Bridge crane transmission system bearing fault diagnosis method based on domain adaptation technology
The bridge crane bearing fault diagnosis method using domain-adaptive technology solves the problems of class imbalance and data drift, reduces data acquisition costs, improves diagnostic accuracy and model generalization ability, and enhances the operational safety and reliability of bridge cranes.
Patent Information
- Application Number
- CN202510035505.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-09
- Publication Date
- 2026-08-25
- Estimated Expiration
- 2045-01-09
AI Technical Summary
Existing bridge crane bearing fault diagnosis technologies suffer from class imbalance, data drift, reliance on extensive prior knowledge and costly data acquisition, low diagnostic accuracy, and insufficient generalization ability. Traditional transfer learning methods have failed to effectively extract discriminative features.
We employ a domain-adaptive approach, constructing a domain-shared feature extraction network. We clean the data using laboratory and real-world data, train the feature extraction model, domain discriminator, and diagnostic model, and optimize neuron parameters by combining maximum mean squared error loss and an improved Softmax loss function to extract cross-domain invariant features and improve diagnostic accuracy.
It significantly reduces data acquisition costs, improves the operational safety and reliability of bridge cranes, enhances fault diagnosis accuracy and model generalization ability, and adapts to bridge crane bearing fault diagnosis under different working conditions.
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Figure CN120197050B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of crane fault diagnosis technology, and in particular to a method for diagnosing bearing faults in the transmission system of a bridge crane based on domain adaptive technology. Background Technology
[0002] Bridge cranes are widely used in factories, construction sites, and ports to handle heavy materials or finished products, and to install or lift large structural components. The transmission system, a core component of the bridge crane, is responsible for transmitting power from the motor to various working mechanisms to achieve material handling. A failure in the transmission system can range from affecting production efficiency and quality to causing further equipment damage or even personal injury. Current bridge crane maintenance still relies on periodic inspections. However, components of the transmission system, such as bearings, even bearings of the same model and made from the same materials from the same manufacturer, can have significantly different remaining service lives under different working conditions, operating habits, and prolonged operation. Repairing the transmission system of a bridge crane before its remaining service life is time-consuming and resource-intensive. Furthermore, because many faults are difficult to detect in their early stages, misdiagnosis and missed diagnosis are common, further impacting production safety. Secondly, if the transmission system has reached the end of its remaining service life and is not inspected, more serious consequences will occur. Therefore, it is necessary to conduct accurate intelligent fault diagnosis on the transmission system of bridge cranes, especially the bearings, in order to improve the reliability and safety of the equipment, while reducing labor costs and achieving the effect of cost reduction and efficiency improvement.
[0003] Traditional bridge crane bearing fault diagnosis primarily relies on signal processing methods. These methods require engineers to possess extremely high theoretical knowledge and mathematical analysis skills. However, their processing efficiency and diagnostic accuracy cannot meet customers' requirements for operational reliability. With the development of deep learning, which can provide accurate diagnostic results based solely on data without requiring excessive prior knowledge, and whose advantage in processing large amounts of data has gradually replaced traditional bridge crane bearing fault diagnosis methods, deep learning-based bridge crane bearing fault diagnosis technology has not been widely adopted. There are two important reasons for this: 1. Class imbalance problem, namely, during the service life of bridge cranes, the vast majority of data collected is positive. 1. The lack of fault sample data makes it impossible for existing models to learn the boundaries of fault classification, resulting in overfitting and affecting the generalization performance of intelligent fault diagnosis. 2. The data drift problem: During the service of bridge cranes, the power and speed output of their transmission systems vary greatly due to different cargo, resulting in significant differences in their operating signals. If the neural network is trained based on the operating signals collected under a certain speed or load condition, the effect is often poor when performing fault diagnosis under other speed or load conditions. Collecting operating signals separately for each task, classifying the signals through manual annotation, and then retraining the neural network will undoubtedly increase the labor cost significantly.
