Multi-task collaborative classification method based on multi-domain fuzzy robust matrix machine

Abstract

The invention discloses a multi-task collaborative classification technology based on a multi-domain fuzzy robust matrix machine, and relates to the field of signal processing and feature recognition. Comprising the following steps: collecting multi-target domain vibration signals in different states; recombining the vibration signals into a symplectic geometry coefficient matrix sample by adopting a symplectic geometry similarity transformation method to serve as the input of a multi-domain fuzzy robust matrix machine; selecting a part of samples as a training set to train a multi-domain fuzzy robust matrix machine; constructing a multi-task optimization model; a multi-constraint problem is converted into a dual problem to be solved through a Lagrange multiplier method; and outputting a classification result according to the decision function. According to the multi-task collaborative classification technology provided by the invention, by designing the multi-domain fuzzy robust matrix machine model, accurate data classification under different tasks can be realized, the generalization performance of the model can be effectively improved, and the influence of isolated data on model classification can be reduced to a certain extent.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and feature recognition, specifically to a multi-task collaborative classification method based on a multi-domain fuzzy robust matrix machine. Background Technology

[0002] In recent years, scholars have proposed various symplectic geometric mode analysis methods based on symplectic geometric theory, which can achieve noise removal while preserving the structured information of the signal. However, both symplectic geometric spectral analysis and symplectic geometric mode decomposition have shortcomings. SGSA is applied to time series analysis, but this method relies on empirical selection of the embedding dimension and does not provide a termination criterion.

[0003] Traditional matrix classification methods struggle to simultaneously model multiple patterns in rotating machinery systems. This is particularly relevant for addressing potential correlations between bearing and gear fault diagnosis tasks, such as shared fault frequencies, and the inability to leverage shared information across different tasks to improve overall classification accuracy.

[0004] Existing learning classification methods:

[0005] Traditional matrix classifiers (such as TWSVM) lack consideration for the correlation between tasks;

[0006] Typical multi-task learning (such as MTL-SVM) lacks low-rank constraints and symplectic geometric feature inputs;

[0007] Existing fuzzy SVM methods lack the combination of multi-task architecture and dual-boundary control, and their computational complexity increases dramatically with the number of tasks.

[0008] The above methods are difficult to apply to unusual samples, such as industrial vibration data which often contain impact noise, leading to distorted classification boundaries. Summary of the Invention

[0009] To address the shortcomings of existing multi-object domain classification methods, this invention provides a multi-domain fuzzy robust matrix machine-based multi-task collaborative classification method. The method provided by this invention can solve classification problems under multiple tasks. Furthermore, constructing a pair of parallel hyperplanes improves the model's computational speed and classification performance. In addition, by introducing a fuzzy function, the robustness of the model is further enhanced, reducing the impact of outlier samples on classification.

[0010] A multi-task collaborative classification technique based on a multi-domain fuzzy robust matrix machine, comprising the following steps:

[0011] Step 1: Collect vibration signals from multiple targets under different conditions;

[0012] Step 2: The vibration signal is reconstructed into a symplectic geometric coefficient matrix sample using the symplectic geometric similarity transformation method, which serves as the input to the multi-domain fuzzy robust matrix machine;

[0013] Step 3: First, select a portion of the samples as the training set, with a random ratio of 0.4-0.5, to train the multi-domain fuzzy robust matrix machine; use the remaining samples as the test set to verify the model performance of the multi-domain fuzzy robust matrix machine.

[0014] Construct a multi-task optimization model for T distinct but related tasks, where the input sample for each task is {(x...} i ,y i ), i = 1, 2, ..., n}, where x i ∈R m×n ,y i ={+1,-1}; then construct the objective function of the multi-task optimization model;

[0015] The objective function is: for T distinct and related tasks, the input samples for each task are {(x... i ,y i ), i = 1, 2, ..., n}, where x i ∈R m×n ,y i ={+1,-1}. The objective function for constructing the multi-domain fuzzy robust matrix mechanism is as follows:

[0016]

