CN111506862B - Rolling bearing fault diagnosis method based on multisource weighting integrated transfer learning - Google Patents

Rolling bearing fault diagnosis method based on multisource weighting integrated transfer learning Download PDF

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CN111506862B
CN111506862B CN202010368012.5A CN202010368012A CN111506862B CN 111506862 B CN111506862 B CN 111506862B CN 202010368012 A CN202010368012 A CN 202010368012A CN 111506862 B CN111506862 B CN 111506862B
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姜洪开
杨懿
王应雷
鲁腾飞
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Abstract

The invention discloses a rolling bearing fault diagnosis method based on multi-source weighting integrated transfer learning. The method comprises the steps of selecting a fault vibration signal of a rolling bearing under a certain working condition as a target domain, selecting a fault vibration signal of the same type of bearing under other working conditions as a source domain, extracting time-frequency domain characteristic quantity of the vibration signal as samples of the target domain and the source domain, and giving corresponding sample weights to the target domain and the source domain; an improved gradient lifting tree (LightGBM) is adopted as a base learner for integrated transfer learning, so that the operation efficiency and accuracy of an algorithm are improved; and updating the sample weight by adopting a weight updating strategy of the TrAdaboost after the multi-source domain improvement, so as to reduce the influence of the negative migration source domain on the migration effect. The diagnosis method has reliable results and good real-time performance, and is suitable for the fault diagnosis of the rolling bearing under the condition of fewer target fault samples.

Description

Rolling bearing fault diagnosis method based on multisource weighting integrated transfer learning
Technical Field
The invention belongs to the field of fault diagnosis of mechanical equipment, and particularly relates to a fault diagnosis method of a rolling bearing.
Background
Rolling bearings are key components in modern rotary machines, and at present, the working conditions of many rotary machines are bad, and the rolling bearings become one of the most vulnerable elements, and once the rolling bearings are out of order, serious consequences are likely to happen, so the fault diagnosis of the rolling bearings is an important research direction in the field of fault diagnosis. At present, many rotary machines are developed towards the directions of high speed and integration, so that the fault characteristic information of the rolling bearing is not easy to collect, the fault sample quantity of the target diagnosis fault characteristic is possibly small, and meanwhile, the development of the sensor is also gradually changed, so that the collected fault information also has the characteristic of multiple sources. Therefore, the existing rolling bearing fault characteristic information has the characteristics of information multisource, small target fault sample size and the like.
Currently, three general methods for fault diagnosis of rolling bearings are mainly used: knowledge-based fault diagnosis, traditional machine learning-based fault diagnosis, deep learning-based fault diagnosis. The fault diagnosis based on knowledge is to build an expert system to diagnose by using the experience and knowledge of the expert, but the fault diagnosis has the defects of difficult acquisition of knowledge, poor self-adaptation capability and the like in practical situations. The fault diagnosis based on the traditional machine learning is to classify and identify the fault characteristics by utilizing the machine learning, commonly has the fault diagnosis based on an artificial neural network or a support vector machine, and has certain application in the field of fault diagnosis, but the methods still have a plurality of defects, such as easy sinking of the artificial neural network into local minima and longer training time; the support vector machine is suitable for learning small samples and is not suitable for learning multi-source large samples with high redundancy. The fault diagnosis based on the deep learning is a hot trend which is rising in recent years, the deep learning has the characteristics of autonomous learning essential characteristics, high diagnosis accuracy and the like, but the deep learning needs a large amount of target fault samples to support, and is not suitable for the condition of less target fault characteristic information.
Most importantly, the conventional machine learning or deep learning method requires that the source domain data and the target domain data are distributed together, and the migration learning can migrate the knowledge learned from the source domain to the target domain, so that the migration learning can solve the diagnosis problem of a small number of fault samples. However, the transfer learning also has the problem of negative transfer, and the negative transfer source domain may seriously affect the effect of the transfer learning, and the conventional TrAdaboost algorithm based on sample transfer has the defects that the source domain cannot be expanded, the source domain cannot be effectively screened and the like although the transfer learning of a small number of fault samples can be realized.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a multi-source domain integrated transfer learning strategy, which can effectively reduce the influence of a negative transfer source domain on the transfer learning effect, and simultaneously uses an improved gradient lifting tree (LightGBM) as an integrated learning base learner to further improve the accuracy and instantaneity of diagnosis, thereby effectively completing the fault diagnosis of the rolling bearing with fault information multi-source property and less target fault sample size.
