CN110686897A - Variable working condition rolling bearing fault diagnosis method based on subspace alignment - Google Patents

Variable working condition rolling bearing fault diagnosis method based on subspace alignment Download PDF

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CN110686897A
CN110686897A CN201910985862.7A CN201910985862A CN110686897A CN 110686897 A CN110686897 A CN 110686897A CN 201910985862 A CN201910985862 A CN 201910985862A CN 110686897 A CN110686897 A CN 110686897A
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张博
李伟
张梦
任勇
佟哲
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China University of Mining and Technology CUMT
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Abstract

一种基于子空间对齐的变工况滚动轴承故障诊断方法，属于机械故障诊断领域。将是不同工况条件下轴承的振动信号放入源领域和目标领域并生成对应的子空间，将样本转换到d维特征向量构建的子空间中通过最小化Bregman散度计算转换矩阵M，使得对齐后源领域子空间ZA＝ZSM与目标领域子空间ZT坐标对齐，从而消除领域间数据分布的差异，最后使用训练后的分类模型对投影后的目标领域样本集合中的样本进行故障诊断。其提供了一种能够消除工况影响，并获取仅反映滚动轴承故障或性能退化的信息的方法，从而使滚动轴承故障的诊断更加准确，具有极高的推广价值。

Figure 201910985862

The invention discloses a fault diagnosis method for a variable working condition rolling bearing based on subspace alignment, belonging to the field of mechanical fault diagnosis. Put the vibration signals of the bearing under different working conditions into the source domain and the target domain and generate the corresponding subspace, convert the samples into the subspace constructed by the d-dimensional eigenvectors, and calculate the transformation matrix M by minimizing the Bregman divergence, so that After alignment, the source domain subspace Z A = Z S M is aligned with the target domain subspace Z T coordinates, so as to eliminate the difference in data distribution between domains, and finally use the trained classification model to perform the projection on the samples in the target domain sample set. Troubleshooting. It provides a method that can eliminate the influence of working conditions and obtain information that only reflects the failure or performance degradation of the rolling bearing, thereby making the diagnosis of the rolling bearing fault more accurate and having extremely high promotion value.

Figure 201910985862

Description

一种基于子空间对齐的变工况滚动轴承故障诊断方法A fault diagnosis method for rolling bearings with variable working conditions based on subspace alignment

技术领域technical field

本发明涉及一种滚动轴承故障诊断方法，尤其是一种基于子空间对齐的变工况滚动轴承故障诊断方法，属于机械故障诊断领域。The invention relates to a fault diagnosis method for a rolling bearing, in particular to a fault diagnosis method for a rolling bearing with variable working conditions based on subspace alignment, and belongs to the field of mechanical fault diagnosis.

背景技术Background technique

滚动轴承是电力、石化、冶金、机械、航空航天以及一些军事工业部门中使用最广泛的机械零件,也是最易损伤的部件之一。它具有效率高、摩擦阻力小、装配方便、润滑易实现等优点,在旋转机械上应用非常普遍,并起着关键作用。旋转机械设备的许多故障都与滚动轴承有着密切的关联。据有关资料统计,机械故障的70％是振动故障,而振动故障中有30％是由滚动轴承引起的。这是因为滚动轴承在机械设备中起着承受载荷和传递载荷的作用,而且工作条件比较恶劣，长期连续工作在高载荷、高转速下，容易受到损害和出现故障。滚动轴承故障引起的直接后果轻则降低和失去系统的某些功能,重则造成严重的甚至是灾难性的事故。因此，滚动轴承的故障诊断方法,一直是机械故障诊断中重点发展的技术之一，具有重要的社会经济意义。Rolling bearings are the most widely used mechanical parts in electric power, petrochemical, metallurgy, machinery, aerospace and some military industrial sectors, and also one of the most vulnerable parts. It has the advantages of high efficiency, low friction resistance, convenient assembly, and easy realization of lubrication. It is widely used in rotating machinery and plays a key role. Many failures of rotating machinery are closely related to rolling bearings. According to relevant statistics, 70% of mechanical failures are vibration failures, and 30% of vibration failures are caused by rolling bearings. This is because rolling bearings play a role in bearing and transmitting loads in mechanical equipment, and the working conditions are relatively poor. Long-term continuous work under high load and high speed is prone to damage and failure. The direct consequences of rolling bearing failures range from reducing and losing some functions of the system to serious or even catastrophic accidents. Therefore, the fault diagnosis method of rolling bearing has always been one of the key development technologies in mechanical fault diagnosis, and has important social and economic significance.

