-th domain discriminator and the c-th domain discriminator respectively; is a source domain sample Probability distribution over category c; c∈{1,2,…,C}; Therefore, the overall loss function of DAAN is expressed as follows: In the formula, θ enc is the parameter of the feature extractor of the encoding layer of the Crossformer model; θ y ,θ g , Respectively represent the label classifier f y , global domain discriminator f g and local domain discriminator f l Parameters in; μ and λ are the parameters that balance f g and f l Hyperparameters of the loss function; define the parameter set According to the overall loss function of DAAN shown in formula (7), the parameter set θ is derived DDAN The gradient expression is as follows: According to the parameter set θ shown in formula (8) DDAN The gradient expression of DAAN is trained using the stochastic gradient descent algorithm. DDAN ; When the overall loss function value of DAAN converges to the expected value, the rolling bearing domain invariant performance degradation features that help improve the domain adaptation ability and generalization performance of the Crossformer model are learned l represents the number of layers of the encoder of the Crossformer model; The Crossformer model uses a dimension segmentation mechanism to train the target domain rolling bearings on performance degradation deep feature sequences Divide into length L seg The process is expressed as follows: In the formula, is the kth segment of dimension d and length L seg ; For convenience, assume that T and τ can be L seg Divide by integer, and then use linear projection and position embedding for each segment to get the corresponding embedding vector h k,d ,Right now: In the formula, represents the linear projection matrix to be learned, d model is the number of rows of the linear projection matrix; Represents the learnable position embedding at position (k, d); after the above operation, a two-dimensional vector is obtained Then, the domain-invariant performance degradation characteristics of the rolling bearing are Input the TSA layer to get the output matrix F of the encoding layer of the Crossformer model enc,l , the process is expressed as follows: Where, TSA(·) represents the encoding function of the TSA layer; Using F enc,0 ,…,F enc,1 ,…,F enc,N To represent the N+1 output matrix of the encoder of the Crossformer model, where F enc,0 =H; after obtaining the N+1 feature matrices output by the encoder, the decoder of the Crossformer model uses a decoding layer with N+1 layers for output prediction; the l-th decoding layer uses the output matrix of the l-th encoding layer as its input to obtain the decoded output of the decoding layer. The process is expressed as: F dec,l =Decoder(F dec,l-1 ,F enc,l ) (12) When l = 0 in formula (12), F dec,l =Decoder(E dec ,F enc,l ),in Represents the learnable position embedding of the decoder; Next, apply linear projection to the output of each layer of the decoder to obtain the prediction matrix of the decoding layer: In formula (13), represents the kth segment in the d-dimensional time series output by the l-th decoding layer; is a weight matrix used to project a vector into a time series segment; in formula (14), Represents the prediction matrix after all segments output by the l-th decoding layer are rearranged; Finally, the prediction matrices of each decoding layer are summed to obtain the final prediction value of the AAET-Crossformer model. The process is expressed as follows: S23, using the policy gradient learning algorithm to train the AAET-Crossformer model; including the following sub-steps: S231, will and θ dec Combined into parameter sets Initialization parameter set S232, training sample sets of multiple source domains and the target domain training sample set At the same time, the AAET-Crossformer model is input to obtain the performance degradation characteristic trend prediction value and T ; S232, use the policy gradient learning algorithm to adjust the parameter set of the AAET-Crossformer model Update the updated parameter set As the initial value of the parameter set for the next training; the specific update method is: define the loss function of the AAET-Crossformer model as the mean square error between its predicted value and the true value in is the predicted value at time t', is the true value at time t'; to update the parameter set The AAET-Crossformer model is used as an intelligent agent that can interact with the environment, and the parameter set of the AAET-Crossformer model is As the state value of the environment; when the agent updates the parameter set In the process of Maximize the cumulative return from the initial state to the terminal state; the cumulative return expression is as follows: In the formula, Is based on strategy The distribution of the generated Markov chain with respect to the state s; Indicates that in a given state s and parameter set The probability of taking any possible action a under represents the immediate reward obtained by taking action a at time t'; according to the policy gradient theorem, equation (16) is converted into a state distribution that does not involve For policy parameter sets The expression form of the derivative is: Following the strategy In the case of generating a complete trajectory, the objective function Gradient The proportional constant relative to the right side of equation (17) is used to update the parameter set When , it can be absorbed by the step length β, so equation (17) is further derived as follows: In the formula, Q π (s, a) represents the state action value function; in order not to change the policy gradient To further reduce the variance of the policy gradient in the case of Subtract a baseline function B(s) from the state; in order to ensure that the baseline function is only related to the state s and has nothing to do with the action a, set For strategy The value of the current state s, then Further expressed as: In the formula, express right The derivative of Q π (s,a), The product of the differences is about To simplify formula (19), Defined as advantage function Rewrite formula (19) into the following form: Timing Differential Error Instead of advantage function To calculate the policy gradient, because is the advantage function An unbiased estimate of The definition is as follows: In the formula, r is the return of environmental feedback, γ is the discount coefficient, For strategy Next state - The value of; therefore, the policy gradient The calculation formula becomes: Therefore, the parameter set The update process is expressed as: The policy gradient Instantiated as the gradient of the inverse of the mean squared error function, the parameter set The update process is expressed as: Comparing equation (23) and equation (24), to make the two equations consistent, let r = 0, Represents the state value function The weight at time t', After the agent interacts with the environment The subsequent update of ; so formula (23) is further derived as: Formula (25) completes the AAET-Crossformer model parameter set The update process; S234, repeat steps S232 and S233 until the mean square error function Less than the training threshold, or the number of training steps reaches the maximum number of training steps, then the parameter set No more updates, i.e. the policy gradient learning algorithm is considered trained to convergence; S3, using the trained AAET-Crossformer model to hierarchically decode and predict the future performance degradation characteristics of the target domain rolling bearing; S4. Combine the performance degradation feature sequence used for target domain training and the predicted performance degradation feature trend value to establish a three-parameter Weibull distribution reliability model to predict the failure threshold time point and remaining service life RUL of the rolling bearing in the target domain; the specific implementation method is: Combine the performance degradation feature sequence used for target domain training And the predicted target domain performance degradation characteristic trend value Establish a reliability model for RUL prediction of rolling bearings in the target domain; The failure rate function λ(t,s) of the rolling bearing is considered to obey the three-parameter Weibull distribution, so the failure rate function is calculated as follows: In the formula, represents the performance degradation feature set, α is the scale parameter, η is the shape parameter, τ' represents the covariate regression parameter, and t represents the time variable; Since the reliability function R(t,s) of the three-parameter Weibull distribution and the failure rate function λ(t,s) satisfy Then, combined with formula (26), the reliability at time t is expressed as: At this point, the establishment of the three-parameter Weibull distribution reliability model is completed; Assume that the starting prediction time is t s The predicted failure threshold of the target domain rolling bearing corresponds to the time t fp , then the predicted RUL of the rolling bearing in the target domain is calculated as: T P =t fp -t s +1×ΔT=R -1 (R fp )-N s ×ΔT+1×ΔT=(N fp -N s +1)×ΔT (28) Where ΔT represents the time interval between two adjacent points in the performance degradation characteristic curve of the target rolling bearing, R fp Represents the reliability value corresponding to the predicted failure threshold point, N s Indicates the starting prediction time point, N fp Represents the predicted failure threshold time point.

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