The invention provides a rolling bearing fault diagnosis method based on multi-source weighting integrated transfer learning. The method comprises the steps of selecting a fault vibration signal of a rolling bearing under a certain working condition as a target domain, selecting a fault vibration signal of the same type of bearing under other working conditions as a source domain, extracting time-frequency domain characteristic quantity of the vibration signal as samples of the target domain and the source domain, and giving corresponding sample weights to the target domain and the source domain; an improved gradient lifting tree (LightGBM) is adopted as a base learner for integrated transfer learning, so that the operation efficiency and accuracy of an algorithm are improved; and updating the sample weight by adopting a weight updating strategy of the TrAdaboost after the multi-source domain improvement, so as to reduce the influence of the negative migration source domain on the migration effect. The diagnosis method has reliable results and good real-time performance, and is suitable for the fault diagnosis of the rolling bearing under the condition of fewer target fault samples.
The technical scheme of the invention is as follows:
the rolling bearing fault diagnosis method based on multi-source weighting integrated transfer learning is characterized by comprising the following steps of: the method comprises the following steps:
step 1: selecting a fault vibration signal of a rolling bearing under a certain working condition as a target domain, selecting a fault vibration signal of the same type of bearing under other working conditions as a source domain, extracting time-frequency domain characteristic quantity of the vibration signal as samples of the target domain and the source domain, and giving corresponding sample weights to the target domain and the source domain;
step 2: adopting an improved gradient lifting tree as a base learner for integrated transfer learning, updating the sample weight by using the target domain and source domain samples and the sample weight obtained in the step 1 and adopting a weight updating strategy of the TrAdaboost after multi-source domain improvement, and training the base learner to obtain a final integrated transfer learner;
step 3: and (3) performing rolling bearing fault diagnosis by using the integrated transfer learner obtained in the step (2).
Further, the time-frequency domain feature quantity of the vibration signal extracted in the step 1 comprises a norm square sum, a standard deviation, a root mean square value, kurtosis, a skew, a waveform index, a mean value, a median, a peak-to-peak value, a maximum value, a square root amplitude value, an absolute mean value, a peak index and a variance.
Further, in step 1, a target fault sample set is selected as a target domain training set D T N auxiliary fault sample sets are selected as source domain training setsSetting the target domain sample weight to omega T Wherein-> The initial value of the target domain sample weight is +.>Wherein n is T Setting N source domain sample weights as +.>Wherein->The initial value of the sample weight of the source domain k isWherein->The number of samples for source field k; the number of fault types in the training set is M, and the target domain label matrix is set as y T The source domain label matrix is->
Further, the specific process of the step 2 is as follows:
step 2.1: with improved gradientLifting tree as base learner, L (x) i ,y i ) To improve the loss function of the gradient-lifted tree when the training set does not have sample weights, for the training set with sample weights ω, the final loss function of the gradient-lifted tree is improved as follows:
L f =∑ω i ·L(x i ,y i )
step 2.2: the sample weight is updated by adopting the TrAdaboost with the multisource domain improved, and the specific implementation process comprises the following steps:
step 2.2.1: setting the iterative times of the algorithm as M, wherein M cannot exceed n SFor the total number of samples in all source domains, a fixed update parameter defining the sample weights of the source domains is beta S The calculation mode is as follows:
step 2.2.2: in the t-th iteration, combining the target domain and the source domain into a training set k, and setting the sample weight of the training set k asTraining set k and sample weights +.>Input base learning deviceObtaining training error of target domain on the base learner as +.>The calculation mode is as follows:
satisfy->Setting the dynamic update parameter of the source domain k sample weight to +.>Wherein the method comprises the steps ofThe sample weights for source field k are updated as:
step 2.2.3: in the t-th iteration, after the sample weights of all source domains are updated, obtaining the total sample weight of the source domainCombining the target domain and all source domains into a training set alpha, and setting the sample weight of the training set alpha as omega α (t)=(ω T (t),ω S (t+1)), training set alpha and sample weight omega thereof α (t) input base learner->Obtaining training error of target domain on the base learner> Satisfy->Setting the dynamic update parameter of the target domain sample weight to +.>Wherein->The sample weight of the target domain is updated as:
step 2.2.4: when t is greater than or equal to M orWhen the iteration is exited, t learners h are obtained i The training error of the corresponding target domain of each learner is +.>Dynamic update parameter is->For the diagnosis of the two classification faults, the final integrated learner h f The method comprises the following steps:
for multi-class fault diagnosisIn order to integrate t learners according to weighted voting, taking the highest predicted value of the vote as the predicted value of a sample to obtain a final integrated learner, and enabling a learner with the predicted value of a training sample being j to be h j The corresponding training error of the target domain is +.>Final ensemble learner h f The method comprises the following steps:
advantageous effects
The beneficial effects of the invention are as follows: the invention adopts an improved gradient lifting tree (LightGBM) as a base learner for integrated transfer learning, thereby improving the operation efficiency and accuracy of the algorithm; meanwhile, the improved TrAdaboost of the multi-source domain is used as an updating strategy of the sample weight, so that the expansibility of the source domain is increased, and the influence of the negative migration source domain on the migration learning effect is reduced. The accuracy and reliability of the method of the invention in bearing fault diagnosis is verified in the examples using the relevant disclosed rolling bearing vibration signals. Compared with the traditional method, the fault diagnosis method has high accuracy and high reliability, and can be applied to the fault diagnosis of the rolling bearing under the condition of fewer target fault samples.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of a method of diagnosing a rolling bearing failure according to the present invention;
figure 2 is a schematic drawing of a collection of a rolling bearing laboratory bench according to the present invention;
FIG. 3 is a time domain diagram of vibration signals of a rolling bearing according to the present invention;
FIG. 4 is a graph of the accuracy of source domain and fault diagnosis of different types according to the present invention;
FIG. 5 is a graph of the accuracy of the fault diagnosis and the different types of target domains according to the present invention;
FIG. 6 is a graph comparing accuracy of the present invention with a conventional machine learning algorithm.
Detailed Description
The following detailed description of embodiments of the invention is exemplary and intended to be illustrative of the invention and not to be construed as limiting the invention.
Referring to fig. 1, the contents of the present invention may be divided into two parts. The first part is to extract the time-frequency domain characteristics of the rolling bearing vibration signals, construct target domain and source domain samples, give corresponding sample weights, and initialize the LightGBM algorithm; and the second part is to update sample weights of the source domain and the target domain by utilizing the TrAdaboost after the multi-source domain improvement, and obtain a final integrated transfer learning classifier after the iteration finishing condition is met, thereby completing the fault diagnosis of the rolling bearing.
Referring to fig. 2, fig. 2 is a schematic structural diagram of a rolling bearing failure experiment table in the example, and the experiment table is composed of a motor, a driving end bearing, a load and an accelerometer.
Referring to fig. 3, fig. 3 is a time domain diagram of a vibration signal of a rolling bearing according to an example, wherein the abscissa represents time in s; the ordinate indicates the vibration amplitude in m/s 2
Referring to fig. 4, fig. 4 is a graph of fault diagnosis accuracy and five different source domains under the same target domain, and the abscissa is the number of recorded results and the ordinate is the fault diagnosis accuracy.
Referring to fig. 5, fig. 5 is a graph of fault diagnosis accuracy and a ratio of the target domain in the total training samples under the same source domain, and the abscissa is the ratio of the number of samples of the target domain in the total training samples and the ordinate is the fault diagnosis accuracy.
Referring to fig. 6, fig. 6 is a graph showing the comparison between the fault diagnosis accuracy of the method and the Support Vector Machine (SVM) according to the present invention in the same positive migration source domain training sample, wherein the abscissa is the duty ratio of the target domain sample in the total training sample, and the ordinate is the fault diagnosis accuracy.
The invention is implemented according to the following steps:
(1) The method comprises the steps of selecting a fault vibration signal of a rolling bearing under a certain working condition as a target domain, selecting a fault vibration signal of the same type of bearing under other working conditions as a source domain, extracting time-frequency domain characteristic quantity of the vibration signal as samples of the target domain and the source domain, and giving corresponding sample weights to the target domain and the source domain;
(2) An improved gradient lifting tree (LightGBM) is adopted as a base learner for integrated transfer learning, so that the operation efficiency and accuracy of an algorithm are improved; and updating the sample weight by adopting a weight updating strategy of the TrAdaboost after the multi-source domain improvement, so as to reduce the influence of the negative migration source domain on the migration effect.