[0017] Where, A=[(γ<a,c> +k) d ,e],A t =[(γ t ,c>+k) d ,e t ],B=[(γ<b,c> +k) d ,e],B t =[(γ t ,c>+k) d ,e t ]. where 'a' represents the positive class samples for all tasks, a t Let b be the positive class samples of task t, and b be the negative class samples of all tasks. t Let S be the negative class sample of task t, and c be the total sample of all tasks, where c = [a; b]. i ,S it (i=+,-) is a diagonal matrix of fuzzy membership values ​​for the task data samples, Υ is the scaling parameter, Σ1 and Σ2 are boundary factors used to control boundary tolerance. c1 and c2 are regularization parameters, κ>1 is the penalty parameter, and n1 and n2 are the sums of positive and negative class samples in each task, respectively. ξ 1t and ξ 2t e is a slack variable t ​​Let T be a column vector containing all 1s in any dimension. T refers to the number of tasks, which we modified in Problem 1. t refers to the t-th task.

[0018] MFRMM considers the impact of different outlier samples on the model, and therefore designs two slack variables. The weight of the first slack variable is set to 1, while the second slack variable considers samples with a higher degree of anomalousness, thus imposing a stronger penalty, so κ > 1.

[0019] In equations (1) and (2), for low-rank constraints, the strength of the low-rank constraint on the weight matrix is ​​limited by the regularization parameters c1 and c2; the weighted nuclear norm term ||W is added to the objective function. i ||,||W it ||(i=+,-) forces the weight matrix W to be reduced in rank to achieve cross-task feature sharing, significantly improving knowledge transfer efficiency.

[0020] Fuzzy membership matrix: S i ,S it (i = +, -) is used to dynamically reduce the weight of abnormal samples;

[0021] Dual boundary factors Σ1 and Σ2 serve as boundary factor control tolerances; independent boundary factors enhance adaptability to data offsets.

[0022] The symplectic geometric similarity transformation satisfies the structure-preserving property of the symplectic matrix, maintaining the time-frequency coupling relationship of the vibration signal. The low-rank constraint, by forcing the minimization of the nuclear norm of the weight matrix W, enables cross-task sharing of the feature subspace.

[0023] Step 4: Transform the multi-constraint problem into a dual problem using the Lagrange multiplier method;

[0024] By using the Lagrange multiplier method, the multi-constrained problem of formula (1) is transformed into an unconstrained problem;

[0025]

[0026] Where, α t ,β t ,χ t ,δ t Let ν1 and ν2 be Lagrange multipliers. Then, based on the Karush-Kuhn-Tucker (KKT) conditions, the following derivation is made:

[0027]

[0028] Where α=[α1,α2,...,α T ].

[0029] Based on formulas (4) and (5), we can derive:

[0030] W + =-[(S + A) T (S + A)+c1I] -1 B T α (11)

[0031]

[0032] The derivation is based on formulas (6) and (7) as follows:

[0033]

[0034] Substituting formulas (10) and (11) into formula (3), the dual problem of formula (1) is transformed as follows:

[0035]

[0036] Where X = B((S) + A) T (S + A)+c1I) -1 B T , H = blkdiag(H1,H2,...,H) T ).

[0037] Similarly, the dual problem of formula (2) can be derived as follows:

[0038]

[0039] Where, K = A((S_B) T (S_B)+c2I) -1 A T , Λ=blkdiag(Λ1,Λ2,...,Λ T );

[0040] Finally, by solving the two quadratic programming problems (14) and (15), the optimal solutions of formulas (1) and (2) can be determined.

[0041] Step 5: Output the classification result based on the decision function;

[0042] For unknown samples in task t, the classification label of the output sample is determined by formula (3).

[0043]

[0044] The decision formula (3) can significantly reduce the amount of computation; the dual problem transformations (14) and (15) reduce the complexity of the formula, thereby improving the training speed.

[0045] Compared with existing known technologies, the technical solution provided by this invention has the following significant advantages:

[0046] This invention proposes a multi-task collaborative classification method based on a multi-domain fuzzy robust matrix machine (MFRMM). By imposing low-rank constraints, this method can automatically mine common feature representations among different tasks, thereby establishing an effective knowledge transfer framework. Specifically,

[0047] 1) Multi-feature information fusion forces the model to determine a subspace structure shared across tasks in the feature space, so that the diagnostic knowledge learned on a certain task can be generalized to other related tasks, which significantly improves the diagnostic performance of the model.

[0048] 2) A domain adaptive boundary factor was designed. By adopting a differentiated penalty strategy, the sample weights are dynamically adjusted according to the abnormal data distribution characteristics of each task, thereby mitigating the excessive influence of samples with different degrees of abnormality on the model decision.

