Rotating machinery fault diagnosis method based on passive multi-target gradient calibration

Abstract

The application discloses a rotating machinery fault diagnosis method based on passive multi-target gradient calibration, sets a rotating machinery fault diagnosis model comprising a feature extractor and a classifier, and adopts a labeled source data sample set to train the rotating machinery fault diagnosis model to obtain a source model; when it is necessary to migrate the source model to a multi-target domain, a no-labeled data sample set under different target domains is collected, then the weight parameters of the classifier are frozen, the weight parameters of the feature extractor are adaptively learned by using the no-labeled data sample set, the parameter updating is carried out based on multi-target gradient correction in the adaptive learning, and finally the rotating machinery fault diagnosis model trained by using the adaptive learning is used to carry out fault diagnosis on the rotating machinery in the target domain. By designing a multi-target gradient constraint strategy, the gradient direction between different domains is forced to be consistent, so that the domain-invariant features are extracted, and the migration diagnosis capability of the rotating machinery fault diagnosis model is improved.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery fault diagnosis technology, and more specifically, relates to a rotating machinery fault diagnosis method based on passive multi-target gradient calibration. Background Technology

[0002] With the development of industrial intelligence and condition monitoring technologies, data-driven fault diagnosis methods have been widely applied. However, in real-world engineering scenarios, due to factors such as changes in equipment operating conditions, environmental disturbances, and sensor differences, there is often a significant distribution shift between training and test data, severely impacting the model's generalization performance. Simultaneously, industrial data often involves enterprise privacy or security restrictions, making it difficult to directly obtain or share source domain data during model deployment. Against this backdrop, Source-free Domain Adaptation (SFDA) methods have gradually become an important technical approach to address the issues of distribution shift and data privacy protection. By utilizing only source model parameters and target domain data to achieve cross-domain knowledge transfer, SFDA shows promising application prospects.

[0003] While existing passive domain adaptive methods have made some progress in fault diagnosis, most research remains limited to single-objective domain scenarios, assuming that the target domain data follows a single distribution. This assumption is often difficult to apply in real-world industrial environments. Because equipment operates under different loads, speeds, or conditions, data collected from the same type of equipment may exhibit multiple heterogeneous distribution characteristics, creating a multi-objective domain problem. In this context, traditional single-objective domain methods struggle to effectively model the differences between these distributions, easily leading to degraded transfer performance or even negative transfer, thus limiting their application in complex industrial scenarios.

[0004] Furthermore, most existing methods optimize from the perspective of feature alignment or loss function design, typically by constructing multiple loss functions to constrain the model learning process. However, they generally overlook the gradient conflict that may arise between different loss functions during optimization. In multi-objective domain scenarios, the optimization objectives corresponding to different domains often have inconsistent or even contradictory gradient directions. This can lead to instability in the model parameter update process, making it difficult to converge to the optimal solution that takes into account the performance of each domain. Moreover, this gradient conflict may exacerbate overfitting of the model to a specific domain, weakening its cross-domain generalization ability. Therefore, how to simultaneously handle the differences in the distribution of multiple objective domains under passive conditions and effectively alleviate the gradient conflict problem between multiple loss functions has become a key technical problem that urgently needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a rotating machinery fault diagnosis method based on passive multi-objective gradient calibration. By designing a multi-objective gradient constraint strategy, the gradient directions between different domains are forced to remain consistent, thereby ensuring the extraction of domain-invariant features and improving the transfer diagnostic capability of the rotating machinery fault diagnosis model.

[0006] To achieve the above-mentioned objectives, this invention proposes two methods for fault diagnosis of rotating machinery based on passive multi-objective gradient calibration. The first method includes the following steps:

[0007] S1: Set up a fault diagnosis model for rotating machinery, including a feature extractor. and classifier For rotating machinery, obtain labeled source data sample sets. Each source data sample includes rotating machinery operating signals. and corresponding fault category labels , , Indicates the number of source data samples; uses the source data sample set. The source model is obtained by training the rotating machinery fault diagnosis model;

[0008] S2: When it is necessary to migrate the source model to a multi-objective domain, collect several working signals of the rotating machinery in each objective domain to obtain the target domain data sample set. , Indicates the first The first target domain One working signal data sample, , Indicates the first Number of data samples in each target domain , Indicates the number of target fields;