[0004] Therefore, new algorithms are still needed to address the impact of class imbalance and data drift in bridge crane bearing health status analysis. However, existing technologies have the following drawbacks: 1. Existing technologies cannot effectively handle large and complex datasets, resulting in low model diagnostic efficiency and success rates. 2. They require a large amount of prior knowledge, which is difficult for non-industry personnel to understand, limiting the development of data science and failing to leverage the advantages of the big data era. 3. Existing technologies do not effectively address the problems of insufficient samples, class imbalance, and data drift, affecting the model's generalization ability and accuracy. 4. Existing technologies rely on large amounts of labeled, high-quality datasets, but data collection is prohibitively expensive, and the collected data often lacks significant labeling, resulting in low diagnostic accuracy. 5. Traditional transfer learning methods rely solely on feature difference measures to extract domain-invariant features, neglecting the extraction of discriminative features. Existing feature difference measures can extract relatively few effective features, often failing to cover all features of bridge crane bearing operating signals. Summary of the Invention
[0005] This invention discloses a method for diagnosing bearing faults in the transmission system of a bridge crane based on domain adaptive technology. The specific method is as follows:
[0006] Obtain bearing data from the operation of the bridge crane in the laboratory as source domain data;
[0007] Obtain bearing data of the bridge crane under actual working conditions as the target domain data;
[0008] Perform data cleaning processing on source domain data and target domain data;
[0009] A domain-shared feature extraction network was trained using cleaned source domain data and target domain data;
[0010] A trained domain-shared feature extraction network is used to diagnose bearing fault categories in the transmission system of a bridge crane.
[0011] Furthermore, the domain-shared feature extraction network includes a feature extraction model, a domain discriminator, and a diagnostic model;
[0012] The feature extraction model extracts the cleaned source domain data and target domain data;
[0013] The domain discriminator distinguishes the differences between the extracted source domain data and the target domain data.
[0014] The diagnostic model is trained using the extracted source domain data and target domain data. The trained diagnostic model diagnoses the bearing fault type of the bridge crane transmission system based on the target domain data.
[0015] Furthermore, the training methods for the feature extraction model, the domain discriminator, and the diagnostic model are as follows:
[0016] Construct the overall loss function for the feature extraction model, the domain discriminator, and the diagnostic model;
[0017] Based on the total loss function, the neuron parameters of the feature extraction model, the domain discriminator, and the diagnostic model are adjusted through backpropagation;
[0018] The goal is to achieve the following: consistency between source domain data features and target data features extracted by the feature extraction model; difficulty for the discriminator to distinguish between source domain data features and target data features; and ease of identification between various fault diagnosis areas.
[0019] Furthermore, the consistency between the source domain data features and the target data features extracted by the feature extraction model is quantified by the source domain-target domain feature extraction consistency evaluation function, the specific formula of which is as follows:
[0020]
[0021] Where n and m are the number of samples in the source domain and the target domain, respectively, and K(·,·) represents the kernel function obtained by weighted summation of Gaussian kernels with different bandwidths obtained by dynamically calculating the kernel bandwidth method;
[0022] These represent the sum of kernel function values for all sample pairs within the source domain, the target domain, and between the source and target domains, respectively.
[0023] Furthermore, the difficulty for the discriminator to distinguish between source domain data features and target data features is quantified by the domain discriminator evaluation function, the specific formula of which is as follows:
[0024]
[0025] Where g i The source domain label is set to 0, and the target domain label is set to 0. i ) represents the probability estimate of the i-th sample output by the domain classifier belonging to the source domain, and m represents the number of samples.
[0026] Furthermore, the ease of identification between various fault diagnosis areas is quantified using a sample health classification evaluation function, the specific formula of which is as follows:
[0027] L csoft =L arc +L soft
[0028] in
[0029]
[0030]
[0031] In the formula, L csoft L is the health classification evaluation function for the samples. arc The value represents the magnitude of the loss, N is the number of samples, and yi is the true label of the i-th sample. Pseudo-labels are used to replace the true labels, and m is a hyperparameter used to increase the distance between classification boundaries, making different samples more widely separated. To increase the cosine value after adding distance, and to increase the decision boundary for the correct category, where n is the category of the health state of the bridge crane bearing, cosθ j The cosine similarity between the feature vector and the weight vector for each class j;
[0032] L softmax The loss function is the standard cross-entropy loss, where N is the number of samples, C is the health status type of the bridge crane bearing, and y is the standard cross-entropy loss. ij p is an indicator variable indicating that the i-th sample belongs to the j-th class. ij Predict the probability that the i-th sample belongs to the j-th class for the model.
