A Fault Diagnosis Method for Rolling Bearings with Different Loads

Abstract

The present invention belongs to the technical field of engineering machinery, and discloses a method for diagnosing rolling bearing faults under different loads, comprising the following steps: Step 1, establishing a PSO-SSTCA migration algorithm; Step 2, using the PSO-SSTCA migration algorithm to shorten the distance between various features of the rolling bearing, and realizing analog classification between different load data; Step 3, using the KNN algorithm, realizing classification of other data sets through existing rolling bearing data sets and their label information; Step 4, diagnosing the current fault state of the bearing through steps 1 to 3. The present invention adaptively adjusts the distribution of calculation features through transfer learning, shortens the data distribution distance of the bearing under different load conditions, and overcomes the problem that fault diagnosis in the prior art is limited to a single stable environment and traditional diagnostic methods are difficult to apply.

Description

Technical Field

[0001] This invention belongs to the field of engineering machinery technology, and specifically relates to a method for diagnosing faults in rolling bearings under different loads. Background Technology

[0002] Bearings in engineering equipment typically operate under varying loads. For example, loaders perform numerous forward, reverse, gear shifting, and shoveling operations within a single work cycle. Their transmission systems, including bearings, gears, and drive shafts, frequently bear varying degrees of external load. In wind power machinery, such as wind turbines, the blade speed needs to be adjusted according to weather conditions to ensure maximum power generation efficiency without damaging the original structure. The loads on these machines often vary significantly, making traditional constant-load-based fault diagnosis methods inaccurate. The large load variation and the enormous data measurement workload for each load condition make it difficult to meet the data volume requirements of current deep learning algorithms. Therefore, the most effective and direct approach is to minimize the data distribution differences between loads, applying diagnostic experience from one load to other load conditions for bearing fault diagnosis. To reduce the variability in bearing data features caused by different loads and environments, transfer learning is used to adaptively adjust the distribution of computational features, shortening the data distribution distance of bearings under different load conditions. Summary of the Invention

[0003] To address the problems existing in the prior art, the purpose of this invention is to propose a fault diagnosis method for rolling bearings under different loads, overcoming the limitations of existing fault diagnosis methods, which are restricted to a single stable environment and are difficult to apply to traditional diagnostic methods.

[0004] To achieve the above objectives, the present invention employs the following technical solutions.

[0005] 1. Transfer Learning Theory

[0006] 1.1. Distance Metrics for Transfer Learning

[0007] Transfer learning refers to learning and research that transfers from an old domain to a new domain based on the correlations between different data, tasks, or features. Its core objective is to find the connections between different domains, thereby enabling the transfer of related tasks.

[0008] Data collected under different load conditions and working environments will inevitably exhibit distributional differences. Therefore, different distance calculation standards are needed to quantify the differences between these different distribution domains. Meanwhile, the transformation from the source domain to the target domain is diverse, and to achieve optimal mapping, relevant metrics need to be introduced for evaluation. Their main uses include: 1) qualitatively determining the correlation between two variables and quantitatively calculating their degree of association; 2) using the calculated values ​​as a basis to continuously improve the correlation between two variables through necessary learning methods. Common metrics include distance metrics and similarity metrics.

[0009] Common metrics for measuring reciprocity in transfer learning include:

[0010] Maximum mean discrepancy (MMD). MMD is the distance between two distributions in a reproducing Hilbert space. Its squared distance expression is:

[0011]

[0012] Where φ(·) represents the kernel mapping, which allows for efficient calculation of the inner product of kernel functions after mapping the original variables. The MMD distance calculation method can use either a single kernel mapping or multiple kernel functions to calculate the spatial distribution distance through linear combination.

[0013] The Hilbert-Schmidt Independence Criterion (HSIC) is used to characterize the independence between two sets of data.

[0014] HSIC(X,Y)=trace(HXHY) (4.8)

[0015] Where X and Y are kernel functions of two sets of data.

[0016] 1.2 TCA Transfer Learning Theory and Algorithm Model

[0017] Domain and task are fundamental concepts in transfer learning. The domain of data feature distribution mainly includes the source domain and the target domain. The former is a collection of knowledge with a large number of learning labels, which is the object to be transferred; the latter is the object that ultimately needs to be assigned knowledge or labels. The task is the main goal of transfer learning, which includes the labels that need to be defined.