滚动轴承在机械设备中往往运行工况多变(载荷、转速等连续地或间歇性地变化)。采集到的传感信号与工况存在直接关联关系。系统变工况运行时，新数据不断涌现，原先可利用的有标签传感数据与新工况条件下的测试样本产生了分布差异。已有的训练样本已经不足以训练得到一个可靠的故障诊断模型。同时，重新标注一批新工况条件下的故障样本不仅费时费力而且非常昂贵。Rolling bearings often have variable operating conditions in mechanical equipment (load, speed, etc. change continuously or intermittently). There is a direct correlation between the collected sensor signals and the working conditions. When the system runs under variable operating conditions, new data emerges constantly, and there is a distribution difference between the previously available labeled sensor data and the test samples under the new operating conditions. The existing training samples are not enough to get a reliable fault diagnosis model. At the same time, re-labeling a batch of fault samples under new operating conditions is not only time-consuming, labor-intensive, but also very expensive.

由于不同工况条件下轴承的振动信号，由于源领域与目标领域存在分布差异，因此源领域训练出来的故障分类器不能直接用于目标领域中的故障分类，这就引起了滚动轴承故障诊断的一个重要问题，即，变工况条件下如何利用少量的有标签训练样本或者源领域数据，建立一个可靠的模型对新工况条件或目标领域数据进行预测，其中源领域数据和目标领域数据可以不具有相同的数据分布。Due to the distribution difference between the source domain and the target domain of the vibration signals of the bearing under different working conditions, the fault classifier trained in the source domain cannot be directly used for fault classification in the target domain, which leads to a problem of rolling bearing fault diagnosis. The important question is how to use a small number of labeled training samples or source domain data to build a reliable model to predict new working conditions or target domain data under variable working conditions, in which the source domain data and target domain data can be different. have the same data distribution.

发明内容SUMMARY OF THE INVENTION

本发明所要解决的技术问题在于克服变工况条件下传感数据分布的差异，提供了一种能够消除工况影响，并获取仅反映滚动轴承故障或性能退化的信息的方法，并精确判断滚动轴承故障的诊断方法。The technical problem to be solved by the present invention is to overcome the difference in the distribution of sensing data under variable working conditions, and to provide a method that can eliminate the influence of working conditions, obtain information that only reflects the fault or performance degradation of the rolling bearing, and accurately judge the fault of the rolling bearing. method of diagnosis.

为了解决上述技术问题，本发明基于子空间对齐的变工况滚动轴承故障诊断方法，其特征在于：In order to solve the above-mentioned technical problems, the present invention provides a fault diagnosis method for rolling bearings with variable working conditions based on subspace alignment, which is characterized in that:

首先采集多个运行中滚动轴承的振动信号作为样本,将部分样本的故障类型标注标签后作为训练数据放入源领域，将部分样本作为测试数据放入目标领域；Firstly, the vibration signals of multiple rolling bearings in operation are collected as samples, and the fault types of some samples are labeled as training data into the source domain, and some samples are placed as test data into the target domain;

使用主成分分析法生成源领域的子空间,ZS∈RD×d和目标领域的子空间ZT∈RD×d，ZS为源领域的PCA特征向量矩阵，ZT为目标领域的PCA特征向量矩阵；Use the principal component analysis method to generate the subspace of the source domain, Z S ∈ R D×d and the subspace Z T ∈ R D×d of the target domain, Z S is the PCA eigenvector matrix of the source domain, and Z T is the target domain PCA eigenvector matrix;

将样本转换到d维特征向量构建的子空间中；Transform the samples into the subspace constructed by the d-dimensional feature vector;

然后，通过最小化Bregman散度

Figure BDA0002236655960000021
计算转换矩阵M，使得对齐后源领域子空间ZA＝ZSM与目标领域子空间ZT坐标对齐，从而消除领域间数据分布的差异，对齐后的振动信号仅反映滚动轴承故障或性能退化的信息；Then, by minimizing the Bregman divergence
Figure BDA0002236655960000021
Calculate the transformation matrix M, so that the source domain subspace Z A = Z S M is aligned with the target domain subspace Z T coordinates after alignment, so as to eliminate the difference in data distribution between domains, and the aligned vibration signal only reflects the failure or performance degradation of the rolling bearing. information;

