CN117252083A - A bearing remaining life prediction method and system that combines degradation stage division and sub-domain adaptation - Google Patents

Abstract

The invention discloses a bearing remaining life prediction method and system that combines degradation stage division and sub-domain adaptation. The method includes the following steps: S1. Construction of a health index curve; S2. Health stage division; S3. Construction and training of a remaining life prediction model. ;S4. Remaining life prediction. The advantage is that it can cleverly correspond to different health stages existing in the life cycle to different subdomains, and disperse the overall differences of global alignment to the stage differences of local alignment. In the migration prediction stage, multi-order measures based on data labels and membership degrees are used to narrow down each degradation stage and complete fuzzy substructure alignment and cross-domain regression. The present invention can achieve finer-grained feature alignment, build a model with better generalization, and at the same time achieve more accurate remaining life prediction.

Description

A bearing remaining life prediction method and system combining degradation stage division and subdomain adaptation

Technical Field

The present invention relates to the technical field of bearing equipment condition monitoring and health management, and in particular to a bearing remaining life prediction method and system combining degradation stage division and subdomain adaptation.

Background Art

Bearings are important components of mechanical equipment. As the running time increases, the performance of bearings will gradually decline, causing failures and even affecting the availability of equipment. How to ensure the safety and reliability of bearings is an important issue at present. Therefore, bearing fault prognostics and health management (PHM) has become a key issue. Bearing PHM aims to monitor the health of the equipment, predict possible problems, and avoid serious failures or accidents. Remaining useful life prediction (RULprediction) is the core part of the PHM task. Its main task is to predict the length of time from the current moment to the loss of operating ability of the running equipment or components, and then formulate preventive maintenance strategies based on the prediction results.

At present, according to the technology used in the prediction process, the remaining life prediction methods of bearings can be roughly divided into two categories: model-based remaining life prediction methods and data-driven remaining life prediction methods. (1) Model-based remaining life prediction methods: Model-based methods use prior knowledge to construct a model to characterize bearing degradation, that is, to construct an empirical model through various mathematical and physical models to predict the remaining life of the bearing. This type of method has good interpretability and can achieve good prediction results when the failure mechanism is fully understood and a suitable model is constructed. However, model-based remaining life prediction methods require a lot of expert knowledge and have poor generalization. The physical properties of bearings are also difficult to fully understand, which limits their application. (2) Data-driven remaining life prediction methods: Data-driven remaining life prediction methods map the degradation process into a relationship function between health status and monitoring data, extract and learn patterns from available data to characterize degradation behavior. Traditional data-driven methods mostly use simple machine learning algorithms for prediction, but the network structure used by this type of algorithm is simple and cannot better mine the potential information between data. With the development of artificial intelligence technology, deep learning has excellent performance in the task of bearing remaining life prediction due to its powerful feature extraction and data processing capabilities.

However, deep learning models require a large amount of high-quality training data to understand the underlying patterns of the data, and require the test data and training data to have the same data distribution. The above assumptions present the following challenges in actual remaining life prediction: (1) First, each device is often in a complex and time-varying working condition, and there is a covariate shift between the training data and the test data. It is impossible to obtain high-quality training data with the same distribution, which leads to a sharp drop in performance when a RUL prediction model predicts other devices. This phenomenon is called the "cross-domain problem." (2) At the same time, the reliability and safety of each device are constantly improving, and it is becoming increasingly difficult to obtain the full life cycle. Incomplete test data and training data will have a greater distribution deviation.

Taking the above challenges into consideration, transfer learning methods based on deep learning models have emerged and have become the focus of research on data-driven methods today.

In the problem of remaining life prediction of bearings under cross-domain conditions, there are differences in the data distribution of the source domain and the target domain. The difference is narrowed by extracting domain-invariant common features of the two domains. However, in practical problems, the overall distribution of the target domain data with missing parts of the cycle will change, resulting in greater differences from the source domain data with complete cycles, making it difficult to directly perform global domain adaptation. In addition, there are different health stages in the entire life cycle of bearings, and each stage has obvious structured characteristics and large distribution differences. Global alignment ignores the differences in the internal structure of the life cycle, which may lead to incorrect matching of different substructures and fail to mine the common potential local features of the data. Therefore, how to accurately predict the remaining life of bearings under incomplete data and cross-domain conditions is a problem that needs to be solved urgently.

Summary of the invention

The object of the present invention is to provide a bearing remaining life prediction method and system combining degradation stage division and subdomain adaptation, so as to solve the above-mentioned problems existing in the prior art.

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

A bearing remaining life prediction method combining degradation stage division and subdomain adaptation includes the following steps:

S1. Construction of health index curve:

Obtain the original data set, extract time domain and frequency domain features of the source domain data and target domain data in the original data set, and perform secondary index optimization and correlation analysis on the obtained multi-dimensional features to obtain a health index curve;

S2. Health stage division:

The time series window weighted clustering algorithm is used to process the health index curve, obtain the health stage label and fuzzy membership of each source domain data and target domain data, and divide them into training set and test set according to the proportion;

S3. Build and train the remaining life prediction model:

The remaining life prediction model includes a fuzzy subdomain feature extractor and a RUL regressor; the training set is input into the remaining life prediction model to train it; during the training process, the total loss is obtained based on the alignment loss of the substructure fuzzy alignment module in the fuzzy subdomain feature extractor and the regression loss of the RUL regressor, and the parameters of the fuzzy subdomain feature extractor and the RUL regressor are optimized by minimizing the total loss, and the trained remaining life prediction model is obtained and saved;

S4. Remaining life prediction:

The test set is input into the trained remaining life prediction model to perform remaining life prediction and obtain the remaining life prediction result.

