CN111829782A - Fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment - Google Patents
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Abstract
The invention discloses a fault diagnosis method based on self-adaptive manifold embedding dynamic distribution alignment, which can effectively avoid the characteristic distortion of data in an original Euclidean space by automatically calculating the optimal subspace dimension and calculating a geodesic flow kernel and the characteristic representation of a manifold after transformation. The method has the advantages of introducing similarity measurement A-distance to define a self-adaptive factor, dynamically adjusting the relative weight of sample data condition distribution and edge distribution, effectively reducing the distribution difference of the source domain samples and the target domain samples, greatly improving the accuracy and effectiveness of rolling bearing fault diagnosis under variable working conditions, along with strong interpretability, low requirement on computer hardware resources, higher execution speed, and excellent diagnosis accuracy, algorithm convergence and parameter robustness. The method is particularly suitable for multi-scene and multi-fault bearing fault diagnosis under variable working conditions, and can be widely applied to fault diagnosis tasks under variable working conditions of complex systems such as machinery, electric power, chemical engineering, aviation and the like.
Description
Technical Field
The invention relates to the technical field of mechanical fault diagnosis and machine learning, in particular to a fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment.
Background
The rolling bearing is widely applied to various important fields of machinery, electric power, chemical engineering, aviation and the like as a key part in industrial production equipment, and meanwhile, the rolling bearing also frequently works in severe environments such as high temperature, high speed, heavy load and the like, so that the rolling bearing is very easy to generate faults such as abrasion, crack, fracture and the like.
Most of the existing bearing fault diagnosis technologies are used for analyzing vibration signals acquired by a sensor, such as fault characteristic frequency extraction, short-time Fourier transform, empirical mode decomposition, sparse representation and the like based on the vibration signals. In addition, a number of improved machine learning algorithms are also used to automatically learn bearing fault features, such as Support Vector Machines (SVMs), Artificial Neural Networks (ANN), Convolutional Neural Networks (CNN), and Automatic Encoders (AE), among others.
However, most of the current fault diagnosis methods are based on a common assumption that training data and test data must satisfy the same distribution, however, under actual complex working conditions, bearing vibration signal distributions acquired by sensors are usually inconsistent, so that the fault diagnosis effect is reduced sharply. Considering that the working principle and the failure mechanism of the rotary machine are similar, the bearing vibration data under the variable working condition can share similar fault characteristics, and the data distribution difference can be well overcome by the self-adaptive transfer learning. In particular, bearing data collected under varying conditions often have different condition distributions and edge distributions. Furthermore, when adaptive distribution alignment is performed in the original euclidean space, data feature distortion inevitably occurs, resulting in an unsatisfactory diagnostic effect of the model.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment, which has high precision and excellent algorithm convergence and parameter robustness. The technical scheme is as follows:
a fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment comprises the following steps:
s10, collecting vibration signals of the bearing under different working conditions, adding various fault type labels of the bearing, taking the data collected under each working condition as a transferable data set, distributing the data in each transferable domain data set under different conditions and edges, then performing data cutting, and obtaining a sample;
s20, carrying out frequency domain processing on the bearing signals by using fast Fourier transform to obtain a source domain data set and a target domain data set, and inputting the source domain data set and the target domain data set as models;
s30, calculating the optimal subspace dimension through a GFK algorithm, and calculating a geodesic flow type kernel matrix and a transformed manifold feature representation;
s40, training a KNN-based classifier to generate preliminary prediction labels of target domain samples, and respectively calculating a maximum mean difference matrix M0And McAnd respectively corresponding to the edge distribution of the sample dataCondition distribution, defining and calculating an adaptive dynamic factor through similarity measurement A-distance;
s50, solving partial derivatives of the target loss function containing the structure risk minimization, the dynamic distribution alignment and the Laplace regularization term to obtain the optimal solution of the coefficient vector of the model, and then solving the secondary prediction label of the target domain sample through a representation theory;
s60, updating the maximum mean difference matrix M by using the secondary prediction label0And McRecalculating the adaptive dynamic factor, and solving a new optimal solution of the objective function to obtain a cubic prediction label of the target domain sample;
and S70, iterating the steps S40-S60 until the algorithm converges, obtaining a final prediction label of the target domain sample, and completing bearing fault diagnosis.