[0009] S3: Classifier in Fault Diagnosis Model for Frozen Rotating Machinery The weight parameters are adopted. Data sample set of target domains For feature extractors The weight parameters are adaptively learned to obtain the adaptively learned rotating machinery fault diagnosis model; in the adaptive learning, feature extractor is performed based on multi-objective gradient correction. Weight parameter update:

[0010] ,

[0011] in, , These represent the feature extractors before and after the update, respectively. The weight parameters, This indicates the preset learning rate. This represents the preset trade-off parameters. , They represent the first The target domain and the first The gradient corresponding to each target domain , They represent the first The target domain and the first The loss function corresponding to each target domain and They represent the first The target domain and the first The Hessian matrix corresponding to each target domain ;

[0012] S4: Use the adaptive learning-trained model to diagnose faults in the working signals of rotating machinery in the target domain.

[0013] The second method includes the following steps:

[0014] S1: Set up a fault diagnosis model for rotating machinery, including a feature extractor. and classifier For rotating machinery, obtain labeled source data sample sets. Each source data sample includes rotating machinery operating signals. and corresponding fault category labels , , Indicates the number of source data samples; uses the source data sample set. The source model is obtained by training the rotating machinery fault diagnosis model;

[0015] S2: When it is necessary to migrate the source model to a multi-objective domain, collect several working signals of the rotating machinery in each objective domain to obtain the target domain data sample set. , Indicates the first The first target domain One working signal data sample, , Indicates the first Number of data samples in each target domain , Indicates the number of target fields;

[0016] S3: Classifier in Fault Diagnosis Model for Frozen Rotating Machinery The weight parameters are adopted. Data sample set of target domains For feature extractors The weight parameters are adaptively learned to obtain the adaptively learned rotating machinery fault diagnosis model; in the adaptive learning, an in-domain gradient alignment update strategy is adopted to realize a feature extractor based on multi-objective gradient correction. The steps for updating weight parameters include:

[0017] S3.1: Let the number of iterations be... ;

[0018] S3.2: The feature extractor obtained from the previous training round Weight parameters As a feature extractor Initial weight parameters , that is to say , That is, the feature extractor in the source model. Weight parameters;

[0019] S3.3: Set the target field number ;

[0020] S3.4: From the first Data sample set of target domains The data sample set of the current training batch is sampled in the middle. ;

[0021] S3.5: Data sample set Input the current rotating machinery fault diagnosis model and calculate the loss function, then calculate the weight parameters. gradient ;

[0022] S3.6: The weight parameters are updated using the following formula. :

[0023] ,

[0024] in, This represents the preset learning rate for the target domain;

[0025] S3.7: Determine if If yes, proceed to step S3.8; otherwise, proceed to step S3.9.

[0026] S3.8: Order Return to step S3.4;

[0027] S3.9: The feature extractor for this training round is updated using the following formula. Weight parameters :

[0028] ,

[0029] in, This indicates the preset learning rate for the training rounds;

[0030] S3.10: Determine whether the adaptive learning termination condition has been met. If yes, adaptive learning ends; otherwise, proceed to step S3.11.

[0031] S3.11: Order Return to step S3.2;

[0032] S4: Use the adaptive learning-trained model to diagnose faults in the working signals of rotating machinery in the target domain.

[0033] This invention relates to a rotating machinery fault diagnosis method based on passive multi-objective gradient calibration. It establishes a rotating machinery fault diagnosis model including a feature extractor and a classifier, and trains it using labeled source data samples to obtain a source model. When it is necessary to transfer the source model to a multi-objective domain, unlabeled data samples from different target domains are collected. Then, the weight parameters of the classifier are frozen, and the weight parameters of the feature extractor are adaptively learned using the unlabeled data samples. During the adaptive learning process, parameters are updated based on multi-objective gradient calibration. Finally, the rotating machinery fault diagnosis model trained through adaptive learning is used to diagnose faults in rotating machinery within the target domain.

[0034] The present invention has the following beneficial effects:

[0035] 1) This invention proposes a passive multi-objective gradient calibration framework and designs a multi-objective gradient constraint strategy to force the gradient directions between different domains to remain consistent, thereby ensuring the extraction of domain-invariant features and improving the transfer diagnostic capability of rotating machinery fault diagnosis models.

[0036] 2) This invention also proposes an inter-domain gradient alignment strategy for passive multi-objective gradient calibration. It achieves multi-objective gradient calibration efficiently through first-order optimization, avoiding the huge computational overhead caused by second-order optimization, and further improving the efficiency of adaptive learning.