[0049] 3) The multi-domain fuzzy robust matrix mechanism constructs a pair of parallel hyperplanes to improve the classification efficiency of the model. Secondly, it constructs a multi-task learning framework to realize multi-task and multi-objective synchronous classification, which significantly improves the generalization performance of the model.

[0050] 4) Finally, the introduction of a fuzzy function improves the robustness of the model's classification. The model is applied to the field of mechanical fault diagnosis, and experimental results show that it has superior classification performance.

[0051] This invention achieves efficient collaborative classification of multiple tasks in mechanical fault diagnosis for the first time through a triple technological innovation of symplectic geometric transformation, multi-feature information fusion, and fuzzy double boundary, breaking through the existing technical bottlenecks in terms of accuracy, robustness, and efficiency. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating a multi-task collaborative classification method based on a multi-domain fuzzy robust matrix machine according to the present invention.

[0053] Figure 2 This is an experimental platform for the vibration characteristics of rolling mill rolls at Anhui University of Technology.

[0054] Figure 3 The average accuracy results for different c values;

[0055] Figure 4 Average accuracy of multi-task classification under different Y and κ values;

[0056] Figure 5The evaluation indicators for the five methods are as follows;

[0057] Figure 6 The average evaluation index value for multiple tasks under the five methods;

[0058] Figure 7 The classification results for five methods include anomalous samples. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] Example 1

[0061] This embodiment of the multi-task collaborative classification technique based on a multi-domain fuzzy robust matrix machine includes the following steps:

[0062] Step 1: Collect vibration signals of rolling bearings and gears under different conditions; the vibration signals of rolling bearings can be obtained by using vibrations at different positions of the inner ring, outer ring, and rolling elements; while gears can include different fault signals such as uniform wear, eccentricity, misalignment, local abnormalities, and tooth pitch error.

[0063] Step 2: The vibration signal is reconstructed into a symplectic geometric coefficient matrix sample using the symplectic geometric similarity transformation method, which serves as the input to the multi-domain fuzzy robust matrix machine;

[0064] Step 3: First, select a portion of the samples as the training set, with a random ratio of 0.4-0.5, to train the multi-domain fuzzy robust matrix machine; use the remaining samples as the test set to verify the model performance of the multi-domain fuzzy robust matrix machine.

[0065] Construct a multi-task optimization model for T distinct but related tasks, where the input sample for each task is {(x...} i ,y i ), i = 1, 2, ..., n}, where x i ∈R m×n ,y i ={+1,-1}; Then, the objective function of the multi-task optimization model is constructed; the objective function of the multi-domain fuzzy robust matrix machine is constructed as follows:

[0066]

[0067] Where, A=[(γ<a,c> +k) d ,e],A t =[(γ <at ,c>+k) d ,e t ],B=[(γ<b,c> +k) d ,e],B t =[(γ t ,c>+k) d ,e t ]. where 'a' represents the positive class samples for all tasks, a t Let b be the positive class samples of task t, and b be the negative class samples of all tasks. t Let S be the negative class sample of task t, c be the total sample of all tasks, and c = [a; b]. i ,S it (i=+,-) is a diagonal matrix of fuzzy membership values ​​for the task data samples, Υ is the scaling parameter, Σ1 and Σ2 are boundary factors used to control boundary tolerance. c1 and c2 are regularization parameters, κ>1 is the penalty parameter, and n1 and n2 are the sums of positive and negative class samples in each task, respectively. ξ 1t and ξ 2t e is a slack variable t It is a column vector in any dimension, where all elements are 1.

[0068] Step 4: Transform the multi-constraint problem into a dual problem using the Lagrange multiplier method;

[0069] By using the Lagrange multiplier method, the multi-constrained problem of formula (1) is transformed into an unconstrained problem;

[0070]

[0071] Where, α t ,β t ,χ t ,δ t Let ν1 and ν2 be Lagrange multipliers. Then, based on the Karush-Kuhn-Tucker (KKT) conditions, the following derivation is made:

[0072]

[0073] Where α=[α1,α2,...,α T ].

