Time-varying cross-domain diagnosis method based on distributed manifold distance distribution difference index

Abstract

The invention relates to a time-varying cross-domain diagnosis method based on a distributed manifold distance distribution difference index, and belongs to the technical field of mechanical equipment fault diagnosis. The method comprises the following steps: S1, acquiring an original vibration signal of mechanical equipment through a sensor, and expanding a sample data set for the acquired original vibration signal by using a sliding sampling technology; s2, an IDMD based on an MELD selection mechanism and EGMG measurement is designed; s3, constructing a fault migration diagnosis model based on the IDMD and the one-dimensional convolutional neural network; s4, inputting the training set into a constructed fault migration diagnosis model, and performing iterative updating training on the model by using a source domain labeled sample classification cross entropy loss function and an IDMD distribution difference loss function between the source domain and a target domain; s5, after repeated iterative training, the error curve tends to be stable, and model training is completed; and inputting the verification set into the trained model for cross-time-varying working condition fault migration diagnosis of the mechanical equipment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical equipment fault diagnosis, and relates to a time-varying cross-domain diagnosis method based on a set-distributed manifold distance distribution difference index. BACKGROUND

[0002] In modern industrial production, stable and efficient operation of mechanical equipment is crucial. In order to make the mechanical equipment achieve and maintain the best service state, it is often necessary to actively or passively adjust its operating parameters, such as speed, load, temperature, etc. These adjustments result in continuous changes in the operating conditions of mechanical equipment, thereby generating a large amount of variable operating condition data.

[0003] In recent years, data-driven intelligent diagnosis models, especially deep learning models, have achieved remarkable success in the field of mechanical fault diagnosis. However, the performance of these models largely depends on a basic assumption that training data and test data come from the same distribution. In actual engineering applications, due to the adjustment of the operating posture of mechanical equipment, the data distribution of monitoring signals such as vibration and noise will change significantly. This difference in data distribution, also known as "domain shift", will inevitably lead to a significant decline in the accuracy and generalization ability of intelligent diagnosis models trained in a certain operating condition in another operating condition.

[0004] To solve this problem, researchers have introduced transfer learning techniques, especially fault transfer diagnosis methods. This method aims to reduce the distribution difference between data from different operating conditions (source domain and target domain), transfer the fault diagnosis knowledge learned from one operating condition to another new operating condition lacking labeled data, and thus improve the adaptability of the model in the variable operating condition environment.

[0005] The core of the fault transfer diagnosis method is how to accurately measure the difference between the source domain and the target domain data distribution. Currently, the mainstream difference measurement indicators include Maximum Mean Discrepancy (MMD), Kullback-Leibler (KL) divergence, Wasserstein distance, etc. These indicators quantify the distance between two distributions by finding a function in the feature space that maximizes the difference between the two distributions. In the training process, the transfer learning model minimizes this difference indicator to learn domain-invariant feature representations, thereby improving the performance of transfer diagnosis.

[0006] However, the existing fault migration diagnosis methods based on these distribution difference indicators have a fundamental limitation: their effectiveness depends entirely on the stability of the data distribution. In other words, these methods only perform well when dealing with migration tasks from one constant operating condition to another. For example, a model is trained in a stable 1000 RPM speed operating condition and then migrated to another stable 1500 RPM speed operating condition. In this "constant-constant" variable operating condition scenario, although the data distributions of the source domain and the target domain are different, they are relatively stable internally.

[0007] In more complex practical engineering environments, the operating conditions of mechanical equipment are often time-varying, i.e., the parameters such as speed and load are continuously and dynamically changing. In this case, the monitoring data no longer conforms to a fixed distribution, but exhibits non-stationary characteristics that change continuously. The traditional distribution difference indicators mathematically assume that the source domain and the target domain each have a static, determinable probability distribution. When time-varying conditions cause the data distribution to continuously drift over time, this basic assumption no longer holds.

[0008] Specifically, for a time-varying system, the data collected in any time period may come from a distribution slightly different from the previous time period. If the entire time-varying process is considered as a target domain, it contains countless continuously changing sub-distributions. Existing difference measurement indicators cannot capture this dynamic and continuous distribution change. They can only calculate the global difference between the distributions of two "frozen" states, thus ignoring the transient process and evolution trend of the distribution change. The failure of this measurement method results in the inability of the transfer learning model to truly learn the fault features that remain unchanged in the time-varying process, and its performance upper limit is fundamentally constrained.