[0037] 3) During source model training, the present invention can also introduce a label smoothing strategy to improve the generalization ability of the model in the source domain pre-training stage, thereby improving the performance of fault diagnosis in the target domain. Attached Figure Description

[0038] Figure 1 This is a flowchart of the first specific implementation of the rotating machinery fault diagnosis method based on passive multi-target gradient calibration of the present invention;

[0039] Figure 2 This is a schematic diagram of the probability prediction distribution for a binary classification task;

[0040] Figure 3 This is a schematic diagram illustrating different alignment mechanisms under gradient conflict;

[0041] Figure 4 This is a flowchart of the second specific implementation of the rotating machinery fault diagnosis method based on passive multi-target gradient calibration of the present invention;

[0042] Figure 5 This is a flowchart of the gradient alignment update within the domain in this invention;

[0043] Figure 6 This is a schematic diagram of the intra-domain gradient alignment update inner and outer loop mechanism in this embodiment. Detailed Implementation

[0044] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0045] Example

[0046] Figure 1 This is a flowchart illustrating the first specific implementation of the rotating machinery fault diagnosis method based on passive multi-objective gradient calibration of the present invention. Figure 1 As shown, the specific steps of the rotating machinery fault diagnosis method based on passive multi-target gradient calibration of the present invention include:

[0047] S101: Pre-trained source model:

[0048] Set up a fault diagnosis model for rotating machinery, including a feature extractor. and classifier For rotating machinery, a labeled source data sample set is obtained. Each source data sample includes rotating machinery operating signals. and corresponding fault category labels , , Indicates the number of source data samples. The source data sample set is used. The source model is obtained by training the rotating machinery fault diagnosis model.

[0049] To prevent overfitting of the model to the source data and to encourage the model to learn more generalized feature representations, thereby providing a better initial decision boundary for the subsequent model adaptation phase on the target data, this embodiment introduces a regularized label smoothing strategy during the pre-training of the source model. Traditional source model training typically uses the standard cross-entropy loss, expressed as:

[0050] (1)

[0051] in, Represents the source data sample set The Middle Data sample source data sample Category The predicted probability, , Indicates the number of fault categories. .

[0052] The optimization objective of Equation (1) is to maximize the predicted probability value at the corresponding label index position, forcing the predicted probability output by the model to approach the one-hot encoded label infinitely. However, this leads to severe overfitting in the source model during feature learning. Consequently, the model often learns non-generalized feature representations private to the source domain, hindering the extraction of domain-invariant features. Figure 2 This is a schematic diagram illustrating the probability prediction distribution for a binary classification task. For example... Figure 2 As shown, given a "difficult-to-learn sample" (prone to misclassification) belonging to category 1 of the target domain. Its predicted probability distribution under the normal decision boundary of the source model is: ,like Figure 2 As shown in (a); to classify it correctly, its minimum correction amount only needs to be... However, in cases of overfitting, its predicted probability distribution will be overly confident. ,like Figure 2 As shown in (b), its minimum correction amount requires Based on the above analysis, it can be seen that a strict decision boundary under overfitting of the source model increases the degree of misfitting of the target domain samples during the model's adaptation phase, thereby causing a serious decline in the model's self-correction ability. ).

[0053] Therefore, to prevent overfitting of the source model, this embodiment introduces a label smoothing strategy during the pre-training stage of the source model. Specifically, instead of using one-hot labels, a smooth label is constructed. :

[0054] (2)

[0055] in, It is the first of the real and unique hot tags One element, The first smooth label One element, Represents the smoothing coefficient. It is the noise probability assigned to all categories.

[0056] Based on this, the optimization loss of the source model pre-training in formula (1) Can be rewritten as loss :

[0057] (3)

[0058] Through the loss function The model no longer blindly pursues 100% confidence, but instead learns to retain a moderate degree of predictive uncertainty. This not only makes the feature representations learned by the source model more generalizable, but also provides a more reliable initialization foundation for subsequent gradient alignment and pseudo-label generation in the target domain.

[0059] S102: Collect multi-target domain data samples:

[0060] When it is necessary to migrate the source model to a multi-objective domain, several operating signals of the rotating machinery in each objective domain are collected to obtain the target domain data sample set. , Indicates the first The first target domain One working signal data sample, , Indicates the first Number of data samples in each target domain , Indicates the number of target domains.