Preferably, the secondary index optimization is specifically to perform an inter-feature difference alignment operation on the multi-dimensional features to obtain a relative index, and then perform an intra-feature compression and smoothing operation on the relative index to obtain a denoising index.

Preferably, the correlation analysis is specifically to use the Pearson correlation coefficient to measure the correlation degree between the data at each moment and the data at the initial moment for the index after secondary optimization, so as to construct a health index.

Preferably, the source domain data is the electromechanical equipment monitoring data collected when the electromechanical equipment with bearings runs to failure; the target domain data is the electromechanical equipment monitoring data when the electromechanical equipment without bearings runs to failure;

The source domain data is supervised data with the remaining life of the bearing as a label; and the target domain data is unsupervised data without the remaining life of the bearing label.

Preferably, step S2 specifically includes the following contents:

S21, dividing the health index curve into windows, using the statistical value of the window to replace the current single point value, to achieve fuzzy smoothing of the health index curve;

S22, clustering the health index curve after fuzzy smoothing, and obtaining the health stage label and fuzzy membership of each source domain data and target domain data by iteratively optimizing the fuzzy membership of each data point and the cluster center of each category;

S23. Divide the source domain data, target domain data and their health stage labels and fuzzy memberships into training sets and test sets in proportion.

Preferably, step S3 specifically includes the following contents:

S31, inputting the training set into the fuzzy subdomain feature extractor, using the deep neural network of the fuzzy subdomain feature extractor to respectively obtain the feature potential representations of the source domain data and the target domain data in the training set, and obtaining the high-dimensional feature matrix corresponding to the source domain data and the target domain data;

S32, inputting the high-dimensional feature matrices corresponding to the source domain data and the target domain data into the substructure fuzzy alignment module of the fuzzy subdomain feature extractor, and obtaining the alignment loss by calculating the FLMMD between the feature matrices of the source domain data and the target domain data, and the FLCORAL between the feature matrices of the source domain data and the target domain data;

S33, inputting the time series feature matrix of the aligned source domain data and the target domain data in the training set output by the fuzzy subdomain feature extractor into the RUL regressor, outputting the remaining life prediction values of the source domain data and the target domain data in the training set, and calculating the mean square error between the source domain remaining life prediction value and the true value as the regression loss;

S34. Calculate the total loss based on the alignment loss and the regression loss;

S35, minimize the total loss, feedback-adjust the network parameters of the fuzzy subdomain feature extractor and the RUL regressor, implement network training of the fuzzy subdomain feature extractor and the RUL regressor, until the training is completed, and obtain the trained remaining life prediction model.

Preferably, step S32 specifically includes the following contents:

S321, first part alignment: based on the fuzzy local maximum mean difference of the maximum mean difference, while considering the probability of each sample belonging to all categories, a more fine-grained fuzzy subdomain alignment is achieved; the FLMMD between the feature matrices of the source domain data and the target domain data is calculated as the first part loss;

S322, the second part of alignment: Fuzzy LocalCORAL based on the second-order statistics Correlation Alignment, while considering the probability of each sample belonging to all categories, fine-grained alignment is performed on the second-order statistics; the FLCORAL of the feature matrix time of the source domain data and the target domain data is calculated as the second part of the loss;

S323. Combining the first part loss and the second part loss, obtain the alignment loss.

Preferably, the fuzzy subdomain feature extractor is a ResNet50 feature extractor.

Preferably, the RUL regressor is a regression predictor based on a fully connected network.

The present invention also aims to provide a bearing remaining life prediction system combining degradation stage division and subdomain adaptation, the system is used to implement any of the above methods, the system comprises:

Curve construction module: used to construct health indicator curve;

Obtain the original data set, extract time domain and frequency domain features of the source domain data and target domain data in the original data set, and perform secondary index optimization and correlation analysis on the obtained multi-dimensional features to obtain a health index curve;

Stage division module: used to divide health stages;

The time series window weighted clustering algorithm is used to process the health index curve, obtain the health stage label and fuzzy membership of each source domain data and target domain data, and divide them into training set and test set according to the proportion;

Prediction model building module: used to build and train the remaining life prediction model;

The remaining life prediction model includes a fuzzy subdomain feature extractor and a RUL regressor; the training set is input into the remaining life prediction model to train it; during the training process, the total loss is obtained based on the alignment loss of the substructure fuzzy alignment module in the fuzzy subdomain feature extractor and the regression loss of the RUL regressor, and the parameters of the fuzzy subdomain feature extractor and the RUL regressor are optimized by minimizing the total loss, and the trained remaining life prediction model is obtained and saved;

Life prediction module: used to predict the remaining life;

The test set is input into the trained remaining life prediction model to perform remaining life prediction and obtain the remaining life prediction result.