将带有故障标签的源领域样本集合经对齐后源领域子空间ZA投影至目标子空间ZT得到投影后的样本集合合，然后使用投影后的样本集合输入标准SVM分类模型进行训练最终获得训练后的SVM分类模型；The source domain sample set with the fault label is aligned and the source domain subspace Z A is projected to the target subspace Z T to obtain the projected sample set set, and then the projected sample set is used to input the standard SVM classification model for training and finally obtained. The trained SVM classification model;

最后使用训练后的SVM分类模型对投影后的目标领域样本集合中的样本进行故障诊断，判断其中每个样本所属的故障类型。Finally, the trained SVM classification model is used to perform fault diagnosis on the samples in the projected target domain sample set, and determine the fault type to which each sample belongs.

生成子空间的具体步骤为：The specific steps to generate the subspace are:

首先通过振动传感器采集多个运行中不同工况条件下轴承的振动信号x∈X，所有的振动信号作为样本集合后,将部分样本的故障类型标注标签后作为训练数据放入源领域，故障类型标签y∈Y＝{1,2,…,K}，将部分样本作为测试数据放入目标领域；First, the vibration signals x ∈ X of the bearings under different working conditions are collected by the vibration sensor. After all the vibration signals are used as a sample set, the fault types of some samples are labeled and put into the source field as training data. Label y∈Y={1,2,…,K}, put some samples into the target field as test data;

然后使用快速傅里叶变换(FFT)分别提取源领域和目标领域中每个样本的长度为D的频域特征，即每个样本振动信号对应的D维幅值系数；Then use the fast Fourier transform (FFT) to extract the frequency domain features of the length D of each sample in the source field and the target field, that is, the D-dimensional amplitude coefficient corresponding to the vibration signal of each sample;

对源领域和目标领域中所有样本的D维幅值系数进行z-normalized归一化处理后，对归一化处理后得到的矩阵分别计算源领域和目标领域样本的协方差矩阵，接着使用主成分分析法(Principal Component Analysis，PCA)对源领域和目标领域样本的协方差矩阵进行特征值分解，均取前d个特征值对应的特征向量构成源领域和目标领域子空间的基向量,即,和

Figure BDA0002236655960000023
从而将样本转换到d维特征向量构建的子空间中，式中：ZS为源领域的PCA特征向量矩阵，代表源领域子空间,ZT为目标领域的PCA特征向量矩阵，代表目标领域子空间，
Figure BDA0002236655960000024
表示D行d列的实数矩阵。After performing z-normalized normalization on the D-dimensional amplitude coefficients of all samples in the source domain and the target domain, calculate the covariance matrices of the source domain and target domain samples respectively for the matrix obtained after normalization, and then use the main Principal Component Analysis (PCA) decomposes the eigenvalues of the covariance matrices of the source domain and target domain samples, and takes the eigenvectors corresponding to the first d eigenvalues to form the basis vectors of the source domain and target domain subspaces, namely , and
Figure BDA0002236655960000023
Thus, the samples are converted into the subspace constructed by the d-dimensional eigenvectors, where Z S is the PCA eigenvector matrix of the source domain, representing the source domain subspace, and Z T is the PCA eigenvector matrix of the target domain, representing the target domain subspace. space,
Figure BDA0002236655960000024
Represents a real matrix with D rows and d columns.

通过子空间对齐消除领域间数据分布的差异的具体步骤为：使用转换矩阵M将源领域子空间ZS向目标领域子空间ZT坐标对齐，源领域子空间ZS经M变化后得到对齐后的源领域子空间记ZA＝ZSM，The specific steps to eliminate the difference of data distribution between domains through subspace alignment are: using the transformation matrix M to align the coordinates of the source domain subspace Z S to the target domain subspace Z T , and the source domain subspace Z S is changed by M to obtain the alignment The source domain subspace denoted Z A = Z S M,

具体的：specific:

利用对齐后源领域子空间ZA与目标领域子空间ZT的Bregman散度

Figure BDA0002236655960000031
Figure BDA0002236655960000032
用以判断变换后的源领域子空间ZA与目标领域子空间ZT坐标是否趋于一致，若两者Bregman散度趋于一致即判断源领域样本和目标领域样本投影到对齐后源领域子空间ZA和目标领域子空间ZT后，其数据坐标对齐；Using the Bregman divergence of the source domain subspace Z A and the target domain subspace Z T after alignment
Figure BDA0002236655960000031
Figure BDA0002236655960000032
It is used to judge whether the coordinates of the transformed source domain subspace Z A and the target domain subspace Z T tend to be consistent. If the Bregman divergences of the two tend to be consistent, it is judged that the source domain samples and the target domain samples are projected to the aligned source domain subspace. After space Z A and target domain subspace Z T , their data coordinates are aligned;