[0061] S103: Adaptive learning based on multi-objective gradient calibration:

[0062] In the adaptive learning phase, the weight parameters of the rotating machinery fault diagnosis model directly inherit from the source model trained in step S101, where the classifier... The weight parameters are kept frozen to preserve the discriminative decision boundary of the source domain to the greatest extent; in contrast, the feature extractor The weight parameters are updated to align the distribution of different target data by adjusting the feature mapping relationship. Therefore, the classifier for the frozen rotating machinery fault diagnosis model is... The weight parameters are adopted. Data sample set of target domains For feature extractors The weight parameters are adaptively learned to obtain the adaptively learned rotating machinery fault diagnosis model.

[0063] During the adaptive learning phase of the model in this invention, due to the strict inaccessibility of the source data, the feature extractor... The parameter updates rely entirely on unlabeled multi-objective data. To drive the model to effectively adapt and learn in the target domain, a set of optimization objectives based on self-supervised learning needs to be constructed first. To extract discriminative features under unsupervised conditions and avoid the risk of model collapse, this embodiment introduces the following three complementary loss functions: First, to reduce the uncertainty of the model's prediction of target domain samples, an entropy minimization strategy is adopted, i.e., entropy minimization loss is introduced. According to the clustering assumption, the decision boundary should pass through the low-density region of the data distribution. Therefore, by minimizing the information entropy of the prediction distribution, the model can be forced to make high-confidence predictions, thereby sharpening the decision boundary. Minimize the entropy loss of each target domain The calculation formula is as follows:

[0064] (4)

[0065] in, This indicates that the current rotating machinery fault diagnosis model is applicable to the first... The first target domain Data samples Category The predicted probability, This indicates the th element in the current training batch. A data sample set for each target domain This indicates the number of data samples in the data sample set.

[0066] Secondly, relying solely on entropy minimization can easily lead the model to predict all samples as belonging to the same category, resulting in mode collapse. To ensure global balance in predicted categories, a diversity loss is introduced, aiming to maximize the entropy of the average predicted distribution within the current batch of samples. Diversified loss of each target domain The calculation formula is as follows:

[0067] (5)

[0068] in, This represents the current training batch data sample set. All data samples in the middle belong to the category The mean of the predicted probability, It is also important to note that maximizing entropy here is equivalent to minimizing this loss.

[0069] Finally, to fully utilize the semantic information of high-confidence samples, a pseudo-label loss is introduced to filter out samples with confidence levels exceeding a threshold. The samples were used as pseudo-labels, and only those with a confidence level exceeding the threshold were considered. The loss is calculated from the samples, thus enabling supervised cross-entropy training. Pseudo-label loss for each target domain The calculation formula is as follows:

[0070] (6)

[0071] in,, Represents data samples pseudo-tags Represents data samples The mask, Indicates an indicator function, This indicates a preset threshold.

[0072] In conclusion, the final number Loss function for each target domain The weighted sum of the above three:

[0073] (7)

[0074] in, , This indicates the preset weight.

[0075] When faced with multiple target domains with statistical differences, simple joint optimization, namely the traditional empirical risk minimization (ERM), still faces serious challenges. Figure 3 This is a schematic diagram illustrating different alignment mechanisms under gradient conflict. For example... Figure 3 As shown, the core of Empirical Risk Minimization (ERM) aims to drive the model parameters to evolve in the overall direction of decreasing the average loss across all target domains. However, the update trajectory of the model parameters is actually driven by the direction and magnitude of the gradients in each domain. Due to the differences in the operating conditions of different target domains, the gradient directions they generate at the same parameter point are often inconsistent, and gradient conflicts may even occur. This gradient conflict can prevent the model parameters from reaching the optimum in the gradient field, causing the model to compromise its learning performance in another domain while attempting to adapt to one domain, i.e., resulting in negative transfer and difficulty in extracting truly generalized domain-invariant features. To address the gradient conflict problem at its root, this invention proposes a Multi-Objective Gradient Calibration (MTGC) mechanism. Its core idea is not to simply pursue the minimization of the average loss like ERM, but to find an update path that keeps the gradient directions of all target domains consistent, such as... Figure 3 As shown in (b).

[0076] In mathematics, the consistency of gradient direction can be achieved by maximizing the inner product of gradients between different target domains. Therefore, this invention designs a gradient alignment loss. Maximizing the gradient inner product (GIP) is mathematically expressed as follows:

[0077] (8)

[0078] (9)

[0079] in, Feature extractor The weight parameters, , They represent the first The target domain and the first The gradient corresponding to each target domain , They represent the first The target domain and the first The loss function corresponding to each target domain .