As a further improvement of the present invention, step S20 specifically includes:
converting a bearing time domain vibration signal into a frequency domain signal through Fast Fourier Transform (FFT), reserving unilateral frequency spectrum information of a frequency domain, and giving a marked source domain data setAnd a target domain data setWherein x issAnd xtRespectively source domain and target domain samples, n and m are corresponding sample numbers, ysIs a source domain sample label, k is a sample feature number, and
as a further improvement of the present invention, the step S30 of calculating the optimal subspace dimension specifically includes:
respectively obtaining subspace data sets P of a source domain and a target domain through principal component analysissAnd PtCalculate PsAnd PtIs combined with the matrix Ps+tAnd separately calculate Ps、PtAnd Ps+tSine included angle alpha therebetweendAnd betadThe subspace inconsistency metric (SDM) c (d) may be expressed as:
C(d)=0.5[sinαd+sinβd]
here, the more similar the source domain and the target domain, the larger the value of c (d), and under the premise of ensuring that the captured variance of one subspace can be transferred to other subspaces, that is: alpha is alphad≠π/2,βdNot equal to pi/2, the optimal subspace dimension d can be calculated by a greedy algorithm*:
d*=min{d|C(d)=1}。
As a further improvement of the present invention, the calculating of the geodesic flow kernel matrix and the transformed manifold feature representation in step S30 specifically includes:
computing PCA subspace PsAnd PtPrincipal angle of (theta)i(0≤θ1≤θ2≤…θdLess than or equal to pi/2), respectively calculating cos thetaiAnd sin θi(i ═ 1,2 ·, d) and as diagonal elements of the diagonal matrix sum Σ, PsIs complemented byAndrepresents a pair of orthogonal matrices and can be found by singular value decomposition of:
further, the geodesic flow kernel matrix G may be calculated by the following formula:
wherein, Λ1To Λ3For a diagonal matrix, the diagonal elements are:
the transformed manifold features are further represented as:
wherein X ═ Xs,Xt]Source domain sample set W after conversionsAnd a target domain sample set WsCan be calculated by the following formula:
as a further improvement of the present invention, the maximum mean difference matrix M is calculated in step S400And McThe method specifically comprises the following steps:
wherein n iscAnd mcAre respectively a source domain DsAnd a target domain DtThe number of samples of the class c tag in (1).
As a further improvement of the present invention, in step S40, an adaptive dynamic factor is defined and calculated by a similarity measure a-distance, which specifically includes:
training a linear two-classifier h on a source domain and a target domain by using a Support Vector Machine (SVM), and representing the loss of the classifier by (h), the similarity measure A-distance across domains can be represented as:
A(Ds,Dt)=2(1-2(h))
the adaptation factor ξ may be defined as:
wherein A isMAnd AcRespectively representing an edge similarity measure and a conditional similarity measure.