据此，通过最小化对齐后源领域子空间ZA与目标领域子空间ZT的Bregman散度

Figure BDA0002236655960000033
计算最优转换矩阵M*，即，M*＝argminM(δAT))，Accordingly, by minimizing the Bregman divergence of the source domain subspace Z A and the target domain subspace Z T after alignment
Figure BDA0002236655960000033
Calculate the optimal transformation matrix M*, that is, M * = argmin M (δ AT )),

由于ZS与ZT均为正交矩阵，且Bregman散度中的F矩阵范数具备正交不变性，因此Bregman散度为：

Figure BDA0002236655960000034
式中，
Figure BDA0002236655960000035
为ZS的转置矩阵；Since Z S and Z T are both orthogonal matrices, and the F matrix norm in the Bregman divergence has orthogonal invariance, the Bregman divergence is:
Figure BDA0002236655960000034
In the formula,
Figure BDA0002236655960000035
is the transpose matrix of Z S ;

综上可得最优转换矩阵

Figure BDA0002236655960000036
In summary, the optimal transformation matrix can be obtained
Figure BDA0002236655960000036

训练分类器的具体步骤为：The specific steps for training the classifier are:

首先将带有故障标签的源领域样本集合

Figure BDA0002236655960000037
经对齐后源领域子空间ZA投影至目标子空间ZT得到投影后的样本集合合
Figure BDA0002236655960000038
式中N表示源领域样本的数量；First set the source domain samples with fault labels
Figure BDA0002236655960000037
After alignment, the source domain subspace Z A is projected to the target subspace Z T to obtain the projected set of samples.
Figure BDA0002236655960000038
where N represents the number of source domain samples;

然后使用投影后的样本集合

Figure BDA0002236655960000039
输入标准SVM分类模型进行训练最终获得训练后的SVM分类模型。Then use the projected set of samples
Figure BDA0002236655960000039
Input the standard SVM classification model for training and finally obtain the trained SVM classification model.

故障诊断具体步骤为：The specific steps for fault diagnosis are:

首先将不带标签的目标领域样本集合

Figure BDA00022366559600000310
投影至目标子空间ZT得到目标领域样本集合M表示目标领域样本的数量，然后使用训练后的SVM分类模型，对投影后的目标领域样本集合
Figure BDA00022366559600000312
中的样本进行故障诊断，判断其中每个样本所属的故障类型。First set the target domain samples without labels
Figure BDA00022366559600000310
Projection to the target subspace Z T to obtain the target domain sample set M represents the number of target domain samples, and then uses the trained SVM classification model to classify the projected target domain sample set
Figure BDA00022366559600000312
The samples in the fault diagnosis are carried out, and the fault type of each sample is judged.

有益效果：Beneficial effects:

本发明通过将源领域中样本与对齐后源领域子空间子空间ZA中数据坐标对齐，将目标领中域样与目标领域子空间ZT中数据坐标对齐的方式，克服变工况条件下传感数据分布的差异，提供了一种能够消除工况影响，获取仅反映滚动轴承故障或性能退化的信息的方法；By aligning the samples in the source field with the data coordinates in the subspace ZA of the source field after alignment, and aligning the samples in the target field with the data coordinates in the subspace ZT of the target field, the invention overcomes the problem of changing working conditions . Differences in the distribution of sensing data provide a method that can eliminate the influence of operating conditions and obtain information that only reflects the failure or performance degradation of rolling bearings;

本发明针对不同工况条件下故障传感数据分布的差异，使用Bregman散度来描述源领域与目标领域的分布差异，通过引入转换矩阵M将源领域子空间ZS对齐至目标领域子空间ZT后最小化领域间的Bregman散度，使得变换后的源领域子空间ZA与目标领域子空间ZT趋近一致，空间相似后，训练数据(源领域)和测试数据(目标领域)的分布差异就变小了，这样源领域训练的模型就能够用于目标领域的诊断；Aiming at the difference in the distribution of fault sensing data under different working conditions, the invention uses Bregman divergence to describe the distribution difference between the source domain and the target domain, and aligns the source domain subspace Z S to the target domain subspace Z by introducing a transformation matrix M After T , the Bregman divergence between domains is minimized, so that the transformed source domain subspace Z A and the target domain subspace Z T tend to be consistent. After the spaces are similar, the difference between the training data (source domain) and test data (target domain) The distribution difference becomes smaller, so that the model trained in the source domain can be used for diagnosis in the target domain;