[0074] Based on formulas (4) and (5), we can derive:

[0075] W + =-[(S + A) T (S + A)+c1I] -1 B T α (11)​

[0076]

[0077] The derivation is based on formulas (6) and (7) as follows:

[0078]

[0079] Substituting formulas (10) and (11) into formula (3), the dual problem of formula (1) is transformed as follows:

[0080]

[0081] Where X = B((S) + A) T (S + A)+c1I) -1 B T , H = blkdiag(H1,H2,...,H) T ).

[0082] Similarly, the dual problem of formula (2) can be derived as follows:

[0083]

[0084] Where, K = A((S_B) T (S_B)+c2I) -1 A T , Λ=blkdiag(Λ1,Λ2,...,Λ T );

[0085] Finally, by solving the two quadratic programming problems (14) and (15), the optimal solutions of formulas (1) and (2) can be determined.

[0086] Step 5: Output the classification result based on the decision function;

[0087] For unknown samples of task t, their predicted labels are determined by formula (3).

[0088]

[0089] To verify the effectiveness of this invention in the field of mechanical fault diagnosis, this embodiment uses a multi-domain fuzzy robust matrix machine to perform pattern recognition on fault samples and provides a series of comparative experiments to illustrate the effectiveness of the method.

[0090] The experimental data used for verification were collected from the roll vibration characteristic experimental platform at Anhui University of Technology. The layout of the experimental platform is as follows: Figure 1As shown, vibration signals of different fault types were collected from the gearbox bearing and the roll bearing to simulate two classification tasks. The experimental setup uses a 3KW three-phase AC variable frequency motor, and vibration signals from different fault locations are collected using an accelerometer.

[0091] Signals of different types from seven bearings were collected under different loads and speeds for two tasks. Details are shown in Tables 1 and 2.

[0092] Table 1 Task 1: Gearbox Bearing Fault Dataset

[0093]

[0094]

[0095] Table 2 Task 2: Roll Bearing Fault Dataset

[0096]

[0097] Before using MFRMM for classification, the original vibration signal needs to be preprocessed. The vibration signal is subjected to a symplectic geometric similarity transformation to obtain a symplectic geometric coefficient matrix, which serves as the input to the model, thus enabling effective multi-task classification.

[0098] Figure 2 This chart shows the average accuracy for different c values; the x-axis represents the c value, decreasing from left to right. The y-axis represents the average accuracy. The initial value is 0.94, and the average accuracy reaches 1 at the top. When the c value is 10... -5 At that time, the peak average accuracy was approximately 0.985.

[0099] Figure 3 The average accuracy of multi-task classification is represented by different values ​​of Y and κ; Y is the scaling parameter, and k is the penalty parameter. The horizontal axis represents Y*0.1 and k, and the vertical axis represents the average accuracy. This indicates the impact of different values ​​of Y and k on the average accuracy of multi-task classification in this application.

[0100] Figure 4 The evaluation index results for the five methods are shown in the bar chart. Each group is distributed from left to right as follows: MFRMM, MTCEMM, MTTPKMC, MT-TBSVM, and MTNPSVM.

[0101] The horizontal axis represents Accuracy, Kappa coefficient, Recall, F1 score, and Precision. The vertical axis represents the five methods.

[0102] MFRMM is the multi-domain fuzzy robust matrix machine of this application; MTCEMM is the multi-task collaborative enhancement matrix machine; MTTPKMC is the multi-task double bouncing ball kernel matrix classifier; MT-TBSVM is the multi-task double-bounded support vector machine; and MTNPSVM is the multi-task non-parallel support vector machine. It can be shown that the evaluation metrics of this application are higher than the other four existing classification methods.

[0103] Figure 5 The average evaluation index value for multiple tasks under five methods; based on Figure 4 The five methods are represented in the pie chart, with each pie chart showing MTNPSVM, MTCEMM, MTTPKMC, MT-TBSVM, and MFRMM from the outside in. The pie chart indicates that the more inward the pie chart, the better the average multi-task performance index.

[0104] Figure 6 The five methods represent classification results with outlier samples. The five corners represent Accuracy, Kappa coefficient, Recall, Flscore, and Precision.

[0105] correspond Figure 4 The five methods are shown in Tables 1 and 2, respectively, for Task 1 and Task 2. Figure 6 From the outside in, the components of Task 1 are MFRMM, MTNPSVM, MTTPKMC, MT-TBSVM, and MTCEMM. Figure 6 Task 1 consists of MFRMM, MTTPKMC, MTCEMM, MTNPSVM, and MT-TBSVM from the outside in.