[0009] In summary, the existing technology has the following key problems:

[0010] (1) Application scenario limitation: The transfer learning fault diagnosis method based on traditional distribution difference measurement is mainly applicable to constant variable operating condition tasks, i.e., migrating from one stable operating condition to another stable operating condition.

[0011] (2) Inability to adapt to time-varying operating conditions: In time-varying operating condition environments where speed, load, and other parameters continuously and dynamically change, the performance of existing methods will significantly decrease or even fail.

[0012] (3) Fundamental defect of measurement indicators: The mathematical assumption of existing distribution difference indicators (i.e., the stability of the distribution within the domain) is broken in time-varying environments, which cannot accurately measure and align the dynamically changing data distribution, thus limiting the performance upper limit of the fault migration diagnosis method.

[0013] Therefore, there is an urgent need for a new technology that can break through the limitations of existing distribution difference measurement methods, accurately measure the distribution difference of data under time-varying working conditions, and thus provide a theoretical basis and technical support for developing intelligent fault migration diagnosis models with higher performance and greater robustness. SUMMARY

[0014] Therefore, the purpose of the present application is to provide a time-varying cross-domain diagnosis method based on the set and scatter manifold distance distribution difference index, which can accurately measure the distribution difference of data under time-varying working conditions.

[0015] To achieve the above purpose, the present application provides the following technical solutions:

[0016] A time-varying cross-domain diagnosis method based on the set and scatter manifold distance distribution difference index, specifically comprising the following steps:

[0017] S1: Collect the original vibration signal of the mechanical equipment through the sensor, and then expand the sample data set using the sliding sampling technology, and divide it into a training set and a validation set;

[0018] S2: Design IDMD based on MELD selection mechanism and EGMG measurement, wherein MELD represents maximum entropy local distribution, EGMG represents integrated Grassmann manifold geodesic, and IDMD represents set and scatter manifold distance;

[0019] S3: Based on IDMD and one-dimensional convolutional neural network, construct a fault migration diagnosis model;

[0020] S4: Input the training set into the constructed fault migration diagnosis model, and use the source domain labeled sample classification cross-entropy loss function and the IDMD distribution difference loss function between the source domain and the target domain to iteratively update and train the model;

[0021] S5: After multiple iterations of training, the error curve tends to be stable, and the model training is completed; input the validation set into the trained model for cross-time-varying working condition fault migration diagnosis of the mechanical equipment.

[0022] Further, in step S2, the MELD selection mechanism is used to adaptively segment multiple local distributions, thereby maximizing the representation of the information of the time-varying overall distribution; subsequently, the EGMG measurement is used to capture the internal distribution difference between the source domain and the target domain in the manifold space under time-varying conditions, thereby accurately realizing fault accurate migration diagnosis under dynamic cross-domain data structure.

[0023] Further, in step S2, the MELD selection mechanism is used to adaptively search for multiple optimal local distributions; first, assume that the distribution of the monitoring signal follows a Gaussian distribution N(u c ,Σ c), the probability density function of which can be expressed as:

[0024]

[0025] where P(x|z=c) represents the sample distribution probability of the c-th Gaussian component; u c and Σ c represent the mean vector and covariance matrix of the c-th sample set; x represents the sample variable, z represents the hidden variable; d represents the sample dimension; subsequently, the internal distribution P o (x) of the entire continuous time-varying monitoring signal can be expressed as:

[0026]

[0027] where θ={ω c ,u c ,Σ c}, c=0, 1, ···, C represents the parameter set, and C is the number of categories; ω c represents the weight of the c-th Gaussian component; the solving of the distribution parameter can be converted into solving the Gaussian mixture model problem.

[0028] Further, in step S2, the solving of the distribution parameter can be converted into solving the Gaussian mixture model problem, specifically: given the sample number n, the optimization objective is defined as:

[0029]

[0030] where c=0, 1, ···, C represents the optimal distribution parameter, and Θ represents the distribution parameter set; after the optimal distribution parameter θ is obtained, the optimal number of Gaussian local distributions is determined according to the following formula:

[0031]

[0032] where IE i represents the information entropy of the i-th Gaussian component, I(·) represents the indicator function, and K represents the discrimination threshold; formula (4) represents that under the condition that IE i >IE j , j=i+1, i+2, ···, i+K, the lowest i is selected as the final number of local distributions

[0033] Further, in step S2, the calculation formula of the information entropy IE i of the i-th Gaussian component is:

[0034]

[0035] where The denoted τ represents the proportion of the i-th Gaussian distribution among all Gaussian distributions; τ represents the control... The temperature coefficient of difference, the smaller the τ, the greater the difference.