[0018] To achieve learning transfer from the source domain to the target domain, Transfer Component Analysis (TCA) introduces the concept of Domain Adaptation: for a source domain that already has labels... Target domain lacking label information Assuming the feature spaces are the same, i.e., X s =X t Similar category spaces (label categories), Y s =Y t Meanwhile, their conditional probabilities are approximately equal, Q s (y s |x s )=Q t (y t |x t However, the marginal distributions of the two domains are not the same, P s (x s )≠P(x t The ultimate goal of TCA transfer learning in achieving domain adaptation is to search for a mapping transformation to project the original data features onto the existing data feature set, thereby reducing the distance between the marginal distributions of the source and target domains.

[0019] DISTANCE(D s D t )≈||P(X s )-P(X t (4.9)

[0020] The goal of this method is to reduce the difference in individual distribution between the source and target domains while minimizing changes to the original data structure, thereby enabling the classification algorithm for the source domain to be implemented as efficiently as possible on the new domain. Therefore, it can be broadly divided into two process objectives:

[0021] (1) Minimize marginal distribution

[0022] Minimize the marginal distribution, even if P(X) s ) and P(X t The closest distance is found between the two domains. Using the MMD distance as a metric to measure the maximum mean difference between the two domains, and employing a suitable kernel mapping function φ, the projected data distribution is brought closer together, i.e., P(φ(X)). s ))≈P(φ(X t The specific calculation method is as follows:

[0023]

[0024] Based on the fact that the squared distance expansion includes a quadratic product, we introduce the kernel function matrix K and the MMD matrix L to solve for the mapping φ:

[0025]

[0026] Finally, a matrix W with a lower dimension than K is used to improve the model's solution efficiency. Therefore, the optimization objective of TCA is transformed into:

[0027]

[0028] (2) Maintain the data characteristics of their respective distribution domains

[0029] To prevent the original data distribution structure from being destroyed after mapping, thus making it difficult to effectively classify the transformed features, additional constraints need to be introduced. The scatter matrix of data can reflect the distribution among individual data points to a certain extent. For a matrix A, its scatter is AHAT, where H is the center matrix, defined as follows:

[0030]

[0031] To maintain the divergence (i.e., variance) of the original data, the following condition must be met:

[0032] W T KHKW = I m (4.14)

[0033] Transfer learning relies on a high degree of similarity between two domains. If there is no similarity, or only a significant dissimilarity, the knowledge learned from the original data may have a negative effect on the classification of new data—a phenomenon known as negative transfer. Different transfer learning methods have their own advantages; choosing the appropriate method is crucial to maximizing transfer efficiency between different feature datasets and avoiding negative transfer.

[0034] 2. Model Optimization Algorithm Combining Pseudo-Label Learning and HSIC Multi-Kernel Function

[0035] 2.1 Introducing HSIC-associated raw data tag information

[0036] The TCA transfer learning method, which adapts to data distribution, can reduce the differences in data distribution to some extent. However, it focuses on the data distribution itself and does not fully consider the label classification information contained in the data. In the engineering field, the original dataset often has relevant state labels, while the new dataset lacks relevant label information. If the existing label information can be utilized, the efficiency of transfer transformation can be improved to some extent, and the distribution of feature data points between the source and target domains can be narrowed.

[0037] As defined in equation (4.8), HSIC can measure the dependency between two datasets. Introducing HSIC to enhance the dependency between data and class labels in the feature space—that is, the semi-supervised transfer learning algorithm (SSTCA)—can utilize the original data label information to improve the transfer effect of data features. Assuming that the feature data in the source domain all contain class labels, and the target domain lacks relevant information, then:

[0038]

[0039] Where n = n1 + n2, (I is the identity matrix, II is the matrix with all elements equal to 1), H is used for centering, K and K yy Let be the kernel matrix of X and Y. A larger value of HSIC(X, Y) indicates a stronger dependency between X and Y. The ultimate goal of introducing HSIC is to maximize:

[0040]

[0041] In the formula, K l The kernel matrix is ​​based on the original data labels, and its inner matrix elements satisfy: The second term is the variance after data mapping. The parameter γ adjusts the balance between the data labels and the variance of the mapped data.