[0080] Given M target domains, the proposed MTGC optimization objective is... It can be defined as:

[0081] (10)

[0082] The first term, ERM, ensures that the model can achieve the intended function of the loss function in each target domain, while the second term, GIP, ensures the consistency of the gradient direction. This represents the preset trade-off parameters. To achieve... First, we need to calculate Relative to model weight parameters gradient:

[0083] (11)

[0084] The specific mathematical expression for the GIP term in the above formula is:

[0085] (12)

[0086] in, and They represent the first The target domain and the first The Hessian matrix corresponding to each target domain , They represent the first The target domain and the first The gradient corresponding to each target domain The model parameters were measured along During the update, the first The degree of interference in each target domain Similarly.

[0087] Therefore, as can be seen from formula (12), by controlling the gradient inner product... The magnitude of the gradient calibrator guides the model parameters to search for a cooperative descent path in the gradient field that satisfies gradient consistency across all target domains, thus avoiding gradient conflicts. Finally, the update rule of the multi-objective gradient calibration strategy can be expressed as follows:

[0088] (13)

[0089] in, This indicates the preset learning rate.

[0090] S104: Target Domain Fault Diagnosis

[0091] The model trained by adaptive learning is used to diagnose faults in the working signals of rotating machinery in the target domain.

[0092] Although the multi-objective gradient calibration (MTGC) strategy proposed in this invention can effectively solve the gradient conflict problem of the traditional ERM update strategy in multi-objective domain scenarios, directly optimizing the objective in formula (10) It will face high complexity. As shown in formula (13), the gradient calculation of GIP involves the calculation of the second derivative Hessian matrix. For deep neural networks with millions of parameters, calculating and storing the Hessian matrix not only requires huge amounts of GPU memory resources ( Space complexity, (This refers to the number of parameters), and its computation time cost increases exponentially with the increase of network depth.

[0093] To achieve gradient consistency constraints while maintaining computational efficiency, this invention further proposes an intra-domain gradient alignment update strategy (IDGA) as an efficient first-order approximation algorithm for multi-objective gradient calibration (MTGC), and further proposes another rotating machinery fault diagnosis method based on passive multi-objective gradient calibration. Figure 4 This is a flowchart illustrating the second specific implementation of the rotating machinery fault diagnosis method based on passive multi-target gradient calibration of the present invention. Figure 4 As shown, the rotating machinery fault diagnosis method based on passive multi-objective gradient calibration of the present invention includes the following steps:

[0094] S401: Pre-trained source model:

[0095] Set up a fault diagnosis model for rotating machinery, including a feature extractor. and classifier For rotating machinery, obtain labeled source data sample sets. Each source data sample includes rotating machinery operating signals. and corresponding fault category labels , , Indicates the number of source data samples; uses the source data sample set. The source model is obtained by training the rotating machinery fault diagnosis model;

[0096] S402: Collect multi-target domain data samples:

[0097] When it is necessary to migrate the source model to a multi-objective domain, several operating signals of the rotating machinery in each objective domain are collected to obtain the target domain data sample set. , Indicates the first The first target domain One working signal data sample, , Indicates the first Number of data samples in each target domain , Indicates the number of target domains.

[0098] S403: Adaptive learning based on intra-domain gradient alignment update:

[0099] Classifier in Fault Diagnosis Model of Frozen Rotating Machinery The weight parameters are adopted. Data sample set of target domains For feature extractors The weight parameters are adaptively learned to obtain the adaptively learned rotating machinery fault diagnosis model. In the adaptive learning, an intra-domain gradient alignment update strategy is used to realize a feature extractor based on multi-objective gradient correction. Weight parameters updated. Figure 5 This is a flowchart of the gradient alignment update within the domain in this invention. For example... Figure 5 As shown, the specific steps of gradient alignment update within the domain in this invention include:

[0100] S501: Set the iteration count .

[0101] S502: Initialize the training parameters for this session:

[0102] The feature extractor obtained from the previous training round Weight parameters As a feature extractor Initial weight parameters , that is to say , That is, the feature extractor in the source model. The weight parameters.

[0103] S503: Set the target field sequence number .

[0104] S504: Sample set of data for the target domain:

[0105] From the Data sample set of target domains The data sample set of the current training batch is sampled in the middle. .

[0106] S505: Calculate the gradient of the loss function:

[0107] Data sample set Input the current rotating machinery fault diagnosis model and calculate the loss function, then calculate the weight parameters. gradient .