The beneficial effects of the present invention are: 1. It can fully and cleverly utilize the stages existing in the life cycle corresponding to different subdomains to disperse the overall differences of global alignment into the stage differences of local alignment. 2. In the health stage division stage, a time series fuzzy clustering algorithm suitable for time series window data is proposed to realize the unified and standardized health indicator construction and stage division process. In the migration stage, a multi-order metric based on data labels and membership is used to bring each degradation stage closer, so as to complete the fuzzy substructure alignment and cross-domain regression. 3. It can achieve more fine-grained feature alignment, build a model with better generalization, and at the same time achieve more accurate remaining life prediction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart showing the principle of a method for predicting the remaining life of a bearing according to an embodiment of the present invention;

FIG2 is a schematic diagram of the basic principle of transfer learning in an embodiment of the present invention;

FIG3 is a schematic diagram of a feature-internal compression and smoothing operation in an embodiment of the present invention;

FIG4 is a schematic diagram of a TWW-FCM according to an embodiment of the present invention;

FIG5 is a schematic diagram of a framework of a fuzzy subdomain adaptive regression network (FSARN) according to an embodiment of the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation methods described herein are only used to explain the present invention and are not used to limit the present invention.

Embodiment 1

As shown in FIG. 1 to FIG. 5 , in this embodiment, a bearing remaining life prediction method combining degradation stage division and subdomain adaptation is provided, comprising the following steps:

1. Construction of health index curve:

The original data set is obtained, and time domain and frequency domain features are extracted from the source domain data and target domain data in the original data set. The obtained multidimensional features are subjected to secondary index optimization and correlation analysis to obtain a health index curve.

The secondary index optimization includes relative index and denoising index. First, the multi-dimensional features are aligned to obtain the relative index, and then the relative index is compressed and smoothed within the features (as shown in Figure 3) to obtain the denoising index.

The correlation analysis is specifically to use the Pearson correlation coefficient to measure the correlation between the data at each moment and the data at the initial moment for the secondary optimized index, and to construct the health index HI.

The source domain data is the monitoring data of electromechanical equipment collected when the electromechanical equipment with bearings runs to failure; the target domain data is the monitoring data of electromechanical equipment without bearings running to failure, which is only the monitoring data collected in the early stage.

The source domain data is supervised data with the remaining life of the bearing as a label; and the target domain data is unsupervised data without the remaining life of the bearing label.

2. Health stage division:

The time series window weighted clustering algorithm (TWW-FCM algorithm) is used to process the health index curve to obtain the health stage label and fuzzy membership of each source domain data and target domain data, and divide them into training set and test set according to the proportion.

As shown in FIG4 , the TWW-FCM algorithm is a clustering algorithm suitable for dividing time series data into stages. After fuzzy smoothing is performed on the HI curve, it is clustered to obtain the health stage label HS and the fuzzy membership. Specifically, the following steps are included:

1. Divide the health index curve into windows, and use the statistical value of the window to replace the current single point value to achieve fuzzy smoothing of the health index curve.

2. Cluster the health indicator curves after fuzzy smoothing, and obtain the health stage label and fuzzy membership of each source domain data and target domain data by iteratively optimizing the fuzzy membership of each data point and the cluster center of each category.

3. Divide the source domain data, target domain data and their health stage labels and fuzzy membership into training sets and test sets in proportion.

3. Build and train the remaining life prediction model:

The remaining life prediction model includes a fuzzy subdomain feature extractor and a RUL regressor; a training set is input into the remaining life prediction model to train it; during the training process, a total loss is obtained based on the alignment loss of the substructure fuzzy alignment module in the fuzzy subdomain feature extractor and the regression loss of the RUL regressor, and the parameters of the fuzzy subdomain feature extractor and the RUL regressor are optimized by minimizing the total loss, and the trained remaining life prediction model is obtained and saved.

The specific steps include:

1. Input the training set into the fuzzy subdomain feature extractor, and use the deep neural network of the fuzzy subdomain feature extractor to obtain the feature potential representations of the source domain data and the target domain data in the training set, and obtain the high-dimensional feature matrix corresponding to the source domain data and the target domain data;

2. The high-dimensional feature matrices corresponding to the source domain data and the target domain data are input into the substructure fuzzy alignment module of the fuzzy subdomain feature extractor, and the alignment loss is obtained by calculating the FLMMD between the feature matrices of the source domain data and the target domain data, and the FLCORAL between the feature matrices of the source domain data and the target domain data.

The high-dimensional feature matrices of the source domain data and the target domain data are input into the substructure fuzzy alignment module to learn the domain-invariant representation of the subdomain level by minimizing the feature distribution differences between substructures. The substructure fuzzy alignment module includes two parts of alignment, specifically:

2.1. Alignment of the first part: Based on the fuzzy local maximum mean discrepancy (FLMMD) of the maximum mean discrepancy (MMD), FLMMD simultaneously considers the probability that each sample belongs to all categories, and realizes a more fine-grained fuzzy subdomain alignment, making the source domain data and the target domain data closer in the mapped feature space; the substructure fuzzy alignment module calculates the FLMMD between the feature matrices of the source domain data and the target domain data as the first part loss

2.2. Alignment in the second part: Fuzzy Local Coral (FLCORAL) based on the second-order statistic Correlation Alignment (CORAL). FLCORAL also considers the probability of each sample belonging to all categories at the same time, and performs fine-grained alignment on the second-order statistics to capture the complex differences between the two domains. The substructure fuzzy alignment module calculates the FLCORAL between the feature matrices of the source domain data and the target domain data as the second part loss.