[0036] Furthermore, in step S2, the EGMG metric specifically includes: embedding multiple subdomains from the source and target domains into a Grassman manifold to obtain their subspace representations. Solve by eigenvalue decomposition of the sample covariance matrix:

[0037] xx T ω i =λ i ω i (6)

[0038] Where d and d′ represent the original sample space dimension and subspace dimension, respectively, and λ i Represent eigenvalues; [represent the source domain] With the i-th subdomain in the target domain Defined as Ψ i (0) and Ψ i (1); Therefore, the geodesic flow between the two domains is expressed as:

[0039]

[0040] In the formula, Ψ i (0) = W S and t represents the position variable; if Ψ i If the expression for (t) can be constructed, then the final geodesic metric (Ψ) is... i ) T x is obtained:

[0041]

[0042] In the formula, and Represents an orthogonal matrix; and In subspace W S and Between the main characters {θ i} i＝1,2,···d The relevant singular diagonal matrix is ​​expressed as follows:

[0043]

[0044] The elements of equation (8) corresponding to Γ(t) and Λ(t) are cos(θ) i t) and sin(θ) i t);

[0045] Due to geodesic metric is an infinite dimensional vector, which is not computable. and the i-th sub-domain in the target domain S and Based on the inner product between vectors i ) T x S and The final IDMD distribution difference index can be defined as:

[0046]

[0047] Further, in step S2, the expressions of the orthogonal matrix and are:

[0048]

[0049] Wherein, SVD represents the singular value decomposition algorithm.

[0050] Further, in step S2, given The mathematical solution expression for solving the integral term is:

[0051]

[0052] The beneficial effects of the present application are that the present application proposes an integrated manifold distance (IDMD) to improve the difference expression capability in dynamic data structure. In the IDMD, first, a maximum entropy local distribution (MELD) selection mechanism is designed to adaptively represent the global distribution information of the time-varying monitoring signal with multiple local distributions; and an integrated Grassmann manifold geodesic (EGMG) metric is constructed to represent the distribution difference information under the internal dynamic data structure. The specific embodiments are as follows:

[0053] 1) Dynamic data structure representation capability is improved: the maximum entropy local distribution (MELD) selection mechanism is used to adaptively segment the local distribution of the time-varying signal, which solves the problem that the traditional method is difficult to capture the non-steady global distribution. The mechanism optimizes the number of local distributions based on information entropy, realizing efficient representation of time-varying signal distribution.

[0054] 2) Nonlinear difference measurement innovation: the integrated Grassmann manifold geodesic (EGMG) metric breaks through the limitation of Euclidean space, and uses the Grassmann manifold geodesic to describe the difference of nonlinear data structure. Experiments show that the diagnostic accuracy is improved by about 40% compared with traditional methods (MMD, etc.), and the average reaches more than 90%.

[0055] ​3) Engineering application value is prominent: in the planetary gearbox fault diagnosis, the method of the application successfully realizes the cross-domain migration from time-varying working condition (such as 0-2400rpm) to constant working condition, and verifies the applicability of the method of the application to complex industrial scenes. Through sliding sampling and covariance matrix feature decomposition, the calculation complexity is significantly reduced.

[0056] Other advantages, objects, and features of the application will be in part apparent and in part pointed out below in the specification, as some of them will be observed from a reading of the specification. The objects and other advantages of the application can be realized and attained by the structure particularly pointed out in the specification. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred embodiments of the present application will be described in detail below with reference to the drawings, in which:

[0058] Figure 1 It is a schematic diagram of the principle of IDMD (Integrated Distance Manifold Distance) ;

[0059] Figure 2 It is a schematic diagram of the principle of Euclidean measurement and geodesic measurement;

[0060] Figure 3 It is a schematic diagram of the structure of the planetary gearbox fault simulation test bed;

[0061] Figure 4 It is a comprehensive comparison of experimental results. DETAILED DESCRIPTION

[0062] The embodiments of the present application will be described below through specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the disclosure of the specification. The present application can also be implemented or applied by different specific embodiments, and the details in the specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be noted that the diagrams provided in the following examples only illustrate the basic concept of the present application in a schematic manner, and the following examples and features in the examples can be combined with each other without conflict.