[0108] S506: Update feature extractor weight parameters:

[0109] The weight parameters are updated using the following formula. :

[0110] (14)

[0111] in, This represents the preset learning rate for the target domain.

[0112] S507: Determine if If yes, proceed to step S508; otherwise, proceed to step S509.

[0113] S508: Order Return to step S504.

[0114] S509: Update the weight parameters for this training round:

[0115] The feature extractor for this training round is updated using the following formula. Weight parameters :

[0116] (15)

[0117] in, This indicates the preset learning rate for the training rounds.

[0118] S510: Determine if the adaptive learning termination condition has been met. If yes, adaptive learning ends; otherwise, proceed to step S511. The adaptive learning termination condition can generally be set to the maximum number of iterations or the convergence of the feature extractor's weight parameters.

[0119] S511: Order Return to step S502.

[0120] It is evident that the gradient alignment update within the domain employs an "inner and outer loop" mechanism for optimization. Figure 6 This is a schematic diagram of the intra-domain gradient alignment update inner and outer loop mechanism in this embodiment. For example... Figure 6 As shown, firstly, in the outer loop phase, the model parameters from the source domain are copied to a temporary model, and the classifier parameters are frozen. Then, in the inner loop phase, the loss function for the corresponding target domain is calculated, and the copied feature extractor parameters are updated accordingly. Finally, the parameter offsets generated by each target domain in the inner loop are calculated. The summation of these values ​​is used as the correction factor in the outer loop, thereby guiding the update of the feature extractor parameters. Therefore, IDGA avoids explicit and complex second-order derivative calculations, implicitly achieving gradient alignment across multiple target domains. The mathematical expression for IDGA update is:

[0121] (16)

[0122] S404: Target Domain Fault Diagnosis

[0123] The model trained by adaptive learning is used to diagnose faults in the working signals of rotating machinery in the target domain.

[0124] Next, the equivalence of the two multi-objective domain gradient correction methods in this invention will be proven. In the following formulas, in order to prove the optimization equivalence between the MTGC update strategy in formula (13) and the IDGA update strategy in formula (16), the gradient in the inner loop is first... At the initial point Perform a first-order Taylor expansion:

[0125] (17)

[0126] in, It is the first The gradient of the target domain at the initial position. It is the first The Hessian matrix of each target domain at its initial position. From step 0 to step 1 The cumulative change in parameters at each step.

[0127] According to the stochastic gradient descent update rule, the change in model parameters can be expressed as:

[0128] (18)

[0129] Then Substituting back into formula (18), we get:

[0130] (19)

[0131] Then the total update amount of the model parameters can be calculated as follows:

[0132] (20)

[0133] Then, in formula (19) Substitute into the above formula:

[0134] (twenty one)

[0135] The first item The first term is the average gradient of all target domains, i.e., the traditional ERM update; the second term is a second-order term based on the Hessian matrix and gradient, which is also the key to achieving multi-target gradient alignment in this invention.

[0136] Finally, it is proven that the second term in formula (21) is consistent with the direction of the GIP gradient. First, we analyze the expected value of the second term in formula (21). Assuming that the order of the target domain is randomly shuffled, we can take the expected value for all possible orders. Under expectation, the index and Covered all The pairing, that is:

[0137] (twenty two)

[0138] Utilizing Hessian's symmetry and the properties of the derivative of the inner product of the gradient:

[0139] (twenty three)

[0140] Therefore, the direction of the second term is... Related.

[0141] More strictly, define specific update components of IDGA Subtract the ERM gradient from the total update amount:

[0142] (twenty four)

[0143] Substituting the previous Taylor expansion result:

[0144] (25)

[0145] The defined gradient distribution alignment loss for:

[0146] (26)

[0147] Therefore, it can be seen that:

[0148] (27)

[0149] In summary, although IDGA only uses first-order gradient calculations, its update direction mathematically implicitly optimizes the inner product term of the second-order gradient. This can be achieved by adjusting the number of inner loop steps. With its learning rate, IDGA can maximize gradient consistency between domains while minimizing the average loss, thus effectively achieving gradient alignment and domain-invariant fault feature learning in multi-objective domains without increasing memory overhead.