As a further improvement of the present invention, step S50 specifically includes:
s51, solving an optimal solution of the objective loss function; the method specifically comprises the following steps:
the structural risk minimization function defined on the source domain can be expressed as:
wherein HKAnd | · | non-conducting phosphorFRespectively representing the reproducible Hilbert space (RKHS) and the Frobenius norm,is the coefficient vector to be solved, tr (-) is the trace of the solving matrix,is a kernel matrix, and Kij=K(wi,wj) In the model, an RBF radial basis kernel function is adopted,is a label matrix composed of source domain sample labels and target domain sample prediction labels,is a diagonal indicating matrix and satisfies:
s52, in order to fully mine the geometric characteristics among the neighboring samples in the manifold space, a Laplace regularization term Lap (D) is added to the objective functions,Dt) Expressed as follows:
wherein L is laplace matrix and L-a-U, a denotes diagonal matrix, andu is a neighbor sample incidence matrix and can be obtained by the following calculation:
here, sim (,) is a similarity function used to evaluate the correlation between two samples, Np(wi) Is any one sample wiP neighbor sample sets;
s53, the fault bearing signal collected under the variable working condition often has different condition distribution and edge distribution, so it is necessary to evaluate the relative importance of the two distributions, the maximum mean difference MMD can evaluate the deviation of the two cross-domain distributions, this text defines a self-adaptive factor xi to dynamically adjust the two distributions, and the source domain D expresses the theory and nuclear skillsAnd a target domain DtDIS (D) of data distributions,Dt) Can be expressed as:
where E [. cndot. ] represents the mean of the samples mapped to the regenerated Hilbert space, and M is the MMD combination matrix of the conditional distribution and the edge distribution, which can be calculated by:
here, when ξ → 0, it indicates that the inter-domain conditional distribution adaptation is more important, and conversely, when ξ → 1, it indicates that the inter-domain edge distribution adaptation is more important;
s54, constructing and solving an objective function to obtain the optimal solution of the coefficient vectorThe method for obtaining the target domain sample label by using the representation theory specifically comprises the following steps:
the Laplace regularization term Lap (D) described aboves,Dt) And a dynamically distributed alignment term DIS (D)s,Dt) Added to the structure risk minimization objective function, a global objective loss function is obtained:
by solving the partial derivatives of the objective functionObtaining an optimal coefficient solution
Wherein, I is a unit diagonal matrix, λ, ρ, and η are regularization parameters of corresponding terms, and a quadratic prediction label of a target domain sample can be obtained by using a representation theory in machine learning:
as a further improvement of the present invention, step S60 specifically includes:
updating the maximum mean difference matrix M with the quadratic prediction label0And McAnd recalculating the self-adaptive dynamic factor, solving a new optimal solution of the objective function, and obtaining a cubic prediction label of the target domain sample by using a representation theory.
As a further improvement of the present invention, the step S10 of collecting vibration signals of the bearing under different working conditions specifically includes: when the bearing rotates and runs under four different working conditions, the vibration signals of the bearing under each working condition are collected through the acceleration sensor.
As a further development of the invention, the four different operating conditions are four different radial loads exerted on the bearing.
The invention has the beneficial effects that:
1. by automatically calculating the optimal subspace dimension and calculating the geodesic flow kernel and the converted manifold feature representation, the feature distortion of data in the original Euclidean space can be effectively avoided.
2. And a self-adaptive factor is defined by introducing similarity measurement A-distance, the relative weight of sample data condition distribution and edge distribution is dynamically adjusted, the distribution difference of the source domain sample and the target domain sample is effectively reduced, and the accuracy and the effectiveness of the fault diagnosis of the rolling bearing under the variable working condition are greatly improved.
3. Compared with the bearing fault diagnosis based on deep learning, the method has the advantages of strong interpretability, lower requirement on computer hardware resources, higher execution speed, and excellent diagnosis accuracy, algorithm convergence and parameter robustness. The method is particularly suitable for multi-scene and multi-fault bearing fault diagnosis under variable working conditions, and can be widely applied to fault diagnosis tasks under variable working conditions of complex systems such as machinery, electric power, chemical engineering, aviation and the like.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment in a preferred embodiment of the present invention;
FIG. 2 is a frequency domain plot of vibration signals for different health states of a bearing in a preferred embodiment of the present invention;
FIG. 3 is a diagram illustrating conditional distribution and edge distribution of cross-domain data according to a preferred embodiment of the present invention;
FIG. 4 is a schematic diagram of a fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment in a preferred embodiment of the present invention;
FIG. 5 is a schematic diagram of the results of fault diagnosis on experimental data in a preferred embodiment of the present invention;
FIG. 6 is a diagram illustrating the convergence result of the fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment according to the preferred embodiment of the present invention;
FIG. 7 is a parameter sensitivity diagram of the fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment in the preferred embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The invention is explained in detail in connection with the actual experimental data:
experimental data a bearing data set from the university of kasseiki storage (CWRU) was used, and a data acquisition system, as shown in fig. 1, included a 2hp motor (1 hp. 746W), a torque sensor, a dynamometer, and electronic control. Faults are introduced in the test bearing roller, the inner ring and the outer ring through an Electric Discharge Machining (EDM) technology, and different fault sizes are set. And collecting vibration data by using an acceleration sensor.