2.3. Combine the first part of the loss and the second part of the loss to obtain the alignment loss. Combine the two parts of the loss of the substructure fuzzy alignment module and use the following formula to calculate the alignment loss:

Where: γ is The weight coefficient of .

3. Input the aligned time series feature matrix of the source domain data and the target domain data in the training set output by the fuzzy subdomain feature extractor into the RUL regressor, output the remaining life prediction values of the source domain data and the target domain data in the training set, and calculate the mean square error (MSE) between the source domain remaining life prediction value and the true value as the regression loss.

4. Calculate the total model loss based on alignment loss and regression loss The following formula is used for calculation:

Where: β is The penalty coefficient.

5. Minimize the total loss, feedback-adjust the network parameters of the fuzzy subdomain feature extractor and the RUL regressor, implement network training of the fuzzy subdomain feature extractor and the RUL regressor, until the training is completed, and obtain the trained remaining life prediction model.

By minimizing the alignment loss It is possible to learn domain-invariant representations and obtain domain-invariant feature matrices between the source domain and the target domain. Specifically, It is used to minimize the first-order moment between the source domain and the target domain. It is used to minimize the second-order moment between the source domain and the target domain, and measures the difference between the two domains by calculating the distance between the covariance of the source sample and the target sample. The two work together to make the data distribution of the source domain and the target domain closer.

For the fuzzy subdomain feature extractor and RUL regressor in series, a total model loss can be obtained Will minimize the total model loss In order to optimize the target, the network parameters of the fuzzy subdomain feature extractor and the RUL regressor are adjusted by feedback to realize the network training of the fuzzy subdomain feature extractor and the RUL regressor until the training termination condition is met and the trained remaining life model is obtained.

In this embodiment, the fuzzy subdomain feature extractor is a ResNet50 feature extractor. The RUL regressor is a regression predictor based on a fully connected network.

4. Remaining life prediction:

The test set is input into the trained remaining life prediction model to perform remaining life prediction and obtain the remaining life prediction result.

The present invention also aims to provide a bearing remaining life prediction system combining degradation stage division and subdomain adaptation, the system is used to implement the method described, the system comprises:

Curve construction module: used to construct health indicator curve;

Obtain the original data set, extract time domain and frequency domain features of the source domain data and target domain data in the original data set, and perform secondary index optimization and correlation analysis on the obtained multi-dimensional features to obtain a health index curve;

Stage division module: used to divide health stages;

The time series window weighted clustering algorithm is used to process the health index curve, obtain the health stage label and fuzzy membership of each source domain data and target domain data, and divide them into training set and test set according to the proportion;

Prediction model building module: used to build and train the remaining life prediction model;

The remaining life prediction model includes a fuzzy subdomain feature extractor and a RUL regressor; the training set is input into the remaining life prediction model to train it; during the training process, the total loss is obtained based on the alignment loss of the substructure fuzzy alignment module in the fuzzy subdomain feature extractor and the regression loss of the RUL regressor, and the parameters of the fuzzy subdomain feature extractor and the RUL regressor are optimized by minimizing the total loss, and the trained remaining life prediction model is obtained and saved;

Life prediction module: used to predict the remaining life;

The test set is input into the trained remaining life prediction model to perform remaining life prediction and obtain the remaining life prediction result.

Embodiment 2

In this embodiment, the execution process of the method of the present invention is described in detail through a specific example:

1. Experimental Dataset Acquisition and Health Indicator (HI) Construction

The data set used in this embodiment is the bearing data set of IEEE PHM Challenge 2012, which is obtained on the PRONOSTIA test platform. The platform consists of three parts: a rotating part, a load part, and a data acquisition part.

The electric power of the rotating part is 250W, and the power is transmitted to the bearing through the rotating shaft. The load part is a pneumatic jack, which provides a dynamic load of 4000N to the bearing, causing the bearing to degrade rapidly. The data acquisition part contains vibration data and temperature data. The vibration sensor consists of two micro accelerometers positioned at 90° to each other, placed on the horizontal axis and the vertical axis respectively. The sampling frequency is 25.6kHz, and 0.1s sampling is performed every 10s, and it stops when the vibration amplitude reaches 20g.

The data set contains three working conditions. The first one is load 4000N, speed 1800rpm, the second one is load 4200N, speed 1650rpm, and the last one is load 5000N, speed 1500rpm. HI creation includes the following steps:

1. Time-frequency statistical feature acquisition:

As shown in Figure 2, in order to fully explore the potential features of time series data, 17 time domain and 8 frequency domain features of the original signal are extracted, so as to study the change trend of the bearing vibration signal from multiple angles. The time domain signal refers to the change characteristics of the signal on the time axis, which can well describe the operation trend of the equipment. The frequency domain signal can well characterize the operation status of the equipment and facilitate the separation and removal of noise information. After a series of time domain and frequency domain feature extraction, the time-frequency feature is expressed as p = {p ₁ ,p ₂ ,…, _pi ,…, _pi }, where I = 25.