[0150] To better illustrate the technical effects of this invention, specific examples were used to experimentally verify it. This experimental verification employed a planetary gearbox fault dataset, which was collected using a dedicated experimental setup. This setup mainly consisted of a three-phase asynchronous motor, a two-stage planetary gearbox, a parallel shaft gearbox, and a magnetic powder brake. To obtain vibration data under different health conditions, an accelerometer was mounted on the surface of the two-stage planetary gearbox housing, and the sampling frequency was set to 5120 Hz. Faults were artificially created on the sun gear, with five health conditions set: normal (NC), surface wear (SW), tooth root crack (RC), tooth surface chipping (CT), and missing tooth (MT). The input speed of the planetary gearbox was adjusted to 1500 rpm, and the load conditions were simulated by adjusting the operating current of the magnetic powder brake, with specific load values ​​of 0, 1.4, and 2.8 N·m. Under each condition, the vibration signal sampling duration was 200 seconds.

[0151] This embodiment introduces several representative fault transfer diagnosis methods as comparative methods to compare their performance with that of the present invention. These comparative methods are divided into three categories: 1) generalization diagnosis methods using only source data (WDCNN, I-Softmax); 2) traditional UDA methods (DDC, DANN, MCD, JDA); 3) SFDA methods (SHOT) where source data is unavailable. To ensure the fairness of the experimental results, all comparative methods adopt the same 1D-CNN backbone network architecture as the present invention. In addition, to reduce the interference of random initialization of model parameter weights on the results, each method is independently trained 5 times on each transfer task, and the mean and standard deviation of the diagnostic accuracy are reported to ensure the reliability of the diagnostic results. Since the two multi-objective domain gradient calibration methods of the present invention are equivalent, this embodiment uses intra-domain gradient alignment update for multi-objective domain gradient calibration, and its learning rate is... Set to 0.001. The value was set to 0.0001, and the optimizer was Adam. Table 1 is a comparison table of the diagnostic performance of the present invention and the comparative method on the planetary gearbox cross-load dataset in this embodiment.

[0152]

[0153] Table 1

[0154] As shown in Table 1, under the condition that source data is unavailable, this invention demonstrates superior cross-domain transfer diagnostic performance. It not only achieves the highest accuracy across all six tasks, but also boasts an average accuracy of 98.06%. Furthermore, it outperforms the best-performing passive domain adaptation method, SHOT, by 5.84%. More noteworthy is the stability of this invention when handling tasks with large-span loads. When faced with large-span loads prone to gradient conflicts, such as 0→2.8 and 2.8→0, even UDA methods that allow access to source data (such as DDC and JDA) exhibit negative transfer due to drastic distribution shifts. In contrast, this invention maintains high accuracies of 97.42% and 96.23%, respectively, with minimal standard deviation across all tasks. This strongly demonstrates that this invention effectively overcomes gradient conflicts caused by large-span distribution shifts at the microscopic level of model updates, stably extracting domain-invariant fault features under passive conditions, and achieving highly reliable fault transfer diagnosis.

[0155] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for fault diagnosis of rotating machinery based on passive multi-objective gradient calibration, characterized in that, Includes the following steps: S1: Set up a fault diagnosis model for rotating machinery, including a feature extractor. and classifier ; For rotating machinery, obtain labeled source data sample sets. Each source data sample includes rotating machinery operating signals. and corresponding fault category labels , , Indicates the number of source data samples; uses the source data sample set. The source model is obtained by training the rotating machinery fault diagnosis model; S2: When it is necessary to migrate the source model to a multi-objective domain, collect several working signals of the rotating machinery in each objective domain to obtain the target domain data sample set. , Indicates the first The first target domain One working signal data sample, , Indicates the first Number of data samples in each target domain , Indicates the number of target fields; S3: Classifier in Fault Diagnosis Model for Frozen Rotating Machinery The weight parameters are adopted. Data sample set of target domains For feature extractors The weight parameters are adaptively learned to obtain the adaptively learned rotating machinery fault diagnosis model; in the adaptive learning, feature extractor is performed based on multi-objective gradient correction. Weight parameter update: ， in, , These represent the feature extractors before and after the update, respectively. The weight parameters, This indicates the preset learning rate. This represents the preset trade-off parameters. , They represent the first The target domain and the first The gradient corresponding to each target domain , They represent the first The target domain and the first The loss function corresponding to each target domain and They represent the first The target domain and the first The Hessian matrix corresponding to each target domain ; S4: Use the adaptive learning-trained model to diagnose faults in the working signals of rotating machinery in the target domain.

2. The method for diagnosing rotating machinery faults according to claim 1, characterized in that, The loss function in the source model training in step S1 The calculation formula is as follows: ， in, Indicates the number of fault categories. Represents the source data sample set The Middle Data sample source data sample Category The predicted probability, , The formula for calculating the smooth label is as follows: ， in, It is the first of the real and unique hot tags. One element, The first smooth label One element, This represents the smoothing coefficient.