[0042] 2.2 Using a combination of multiple kernel functions to replace a single kernel function

[0043] Through the above process, label information can be introduced on the basis of the original TCA algorithm. However, the original TCA algorithm uses a parameterized kernel mapping method when minimizing the edge distribution. This method first gives the kernel function and then directly obtains the kernel matrix based on the kernel function. Since different kernel functions correspond to different mappings, the choice of kernel function will directly affect φ(X). s ) and φ(X T The similarity of distributions. Common kernel functions include:

[0044] Gaussian kernel function

[0045]

[0046] Linear kernel

[0047] k(x, y) = x T y+c (4.18)

[0048] Polynomial Kernel

[0049] k(x, y) = (ax T y+c) d (4.19)

[0050] A single kernel function provides limited mapping features, making it difficult to meet the transformation requirements between various spatial domains. To improve the transfer capability under different load environments, combining different kernel functions with certain weights can achieve better mapping results. Common combinations of multiple kernel functions include multiplication and addition. For example, consider the combination of a polynomial kernel function and a Gaussian kernel function:

[0051] Multiplication kernel:

[0052] K i，j =K Poly (x i x j )·K Guassian (x i x j (4.20)

[0053] Addition kernel:

[0054] K i，j =aK Poly (x i x j )+(1-a)K Gaussian (x i x j (4.21)

[0055] Wherein, according to the definition of the Gaussian kernel function, when x i =x j At that time, K Guassian (x i x j =0. In the additive kernel, weight coefficients are introduced between different kernel functions. For different transfer tasks, the value of these coefficients needs to be adjusted according to certain metrics to achieve better feature transfer results.

[0056] 2.3 Optimizing the weight coefficients of the multi-kernel function using particle swarm optimization algorithm and pseudo-label learning

[0057] Pseudo-labels refer to the preliminary predicted labels for the unlabeled portions of the original data using a classification algorithm. When data samples are scarce, appropriately including pseudo-labeled data as part of the training data can improve the accuracy of model training to some extent. After obtaining a portion of the target domain pseudo-labels through a preliminary machine learning classification algorithm, the conditional probability distribution probability MMD distance between the source and target domains can be calculated:

[0058]

[0059] Conditional probability distribution focuses on the intra-class similarity of data features. By minimizing the distance between the conditional probability distributions of the source and target domains, intra-class features can be better utilized, and the migration effect of features under different loads of rolling bearings can be further optimized.

[0060] Combining multiple kernel functions requires determining different combinations based on the specific target task. The selection of this combination often necessitates multiple calculations and comparisons to arrive at the optimal solution. Since Particle Swarm Optimization (PSO) excels at handling tasks requiring optimal values ​​for multiple parameters, this section uses the pseudo-label target domain data from each calculation as a basis to calculate the conditional distribution probability (MMD) distance between the source and target domains. This distance is then used as the PSO fitness function. Minimizing this distance is the objective of selecting the weight coefficient 'a' for the multiple kernel functions. Finally, through collaborative comparative optimization among particle swarms, the optimal coefficient is searched to find the best solution for constructing the multiple kernel functions in this transfer task.

[0061] 2.4 Local Information Preservation

[0062] Similar to TCA, semi-supervised transfer learning algorithms also require adding distance constraints to the target kernel matrix to preserve local geometry. That is, ensuring that the relative distances between two points in space remain unchanged after mapping. Define the proximity matrix M, with each element... Where, d ij Let be the distance between two points in space. Define a diagonal matrix D, where . Given L′=DM, the constraints that need to be added to the original mapping transformation are:

[0063]

[0064] Based on the above analysis, the ultimate goal of the PSO-optimized SSTCA algorithm is to find a suitable matrix W to solve the following objective function:

[0065]

[0066] Following the TCA approach, the problem can be transformed into:

[0067]

[0068] The above equation is subjected to eigenvalue decomposition. The eigenvectors corresponding to the top m eigenvalues ​​are selected based on their magnitude to form a matrix W. Then, the particle swarm optimization algorithm is used to further reduce the intra-class spacing of the data features, thus obtaining the optimal mapping data after the transfer transformation. The overall algorithm steps are shown below.