2. Secondary feature index extraction:

There are individual differences between the features extracted in step 1, so there is no same starting height between the features, and there are false fluctuations and noise inside. In order to eliminate these effects, the present invention proposes two secondary optimization feature indicators, the relative indicator and the denoising indicator. The role of the relative indicator is to eliminate individual differences, close the distribution gap, and align various feature vectors. Because the starting position heights of various statistical features are different, there is a relative gap in the early flat data part, and the absolute range of change is affected. The formula shown in (1) is used for calculation:

Among them, _pi represents a feature, i represents the feature number, and p _norm represents the average number of features under stable operation. K represents the duration of the stable phase. After the inter-individual difference alignment operation, the time-frequency feature becomes a relative index p _r ={p _r1 ,p _r2 ,…,p _ri ,…,p _rI }.

The denoising index is to reduce abnormal data points, accurately compress the fluctuation range of local sequences, and ensure the monotonicity of data trends. The calculation formula of the i-th denoising index p _di in the sliding window is:

Where p _rj is the jth data of the relative index obtained by formula (1), wi is the length of the sliding window, and _xi is the i-th data of the time series corresponding to p _r . _ki and _bi are the parameters of the linear regression model fitted on the i-th sliding window, which can be obtained by the least squares method. Formulas (3) and (4) represent the closed form expressions of _ki and _bi respectively. _Hi is the sliding window sample after compressing the local sequence fluctuations. Its expression is shown in formula (5). _Di is the starting point of _Hi :

Where y is the value of p _r . min(H _i ) and max(H _i ) represent the upper and lower bounds of the indicator, which are used to reduce the impact of abnormal data on the trend. They can be expressed as follows:

min(H _i )＝μ-3σ

max(H _i )＝μ+3σ

In formula (6), μ and σ are the mean and standard deviation of _Wi, respectively. After the relative index undergoes intra-individual compression and smoothing operation, the denoising index _pd = { _pd1 , _pd2 , …, _pri , …, _pdI } is obtained.

The obtained denoising index _pd is the final data p′ obtained after the secondary feature index extraction operation.

3. Construct HI curve:

HI is an indicator that reflects the change in health status throughout the life cycle, and is usually represented as a curve with a trend. Since bearing degradation is a gradual process, the initial stage is considered to be in a normal state. As operational faults occur, the data in the degradation stage deviates from the normal state data, and its correlation with the initial state will also change. Therefore, the correlation between the data in the later operation stage and the initial stage can be reflected as a set of data points in different health stages. Therefore, the present invention performs a correlation analysis on the transformed 25-dimensional features, and uses the Pearson correlation coefficient to effectively measure the degree of correlation of the data at two time points, obtains the trend of changes on the time axis, and constructs a universal HI. The specific approach is: select the starting part of the optimized 25-dimensional secondary feature index p′ as the base value of the normal state, and then calculate the Pearson correlation coefficient between the starting moment and other moments as the HI to measure the equipment status, which is expressed as follows:

Take the source domain dataset as an example, where x and y represent the multidimensional feature vectors at different time points after processing, x, y = p′ _j , p′ _k , j, k∈{1,2,…,N _s }. By calculating the Pearson coefficient in sequence, we can obtain the correlation coefficient vector R = {r ₁₁ ,r ₁₂ ,…,r _1N }, that is, the HI curve. The HI curve will serve as the basis for subsequent HS division and as one of the features input into the deep migration network.

2. Health Stage (HS) Division

Considering that the fault threshold indicators of various types of bearings are usually different, it is necessary to establish an adaptive HS division method. The present invention proposes a time-series window weighted clustering method (Time-series Window Weighted Fuzzy C-Means Algorithm, TWW-FCM). Since the HI curve obtained previously has local noise and fluctuations, the traditional FCM algorithm usually makes incorrect classifications for the judgment of noise points, resulting in problems of discontinuity of healthy stages such as short-term mutations or "false stages". Therefore, the current single-point prediction is not reliable, and it is necessary to use other points within a certain range before and after to determine the stage. Therefore, TWW-FCM suitable for stage division of time series data is proposed, and its principle diagram is shown in Figure 4. The specific process is as follows:

First, the HI curve needs to be divided into windows, and the statistical value of the window is used to replace the current single point value, so that the data can not only reflect the state within a period of time, but also be smoother and more continuous, reducing the mutation and oscillation of the data, so as to be more in line with the law of equipment degradation, which is conducive to data analysis and modeling. The present invention selects the Gaussian function as the window for processing, which is defined as:

Among them, _ri is the i-th value on the HI curve, μ represents the mean of the sample, and σ represents the standard deviation of the sample. Subsequently, the data is processed by windowing. For each data point _ri , the value of the Gaussian function at this point is used as the weight, and all data points in the window are weighted averaged. The processed HI, i.e., sequence G, is expressed by formula (9):

G＝(g ₁ ,g ₂ ,…,g _N ) (9)

After fuzzy smoothing of the HI curve, clustering is performed to obtain the health stage index. First, the number of clusters N is determined, and the membership value u _ij of each data point to each cluster is randomly initialized. The membership u _ij of each data point i represents the degree to which the data point i belongs to the jth cluster. It is a value between 0 and 1. The calculation of the fuzzy membership u _ij is shown in formula (10):