本发明克服了变工况条件下传感数据分布的差异，提供了一种能够消除工况影响，并获取仅反映滚动轴承故障或性能退化的信息的方法，从而使滚动轴承故障的诊断更加准确，具有极高的推广价值。The invention overcomes the difference in the distribution of sensing data under variable working conditions, and provides a method that can eliminate the influence of working conditions and obtain information that only reflects the fault or performance degradation of the rolling bearing, thereby making the fault diagnosis of the rolling bearing more accurate, and has the advantages of High promotional value.

附图说明Description of drawings

图1为本发明的基于子空间对齐的变工况滚动轴承故障诊断方法的示意图。FIG. 1 is a schematic diagram of a fault diagnosis method for a rolling bearing with variable working conditions based on subspace alignment according to the present invention.

图2为本发明的基于子空间对齐的变工况滚动轴承故障诊断方法坐标对齐的示意图。FIG. 2 is a schematic diagram of coordinate alignment of the subspace alignment-based fault diagnosis method for a rolling bearing with variable working conditions of the present invention.

图3为本发明的基于子空间对齐的变工况滚动轴承故障诊断方法的流程示意图。FIG. 3 is a schematic flowchart of the fault diagnosis method for a rolling bearing with variable working conditions based on subspace alignment according to the present invention.

具体实施方式Detailed ways

下面将结合附图对本发明的实施例作详细说明。The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

如图1所示，本发明的一种基于子空间对齐的变工况滚动轴承故障诊断方法，As shown in FIG. 1, a fault diagnosis method for a rolling bearing with variable working conditions based on subspace alignment of the present invention,

首先采集多个运行中滚动轴承的振动信号作为样本,将部分样本的故障类型标注标签后作为训练数据放入源领域，将部分样本作为测试数据放入目标领域；Firstly, the vibration signals of multiple rolling bearings in operation are collected as samples, and the fault types of some samples are labeled as training data into the source domain, and some samples are placed as test data into the target domain;

使用主成分分析法生成源领域的子空间,ZS∈RD×d和目标领域的子空间ZT∈RD×d，ZS为源领域的PCA特征向量矩阵，ZT为目标领域的PCA特征向量矩阵；Use the principal component analysis method to generate the subspace of the source domain, Z S ∈ R D×d and the subspace Z T ∈ R D×d of the target domain, Z S is the PCA eigenvector matrix of the source domain, and Z T is the target domain PCA eigenvector matrix;

将样本转换到d维特征向量构建的子空间中；Transform the samples into the subspace constructed by the d-dimensional feature vector;

然后通过最小化Bregman散度

Figure BDA0002236655960000041
计算转换矩阵M，使得对齐后源领域子空间ZA＝ZSM与目标领域子空间ZT坐标对齐，从而消除领域间数据分布的差异，对齐后的振动信号仅反映滚动轴承故障或性能退化的信息；Then by minimizing the Bregman divergence
Figure BDA0002236655960000041
Calculate the transformation matrix M, so that the source domain subspace Z A = Z S M is aligned with the target domain subspace Z T coordinates after alignment, so as to eliminate the difference in data distribution between domains, and the aligned vibration signal only reflects the failure or performance degradation of the rolling bearing. information;

将带有故障标签的源领域样本集合经对齐后源领域子空间ZA投影至目标子空间ZT得到投影后的样本集合合，然后使用投影后的样本集合输入标准SVM分类模型进行训练最终获得训练后的SVM分类模型；The source domain sample set with the fault label is aligned and the source domain subspace Z A is projected to the target subspace Z T to obtain the projected sample set set, and then the projected sample set is used to input the standard SVM classification model for training and finally obtained. The trained SVM classification model;

最后使用训练后的SVM分类模型对投影后的目标领域样本集合中的样本进行故障诊断，判断其中每个样本所属的故障类型。Finally, the trained SVM classification model is used to perform fault diagnosis on the samples in the projected target domain sample set, and determine the fault type to which each sample belongs.