In this embodiment, a bearing vibration signal with a sampling frequency of 12KHz is selected as original data, the model of the bearing is 6205-2RS JEM, bearing faults are divided into four types, namely normal, inner ring fault, roller fault and outer ring fault, and the fault size in each fault state includes 3 sizes: 0.007 inches, 0.014 inches and 0.021 inches, so there are a total of 3 x 3+ 1-10 health states, sampling 100 signal samples per operating state, each signal being 1024 points in length. The test bearing is subjected to 3 kinds of radial loads, namely 0hp, 1hp, 2hp and 3hp respectively, the rotating speed of the bearing slightly changes under each kind of load, the 10 bearing health state data are collected under any load and are taken as a transferable domain, and specifically, the domains under different loads are represented as: l0 ═ 0hp/1797rpm, L1 ═ 1hp/1772rpm, L2 ═ 2hp/1750rpm, and L3 ═ 3hp/1730 rpm. Specific bearing data can be found in table 1.
Table 1 description of 10 failed bearings per migratable domain
As shown in fig. 1, the method for diagnosing a fault based on adaptive manifold embedding dynamic distribution alignment according to the present invention includes the following steps:
s10, collecting vibration signals of the bearing under different working conditions, adding various fault type labels of the bearing, taking the data collected under each working condition as a transferable data set, distributing the data in each transferable domain data set according to different conditions and edges, then performing data cutting, and obtaining samples.
Wherein, gather bearing vibration signal under the different operating modes, specifically include: when the bearing rotates and runs under four different working conditions, the vibration signals of the bearing under each working condition are collected through the acceleration sensor. The four different operating conditions are four different radial loads applied to the bearing.
Specifically, when the test bearing rotates and runs under four different radial loads (0hp, 1hp, 2hp and 3hp), a bearing time domain signal under each load is collected through an acceleration sensor, various fault type labels (10 types) of the bearing are added, as shown in the above table 1, data collected under each load is taken as a transferable domain, data of each domain are subjected to different conditions and edge distribution, data are cut according to the above experimental description, and a sample is obtained, wherein any two of the four transferable domains can define two bidirectional transfer tasks, namely, L0 → L1, L0 → L2, L0 → L3; l1 → L0, L1 → L2, L1 → L3; l2 → L0, L2 → L1, L2 → L3; l3 → L0, L3 → L1, L3 → L2, a total of 12 migration tasks, with the left side of the arrow being the labeled source domain and the right side being the unlabeled target domain, are diagnostic objects to be identified.
And S20, carrying out frequency domain processing on the bearing signals by using fast Fourier transform to obtain a source domain data set and a target domain data set, and taking the source domain data set and the target domain data set as model input.
Specifically, a bearing time domain vibration signal is converted into a frequency domain signal through Fast Fourier Transform (FFT), and single-side frequency spectrum information of a frequency domain is reserved; namely, the number of the input sample feature points is 512, and the bearing frequency domain signals in different health states are shown in fig. 2.
In particular, given a labeled source domain datasetAnd a target domain data setWherein x issAnd xtRespectively source domain and target domain samples, n and m are corresponding sample numbers, ysIs a source domain sample label, k is a sample feature number, andthe basic assumption is that: feature space xs=xtAnd a label space ys=ytConditional distribution Qs(ys(x)|xs)≠Qt(yt(x)|xt) And edge distribution Ps(xs)≠Pt(xt). The method aims at constructing a cross-domain classifier through manifold feature learning and dynamic distribution alignmentTo predict the target domain label under variable working conditions
And S30, calculating the optimal subspace dimension through a GFK algorithm, and calculating a geodesic flow type kernel matrix and a transformed manifold feature representation.