[0106] This invention extracts the symplectic geometric coefficient matrix of the vibration signal through symplectic geometric similarity transformation as input, and constructs a multi-task optimization model that integrates multiple feature information, fuzzy membership weighting, and dual boundary factors. This addresses the problems of weak multi-task correlation, noise sensitivity, and low computational efficiency in mechanical fault diagnosis. Experiments show that this method improves the accuracy of bearing fault multi-task classification by 5-8% and significantly enhances robustness to abnormal samples.

[0107] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A multi-task collaborative classification method based on a multi-domain fuzzy robust matrix machine, characterized in that: Includes the following steps: Step 1: Collect vibration signals from multiple targets under different conditions; Step 2: The vibration signal is reconstructed into a symplectic geometric coefficient matrix sample using the symplectic geometric similarity transformation method, which serves as the input to the multi-domain fuzzy robust matrix machine; Step 3: Construct a multi-task optimization model for T distinct but related tasks, where the input sample for each task is {(x... i ,y i ), i = 1, 2, ..., n}, where x i ∈R m×n ,y i ={+1,-1}; then construct the objective function of the multi-task optimization model; The objective function is: Where, A=[(γ<a,c> +k) d ,e],A t =[(γ t ,c>+k) d ,e t ],B=[(γ<b,c> +k) d ,e],B t =[(γ t ,c>+k) d ,e t ]; a represents the positive class samples for all tasks, a t Let b be the positive class samples of task t, and b be the negative class samples of all tasks. t Let W be the negative class sample of task t, and let c be the total sample of all tasks, i.e., c = [a; b]; i W it (i = +, -) is the weight matrix; T is the total number of samples. S is the transpose of any column vector; i ,S it (i=+,-) is a diagonal matrix of fuzzy membership values ​​for the task data samples, Υ is the scaling parameter, Σ1 and Σ2 are boundary factors used to control boundary tolerance; c1 and c2 are regularization parameters, κ>1 is the penalty parameter, and n1 and n2 are the sums of positive and negative samples in each task, respectively; ξ 1t and ξ 2t e is a slack variable t It is a column vector with all elements being 1 in any dimension;​​ Step 4: Transform the multi-constraint problem into a dual problem using the Lagrange multiplier method; Step 5: Output the classification result based on the decision function; Among them, W it Let b be any weight matrix t , where x is the bias and x is the new input sample.

2. The multi-task collaborative classification method based on a multi-domain fuzzy robust matrix machine according to claim 1, characterized in that, In step 3, a portion of the samples need to be selected as the training set, with a random ratio of 0.4-0.5, to train the multi-domain fuzzy robust matrix machine; the remaining samples are used as the test set to verify the model performance of the multi-domain fuzzy robust matrix machine.

3. The multi-task collaborative classification method based on a multi-domain fuzzy robust matrix machine according to claim 2, characterized in that: In step 4, the multi-constrained problem of formula (1) is transformed into an unconstrained problem using the Lagrange multiplier method: Where, α t ,β t ,χ t ,δ t ν1,ν2 are Lagrange multipliers; then, based on the Karush-Kuhn-Tucker conditions, it is derived as follows: Where, α=[α1,α2,...,α T ]; Based on formulas (5) and (6), the derivation is as follows: W + =-[(S + A) T (S + A)+c1I] -1 B T a (11) Based on formulas (7) and (8), the derivation is as follows: Substituting formulas (11) and (12) into formula (4), the dual problem of formula (1) is transformed as follows: where, X = B((S + A) T (S + A)+c1I) -1 B T , Η t = B t ((S +t A t ) T (S +t A t ) / T + c1I t / T) -1 B t T , Η = blkdiag(Η1, Η2,..., Η T ); Similarly, the dual problem of formula (2) is transformed as follows: where \(K = A((S - B) T (S - B)+c2I) -1 A T , \(\Lambda = A t ((S -t B t ) T (S -t B t )+c2I) -1 A t T , \(\Lambda = blkdiag(\Lambda_1,\Lambda_2,...,\Lambda T ) Finally, by solving formulas (14) and (15), the optimal solutions for formulas (1) and (2) can be determined.

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