[0069]

[0070] Compared with the prior art, the beneficial effects of the present invention are: by using transfer learning to adaptively adjust the distribution of computational features, the data distribution distance of bearings under different load conditions is shortened, overcoming the problem that fault diagnosis in the prior art is limited to a single stable environment and traditional diagnostic methods are difficult to apply. Attached Figure Description

[0071] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0072] Figure 1 shows the four-dimensional features of datasets D and C after PCA mapping;

[0073] Figure 1(a) shows data feature 1 after PCA mapping;

[0074] Figure 1(b) shows data feature 2 after PCA mapping;

[0075] Figure 1(c) shows data feature 3 after PCA mapping;

[0076] Figure 1(d) shows data feature 4 after PCA mapping;

[0077] Figure 2 shows the four-dimensional features of datasets D and C after transfer transformation;

[0078] Figure 2(a) shows data feature A after the transfer mapping;

[0079] Figure 2(b) shows the data feature B after the transfer mapping;

[0080] Figure 2(c) shows the data feature C after the transfer mapping;

[0081] Figure 2(d) shows the data feature D after the transfer mapping;

[0082] Figure 3 This is the fault diagnosis interface;

[0083] Figure 4 The diagnostic accuracy of each algorithm under single-load conditions;

[0084] Figure 5 The diagnostic accuracy of each algorithm under multiple-to-single load conditions. Detailed Implementation

[0085] The embodiments of the present invention will be described in detail below with reference to examples. However, those skilled in the art will understand that the following examples are only for illustrating the present invention and should not be regarded as limiting the scope of the present invention.

[0086] 1. Transfer Learning Theory

[0087] 1.1. Distance Metrics for Transfer Learning

[0088] Transfer learning refers to learning and research that transfers from an old domain to a new domain based on the correlations between different data, tasks, or features. Its core objective is to find the connections between different domains, thereby enabling the transfer of related tasks.

[0089] Data collected under different load conditions and working environments will inevitably exhibit distributional differences. Therefore, different distance calculation standards are needed to quantify the differences between these different distribution domains. Meanwhile, the transformation from the source domain to the target domain is diverse, and to achieve optimal mapping, relevant metrics need to be introduced for evaluation. Their main uses include: 1) qualitatively determining the correlation between two variables and quantitatively calculating their degree of association; 2) using the calculated values ​​as a basis to continuously improve the correlation between two variables through necessary learning methods. Common metrics include distance metrics and similarity metrics.

[0090] Common metrics for measuring reciprocity in transfer learning include:

[0091] Maximum mean discrepancy (MMD). MMD is the distance between two distributions in a reproducing Hilbert space. Its squared distance expression is:

[0092]

[0093] Where φ(·) represents the kernel mapping, which allows for efficient calculation of the inner product of kernel functions after mapping the original variables. The MMD distance calculation method can use either a single kernel mapping or multiple kernel functions to calculate the spatial distribution distance through linear combination.

[0094] The Hilbert-Schmidt Independence Criterion (HSIC) is used to characterize the independence between two sets of data.

[0095] HSIC(X,Y)=trace(HXHY) (4.8)

[0096] Where X and Y are kernel functions of two sets of data.

[0097] 1.2 TCA Transfer Learning Theory and Algorithm Model

[0098] Domain and task are fundamental concepts in transfer learning. The domain of data feature distribution mainly includes the source domain and the target domain. The former is a collection of knowledge with a large number of learning labels, which is the object to be transferred; the latter is the object that ultimately needs to be assigned knowledge or labels. The task is the main goal of transfer learning, which includes the labels that need to be defined.

[0099] To achieve learning transfer from the source domain to the target domain, Transfer Component Analysis (TCA) introduces the concept of Domain Adaptation: for a source domain that already has labels... Target domain lacking label information Assuming the feature spaces are the same, i.e., X s =X t Similar category spaces (label categories), Y s =Y t Meanwhile, their conditional probabilities are approximately equal, Q s (y s |x s )=Q t (y t |x t However, the marginal distributions of the two domains are not the same, P s (x s )≠P(x t The ultimate goal of TCA transfer learning in achieving domain adaptation is to search for a mapping transformation to project the original data features onto the existing data feature set, thereby reducing the distance between the marginal distributions of the source and target domains.