[0033] Furthermore, the specific formula for the total loss function is as follows:
[0034] L Total =L csoft +nL d +LMSD
[0035] Right now
[0036]
[0037] Among them, L Total Let L be the total loss function. csoft L is the health classification evaluation function for the samples. d L is the evaluation function for the domain discriminator. MSD θ is the consistency evaluation function for feature extraction from the source and target domains; n is the hyperparameter for determining the adaptive efficiency of the domain; θ is the hyperparameter for the adaptive efficiency of the domain. f θ c θ d These represent the neuron parameters of the feature extraction model, the diagnostic model, and the domain discriminator, respectively.
[0038] Furthermore, through backpropagation, the neuron parameters of the feature extraction model, the domain discriminator, and the diagnostic model are adjusted, as shown in the following formula:
[0039]
[0040]
[0041]
[0042] Where ε is the learning rate.
[0043] Furthermore, the failure categories of bearings in the transmission system of bridge cranes include: inner ring failure, outer ring failure, and ball failure.
[0044] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:
[0045] 1. The proposed intelligent fault diagnosis method for bridge cranes based on domain adaptive technology can solve the problems of insufficient fault data, lack of labeled data, and large amount of noise affecting the accuracy of fault diagnosis in real-world environments. The method can significantly reduce data acquisition costs and greatly improve the operational safety and reliability of bridge cranes.
[0046] 2. The SCAD algorithm based on maximum mean square difference loss and improved Softmax loss is more robust than conventional adaptive methods based on KL divergence, maximum mean difference, and deep correlation comparison, and is more in line with the actual operating logic of bridge cranes, resulting in high diagnostic accuracy.
[0047] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description
[0048] The accompanying drawings of this invention are described below.
[0049] Figure 1 This is a schematic diagram of the overall process.
[0050] Figure 2 This is a diagram illustrating the scale of bearing failure.
[0051] Figure 3 This is a schematic diagram of bearing vibration signals.
[0052] Figure 4 A comparison chart of the classification boundaries of the original Softmax function and the C-softmax function. Detailed Implementation
[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0054] A method for diagnosing bearing faults in the transmission system of a bridge crane based on domain-adaptive technology, such as... Figure 1 As shown, the specific steps are as follows:
[0055] S1. Obtain bearing data of the bridge crane operating in the laboratory as source domain data.
[0056] S2. Obtain the bearing data of the bridge crane under actual working conditions as the target domain data.
[0057] In steps S1 and S2, the source domain dataset used to train the subsequent model comes from sensor data collection records of the laboratory bearing operation. The bearing fault appearance is as follows: Figure 2 As shown. These are labeled standard data used to characterize bearing health. They include inner ring faults IF1~IF4, outer ring faults OF1~OF4, ball faults RF1~RF4, and normal conditions. The specific data format is as follows:
[0058] IF1: Inner ring fault size 1, 0.43 (mm)
[0059] IF2: Inner ring fault size 2, 1.01 (mm)
[0060] IF3: Inner ring fault size 3, 1.56 (mm)
[0061] IF4: Inner ring fault size 4, 2.03 (mm)
[0062] OF1: Outer ring fault size 1, 0.42 (mm)
[0063] OF2: Outer ring fault size 2, 0.86 (mm)
[0064] OF3: Outer ring fault size 3, 1.55 (mm)
[0065] OF4: Outer ring fault size 4, 1.97 (mm)
[0066] RF1: Ball bearing failure size 1, 0.49 (mm)
[0067] RF2: Ball bearing failure size 2, 1.16 (mm)
[0068] RF3: Ball bearing failure size 3, 1.73 (mm)
[0069] RF4: Ball bearing failure size 4, 2.12 (mm)
[0070] S3. Perform data cleaning processing on the source domain data and the target domain data.