[0063] The drawings are only used for illustrative explanation, and the representation is only a schematic diagram, not a physical diagram, and cannot be understood as a limitation of the present application; in order to better illustrate the embodiments of the present application, some components in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some known structures and their descriptions in the drawings may be omitted.

[0064] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it is understood that if the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "front", "back" and the like are based on the orientations or positional relationships shown in the drawings, they are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only used for exemplary illustration, and cannot be understood as a limitation on the present application, for those skilled in the art, the specific meanings of the above terms can be understood according to the specific circumstances.

[0065] Please refer to Figures 1-4 , the embodiment of the present application provides a time-varying cross-domain diagnosis method based on IDMD distance distribution difference index, and the flow is as follows:

[0066] Step 1: Collect the original vibration signal of the planetary gear box on the mechanical equipment through the acceleration sensor, so as to construct the subsequent migration diagnosis task. Then, the original vibration signal collected is expanded by using the sliding sampling technology to expand the sample data set.

[0067] Step 2: Design IDMD based on maximum entropy local distribution (MELD) selection mechanism and integrated Grassmann manifold geodesic (EGMG), as shown in Figure 1 .

[0068] Figure 1 IDMD designs maximum entropy local distribution (MELD) selection mechanism and integrated Grassmann manifold geodesic (EGMG) measurement two core methods. MELD selection mechanism is used to adaptively segment multiple local distributions, so as to maximize the information representing the time-varying overall distribution; then, EGMG measurement is used to capture the internal distribution difference between the source domain and the target domain in the manifold space under the time-varying condition, so as to accurately realize the fault accurate migration diagnosis under the dynamic cross-domain data structure.

[0069] 1) Maximum entropy-based local distribution (MELD) selection mechanism

[0070] The prerequisite for the effectiveness guarantee of IDMD needs to represent the distribution information of the continuous time-varying monitoring signal to the maximum extent, therefore, the MELD selection mechanism is used to adaptively search for multiple optimal local distributions. First, assume that the distribution of the monitoring signal obeys the Gaussian distribution N(u c ,Σ c ), and its probability density function can be expressed as:

[0071]

[0072] In the formula, P(x|z=c) represents the sample distribution probability of the c-th Gaussian component; u c and Σ c Let represent the mean vector and covariance matrix of the c-th sample set; d represents the sample dimension. Subsequently, the intrinsic distribution P of the entire continuous time-varying monitoring signal... o (x) can be represented as:

[0073]

[0074] In the formula, θ={ω c ,u c ,Σ c}, c = 0, 1, ..., C represents the parameter set, where C is the number of categories; ω c This represents the weight of the c-th Gaussian component. Solving for the distribution parameters can be transformed into solving a Gaussian mixture model problem. Given the number of samples n, the optimization objective can be defined as:

[0075]

[0076] In the optimal distribution parameters After obtaining c = 0, 1, ..., C, the next step is to determine the number of Gaussian local distributions. Because Let represent the proportion of the c-th Gaussian distribution among all Gaussian distributions, then the number of optimal local distributions... The solution can be obtained using the following formula:

[0077]

[0078] In the formula, IE C represent The information entropy of a Gaussian component; τ represents the information entropy used for control. The smaller the temperature coefficient of the difference, the greater the difference. According to equation (4), it can be seen that... This is impossible to achieve in actual calculations. Therefore, equation (4) is reformulated as:

[0079]

[0080] In the formula, I(·) represents the indicator function; K represents the discrimination threshold. Overall, equation (5) indicates that in IE... i >IE j Given j = i+1, i+2, ..., i+K, select the lowest i as the final number of elements in the local distribution.

[0081] 2) Ensemble Grassmann manifold geodesic (EGMG) metric

[0082] By sampling C local distribution parameters, C sub-domains in the time-varying target domain can be obtained As shown in the following formula:

[0083]

[0084]

[0085] In the formula, represents the chi-square distribution under the given sample dimension d and confidence level a; is obtained by sampling from the distribution N(u c ,Σ c ) with 1-a confidence level, which also means that the sub-domain is located in the hypersphere.

[0086] Most of the current distribution difference measurement methods are based on Euclidean measurement, which usually assumes that the data sample space is linear and uniform. This assumption does not match the complex nonlinear structure of real-world data samples. Therefore, the EGMG metric based on Grassmann manifold geodesic measurement is proposed, as shown in Figure 2 Geodesic measurement considers the nonlinear geometric structure of data space and can more accurately reflect the inherent distribution difference.