如图3所示，一种基于子空间对齐的变工况滚动轴承故障诊断方法具体步骤为：As shown in Figure 3, the specific steps of a fault diagnosis method for a rolling bearing with variable working conditions based on subspace alignment are:

步骤一、生成子空间：Step 1. Generate subspace:

首先通过振动传感器采集多个运行中不同工况条件下轴承的振动信号x∈X，所有的振动信号作为样本集合后,将部分样本的故障类型标注标签后作为训练数据放入源领域，故障类型标签y∈Y＝{1,2,…,K}，将部分样本作为测试数据放入目标领域；First, the vibration signals x ∈ X of the bearings under different working conditions are collected by the vibration sensor. After all the vibration signals are used as a sample set, the fault types of some samples are labeled and put into the source field as training data. Label y∈Y={1,2,…,K}, put some samples into the target field as test data;

然后使用快速傅里叶变换(FFT)分别提取源领域和目标领域中每个样本的长度为D的频域特征，即每个样本振动信号对应的D维幅值系数；Then use the fast Fourier transform (FFT) to extract the frequency domain features of the length D of each sample in the source field and the target field, that is, the D-dimensional amplitude coefficient corresponding to the vibration signal of each sample;

对源领域和目标领域中所有样本的D维幅值系数进行z-normalized归一化处理后，对归一化处理后得到的矩阵分别计算源领域和目标领域样本的协方差矩阵，接着使用主成分分析法(Principal Component Analysis，PCA)对源领域和目标领域样本的协方差矩阵进行特征值分解，均取前d个特征值对应的特征向量构成源领域和目标领域子空间的基向量,即,

Figure BDA0002236655960000051
和
Figure BDA0002236655960000052
从而将样本转换到d维特征向量构建的子空间中，式中：ZS为源领域的PCA特征向量矩阵，代表源领域子空间,ZT为目标领域的PCA特征向量矩阵，代表目标领域子空间，
Figure BDA0002236655960000053
表示D行d列的实数矩阵。After performing z-normalized normalization on the D-dimensional amplitude coefficients of all samples in the source domain and the target domain, calculate the covariance matrices of the source domain and target domain samples respectively for the matrix obtained after normalization, and then use the main Principal Component Analysis (PCA) decomposes the eigenvalues of the covariance matrices of the source domain and target domain samples, and takes the eigenvectors corresponding to the first d eigenvalues to form the basis vectors of the source domain and target domain subspaces, namely ,
Figure BDA0002236655960000051
and
Figure BDA0002236655960000052
Thus, the samples are converted into the subspace constructed by the d-dimensional eigenvectors, where Z S is the PCA eigenvector matrix of the source domain, representing the source domain subspace, and Z T is the PCA eigenvector matrix of the target domain, representing the target domain subspace. space,
Figure BDA0002236655960000053
Represents a real matrix with D rows and d columns.

步骤二、通过子空间对齐消除领域间数据分布的差异：Step 2: Eliminate the differences in data distribution between fields through subspace alignment:

如图2所示，使用转换矩阵M将源领域子空间ZS向目标领域子空间ZT坐标对齐，源领域子空间ZS经M变化后得到对齐后的源领域子空间记ZA＝ZSM，As shown in Figure 2, use the transformation matrix M to align the coordinates of the source domain subspace Z S to the target domain subspace Z T , and the source domain subspace Z S is changed by M to obtain the aligned source domain subspace Z A =Z S M,

具体的：specific:

利用对齐后源领域子空间ZA与目标领域子空间ZT的Bregman散度

Figure BDA0002236655960000054
Figure BDA0002236655960000055
用以判断变换后的源领域子空间ZA与目标领域子空间ZT坐标是否趋于一致，若两者Bregman散度趋于一致即判断源领域样本和目标领域样本投影到对齐后源领域子空间ZA和目标领域子空间ZT后，其数据坐标对齐；Using the Bregman divergence of the source domain subspace Z A and the target domain subspace Z T after alignment
Figure BDA0002236655960000054
Figure BDA0002236655960000055
It is used to judge whether the coordinates of the transformed source domain subspace Z A and the target domain subspace Z T tend to be consistent. If the Bregman divergences of the two tend to be consistent, it is judged that the source domain samples and the target domain samples are projected to the aligned source domain subspace. After space Z A and target domain subspace Z T , their data coordinates are aligned;

据此，通过最小化对齐后源领域子空间ZA与目标领域子空间ZT的Bregman散度

Figure BDA0002236655960000056
计算最优转换矩阵M*，即，M*＝argminM(δAT))，Accordingly, by minimizing the Bregman divergence of the source domain subspace Z A and the target domain subspace Z T after alignment
Figure BDA0002236655960000056
Calculate the optimal transformation matrix M*, that is, M * = argmin M (δ AT )),