In the formula, ‖·‖ represents the Euclidean distance norm index between the feature sample _xj and the cluster center _ci , and q represents the fuzzy factor. Then, based on the fuzzy membership of each data point, the center point of each cluster is calculated as C = ( _c1 , _c2 , ..., _ci , ... _cN ). For the i-th cluster, the common coordinates of its center point _ci are calculated by formula (11):

TWW-FCM optimizes the membership value and the cluster center of each category through an iterative process to minimize the objective function J until the stopping condition is met. The objective function J and the corresponding constraints are shown in formula (12):

_{0≤uij≤1,1≤i≤C} ,1≤j≤N (12)

Since each cluster center is initially randomly initialized at the beginning of the iteration process, the iteration is stopped when a local minimum or saddle point of the objective function is obtained. The stopping condition is defined as the change of the membership matrix between two consecutive iteration steps meets the termination threshold ε. The convergence condition is expressed as follows:

||U ^k+1 -U ^k ||<ε (13)

Finally, after processing by the TWW-FCM algorithm, the health stage c _i ∈ (1, 2, …, N) to which each data point belongs and the corresponding fuzzy membership _ui = ( _ui1 , _ui2 , …, _uiN ) are obtained. The health stage label and the fuzzy membership matrix will be used as the input data of the deep migration network.

3. Fuzzy subdomain feature extractor for deep feature extraction and feature alignment:

The fuzzy subdomain feature extractor combines the health stage category and corresponding fuzzy membership of each data point to perform deep feature extraction and feature alignment on the acquired multidimensional time-frequency features. Unlike the general subdomain adaptation that uses a certain domain label, the present invention introduces the uncertainty of the stage into the subdomain adaptation, and uses the fuzzy membership generated in the TWW-FCM algorithm to represent the probability that a sample belongs to each subdomain, thereby achieving better subdomain adaptation. First, a deep neural network is used to obtain the feature potential representation of the source domain and target domain data, and then the feature representation of the source domain and the target domain is input into the substructure fuzzy alignment module (SFAM), and the domain-invariant representation of the subdomain level is learned by minimizing the domain differences between substructures. In the present invention, SFAM includes two multi-order subdomain metric distances: Fuzzy Local Maximum Mean Discrepancy (FLMMD) and Fuzzy Local CORAL (FLCORAL).

First, FLMMD is explained. MMD is a non-parametric distance estimation used to measure the difference between two distributions and is widely used in domain adaptation. The original MMD focuses on measuring the overall distribution difference, while ignoring the category information of each subdomain in a domain. The FLMMD proposed in this invention considers the probability of each sample belonging to all categories at the same time, realizes a finer-grained fuzzy subdomain alignment, and makes the source domain and target domain data closer in the mapped feature space.

Assuming the source domain and target domain Among them, x ^S , x ^T are the source domain and target domain samples, u ^S , u ^T are the corresponding fuzzy membership of the source domain and target domain samples, and x ^T is the source domain label. _DS and _DT are divided into N healthy stages, that is, the subdomains are and Where n∈1,2,…,N is the class label. The FLMMD between two distributions p and q is defined as the expected reproducing kernel Hilbert space (RKHS) distance between the mean embeddings in each subdomain. Therefore, the square form of MMD is shown in Equation (14):

Among them, x ^S and x ^T are and The samples in , p ⁽ⁿ⁾ and q ⁽ⁿ⁾ are and distribution. φ(·) represents some function that maps the input to an RKHS with feature kernel k, k(x ^S ,x ^T )＝<φ(x ^S ),φ(x ^T )>. Assuming that each sample belongs to each category according to the weight w ⁿ , its unbiased estimate is expressed as:

in, and They represent the and The weight of . and are all equal to 1, and is the weighted sum over category n. For sample x _i , the weight in FLMMD The calculation of is shown in formula (16):

Among them, u _in is the membership of the nth element of vector u _i . Since the stage fuzzy membership can well reflect the The probability distribution of different health stages, therefore, the present invention uses fuzzy membership and Calculate sample weights and

Although MMD is the most commonly used metric in domain adaptation, MMD only calculates the first-order moment and may not be able to fully capture the complex differences between the two domains. Therefore, the present invention introduces the second-order statistic CORAL loss between the source features and the target features. Specifically, the CORAL loss measures the difference between the two domains by calculating the distance between the covariance of the source sample and the target sample. The present invention proposes that the FLCORAL loss can enable the model to more comprehensively consider the fuzzy differences between subdomains, thereby further improving the generalization performance of the model. The calculation formula of the CORAL loss is as follows:

in, represents the Frobenius norm of the square matrix. ^{V S} and V ^T are the covariance matrices of the source data and target data with dimension d, which can be calculated by formula (18):

Where 1 is a column vector with all elements equal to 1, n _S and n _T represent the number of source data and target data respectively. By giving weights to sample data, more fine-grained subdomain information is introduced to achieve a closer second-order statistical distance at the subdomain level. Its unbiased estimate is expressed as:

in, Represents input data and The covariance matrix of . Consistent with FLMMD, the weights of source and target domain samples are and It can be calculated by the fuzzy membership u _i :

In order to align the hidden features of the source domain and the target domain, we need to activate the hidden states h ^T and h ^S . In a batch, given n _b from the source domain of labeled samples, and _bn from the target domain unlabeled samples, where _nb represents the batch size. As shown in Figure 5, the feature extractor in the FSARN network will generate the activated hidden state as well as Since we cannot directly calculate φ(·), the two distances FLMMD and FLCORAL are calculated by formula (21):

where k _mmd (·,·) and k _coral (·,·) represent the kernel functions of FLMMD and FLCORAL, respectively. After obtaining the estimated value of the weighted distribution difference between the source and target domains, each corresponding subdomain can be aligned by minimizing the difference between them.