Wherein, calculating the optimal subspace dimension specifically comprises:
respectively obtaining subspace data sets P of a source domain and a target domain through principal component analysissAnd PtCalculate PsAnd PtIs combined with the matrix Ps+tAnd separately calculate Ps、PtAnd Ps+tSine included angle alpha therebetweendAnd betadThe subspace inconsistency metric (SDM) c (d) may be expressed as:
C(d)=0.5[sinαd+sinβd]
here, the more similar the source domain and the target domain, the larger the value of c (d), and under the premise of ensuring that the captured variance of one subspace can be transferred to other subspaces, that is: alpha is alphad≠π/2,βdNot equal to pi/2, the optimal subspace dimension d can be calculated by a greedy algorithm*:
d*=min{d|C(d)=1}。
The method for calculating the geodesic flow type core matrix and the manifold feature representation after transformation specifically comprises the following steps:
computing PCA subspace PsAnd PtPrincipal angle of (theta)i(0≤θ1≤θ2≤…θdLess than or equal to pi/2), respectively calculating cos thetaiAnd sin θi(i ═ 1,2 ·, d) and as diagonal elements of the diagonal matrix sum Σ, PsIs complemented byAndrepresents a pair of orthogonal matrices and can be found by singular value decomposition of:
further, the geodesic flow kernel matrix G may be calculated by the following formula:
wherein, Λ1To Λ3For a diagonal matrix, the diagonal elements are:
the transformed manifold features are further represented as:
wherein X ═ Xs,Xt]Source domain sample set W after conversionsAnd a target domain sample set WsCan be calculated by the following formula:
s40, training a KNN-based classifier to generate preliminary prediction labels of target domain samples, and respectively calculating a maximum mean difference matrix M0And McAnd respectively corresponding to the edge distribution and the condition distribution of the sample data, and defining and calculating the self-adaptive dynamic factor through the similarity measurement A-distance.
Wherein a KNN-based classifier is trained to generate a preliminary prediction label of the target domain sample, wherein the number of nearest neighbor samples is set to 1, KNN is only used in the preliminary prediction, and all the subsequent target domain labels are generated by iteration.
Wherein the maximum mean difference matrix M is calculated separately0And McThe method specifically comprises the following steps:
wherein n iscAnd mcAre respectively a source domain DsAnd a target domain DtThe number of samples in the class c label, n and m are the source domain DsAnd a target domain DtNumber of samples, n-m-1000, nc=mc=100。
The method comprises the following steps of defining and calculating an adaptive dynamic factor through a similarity measurement A-distance, and specifically comprises the following steps:
training a linear two-classifier h on a source domain and a target domain by using a Support Vector Machine (SVM), and representing the loss of the classifier by (h), the similarity measure A-distance across domains can be represented as:
A(Ds,Dt)=2(1-2(h))
the adaptation factor ξ may be defined as:
wherein A isMAnd AcRespectively representing an edge similarity measure and a conditional similarity measure. Calculation of AMWhen the training is needed, only the data of the source domain and the data of the target domain are respectively regarded as a whole, and two classification training is carried out; calculation of AcIn the method, the data of the c-type labels in the source domain and the target domain are respectively considered as a whole, and the binary training is carried out, namely 10 times (10 labels) of binary tasks need to be executed, and the average value of 10 average absolute errors (h), namely A, is calculatedc。
S50, solving partial derivatives of the target loss function containing the structure risk minimization, the dynamic distribution alignment and the Laplace regularization term to obtain the optimal solution of the coefficient vector of the model, and then solving the quadratic prediction label of the target domain sample through a representation theory. The method specifically comprises the following steps:
s51, solving an optimal solution of the objective loss function; the method specifically comprises the following steps:
the structural risk minimization function defined on the source domain can be expressed as:
wherein HKAnd | · | non-conducting phosphorFRespectively representing the reproducible Hilbert space (RKHS) and the Frobenius norm,is the coefficient vector to be solved, tr (-) is the trace of the solving matrix,is a kernel matrix, and Kij=K(wi,wj) In the model, an RBF radial basis kernel function is adopted,is a label matrix composed of source domain sample labels and target domain sample prediction labels,is a diagonal indicating matrix and satisfies:
s52, in order to fully mine the geometric characteristics among the neighboring samples in the manifold space, a Laplace regularization term Lap (D) is added to the objective functions,Dt) Expressed as follows:
wherein L is laplace matrix and L-a-U, a denotes diagonal matrix, andu is a neighbor sample incidence matrix and can be obtained by the following calculation:
here, sim (,) is a similarity function used to evaluate the correlation between two samples, Np(wi) Is any one sample wiP neighbor sample sets;
s53, the fault bearing signals collected under the variable working condition often have different condition distributions and edge distributions, so that the relative importance of the two distributions needs to be evaluated, and the maximum mean difference MMD can evaluate the deviation of the two cross-domain distributions, which is defined in the textDefining an adaptive factor xi to dynamically regulate two distributions, which are expressed by theory and kernel technique, source domain DsAnd a target domain DtDIS (D) of data distributions,Dt) Can be expressed as:
where E [. cndot. ] represents the mean of the samples mapped to the regenerated Hilbert space, and M is the MMD combination matrix of the conditional distribution and the edge distribution, which can be calculated by:
here, when ξ → 0, it indicates that the inter-domain conditional distribution adaptation is more important, and conversely, when ξ → 1, it indicates that the inter-domain edge distribution adaptation is more important;
s54, constructing and solving an objective function to obtain the optimal solution of the coefficient vectorThe method for obtaining the target domain sample label by using the representation theory specifically comprises the following steps:
the Laplace regularization term Lap (D) described aboves,Dt) And a dynamically distributed alignment term DIS (D)s,Dt) Added to the structure risk minimization objective function, a global objective loss function is obtained:
by solving the partial derivatives of the objective functionObtaining an optimal coefficient solution
Wherein, I is a unit diagonal matrix, λ, ρ, and η are regularization parameters of corresponding terms, and a quadratic prediction label of a target domain sample can be obtained by using a representation theory in machine learning:
s60, updating the maximum mean difference matrix M by using the secondary prediction label0And McAnd recalculating the self-adaptive dynamic factor, and solving a new optimal solution of the objective function to obtain a cubic prediction label of the target domain sample. The method specifically comprises the following steps:
updating the maximum mean difference matrix M with the quadratic prediction label0And McAnd recalculating the self-adaptive dynamic factor, solving a new optimal solution of the objective function, and obtaining a cubic prediction label of the target domain sample by using a representation theory.
And S70, iterating the steps S40-S60 until the algorithm converges, obtaining a final prediction label of the target domain sample, and completing bearing fault diagnosis. The method specifically comprises the following steps:
iterating the steps S40-S60 until the algorithm converges, namely the prediction result is not changed any more, and obtaining the final prediction label of the target domain sample
Based on the above steps, fig. 4 shows a schematic block diagram of a diagnostic method corresponding to the present invention, fig. 5 is a diagnostic result of 12 migration tasks, the diagnostic result indicates that the average precision of the diagnostic tasks under 12 variable conditions is close to 100%, fig. 6 and fig. 7 respectively show detailed displays based on the experimental result, as can be seen from fig. 6, the present invention can realize algorithm convergence within a very short number of iterations when different migration diagnostic tasks are executed, fig. 7 fully illustrates that the present invention has good robustness to algorithm hyper-parameters while ensuring high diagnostic precision, i.e., when the present invention is used for a diagnostic task outside an experiment, excellent classification effect can be obtained without rich prior knowledge.