由于ZS与ZT均为正交矩阵，且Bregman散度中的F矩阵范数具备正交不变性，因此Bregman散度为：

Figure BDA0002236655960000057
式中，
Figure BDA0002236655960000058
为ZS的转置矩阵；Since Z S and Z T are both orthogonal matrices, and the F matrix norm in the Bregman divergence has orthogonal invariance, the Bregman divergence is:
Figure BDA0002236655960000057
In the formula,
Figure BDA0002236655960000058
is the transpose matrix of Z S ;

综上可得最优转换矩阵

Figure BDA0002236655960000059
In summary, the optimal transformation matrix can be obtained
Figure BDA0002236655960000059

步骤三、训练分类器：Step 3. Train the classifier:

首先将带有故障标签的源领域样本集合

Figure BDA00022366559600000510
经对齐后源领域子空间ZA投影至目标子空间ZT得到投影后的样本集合合
Figure BDA00022366559600000511
式中N表示源领域样本的数量；First set the source domain samples with fault labels
Figure BDA00022366559600000510
After alignment, the source domain subspace Z A is projected to the target subspace Z T to obtain the projected set of samples.
Figure BDA00022366559600000511
where N represents the number of source domain samples;

然后使用投影后的样本集合

Figure BDA0002236655960000061
输入标准SVM分类模型进行训练最终获得训练后的SVM分类模型。Then use the projected set of samples
Figure BDA0002236655960000061
Input the standard SVM classification model for training and finally obtain the trained SVM classification model.

步骤四、故障诊断：Step 4. Troubleshooting:

首先将不带标签的目标领域样本集合

Figure BDA0002236655960000062
投影至目标子空间ZT得到目标领域样本集合
Figure BDA0002236655960000063
M表示目标领域样本的数量，然后使用训练后的SVM分类模型，对投影后的目标领域样本集合中的样本进行故障诊断，判断其中每个样本所属的故障类型。First set the target domain samples without labels
Figure BDA0002236655960000062
Projection to the target subspace Z T to obtain the target domain sample set
Figure BDA0002236655960000063
M represents the number of target domain samples, and then uses the trained SVM classification model to classify the projected target domain sample set The samples in the fault diagnosis are carried out, and the fault type of each sample is judged.

为了度量源领域样本与目标领域样本之间的相似度，本方法定义了以下相似度函数Sim(XS,XT)，即，Sim(XS,XT)＝XSZAZ′TX′T。In order to measure the similarity between the source domain samples and the target domain samples, the method defines the following similarity function Sim(X S , X T ), that is, Sim(X S , X T )=X S Z A Z′ T X' T .

该相似度函数Sim(XS,XT)的结果可以直接用于K-近邻分类算法,但不能直接用与训练SVM分类模型。在使用LIBSVM软件时，本方法将Sim(XS,XT)用作核矩阵训练SVM分类模型。为了防止出现过拟合问题，本方法使用了交叉验证的方法寻找最佳的模型参数。The result of the similarity function Sim(X S , X T ) can be directly used in the K-nearest neighbor classification algorithm, but cannot be used directly in training the SVM classification model. When using the LIBSVM software, the method uses Sim(X S , X T ) as the kernel matrix to train the SVM classification model. In order to prevent overfitting, this method uses cross-validation to find the best model parameters.

Claims (5)