[0100] DISTANCE(D s D t )≈||P(X s )-P(X t (4.9)

[0101] The goal of this method is to reduce the difference in individual distribution between the source and target domains while minimizing changes to the original data structure, thereby enabling the classification algorithm for the source domain to be implemented as efficiently as possible on the new domain. Therefore, it can be broadly divided into two process objectives:

[0102] (3) Minimize marginal distribution

[0103] Minimize the marginal distribution, that is, minimize the distance between P(Xs) and P(Xt). Use the MMD distance as a metric to measure the maximum mean difference between two domains. Utilize a suitable kernel mapping function φ to narrow the projected data distribution, i.e., P(φ(Xs)) ≈ P(φ(Xt)). The specific calculation method is as follows:

[0104]

[0105] Based on the fact that the squared distance expansion includes a quadratic product, we introduce the kernel function matrix K and the MMD matrix L to solve for the mapping φ:

[0106]

[0107] Finally, a matrix W with a lower dimension than K is used to improve the model's solution efficiency. Therefore, the optimization objective of TCA is transformed into:

[0108]

[0109] (4) Maintain the data characteristics of their respective distribution domains

[0110] To prevent the original data distribution structure from being destroyed after mapping, thus making it difficult to effectively classify the transformed features, additional constraints need to be introduced. The scatter matrix of data can reflect the distribution among individual data points to a certain extent. For a matrix A, its scatter is AHAT, where H is the center matrix, defined as follows:

[0111]

[0112] To maintain the divergence (i.e., variance) of the original data, the following condition must be met:

[0113] W T KHKW = I m (4.14)

[0114] Transfer learning relies on a high degree of similarity between two domains. If there is no similarity, or only a significant dissimilarity, the knowledge learned from the original data may have a negative effect on the classification of new data—a phenomenon known as negative transfer. Different transfer learning methods have their own advantages; choosing the appropriate method is crucial to maximizing transfer efficiency between different feature datasets and avoiding negative transfer.

[0115] 2. Model Optimization Algorithm Combining Pseudo-Label Learning and HSIC Multi-Kernel Function

[0116] 2.1 Introducing HSIC-associated raw data tag information

[0117] The TCA transfer learning method, which adapts to data distribution, can reduce the differences in data distribution to some extent. However, it focuses on the data distribution itself and does not fully consider the label classification information contained in the data. In the engineering field, the original dataset often has relevant state labels, while the new dataset lacks relevant label information. If the existing label information can be utilized, the efficiency of transfer transformation can be improved to some extent, and the distribution of feature data points between the source and target domains can be narrowed.

[0118] As defined in equation (4.8), HSIC can measure the dependency between two datasets. Introducing HSIC to enhance the dependency between data and class labels in the feature space—that is, the semi-supervised transfer learning algorithm (SSTCA)—can utilize the original data label information to improve the transfer effect of data features. Assuming that the feature data in the source domain all contain class labels, and the target domain lacks relevant information, then:

[0119]

[0120] Where n = n1 + n2, (I is the identity matrix, II is the matrix with all elements equal to 1), H is used for centering, K and K yy Let be the kernel matrix of X and Y. A larger value of HSIC(X, Y) indicates a stronger dependency between X and Y. The ultimate goal of introducing HSIC is to maximize:

[0121]

[0122] In the formula, K l The kernel matrix is ​​based on the original data labels, and its inner matrix elements satisfy: The second term is the variance after data mapping. The parameter γ adjusts the balance between the data labels and the variance of the mapped data.

[0123] 2.2 Using a combination of multiple kernel functions to replace a single kernel function

[0124] Through the above process, label information can be introduced on the basis of the original TCA algorithm. However, the original TCA algorithm uses a parameterized kernel mapping method when minimizing the edge distribution. This method first gives the kernel function and then directly obtains the kernel matrix based on the kernel function. Since different kernel functions correspond to different mappings, the choice of kernel function will directly affect φ(X). S ) and φ(X T The similarity of distributions. Common kernel functions include:

[0125] Gaussian kernel function

[0126]

[0127] Linear kernel

[0128] k(x, y) = x T y+c (4.18)

[0129] Polynomial Kernel

[0130] k(x, y) = (ax T y+c) d (4.19)