In summary, the bearing fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment under variable working conditions can effectively avoid the characteristic distortion of data in the original Euclidean space by automatically calculating the optimal subspace dimension and calculating the geodesic flow kernel and the characteristic representation of the manifold after transformation. And a self-adaptive factor is defined by introducing similarity measurement A-distance, the relative weight of sample data condition distribution and edge distribution is dynamically adjusted, the distribution difference of the source domain sample and the target domain sample is effectively reduced, and the accuracy and the effectiveness of the fault diagnosis of the rolling bearing under the variable working condition are greatly improved. Compared with the bearing fault diagnosis based on deep learning, the method has the advantages of strong interpretability, lower requirement on computer hardware resources, higher execution speed, and excellent diagnosis accuracy, algorithm convergence and parameter robustness. The method is particularly suitable for multi-scene and multi-fault bearing fault diagnosis under variable working conditions, and can be widely applied to fault diagnosis tasks under variable working conditions of complex systems such as machinery, electric power, chemical engineering, aviation and the like.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. A fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment is characterized by comprising the following steps:
s10, collecting vibration signals of the bearing under different working conditions, adding various fault type labels of the bearing, taking the data collected under each working condition as a transferable data set, distributing the data in each transferable domain data set under different conditions and edges, then performing data cutting, and obtaining a sample;
s20, carrying out frequency domain processing on the bearing signals by using fast Fourier transform to obtain a source domain data set and a target domain data set, and inputting the source domain data set and the target domain data set as models;
s30, calculating the optimal subspace dimension through a GFK algorithm, and calculating a geodesic flow type kernel matrix and a transformed manifold feature representation;
s40, training a KNN-based classifier to generate preliminary prediction labels of target domain samples, and respectively calculating a maximum mean difference matrix M0And McRespectively corresponding to the edge distribution and the condition distribution of the sample data, and defining and calculating a self-adaptive dynamic factor through the similarity measurement A-distance;
s50, solving partial derivatives of the target loss function containing the structure risk minimization, the dynamic distribution alignment and the Laplace regularization term to obtain the optimal solution of the coefficient vector of the model, and then solving the secondary prediction label of the target domain sample through a representation theory;
s60, updating the maximum mean difference matrix M by using the secondary prediction label0And McRecalculating the adaptive dynamic factor, and solving a new optimal solution of the objective function to obtain a cubic prediction label of the target domain sample;
and S70, iterating the steps S40-S60 until the algorithm converges, obtaining a final prediction label of the target domain sample, and completing bearing fault diagnosis.
2. The fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 1, wherein the step S20 specifically includes:
converting a bearing time domain vibration signal into a frequency domain signal through Fast Fourier Transform (FFT), reserving unilateral frequency spectrum information of a frequency domain, and giving a marked source domain data setAnd a target domain data setWherein x issAnd xtRespectively source domain and target domain samples, n and m are corresponding sample numbers, ysIs a source domain sample label, k is a sample feature number, and
3. the fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 1, wherein the step S30 of calculating the optimal subspace dimension specifically includes:
respectively obtaining subspace data sets P of a source domain and a target domain through principal component analysissAnd PtCalculate PsAnd PtIs combined with the matrix Ps+tAnd separately calculate Ps、PtAnd Ps+tSine included angle alpha therebetweendAnd betadThe subspace inconsistency metric (SDM) c (d) may be expressed as:
C(d)=0.5[sinαd+sinβd]
here, the more similar the source domain and the target domain, the larger the value of c (d), and under the premise of ensuring that the captured variance of one subspace can be transferred to other subspaces, that is: alpha is alphad≠π/2,βdNot equal to pi/2, the optimal subspace dimension d can be calculated by a greedy algorithm*:
d*=min{d|C(d)=1}。
4. The fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 3, wherein the step S30 of calculating the geodesic flow kernel matrix and the transformed manifold feature representation specifically comprises:
computing PCA subspace PsAnd PtPrincipal angle of (theta)i(0≤θ1≤θ2≤…θdLess than or equal to pi/2), respectively calculating cos thetaiAnd sin θi(i ═ 1,2 ·, d) and as diagonal elements of the diagonal matrix sum Σ, PsIs complemented byAndrepresents a pair of orthogonal matrices and can be found by singular value decomposition of:
further, the geodesic flow kernel matrix G may be calculated by the following formula:
wherein, Λ1To Λ3For a diagonal matrix, the diagonal elements are:
the transformed manifold features are further represented as:
wherein X ═ Xs,Xt]Source domain sample set W after conversionsAnd a target domain sample set WsCan be calculated by the following formula:
5. the fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment of claim 1, wherein the maximum mean difference matrix M is calculated in step S400And McThe method specifically comprises the following steps:
wherein n iscAnd mcAre respectively a source domain DsAnd a target domain DtThe number of samples of the class c tag in (1).