3. The method for diagnosing rotating machinery faults according to claim 1, characterized in that, The loss function for each target domain in the adaptive learning process in step S3 The following formula is used for calculation: ， in, , Indicates the preset weight. , , They represent the first The entropy minimization loss, diversification loss, and pseudo-label loss for each target domain are calculated using the following formulas: ， in, This indicates that the current rotating machinery fault diagnosis model is applicable to the first... The first target domain Data samples Category The predicted probability, Indicates the first in the current training batch A data sample set for each target domain This indicates the number of data samples in the data sample set. ， in, This represents the current training batch data sample set. All data samples in the middle belong to the category The mean of the predicted probability, ; ， in, Represents data samples pseudo-tags Represents data samples The mask, Indicates an indicator function, This indicates a preset threshold.

4. A method for fault diagnosis of rotating machinery based on passive multi-objective gradient calibration, characterized in that, Includes the following steps: S1: Set up a fault diagnosis model for rotating machinery, including a feature extractor. and classifier ; For rotating machinery, obtain labeled source data sample sets. Each source data sample includes rotating machinery operating signals. and corresponding fault category labels , , Indicates the number of source data samples; uses the source data sample set. The source model is obtained by training the rotating machinery fault diagnosis model; S2: When it is necessary to migrate the source model to a multi-objective domain, collect several working signals of the rotating machinery in each objective domain to obtain the target domain data sample set. , Indicates the first The first target domain One working signal data sample, , Indicates the first Number of data samples in each target domain , Indicates the number of target fields; S3: Classifier in Fault Diagnosis Model for Frozen Rotating Machinery The weight parameters are adopted. Data sample set of target domains For feature extractors The weight parameters are adaptively learned to obtain the adaptively learned rotating machinery fault diagnosis model; in the adaptive learning, an in-domain gradient alignment update strategy is adopted to realize a feature extractor based on multi-objective gradient correction. The steps for updating weight parameters include: S3.1: Let the number of iterations be... ; S3.2: The feature extractor obtained from the previous training round Weight parameters As a feature extractor Initial weight parameters , that is to say , That is, the feature extractor in the source model. Weight parameters; S3.3: Set the target field number ; S3.4: From the first Data sample set of target domains The data sample set of the current training batch is sampled in the middle. ; S3.5: Set up a data sample set Input the current rotating machinery fault diagnosis model and calculate the loss function, then calculate the weight parameters. gradient ; S3.6: The weight parameters are updated using the following formula. : ， in, This represents the preset learning rate for the target domain; S3.7: Determine if If yes, proceed to step S3.8; otherwise, proceed to step S3.

9. S3.8: Order Return to step S3.4; S3.9: The feature extractor for this training round is updated using the following formula. Weight parameters : ， in, This indicates the preset learning rate for the training rounds; S3.10: Determine whether the adaptive learning termination condition has been met. If yes, adaptive learning ends; otherwise, proceed to step S3.

11. S3.11: Order Return to step S3.2; S4: Use the adaptive learning-trained model to diagnose faults in the working signals of rotating machinery in the target domain.

5. The method for diagnosing rotating machinery faults according to claim 4, characterized in that, The loss function in the source model training in step S1 The calculation formula is as follows: ， in, Indicates the number of fault categories. Represents the source data sample set The Middle Data sample source data sample Category The predicted probability, , The formula for calculating the smooth label is as follows: ， in, It is the first of the real and unique hot tags. One element, The first smooth label One element, This represents the smoothing coefficient.

6. The method for diagnosing rotating machinery faults according to claim 4, characterized in that, The loss function for each target domain in the adaptive learning process in step S3 The following formula is used for calculation: ， in, , Indicates the preset weight. , , They represent the first The entropy minimization loss, diversification loss, and pseudo-label loss for each target domain are calculated using the following formulas: ， in, This indicates that the current rotating machinery fault diagnosis model is applicable to the first... The first target domain Data samples Category The predicted probability, Indicates the first in the current training batch A data sample set for each target domain This indicates the number of data samples in the data sample set. ， in, This represents the current training batch data sample set. All data samples in the middle belong to the category The mean of the predicted probability, ; ， in, Represents data samples pseudo-tags Represents data samples The mask, Indicates an indicator function, This indicates a preset threshold.

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