[0087] Since directly measuring geodesic in the sample space will cause high computational complexity, multiple sub-domains in the source domain and the target domain are embedded into the Grassmann manifold to obtain their subspace representations can be solved by eigenvalue decomposition of the sample covariance matrix:

[0088] xx T ω i = λ i ω i (8)

[0089] Figure 2 In the formula, the i-th sub-domain in the source domain and the target domain is defined as Ψ i (0) and Ψ i (1). Therefore, the geodesic flow between the two domains can be represented as:

[0090]

[0091] In the formula, Ψ i (0) = W S and If Ψ i The expression for (t) can be constructed, then the final geodesic metric (Ψ) can be obtained. i ) T x can also be obtained:

[0092]

[0093] In the formula, and Representing an orthogonal matrix:

[0094]

[0095] In the formula, and In subspace W S and Between the main characters {θ i} i＝1,2,···d The relevant singular diagonal matrix is ​​expressed as follows:

[0096]

[0097] The elements of equation (10) corresponding to Γ(t) and Λ(t) are cos(θ) i t) and sin(θ) i t). Due to geodesic measurement It is an infinite-dimensional vector, which is not computable. Given from the source domain... and the i-th subdomain in the target domain sample vector x S and Based on (Ψ) i ) T x S and The inner product of vectors, the final IDMD distribution difference index can be defined as:

[0098]

[0099] Given Integral terms For example, the detailed mathematical solution expression is as follows:

[0100]

[0101] Step 3: Based on the collector-distribution manifold distance and a one-dimensional convolutional neural network, construct a fault migration diagnosis model to verify the effectiveness of the proposed collector-distribution manifold distance.

[0102] Step 4: Input the segmented training samples into the constructed fault transfer diagnosis model, and use the source domain labeled sample classification cross-entropy loss function and the IDMD distribution difference loss function between the source domain and the target domain to iteratively update and train the transfer model.

[0103] Step 5: After multiple iterations of training, the error curve tends to stabilize, the model training is complete, and the trained transfer model will be used for fault transfer diagnosis of planetary gearbox under time-varying operating conditions.

[0104] The above is the flowchart of the time-varying cross-domain diagnostic method based on the distribution difference index of the distributed manifold distance (IDMD) proposed in this invention. The effectiveness of the above method will be verified by experiments below.

[0105] Verification experiment:

[0106] The original vibration signals of the planetary gearbox collected in this experiment came from... Figure 3 The self-test simulation test bench shown consists mainly of a drive motor, a single-stage planetary gearbox, a magnetic powder brake, and a controller. The simulated faulty component is the planetary gear in the gearbox. Vibration monitoring signals covering six health states were collected: normal state (NC), surface spalling (SP), root crack (RC), tooth wear (TW), micropitting (MP), and tooth fracture (TF). The sampling frequency of the accelerometer was set to 16384Hz. Three time-varying speed states were simulated: 0–600 rpm (V1), 0–1200 rpm (V2), and 0–2400 rpm (V3), with rates of change of 100 rpm / s, 200 rpm / s, and 400 rpm / s, respectively. Finally, a constant speed state of 600 rpm (C) was also simulated. The sample dimension was set to 3072 to ensure that each sample contained at least one fault cycle. Sliding sampling was used to divide the sample size for each health state into 1000 samples. Based on the monitoring signals collected above, six time-varying migration diagnostic tasks can be constructed, namely V1→C, V2→C, V3→C, C→V1, C→V2 and C→V3.

[0107] Comparative experiment:

[0108] To demonstrate the superiority of the time-varying cross-domain diagnostic method based on the distribution difference index of the collector-distribution manifold distance (IDMD) of this invention, it was compared with cross-domain diagnostic methods based on current classic distribution difference indices (MMD, MMSD, CORAL, A, and HΔH). The experimental results are as follows: Figure 4 As shown. From Figure 4It can be seen that the IDMD distance distribution difference index has higher migration diagnosis precision and stronger generalization ability. In particular, the average diagnosis accuracy of IDMD reaches more than 90%; compared with other migration diagnosis methods, the diagnosis accuracy is improved by about 40%.

[0109] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the purpose and scope of the technical solutions, which should be covered in the scope of the claims of the present application.