[0131] A single kernel function provides limited mapping features, making it difficult to meet the transformation requirements between various spatial domains. To improve the transfer capability under different load environments, combining different kernel functions with certain weights can achieve better mapping results. Common combinations of multiple kernel functions include multiplication and addition. For example, consider the combination of a polynomial kernel function and a Gaussian kernel function:

[0132] Multiplication kernel:

[0133] K i，j =K Poly (x i x j )·K Guassian (x i x j (4.20)

[0134] Addition kernel:

[0135] K i，j =aK Poly (x i x j )+(1-a)K Gaussian (x i x j (4.21)

[0136] Wherein, according to the definition of the Gaussian kernel function, when x i =x j At that time, K Guassian (x i x j =0. In the additive kernel, weight coefficients are introduced between different kernel functions. For different transfer tasks, the value of these coefficients needs to be adjusted according to certain metrics to achieve better feature transfer results.

[0137] 2.3 Optimizing the weight coefficients of the multi-kernel function using particle swarm optimization algorithm and pseudo-label learning

[0138] Pseudo-labels refer to the preliminary predicted labels for the unlabeled portions of the original data using a classification algorithm. When data samples are scarce, appropriately including pseudo-labeled data as part of the training data can improve the accuracy of model training to some extent. After obtaining a portion of the target domain pseudo-labels through a preliminary machine learning classification algorithm, the conditional probability distribution probability MMD distance between the source and target domains can be calculated:

[0139]

[0140] Conditional probability distribution focuses on the intra-class similarity of data features. By minimizing the distance between the conditional probability distributions of the source and target domains, intra-class features can be better utilized, and the migration effect of features under different loads of rolling bearings can be further optimized.

[0141] Combining multiple kernel functions requires determining different combinations based on the specific target task. The selection of this combination often necessitates multiple calculations and comparisons to arrive at the optimal solution. Since Particle Swarm Optimization (PSO) excels at handling tasks requiring optimal values ​​for multiple parameters, this section uses the pseudo-label target domain data from each calculation as a basis to calculate the conditional distribution probability (MMD) distance between the source and target domains. This distance is then used as the PSO fitness function. Minimizing this distance is the objective of selecting the weight coefficient 'a' for the multiple kernel functions. Finally, through collaborative comparative optimization among particle swarms, the optimal coefficient is searched to find the best solution for constructing the multiple kernel functions in this transfer task.

[0142] 2.4 Local Information Preservation

[0143] Similar to TCA, semi-supervised transfer learning algorithms also require adding distance constraints to the target kernel matrix to preserve local geometry. That is, ensuring that the relative distances between two points in space remain unchanged after mapping. Define a proximity matrix M, where each element... Where, d ij Let be the distance between two points in space. Define a diagonal matrix D, where . Given L′=DM, the constraints that need to be added to the original mapping transformation are:

[0144]

[0145] Based on the above analysis, the ultimate goal of the PSO-optimized SSTCA algorithm is to find a suitable matrix W to solve the following objective function:

[0146]

[0147] Following the TCA approach, the problem can be transformed into:

[0148]

[0149] The above equation is subjected to eigenvalue decomposition. The eigenvectors corresponding to the top m eigenvalues ​​are selected based on their magnitude to form a matrix W. Then, the particle swarm optimization algorithm is used to further reduce the intra-class spacing of the data features, thus obtaining the optimal mapping data after the transfer transformation. The overall algorithm steps are shown below.

[0150]

[0151] To simulate the fault classification and diagnosis of rolling bearings under different load conditions, this embodiment constructs data sets for each load condition based on laboratory bearing data (CWRU), as shown in Table 1.

[0152] Table 1. Construction of the Rolling Bearing Vibration Signal Dataset under Variable Load Conditions

[0153]

[0154] The data set comprises four categories: A, B, C, and D, corresponding to vibration signal information of rolling bearings under loads of 0HP, 1HP, 2HP, and 3HP, respectively. Each data set includes fault-free conditions and fault data for the inner ring, rolling elements, and outer ring under different fault levels. The sample size "10" indicates that 10 signal segments were extracted from the reconstructed signal data. Each segment contains 2400 sampling points. After sparse reconstruction and feature extraction calculations on these 10 signal segments, each data set ultimately yields a 90 (or 100)*18 dimensional rolling bearing feature database. The feature forms extracted from each signal segment are shown in Tables (3.5-3.7). Due to differences in data distribution among the data sets, the PSO-SSTCA algorithm is used to shorten the distance between features, achieving analogical classification between data under different loads.