The method comprises the following steps of selecting a fault vibration signal of a rolling bearing under a certain working condition as a target domain, selecting a fault vibration signal of the same bearing under other working conditions as a source domain, extracting time-frequency domain characteristic quantity of the vibration signal as samples of the target domain and the source domain, and giving corresponding sample weights to the target domain and the source domain, and the method comprises the following steps:
step 1: collecting fault vibration signals of the rolling bearing, extracting 14 time-frequency domain statistical characteristics of the vibration signals, namely norm square sum, standard deviation, root mean square value, kurtosis, skewness, waveform index, mean value, median, peak-to-peak value, maximum value, root mean square amplitude value, absolute mean value, peak index and variance, and forming a 14-dimensional feature vector;
step 2: selecting a target fault sample set as a target domain training set D T N auxiliary fault sample sets are selected as source domain training sets
Step 3: setting the target domain sample weight to omega T WhereinThe initial value of the target domain sample weight is +.>Wherein n is T Setting N source domain sample weights as the sample number of the target domainWherein->Sample weight initialization for source field kThe value is +.> Wherein->The number of samples for source field k;
step 4: the number of fault types in the training set is M, and the target domain label matrix is set as y T The source domain label matrix is
The improved gradient lifting tree (LightGBM) is adopted as a base learner for integrated transfer learning, so that the operation efficiency and accuracy of an algorithm are improved; the sample weight is updated by adopting a weight updating strategy of the TrAdaboost after the multi-source domain improvement, the influence of the negative migration source domain on the migration effect is reduced, and the method comprises the following steps:
step 1: using an improved gradient-lifted tree (LightGBM) as a base learner in the next step, L (x) i ,y i ) For the loss function of the LightGBM when the training set does not have sample weights, the final loss function of the LightGBM for the training set with sample weights ω is:
L f =∑ω i ·L(x i ,y i ) (1)
step 2: the sample weight is updated by adopting the TrAdaboost with the multisource domain improved, and the specific implementation process comprises the following steps:
step 2.1: setting the iterative times of the algorithm as M, wherein M cannot exceed n SFor the total number of samples in all source domains, a fixed update parameter defining the sample weights of the source domains is beta S The calculation mode is as follows:
step 2.2: in the t-th iteration, combining the target domain and the source domain into a training set k, and setting the sample weight of the training set k asTraining set k and sample weights +.>Input base learning deviceObtaining training error of target domain on the base learner as +.>The calculation mode is as follows:
provision for provision ofMust meet->Setting the dynamic update parameter of the source domain k sample weight to +.>Wherein the method comprises the steps ofThe sample weights for source field k are updated as:
step 2.3: in the t-th iteration, all source domainsAfter the sample weights are updated, the total source domain sample weight is obtainedCombining the target domain and all source domains into a training set alpha, and setting the sample weight of the training set alpha as +.>Training set alpha and sample weight omega thereof α (t) input base learner->Obtaining training error of target domain on the base learner>The calculation mode is as shown in formula (3) and +.>Must meet->Setting the dynamic update parameter of the target domain sample weight to +.>Wherein->The sample weight of the target domain is updated as:
step 2.4: when t is greater than or equal to M orWhen the iteration is exited, t learners h are obtained i The training error of the corresponding target domain of each learner is +.>Dynamic update parameter is->For the diagnosis of the two classification faults, the final integrated learner h f The method comprises the following steps:
for multi-class fault diagnosisIn order to integrate t learners according to weighted voting, taking the highest predicted value of the vote as the predicted value of a sample to obtain a final integrated learner, and enabling a learner with the predicted value of a training sample being j to be h j The corresponding training error of the target domain is +.>Final ensemble learner h f The method comprises the following steps:
and then, the obtained integrated transfer learner can be used for completing the fault diagnosis of the rolling bearing.