[0071] In step S3, the target domain data is automatically collected by the bridge crane moving equipment monitoring system. Since the moving equipment monitoring system may be affected by wind disturbance, abnormal operation by on-site operators, abnormal shaking of the working environment, etc. when collecting operating data, the sensing equipment may collect noise signals of different degrees, or be affected by electromagnetic signal interference or data loss during data transmission and storage, which affects the performance of the intelligent fault diagnosis model. Therefore, before inputting the data into the model, the bearing vibration signal is first denoised and missing values are filled by data cleaning.
[0072] The specific method involves feeding the data into a data cleaning network. The network will adopt different data cleaning strategies based on the amount of data. If the amount of data is sufficient for training, the entire column containing obviously abnormal or missing data will be deleted. If the amount of data is small, adopting the deletion strategy will affect the generalization performance of the network. Therefore, the nearest value mean interpolation method is used to fill in the data.
[0073] S4. Train the domain-shared feature extraction network using the cleaned source domain data and target domain data.
[0074] In step S4, the domain-shared feature extraction network includes a feature extraction model, a domain discriminator, and a diagnostic model. The feature extraction model extracts cleaned source domain data and target domain data. The domain discriminator distinguishes the differences between the extracted source domain data and target domain data. The diagnostic model is trained using the extracted source domain data and target domain data, and the trained diagnostic model diagnoses the bearing fault category of the bridge crane transmission system based on the target domain data.
[0075] The feature extraction model is trained to extract common features from the source and target domains. The parameters of the network structure are shown in Table 1 below:
[0076]
[0077] Features extracted by the convolutional neural network are mapped onto a high-dimensional Hilbert space using kernel methods. Network optimization aims to obtain domain-invariant features. Simultaneously, it is hoped that these extracted domain-invariant features will achieve high accuracy on the health status classifier.
[0078] The training steps for the feature extraction model, the domain discriminator, and the diagnostic model are as follows:
[0079] S41. Construct the total loss function for the feature extraction model, the domain discriminator, and the diagnostic model.
[0080] In step S41, the total loss function includes the following three parts:
[0081] S411, Consistency Evaluation Function for Source Domain and Target Domain Feature Extraction MSD It is used to measure the difference between features extracted from source domain data and features extracted from target domain data.
[0082] Let the features extracted from the source domain be: S(f)={G f (x;θ f ) |x~S(x)} represents the data distribution of the source domain, T(f)={G f (x;θ f G represents the distribution of data in the target domain, where G |x~T(x)}. f (x;θ f ) represents the features after passing through the domain-shared feature extraction network, θ f Let represent the parameters of the domain-shared feature extractor, x represent a sample, S represent the source domain, T represent the target domain, x ~ S(x) represents the probability distribution of the sample following the source domain, and x ~ T(x) represents the probability distribution of the sample following the target domain. Since the source domain data is collected from the laboratory and the target domain data is obtained from the actual working conditions of a bridge crane, there is a domain drift phenomenon, i.e., S(x) ≠ T(x).
[0083] To facilitate the calculation of the similarity between the feature sets of two samples, a Gaussian kernel matrix is constructed using dynamic bandwidth calculation. Then, submatrices within the source domain, the target domain, and the cross-domain domain are extracted from the joint kernel matrix. The difference formed by the mean square error of these submatrices is calculated, and this difference is returned as the loss value to guide the training of the model.
[0084] The formula for the maximum mean squared error loss function is as follows:
[0085]
[0086] Where n and m are the number of samples in the source and target domains, respectively, and K(·,·) represents the kernel function obtained by weighted summation of Gaussian kernels with different bandwidths obtained through the dynamic calculation of kernel bandwidth. These represent the sum of kernel function values for all sample pairs within the source domain, the target domain, and between the source and target domains, respectively.
[0087] Where S and T represent the source domain feature distribution and the target domain feature distribution, respectively. The significance of this loss function is that when the network performs backpropagation, the network parameters for extracting domain-shared features can be adjusted according to the loss function so that the maximum mean square difference of the extracted features in the regenerated Hilbert space is minimized, that is, cross-domain invariant features can be extracted.
[0088] Figure 3 This is a schematic diagram of the bearing vibration signal. As can be seen, its mean is near 0. Therefore, using the traditional maximum mean difference to extract the neighborhood-invariant features will result in a significant loss of information. However, using the maximum mean squared error loss function can effectively improve this problem and enhance the generalization performance of the model.