4. RUL regressor for RUL prediction:

The RUL regressor is a prediction network with three fully connected layers. It performs RUL prediction by receiving the features obtained by the feature extractor. The final result is expressed as:

y _t =σ(w _o g _t +b _o ) (22)

in represents the output sequence of the fuzzy subdomain feature extractor at time t, y _t is the RUL prediction result at time t, σ(·) is the sigmoid function, represents a trainable parameter, and b _o is a scalar. The regressor uses mean-square error (MSE) as the regression loss function:

in and The samples are The target regression value and estimated value of .

In order to narrow the distance between the source domain and the target domain and optimize the prediction results of the model, it is necessary to solve the problem shown in the following formula (24):

where J(·,·) represents the loss function between the target domain RUL true value y _i and the predicted value f(x _i ), Used to measure all subdomain differences between the source domain and the target domain.

In summary, the loss of FSARN consists of two parts: fuzzy subdomain alignment loss And RUL prediction loss Objective Function It is expressed as:

Among them, β is the weight coefficient of subdomain alignment loss, and γ is the weight coefficient of CORAL loss. Therefore, subdomain adaptation and regression fitting are performed simultaneously, and the solution formula is shown in (26):

In the proposed deep network, by minimizing the subdomain alignment loss, the network can bring the source domain and target domain data closer by minimizing the difference between the subdomains; and learn the RUL prediction knowledge in the source domain by minimizing the RUL prediction loss. During the training process of the neural network model, the back propagation method is used for parameter update, and the stochastic gradient descent (SGD) algorithm is used as weight optimization to update the network parameters. At each step of training, the model parameters are updated by formula (27):

Where η represents the learning rate, which represents the learning steps taken by the SGD algorithm as the training progresses. _{θ E} and θ _R are the parameters of the feature extractor and RUL predictor, respectively. By minimizing the gradient using the loss function, the data distribution of the source domain and the target domain are pulled as close as possible, and the high-level features in the hidden layer can be automatically learned to perform RUL prediction on the unlabeled target domain data.

In the remaining life prediction method based on domain adaptation, the existing methods mostly focus on the global alignment of the source domain and the target domain, while ignoring the local information contained in the health stage. Local-based alignment can achieve more fine-grained feature alignment and enhance the applicability and applicability of the model. However, how to mine the common potential characteristics of the data when the target domain data is incomplete and the health status of each health stage is quite different is a difficult problem. The present invention proposes a bearing remaining life prediction method that combines degradation stage division and subdomain adaptation. Through a fuzzy subdomain adaptation regression network (Fuzzy Subdomain Adaptation Regression Network, FSARN), it uses multi-order metrics based on data labels and membership to bring each degradation stage closer, complete fuzzy substructure alignment and cross-domain regression, and improve the accuracy of prediction and the generalization of the model.

By adopting the above technical solution disclosed in the present invention, the following beneficial effects are obtained:

The present invention provides a method and system for predicting the remaining life of a bearing that combines degradation stage division and subdomain adaptation, which can fully and cleverly utilize the stages existing in the life cycle to correspond to different subdomains, and disperse the overall differences of global alignment into the stage differences of local alignment. In the health stage division stage, a time series fuzzy clustering algorithm suitable for time series window data is proposed to realize the unified and standardized health indicator construction and stage division process. In the migration stage, multi-order metrics based on data labels and membership are used to bring each degradation stage closer, so as to complete fuzzy substructure alignment and cross-domain regression. It can achieve more fine-grained feature alignment, build a model with better generalization, and at the same time achieve more accurate remaining life prediction.

The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be considered as the scope of protection of the present invention.

Claims (10)

1. A bearing residual life prediction method combining degradation phase division and sub-domain self-adaption is characterized in that: comprises the following steps of the method,

s1, constructing a health index curve:

acquiring an original data set, extracting time domain and frequency domain characteristics of source domain data and target domain data in the original data set, and performing secondary index optimization and correlation analysis on the obtained multidimensional characteristics to acquire a health index curve;

s2, health stage division:

processing the health index curve by adopting a time sequence window weighted clustering algorithm, obtaining the health stage labels and the fuzzy membership degree of each source domain data and each target domain data, and dividing the health stage labels and the fuzzy membership degree into a training set and a testing set according to a proportion;

s3, constructing and training a residual life prediction model:

the residual life prediction model comprises a fuzzy subdomain feature extractor and a RUL regressive; inputting the training set into a residual life prediction model to train the residual life prediction model; in the training process, based on the alignment loss of a sub-structure fuzzy alignment module in a fuzzy subdomain feature extractor and the regression loss of an RUL regressive, obtaining a model total loss, optimizing parameters of the fuzzy subdomain feature extractor and the RUL regressive by minimizing the model total loss, and obtaining and storing a trained residual life prediction model;

S4, residual life prediction:

and inputting the test set into a trained residual life prediction model to perform residual life prediction, and obtaining a residual life prediction result.

2. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: the secondary index optimization is specifically that the inter-characteristic difference alignment operation is carried out on the multidimensional characteristics to obtain relative indexes, and then the intra-characteristic compression smoothing operation is carried out on the relative indexes to obtain denoising indexes.

3. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: the correlation analysis is specifically to use the pearson correlation coefficient to measure the correlation degree of the data at each moment and the data at the initial moment on the index after the secondary optimization, and construct the health index.

4. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: the source domain data are electromechanical equipment monitoring data acquired when electromechanical equipment with a bearing runs to failure; the target domain data is monitoring data of electromechanical equipment from the operation of the electromechanical equipment without the bearing to the fault;

The source domain data are supervised data with the residual life of the bearing as a label; the target domain data is unsupervised data without a bearing remaining life tag.

5. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: step S2 specifically includes the following,

s21, dividing the health index curve into windows, and replacing the current single-point numerical value with the statistical value of the windows to realize fuzzy smoothing of the health index curve;

s22, clustering the health index curves subjected to fuzzy smoothing, and obtaining health stage labels and fuzzy membership degrees of the health stage labels of the source domain data and the target domain data through iterative optimization of fuzzy membership degrees of the data points and clustering centers of the categories;

s23, dividing the source domain data, the target domain data, the health-stage labels to which the source domain data and the target domain data belong and the fuzzy membership degree into a training set and a testing set in proportion.

6. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: step S3 specifically includes the following,

s31, inputting a training set into a fuzzy subdomain feature extractor, and respectively acquiring feature potential representations of source domain data and target domain data in the training set by using a deep neural network of the fuzzy subdomain feature extractor to acquire high-dimensional feature matrixes corresponding to the source domain data and the target domain data;

S32, inputting high-dimensional feature matrixes corresponding to the source domain data and the target domain data into a substructure fuzzy alignment module of a fuzzy subdomain feature extractor, and acquiring alignment loss by calculating FLMMD between the feature matrixes of the source domain data and the target domain data and FLCORAL between the feature matrixes of the source domain data and the target domain data and the feature matrix time of the source domain data and the target domain data;

s33, inputting the time sequence feature matrix of the aligned source domain data and the target domain data in the training set, which are output by the fuzzy subdomain feature extractor, into an RUL regressive device, outputting the residual life predicted value of the source domain data and the target domain data in the training set, and calculating the mean square error of the residual life predicted value and the true value of the source domain as regression loss;

s34, calculating the total loss of the model according to the alignment loss and the regression loss;

and S35, minimizing the total loss of the model, and feeding back and adjusting network parameters of the fuzzy subdomain feature extractor and the RUL regressive to realize network training of the fuzzy subdomain feature extractor and the RUL regressive until the training is completed, so as to obtain a trained residual life prediction model.

7. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 6, wherein: step S32 specifically includes the following,

S321, alignment of the first portion: fuzzy local maximum mean value difference based on the maximum mean value difference, and meanwhile, the probability that each sample belongs to all categories is considered, so that the alignment of fuzzy subdomains with finer granularity is realized; calculating FLMMD between the source domain data and the target domain data feature matrix as a first partial loss;

s322, aligning the second part: fine granularity alignment is performed on the second order statistics based on Fuzzy Local CORAL of the second order statistics Correlation Alignment while considering the probability that each sample belongs to all categories; calculating FLCORAL between the source domain data and the target domain data feature matrix as a second partial loss;

s323, integrating the first partial loss and the second partial loss to obtain the alignment loss.

8. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: the fuzzy subdomain feature extractor is a ResNet50 feature extractor.

9. The method for predicting bearing residual life by combining degradation phase division and sub-domain adaptation according to claim 1, wherein: the RUL regressor is a regression predictor based on a fully connected network.

10. A bearing residual life prediction system combining degradation phase division and sub-domain self-adaption is characterized in that: a system for implementing the method of any one of the preceding claims 1 to 9, said system comprising,

and a curve construction module: the method is used for constructing a health index curve;

acquiring an original data set, extracting time domain and frequency domain characteristics of source domain data and target domain data in the original data set, and performing secondary index optimization and correlation analysis on the obtained multidimensional characteristics to acquire a health index curve;

the stage division module: for dividing the health phase;

processing the health index curve by adopting a time sequence window weighted clustering algorithm, obtaining the health stage labels and the fuzzy membership degree of each source domain data and each target domain data, and dividing the health stage labels and the fuzzy membership degree into a training set and a testing set according to a proportion;

the prediction model building module: the method is used for constructing and training a residual life prediction model;

the residual life prediction model comprises a fuzzy subdomain feature extractor and a RUL regressive; inputting the training set into a residual life prediction model to train the residual life prediction model; in the training process, based on the alignment loss of the sub-structure fuzzy alignment module in the fuzzy subdomain feature extractor and the regression loss of the RUL regressive, acquiring total loss, optimizing parameters of the fuzzy subdomain feature extractor and the RUL regressive by minimizing the total loss, and acquiring and storing a trained residual life prediction model;

Life prediction module: for predicting remaining life;

and inputting the test set into a trained residual life prediction model to perform residual life prediction, and obtaining a residual life prediction result.