[0155] To demonstrate the feature mapping capability of transfer learning algorithms, Principal Component Analysis (PCA), a commonly used linear feature reduction method, is used for comparison. Transfer diagnosis is performed pairwise on four datasets A, B, C, and D with different loads, resulting in 12 single-load judgment tasks. Taking the transfer transformation from dataset D to C, where features are relatively obvious, as an example, the original feature data are compared after undergoing PCA and transfer learning transformations. To facilitate the visualization of the calculated features, the low-dimensional space after mapping is set to four dimensions, and the representations of each feature are shown in Figures 1 and 2.

[0156] Referring to Figures 1 and 2, numbers 1 through 7 represent: normal operating condition, inner ring, rolling element, and outer ring failure condition at 0.1778 mm, and inner ring, rolling element, and outer ring failure condition at 0.5334 mm, respectively. Observing the feature relationship diagrams above, it can be found that after principal component analysis (PCA) transformation, only feature 1, with the largest contribution rate, achieves a clear distinction between various operating conditions and the alignment of the distributions of different datasets D and C (different loads). The remaining features show significant feature misalignment, making it difficult to effectively distinguish different bearing operating conditions. The reason for this is that there are often nonlinear relationships between the multi-source data features of bearing vibration signals under different loads, while PCA is a linear dimensionality reduction method, thus leading to feature mappings in other dimensions that are unrelated to the original operating conditions. However, after the transfer mapping transformation, the two different datasets exhibit approximately the same feature change trend.

[0157] The above results indicate that the PSO-SSTCA method can effectively reduce the differences in characteristic distribution caused by different loads and improve the efficiency of bearing classification and diagnosis under complex load conditions.

[0158] Based on two datasets with similar trend of feature changes, common machine learning algorithms can be used to classify other datasets using existing datasets and their label information. K-Nearest Neighbor (KNN), as a type of supervised learning classification algorithm, is simple, efficient, and has low training costs, making it suitable for classifying data samples where fault conditions such as bearings overlap.

[0159] Based on the above feature transfer process and algorithm, these are integrated into a rolling bearing fault diagnosis module. The module interface is as follows: Figure 3 As shown, this module aims to diagnose the current fault state of the bearing by preprocessing the data signal using a transfer learning algorithm and then training and classifying it with different load data. Finally, combining the fault diagnosis type and manual adjustments, the results of each training diagnosis are added to the existing expert database, thereby continuously improving the training model and increasing the overall accuracy of bearing fault diagnosis.

[0160] refer to Figure 3 In this diagnostic interface, click "Load Signal File" to select the signal data file to be diagnosed. In the parameter adjustment, set the particle swarm optimization parameters, sparsity parameters, and finally, the KNN classification parameters. During the diagnostic process, the system automatically performs sparse reconstruction and feature extraction on the input data file, and performs a transfer mapping transformation between the extracted features and the existing database file to reduce data distribution differences. Finally, the transformed common data is input into the KNN algorithm to complete fault classification in the target domain. The "Partial Feature Trend Map" simply displays the bearing operating condition feature point map currently stored in the database and the input signal feature lines; different operating conditions have their corresponding feature ranges. Figure 3The high degree of overlap between the central feature line and the green feature point on the right indicates that the final diagnosis is "rolling element failure". After completing the diagnosis, you can click "Add to Expert Database for Learning" to incorporate the diagnosis results into the database, thereby continuously expanding the number of database samples and improving the classification accuracy.

[0161] In practical engineering, diagnosis between single loads is rather idealistic, failing to consider the mutual influence between different loads. Furthermore, the data collected in most cases includes datasets covering multiple load conditions. Combining multiple data features can improve the model's transfer applicability to some extent. Therefore, multi-single load datasets were added for comparative calculations. The processing capabilities of feature data were compared by contrasting unprocessed raw vibration signal input, sparsely reconstructed signal data (sparse signal) directly input, reconstructed signal combined with the original TCA algorithm feature transfer (sparse + TCA), and reconstructed signal combined with an optimized transfer learning algorithm (sparse + PSO-SSTCA). The KNN algorithm was used to classify the processed data features, and the fault accuracy was as follows: Figure 4 , Figure 5 As shown.