Based on the method, the effectiveness of the method in the fault diagnosis of the rolling bearing is verified by adopting rolling bearing vibration data disclosed by a certain college. The schematic diagram of the experimental platform is shown in fig. 2, and different data types are set by different fault depths, different fault positions and different sensor arrangement directions. The driving end is a deep groove ball bearing with the model number of 6205-2RSJEMSKF, and the fan end is a deep groove ball bearing with the model number of 6203-2 RSJEMSKF. The fault depth varies from 0.007 inches to 0.028 inches. The data types include normal, inner ring failure, outer ring failure and rolling body failure. The motor loads are respectively 1797 rpm, 1772 rpm, 1750 rpm and 1730 rpm, and the motor speeds are respectively corresponding to 0,1, 2 and 3 HP.
Fig. 3 is a time domain plot of vibration signals of a rolling bearing as referred to in the example, wherein four data types are selected, namely, no load, normal signals at 1797 rpm, and inner ring faults, rolling body faults and outer ring faults with a fault depth of 0.007 inches under the same conditions, each data type taking 12000 data points and sampling frequency of 12000hz.
The data points are segmented, 512 data points in each segment are obtained, 14 time-frequency domain statistical characteristics of vibration signals are extracted, and 14-dimensional feature vectors are respectively formed by norm square sum, standard deviation, root mean square value, kurtosis, skewness, waveform index, mean value, median, peak-to-peak value, maximum value, root-to-square amplitude value, absolute average value, peak index and variance and serve as one sample. Taking a normal signal with no load and 1797 rpm of a target domain and an inner ring fault, a rolling body fault and an outer ring fault with the fault depth of 0.007 inch under the same condition, wherein each fault type comprises 10 samples; taking a source domain 1 as a passive domain sample; taking a source domain 2 as a normal signal without load at the rotating speed of 1797 r/min and an inner ring fault, a rolling body fault and an outer ring fault with the fault depth of 0.021 inch under the same condition, wherein each fault type comprises 200 samples, and the source domain 2 is a proven positive migration source domain; taking a source domain 3 as an inner ring fault with no load and fault depth of 0.007,0.014,0.021,0.028 inches at 1797 rpm, wherein each fault type comprises 200 samples, and the source domain 3 is a proven negative migration source domain; taking a source field x proved to be in positive migration, wherein the source field x is a normal signal with a load of 1HP and a rotating speed of 1772 r/min, and an inner ring fault, a rolling body fault and an outer ring fault with a fault depth of 0.014 inch under the same condition, and each fault type comprises 200 samples; taking a source domain y proved to be negative migration as a rolling body fault with a load of 2HP and a fault depth of 0.007,0.014,0.021,0.028 inches at 1750 revolutions per minute, wherein each fault type comprises 200 samples; the source domain 4 is a multi-source domain consisting of a source domain 3, a source domain 2 and a source domain x; the source taking domain 5 is a multi-source domain consisting of a source domain 3, a source domain 2 and a source domain y.
Fig. 4 is a graph of five different source domains and fault diagnosis accuracy for the same target domain, the selected target domain has a ratio of 0.05 in the total training sample, and five average diagnosis accuracy records for each source domain form the graph. From the graph, it can be seen that the single positive migration source domain can improve the fault diagnosis accuracy, and the single negative migration source domain can reduce the fault diagnosis accuracy, and the fault diagnosis accuracy of the multi-source domain including the positive migration source domain is better than Shan Yuanyu, and the more the positive migration source domains are, the higher the fault diagnosis accuracy is.
Fig. 5 is a graph of fault diagnosis accuracy and the ratio of the target domain in the total training sample under the same source domain, wherein for convenience of presentation, the selected source domain is the positive migration source domain, the ratio of the target domain sample number in the total training sample is 0.02,0.03,0.04,0.05,0.10,0.20,0.30,0.40,0.50,0.60,0.70,0.80,0.90,1.0, and the graph is recorded for fault diagnosis average accuracy of the method. The graph shows that the fault diagnosis accuracy is positively correlated with the target domain sample ratio, and the method has good fault diagnosis accuracy when the total training sample ratio of the target domain sample number is more than 0.04.
Fig. 6 is a graph of the comparison of the fault diagnosis accuracy of the proposed method and the Support Vector Machine (SVM) for the same positive migration source domain training samples, with the abscissa being the duty ratio of the target domain samples in the total training samples and the ordinate being the fault diagnosis accuracy. It can be seen that when the target domain sample ratio is very low, the fault diagnosis accuracy of the SVM is low, and the method has great advantages compared with the method.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention.