Claims

1. A time-varying cross-domain diagnostic method based on the difference index of distance distribution in a distributed manifold, characterized in that, The method specifically includes the following steps: S1: Collect raw vibration signals of mechanical equipment through sensors, and then expand the sample dataset using sliding sampling technology, dividing it into training set and validation set; S2: Design an IDMD based on the MELD selection mechanism and the EGMG metric, where MELD represents the local maximum entropy distribution, EGMG represents the integrated Grassman manifold geodesic, and IDMD represents the distance between the collection and distribution manifolds. S3: Construct a fault migration diagnosis model based on IDMD and one-dimensional convolutional neural network; S4: Input the training set into the constructed fault transfer diagnosis model, and use the source domain labeled sample classification cross-entropy loss function and the IDMD distribution difference loss function between the source domain and the target domain to iteratively update and train the model; S5: After multiple iterations of training, the error curve tends to stabilize, and the model training is complete; input the validation set into the trained model for fault migration diagnosis of mechanical equipment under time-varying operating conditions.

2. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 1, characterized in that, In step S2, the MELD selection mechanism is used to adaptively segment multiple local distributions to maximize the representation of information about the time-varying overall distribution. Subsequently, the EGMG metric is used to capture the inherent distributional differences between the source and target domains in the manifold space under time-varying conditions, thereby accurately realizing fault migration diagnosis under dynamic cross-domain data structures.

3. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 1 or 2, characterized in that, In step S2, the MELD selection mechanism is used to adaptively search for multiple optimal local distributions; first, it is assumed that the distribution of the monitored signal follows a Gaussian distribution N(u c ,Σ c Its probability density function is expressed as: In the formula, P(x|z=c) represents the sample distribution probability of the c-th Gaussian component; u c and Σ c Let represent the mean vector and covariance matrix of the c-th sample set; x represents the sample variables, z represents the latent variables; d represents the sample dimension; subsequently, the intrinsic distribution P of the entire continuous time-varying monitoring signal. o (x) is represented as: In the formula, θ={ω c ,u c ,Σ c }, c = 0, 1, ..., C represents the parameter set, where C is the number of categories; ω c This represents the weight of the c-th Gaussian component; solving for the distribution parameters is transformed into solving a Gaussian mixture model problem.

4. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 3, characterized in that, In step S2, solving for the distribution parameters is transformed into solving a Gaussian mixture model problem. Specifically, given the number of samples n, the optimization objective is defined as: in, c = 0, 1, ..., C represents the optimal distribution parameters, Θ represents the set of distribution parameters; in the optimal distribution parameters... After obtaining the result, the number of optimal Gaussian local distributions is determined by solving the following formula. In the formula, IE i Let I(·) represent the information entropy of the i-th Gaussian component, I(·) represent the indicator function, and K represent the discrimination threshold; Equation (4) indicates that in IE i >IE j Given j = i+1, i+2, ..., i+K, select the lowest i as the final number of elements in the local distribution.

5. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 4, characterized in that, In step S2, the information entropy IE of the i-th Gaussian component i The calculation formula is: in, The denoted τ represents the proportion of the i-th Gaussian distribution among all Gaussian distributions; τ represents the control... The temperature coefficient of the difference.

6. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 4, characterized in that, In step S2, the EGMG metric specifically includes: embedding multiple subdomains from the source and target domains into a Grassman manifold to obtain their subspace representations. Solve by eigenvalue decomposition of the sample covariance matrix: xx T oh i =λ i oh i (6) Where d and d′ represent the original sample space dimension and subspace dimension, respectively, and λ i Represent eigenvalues; [represent the source domain] With the i-th subdomain in the target domain Defined as Ψ i (0) and Ψ i (1); Therefore, the geodesic flow between the two domains is expressed as: In the formula, Ψ i (0) = W S and t represents the position variable; if Ψ i If the expression for (t) can be constructed, then the final geodesic metric (Ψ) is... i ) T x is obtained: In the formula, and Represents an orthogonal matrix; and In subspace W S and Between the main characters {θ i } i＝1,2,···d The relevant singular diagonal matrix is ​​expressed as follows: The elements of equation (8) corresponding to Γ(t) and Λ(t) are cos(θ) i t) and sin(θ) i t); Given from the source domain and the i-th subdomain in the target domain sample vector x S and Based on (Ψ) i ) T x S and The inner product between vectors, the final IDMD distribution difference index. Defined as:

7. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 6, characterized in that, In step S2, the orthogonal matrix and The expression is: Here, SVD stands for Singular Value Decomposition.

8. The time-varying cross-domain diagnostic method based on the difference index of distribution manifold distance according to claim 6, characterized in that, In step S2, given Solving for the integral term The mathematical expression for solving this problem is:

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