[0162] Through the Figure 4 , Figure 5 The data comparison reveals that the accuracy of unprocessed raw data in variable load fault diagnosis is generally low. This is due to background noise interference and the distribution differences of data under different loads. After sparse reconstruction, the traditional TCA method can, to some extent, resolve the gaps between data caused by environmental factors. However, because it does not fully utilize the fault labels in the raw data, there is a certain degree of randomness in feature mapping, and its final accuracy is also affected by the choice of the initial kernel function. The semi-supervised transfer learning algorithm with particle swarm optimization (PSO-SSTCA) solves the above problems. Finally, by calculating the average accuracy of each method, we can obtain the following results: Under the single-single variable load environment, the average accuracy calculated by directly inputting the original data is 51.75%, 75.17% for sparse signal data, 81.25% for sparse signal plus the original TCA algorithm, and 85.92% for sparse signal plus PSO-SSTCA. Under the multi-single load environment, the accuracy is 61.67%, 68.58%, 81.25%, and 88%, respectively, indicating that the accuracy of the PSO-SSTCA method is improved compared to the previous methods.

[0163] Although the present invention has been described in detail in this specification with general description and specific embodiments, some modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention are within the scope of protection claimed by the present invention.

Claims

1. A method for diagnosing rolling bearing faults under different loads, characterized in that: The following steps are involved: Step 1, establish the PSO-SSTCA migration algorithm; Sub-step 1.1, introduce HSIC into the TCA transfer learning algorithm to enhance the dependency between data and category labels in the feature space, and establish the SSTCA semi-supervised transfer learning algorithm; Sub-step 1.2, using a combination of multiple kernel functions instead of a single kernel function; Specifically, the mapping features of a single kernel function are limited and it is difficult to meet the migration and transformation requirements between multiple different spatial domains. In order to improve the migration capability under various load environments, different kernel functions can be combined with certain weights to achieve better mapping effects. Specifically, an additive kernel, such as formula (1), is used instead of a single kernel function; K i，j =aK Poly (x) i ,x j )+(1-a)K Guassian (x) i ,x j ) (1) According to the Gaussian kernel function definition, when x i =x j When K Guassian (x i , x j )=0; Sub-step 1.3, selecting the optimal multi-core function weight coefficient through PSO particle swarm optimization algorithm and pseudo-label learning, and constructing the optimal multi-core function; Specifically, Sub-step 1.3.1, obtain a part of the target domain pseudo labels through a preliminary machine learning classification algorithm, such as the KNN algorithm; Sub-step 1.3.2, calculate the conditional distribution probability MMD distance between the source domain and the target domain; Sub-step 1.3.3, taking the conditional distribution probability MMD distance between the source domain and the target domain as the fitness function of the PSO particle swarm optimization algorithm, taking minimizing the conditional distribution probability MMD distance as the goal of the PSO particle swarm optimization algorithm, searching for the optimal multi-core function weight coefficient through collaborative comparison optimization between particle swarms, and taking the optimal multi-core function weight coefficient as the optimal solution for the multi-core function construction method; Sub-step 1.4, combining sub-steps 1.1 to 1.3, is based on the SSTCA semi-supervised transfer learning algorithm optimized by the PSO particle swarm optimization algorithm, namely the PSO-SSTCA migration algorithm. Its ultimate goal is to find a suitable matrix W to solve the following objective function: Minutes W tr(W T KLKW)+μtr(W T In)+λ(In T KL′KW) Then, following the idea of ​​the TCA transfer learning algorithm, the problem is transformed into: Perform eigenvalue decomposition on the above formula, take the eigenvectors corresponding to the first m eigenvalues ​​according to their size to form a matrix W, and then use the PSO particle swarm optimization algorithm to further reduce the intra-class spacing of data features to obtain the optimal mapping data after migration transformation; Step 2, use the PSO-SSTCA migration algorithm to shorten the distance between the various features of the rolling bearing and realize analogy classification between different load data; Step 3, using the KNN algorithm, classify other data sets through the existing rolling bearing data set and its label information; Step 4: Diagnose the current fault status of the bearing through steps 1 to 3.

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