[0089] S412, Sample Health Classification Evaluation Function L csoft It is used to measure the accuracy of features extracted from source domain data using the same feature extractor in a fault classification task.
[0090] This improved Softmax step is named C-Softmax. The reason for proposing the C-Softmax function is that the objective of conventional Softmax optimization is merely to correctly classify known samples, without requiring features to have small intra-class distances and large inter-class distances. Thus, during knowledge transfer, unseen samples in the target domain may exist near the classification boundary, leading to misclassification when diagnosing faults in bridge crane bearings. Taking a binary classification problem as an example... Figure 4 As shown.
[0091] Sample health classification evaluation function L csoft , by L arc and L softmax We obtain the weighted sum.
[0092]
[0093] Among them, L arc The value represents the magnitude of the loss, N is the number of samples, yi is the true label of the i-th sample (in this invention, pseudo-labels are used instead of true labels), and m is a hyperparameter used to increase the distance between classification boundaries, making different samples more distant. The cosine value after adding distance is used to increase the decision boundary for the correct class, where n is the class of health status of the bridge crane bearing, and cosθ j The cosine similarity between the feature vector and the weight vector for each class j.
[0094]
[0095] Among them, L softmax The loss function is the standard cross-entropy loss, where N is the number of samples, C is the health status type of the bridge crane bearing, and y is the standard cross-entropy loss. ij p is an indicator variable indicating that the i-th sample belongs to the j-th class. ij The model predicts the probability that the i-th sample belongs to the j-th class. In this invention, L is used alone. arc The loss can be significant due to a large initial classification error, affecting network convergence. Therefore, it is necessary to combine L... softmax Loss, and then, based on the model having a certain degree of accuracy, using L arc The loss is adjusted based on the distribution of the features, therefore the improved classification loss formula is as follows:
[0096] L csoft =L arc +L soft
[0097] Among them, L csoft To improve classification loss.
[0098] S413, Domain Discriminator Evaluation Function L d This makes it difficult for the domain discriminator to distinguish between the two domains.
[0099]
[0100] Where g i The source domain is labeled; in this invention, the source domain label is set to 1, and the target domain label is set to 0. d(x) i ) represents the probability estimate of the i-th sample output by the domain classifier belonging to the source domain, and m represents the number of samples. During the training process, we use gradient inversion to maximize this loss, so that the domain classifier cannot determine the true labels of the source and target domains, thereby achieving the purpose of extracting domain-invariant features.
[0101] S42. Based on the total loss function, adjust the neuron parameters of the feature extraction model, the domain discriminator, and the diagnostic model through backpropagation.
[0102] In step S42, the overall optimization objective of the network is to enable the network to extract common features from both laboratory bearing data and actual bridge crane operating data. These common features should exhibit small intra-class distances and large inter-class distances, thus possessing sufficient discriminative power. Therefore, the overall loss of the network can be represented by the following formula:
[0103] L Total =L csoft +nL d +L MSD
[0104] Where n is a hyperparameter for determining the adaptive efficiency of the domain, and after clarifying the above loss function, i.e., the optimization objective, let θ f θ c θ d Let represent the parameters of the domain-shared feature extractor, the health status classifier, and the domain classifier, respectively. Then, the total loss function can be re-given by the following formula:
[0105]
[0106] This embodiment trains the proposed network using stochastic gradient descent and updates the network parameters through backpropagation. The stochastic gradient descent method is used to update θ. f θ c θ d The process can be performed using a formula:
[0107]
[0108]
[0109]
[0110] Where ε is the learning rate.
[0111] S43. Until the consistency between the source domain data features and target data features extracted by the feature extraction model, the difficulty of the discriminator in distinguishing between the source domain data features and target data features, and the ease of identification between various fault diagnosis areas all reach the preset goals.
[0112] S5. Use the trained domain-shared feature extraction network to diagnose the bearing fault categories of the bridge crane transmission system.