1. A variable working condition rolling bearing fault diagnosis method based on subspace alignment is characterized by comprising the following steps:
firstly, collecting vibration signals of a plurality of rolling bearings in operation as samples, labeling fault types of partial samples as training data, and putting the training data into a source field, and putting partial samples as test data into a target field;
generation of subspace, Z, of source domain using principal component analysisS∈RD×dAnd subspace Z of the target domainT∈RD×d，ZSIs a PCA eigenvector matrix, Z, of the source domainTIs a PCA characteristic vector matrix of the target field;
converting the sample into a subspace constructed by the d-dimensional feature vector;
then, by minimizing Bregman divergence
Figure FDA0002236655950000011
Computing a transformation matrix M such that the post-source-domain subspace Z is alignedA＝ZSM and target Domain subspace ZTThe coordinates are aligned, so that the difference of data distribution among the fields is eliminated, and the aligned vibration signals only reflect the information of rolling bearing faults or performance degradation;
aligning the source domain sample set with the fault label to obtain a source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set, inputting the projected sample set into a standard SVM classification model for training, and finally obtaining a trained SVM classification model;
and finally, carrying out fault diagnosis on the samples in the projected target field sample set by using the trained SVM classification model, and judging the fault type of each sample.
2. The variable working condition rolling bearing fault diagnosis method based on subspace alignment as claimed in claim 1, wherein the specific steps of generating the subspace are as follows:
firstly, acquiring vibration signals X belonging to X of a bearing under different working conditions in a plurality of running processes by using a vibration sensor, taking all vibration signals as a sample set, marking fault types of partial samples as labels, then putting the labels into a source field as training data, taking the fault type labels Y belonging to {1,2, …, K }, and putting partial samples into a target field as test data;
then, respectively extracting frequency domain characteristics with the length of D of each sample in the source field and the target field by using Fast Fourier Transform (FFT), namely a D-dimensional amplitude coefficient corresponding to each sample vibration signal;
for source domain and target domainAfter Z-normalized normalization processing is carried out on the D-dimensional amplitude coefficients of all samples, covariance matrixes of the source field samples and the target field samples are respectively calculated on the matrixes obtained after the normalization processing, then characteristic value decomposition is carried out on the covariance matrixes of the source field samples and the target field samples by using Principal Component Analysis (PCA), characteristic vectors corresponding to the first D characteristic values are all taken to form base vectors of subspace of the source field samples and the target field samples, namely,
Figure FDA0002236655950000012
and
Figure FDA0002236655950000013
thus, the samples are converted into a subspace constructed by d-dimensional feature vectors, wherein: zSIs a PCA eigenvector matrix of the source domain, representing a source domain subspace, ZTIs a PCA eigenvector matrix of the target domain, representing the target domain subspace,
Figure FDA0002236655950000014
a matrix of real numbers representing D rows and D columns.
3. The variable working condition rolling bearing fault diagnosis method based on subspace alignment according to claim 1, wherein the specific step of eliminating the difference of data distribution among the fields through subspace alignment is as follows: transforming the source-domain subspace Z using a transformation matrix MSTo a target domain subspace ZTCoordinate alignment, source domain subspace ZSObtaining aligned source domain subspace notation Z after M changesA＝ZSM，
Specifically, the method comprises the following steps:
utilizing aligned back source domain subspace ZAAnd target domain subspace ZTBregman divergence of
Figure FDA0002236655950000021
Figure FDA0002236655950000022
For determining transformed source-domain subspace ZAAnd target domain subspace ZTWhether the coordinates tend to be consistent or not is judged, if the Bregman divergence of the two samples tends to be consistent, the source field sample and the target field sample are projected to the aligned source field subspace ZAAnd a target domain subspace ZTThen, aligning the data coordinates;
accordingly, by minimizing the aligned back-source-domain subspace ZAAnd target domain subspace ZTBregman divergence of
Figure FDA0002236655950000023
Calculating an optimal transformation matrix M, i.e. M*＝argminM(δAT))，
Due to ZSAnd ZTAre all orthogonal matrices and the F matrix norm in Bregman divergence has orthogonal invariance, so Bregman divergence is:
Figure FDA0002236655950000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002236655950000025
is ZSThe transposed matrix of (2);
to sum up, the optimal transformation matrix can be obtained
Figure FDA0002236655950000026
4. The subspace alignment-based variable working condition rolling bearing fault diagnosis method according to claim 1, characterized in that the training classifier comprises the following specific steps:
first, a source domain sample with a fault label is collected
Figure FDA0002236655950000027
Aligned post-source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set
Figure FDA0002236655950000028
Wherein N represents the number of source domain samples;
the projected sample set is then used
Figure FDA0002236655950000029
And inputting a standard SVM classification model for training to finally obtain the trained SVM classification model.
5. The variable working condition rolling bearing fault diagnosis method based on subspace alignment according to claim 1 or 4, characterized in that the fault diagnosis comprises the following specific steps:
firstly, collecting target domain samples without labels
Figure FDA00022366559500000210
Projection into target subspace ZTObtaining a set of target domain samples
Figure FDA00022366559500000211
M represents the number of target field samples, and then the trained SVM classification model is used for collecting the projected target field samples
Figure FDA00022366559500000212
The samples in (1) are subjected to fault diagnosis, and the fault type of each sample is judged.
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