Claims (2)

1. A rolling bearing fault diagnosis method based on multi-source weighting integrated transfer learning is characterized by comprising the following steps of: the method comprises the following steps:
step 1: selecting a fault vibration signal of a rolling bearing under a certain working condition as a target domain, selecting a fault vibration signal of the same type of bearing under other working conditions as a source domain, extracting time-frequency domain characteristic quantity of the vibration signal as samples of the target domain and the source domain, and giving corresponding sample weights to the target domain and the source domain;
the extracted time-frequency domain characteristic quantity of the vibration signal comprises a norm square sum, a standard deviation, a root mean square value, kurtosis, a skewness, a waveform index, a mean value, a median, a peak-to-peak value, a maximum value, a root mean square amplitude value, an absolute average value, a peak index and a variance;
step 2: adopting an improved gradient lifting tree as a base learner for integrated transfer learning, updating the sample weight by using the target domain and source domain samples and the sample weight obtained in the step 1 and adopting a weight updating strategy of the TrAdaboost after multi-source domain improvement, and training the base learner to obtain a final integrated transfer learner;
the specific process of updating the sample weight by adopting the weight updating strategy of the TrAdaboost after the multi-source domain improvement is as follows:
step 2.1: improved gradient lifting tree is used as a base learner, L (x i ,y i ) To improve the loss function of the gradient-lifted tree when the training set does not have sample weights, for the training set with sample weights ω, the final loss function of the gradient-lifted tree is improved as follows:
L f =∑ω i ·L(x i ,y i )
step 2.2: the sample weight is updated by adopting the TrAdaboost with the multisource domain improved, and the specific implementation process comprises the following steps:
step 2.2.1: setting the iterative times of the algorithm as M, wherein M cannot exceed n SFor the total number of samples in all source domains, a fixed update parameter defining the sample weights of the source domains is beta S The calculation mode is as follows:
step 2.2.2: in the t-th iteration, combining the target domain and the source domain into a training set k, and setting the sample weight of the training set k asTraining set k and sample weights +.>Input base learner->x-y, the training error of the target domain on the base learner is +.>The calculation mode is as follows:
satisfy->Setting the dynamic update parameter of the source domain k sample weight to +.>Wherein->The sample weights for source field k are updated as:
step 2.2.3: in the t-th iteration, after the sample weights of all source domains are updated, obtaining the total sample weight of the source domainCombining the target domain and all source domains into a training set alpha, and setting the sample weight of the training set alpha as omega α (t)=(ω T (t),ω S (t+1)), training set alpha and sample weight omega thereof α (t) input base learner->x-y, obtaining training error of target domain on the basic learner> Satisfy->Setting the dynamic update parameter of the target domain sample weight to +.>Wherein->The sample weight of the target domain is updated as:
step 2.2.4: when t is greater than or equal to M orWhen the iteration is exited, t learning resultsDevice h i The training error of the corresponding target domain of each learner is +.>Dynamic update parameter is->For the diagnosis of the two classification faults, the final integrated learner h f The method comprises the following steps:
for multi-class fault diagnosisIn order to integrate t learners according to weighted voting, taking the highest predicted value of the vote as the predicted value of a sample to obtain a final integrated learner, and enabling a learner with the predicted value of a training sample being j to be h j The corresponding training error of the target domain is +.>Final ensemble learner h f The method comprises the following steps:
step 3: and (3) performing rolling bearing fault diagnosis by using the integrated transfer learner obtained in the step (2).
2. The rolling bearing fault diagnosis method based on multi-source weighting integrated transfer learning according to claim 1, wherein the method comprises the following steps: in step 1, a target fault sample set is selected as a target domain training set D T N auxiliary fault sample sets are selected as source domain training setsSetting the target domain sample weight to omega T Wherein->The initial value of the target domain sample weight is +.>Wherein n is T Setting N source domain sample weights as +.>Wherein->The initial value of the sample weight of the source domain k isWherein->The number of samples for source field k; the number of fault types in the training set is M, and the target domain label matrix is set as y T The source domain label matrix is->
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