[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
Claims
1. A method for diagnosing bearing faults in a bridge crane transmission system based on domain adaptive technology, characterized in that, The specific method is as follows: Obtain bearing data from the operation of the bridge crane in the laboratory as source domain data; Obtain bearing data of the bridge crane under actual working conditions as the target domain data; Perform data cleaning processing on source domain data and target domain data; A domain-shared feature extraction network was trained using cleaned source domain data and target domain data; The trained domain-shared feature extraction network is used to diagnose bearing fault categories in the transmission system of a bridge crane. Domain-shared feature extraction networks include feature extraction models, domain discriminators, and diagnostic models; The feature extraction model extracts the cleaned source domain data and target domain data; The domain discriminator distinguishes the differences between the extracted source domain data and the target domain data. The diagnostic model is trained using the extracted source domain data and target domain data. The trained diagnostic model diagnoses the bearing fault type of the bridge crane transmission system based on the target domain data. The training methods for the feature extraction model, the domain discriminator, and the diagnostic model are as follows: Construct the overall loss function for the feature extraction model, the domain discriminator, and the diagnostic model; Based on the total loss function, the neuron parameters of the feature extraction model, the domain discriminator, and the diagnostic model are adjusted through backpropagation; Until the consistency between the source domain data features and target data features extracted by the feature extraction model, the difficulty of the discriminator in distinguishing between source domain data features and target data features, and the ease of identification between various fault diagnosis areas all reach the preset goals; The consistency between the source domain features and the target domain features extracted by the feature extraction model is quantified by the consistency evaluation function of source domain and target domain feature extraction, and the specific formula is as follows: in, and These are the number of samples in the source domain and the target domain, respectively. This represents the kernel function obtained by weighted summation of Gaussian kernels with different bandwidths obtained through a dynamic calculation method of kernel bandwidth; These represent the sum of kernel function values for all sample pairs within the source domain, the target domain, and between the source and target domains, respectively.
2. The method for diagnosing bearing faults in a bridge crane transmission system based on domain adaptive technology as described in claim 1, characterized in that, The difficulty for a discriminator to distinguish between source domain data features and target data features is quantified by a domain discriminator evaluation function, the specific formula of which is as follows: in The source domain label is set to 0, and the target domain label is set to 0. The output of the domain classifier The probability estimate of a sample belonging to the source domain. Indicates the number of samples.
3. The method for diagnosing bearing faults in a bridge crane transmission system based on domain adaptive technology as described in claim 1, characterized in that, The ease of identification between various fault diagnosis areas is quantified using a sample health classification evaluation function, the specific formula of which is as follows: in In the formula, For the health classification evaluation function of the samples, This represents the magnitude of the loss value, where N is the number of samples. For the first The true label of each sample; Using pseudo-labels to replace real labels, This is a hyperparameter used to increase the distance between classification boundaries, making different samples more distant. To increase the cosine value after adding distance, the decision boundary for the correct class is increased. The category of health condition for bridge crane bearings. The cosine similarity between the feature vector and the weight vector for each class j; The loss is the standard cross-entropy loss, and C represents the health state type of the bridge crane bearing. It is the first The sample belongs to the first Class indicator variables, For the model to predict the first The sample belongs to the first The probability of a class.
4. The method for diagnosing bearing faults in a bridge crane transmission system based on domain adaptive technology as described in claim 3, characterized in that, The specific formula for the total loss function is as follows: Right now in, For the total loss function, For the health classification evaluation function of the samples, For the evaluation function of the domain discriminator, Extract a consistency evaluation function for the features of the source domain and the target domain; To determine the hyperparameters for the degree of domain adaptability, , , These represent the neuron parameters of the feature extraction model, the diagnostic model, and the domain discriminator, respectively.
5. The method for diagnosing bearing faults in a bridge crane transmission system based on domain adaptive technology as described in claim 4, characterized in that, The neuron parameters of the feature extraction model, the domain discriminator, and the diagnostic model are adjusted through backpropagation, using the following formulas: in, This is the learning rate.
6. The method for diagnosing bearing faults in a bridge crane transmission system based on domain adaptive technology as described in claim 1, characterized in that, The types of bearing failures in the transmission system of bridge cranes include: inner ring failure, outer ring failure, and ball failure.