6. The fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 5, wherein the step S40 defines and calculates an adaptive dynamic factor by a similarity measure a-distance, which specifically includes:
training a linear two-classifier h on a source domain and a target domain by using a Support Vector Machine (SVM), and representing the loss of the classifier by (h), the similarity measure A-distance across domains can be represented as:
A(Ds,Dt)=2(1-2(h))
the adaptation factor ξ may be defined as:
wherein A isMAnd AcRespectively representing an edge similarity measure and a conditional similarity measure.
7. The fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 1, wherein the step S50 specifically includes:
s51, solving an optimal solution of the objective loss function; the method specifically comprises the following steps:
the structural risk minimization function defined on the source domain can be expressed as:
wherein HKAnd | · | non-conducting phosphorFRespectively representing the reproducible Hilbert space (RKHS) and the Frobenius norm,is the coefficient vector to be solved, tr (-) is the trace of the solving matrix,is a kernel matrix, and Kij=K(wi,wj) In the model, an RBF radial basis kernel function is adopted,is a label matrix composed of source domain sample labels and target domain sample prediction labels,is a diagonal indicating matrix and satisfies:
s52, in order to fully mine the geometric characteristics among the neighboring samples in the manifold space, a Laplace regularization term Lap (D) is added to the objective functions,Dt) Expressed as follows:
wherein L is laplace matrix and L-a-U, a denotes diagonal matrix, andu is a neighbor sample incidence matrix and can be obtained by the following calculation:
here, sim (,) is a similarity function used to evaluate the correlation between two samples, Np(wi) Is any one sample wiP neighbor sample sets;
s53, the fault bearing signal collected under the variable working condition often has different condition distribution and edge distribution, so it is necessary to evaluate the relative importance of the two distributions, the maximum mean difference MMD can evaluate the deviation of the two cross-domain distributions, this text defines a self-adaptive factor xi to dynamically adjust the two distributions, and the source domain D expresses the theory and nuclear skillsAnd a target domain DtDIS (D) of data distributions,Dt) Can be expressed as:
where E [. cndot. ] represents the mean of the samples mapped to the regenerated Hilbert space, and M is the MMD combination matrix of the conditional distribution and the edge distribution, which can be calculated by:
here, when ξ → 0, it indicates that the inter-domain conditional distribution adaptation is more important, and conversely, when ξ → 1, it indicates that the inter-domain edge distribution adaptation is more important;
s54, constructing and solving an objective function to obtain the optimal solution of the coefficient vectorThe method for obtaining the target domain sample label by using the representation theory specifically comprises the following steps:
the Laplace regularization term Lap (D) described aboves,Dt) And a dynamically distributed alignment term DIS (D)s,Dt) Added to the structure risk minimization objective function, a global objective loss function is obtained:
by solving the partial derivatives of the objective functionObtaining an optimal coefficient solution
Wherein, I is a unit diagonal matrix, λ, ρ, and η are regularization parameters of corresponding terms, and a quadratic prediction label of a target domain sample can be obtained by using a representation theory in machine learning:
8. the fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 1, wherein the step S60 specifically includes:
updating the maximum mean difference matrix M with the quadratic prediction label0And McAnd recalculating the self-adaptive dynamic factor, solving a new optimal solution of the objective function, and obtaining a cubic prediction label of the target domain sample by using a representation theory.
9. The fault diagnosis method based on adaptive manifold embedding dynamic distribution alignment as claimed in claim 1, wherein the step S10 of collecting vibration signals of the bearing under different operating conditions specifically includes: when the bearing rotates and runs under four different working conditions, the vibration signals of the bearing under each working condition are collected through the acceleration sensor.
10. The method of claim 9, wherein the four different operating conditions are four different radial loads applied to the bearing.
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