Physical enhancement federal continuous fault diagnosis method for complex electromechanical system

Abstract

The invention discloses a physical enhancement federation continuous fault diagnosis method for a complex electromechanical system, and belongs to the technical field of electromechanical system fault diagnosis. The method aims at solving the problem that an existing complex electromechanical system fault diagnosis method has the contradiction between privacy protection and distributed training. According to the method, continuous fault diagnosis of the complex electromechanical system is carried out based on a federated diagnosis system, and a server side distributes a generator and a global model to each client side for the client side to carry out continuous learning; the generator synthesizes the potential noise vector obeying normal distribution, the working condition vector encoding the working condition information and the classification label representing the fault type as input and outputs a synthesized vibration signal; in the federated learning process, the client determines whether to select the historical generator into a playback set according to the physical similarity between a current task and a historical task, the client generates synthetic samples from the playback generator set to construct a playback buffer area, and the number of the synthetic samples generated by each historical generator is distributed according to a preset proportion.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical system fault diagnosis technology, and relates to a method for continuous fault diagnosis of electromechanical systems. Background Technology

[0002] Rotating machinery is a common and complex electromechanical system in industrial fields, and a core component of industrial systems. Timely and accurate fault diagnosis can prevent unexpected downtime and ensure system safety and efficiency. With the development of deep learning, fault diagnosis methods based on deep models have become a research hotspot in this field. However, existing technologies still face many challenges in practical industrial deployments.

[0003] First, there are data privacy and distributed bottlenecks. Traditional deep diagnostic models rely on centralized training, requiring the collection of vibration data from various devices. However, in industrial scenarios, data is usually stored in different sites, forming data silos, and due to privacy regulations, raw data cannot be shared across sites. This makes it difficult to apply centralized models in real-world industrial environments.

[0004] Second, it faces the challenges of dynamic changes in operating conditions and catastrophic forgetting. The operating conditions of rotating machinery used to represent complex electromechanical systems (such as speed and load) are dynamically adjusted according to production demands, and the types of faults may gradually increase as equipment ages. Most existing federated learning methods assume that the task is static and the client participates synchronously, making them unable to adapt to dynamic operating conditions. When the model learns new operating conditions or new fault knowledge, it is prone to losing its ability to judge historical tasks, i.e., the phenomenon of "catastrophic forgetting" occurs. At the same time, the spectral drift of vibration signals caused by changes in operating conditions will also reduce the model's generalization performance.

[0005] Third, there are issues of missing physical information and negative transfer. The vibration signals of rotating machinery, as a complex electromechanical system, are governed by physical laws. For example, bearing faults exhibit inner ring fault characteristic frequencies (BPFI), outer ring fault characteristic frequencies (BPFO), and ball spin frequencies (BSF), which are determined by the bearing's geometric parameters and are unaffected by external operating conditions. However, existing federated continuous learning methods (such as FedCIL and MFCL) are mostly designed for visual or language tasks, neglecting the physical driving characteristics of vibration signals. On the one hand, the failure to utilize prior physical knowledge makes the model sensitive to spectral drift; on the other hand, the lack of consideration for the physical similarity between tasks, and the blind application of knowledge transfer, easily leads to negative transfer (such as forced transfer between tasks at different speeds), further deteriorating diagnostic performance.

[0006] To address these issues, the industry urgently needs a distributed fault diagnosis method that can integrate physical prior knowledge, protect data privacy, and resist catastrophic forgetting. Summary of the Invention

[0007] This invention addresses the contradiction between privacy protection and distributed training in existing fault diagnosis methods for complex electromechanical systems, as well as the problem of poor generalization caused by the lack of physical information.

[0008] A physically-enhanced federated continuous fault diagnosis method for complex electromechanical systems is provided, which performs continuous fault diagnosis of complex electromechanical systems based on a federated diagnostic system; the federated diagnostic system includes a server and M geographically distributed clients.

[0009] The server aggregates the local model parameters uploaded by the client and generates the trained generator. With global model Distributed to various clients for continuous learning; the generator With a potential noise vector that follows a normal distribution Operating condition vector of encoded operating condition information and classification labels representing fault types The synthesized vibration signal is used as input and output; the working condition vector encodes the working condition information. The subscript j corresponds to the task index, and j in the generator also represents the generator corresponding to each task. For the rotational speed and load parameters of complex electromechanical systems under the corresponding tasks;

[0010] Each client corresponds to one industrial site, and the client uses a local model for tasks. For fault identification, the local model includes a shared encoder and a task-specific classification head. During federated learning, clients do not share raw data but interact through local model parameters or gradients to collaboratively optimize the global model. ;

[0011] During federated learning, the client locally stores the generator set obtained after global aggregation and synchronization following training for each task. Meanwhile, the client determines the current task. With historical mission physical similarity Decide whether to use the history generator Selected for replay set, when When the playback threshold is exceeded, the history generator... Once selected for playback, the client generates synthetic samples from the playback generator set to construct a playback buffer. The number of synthetic samples generated by each historical generator is allocated according to a preset ratio.

[0012] Furthermore, the processing of the local model includes:

[0013] First, the vibration signal sequence The feature vector is fed into a shared encoder to extract the feature vector. The shared encoder consists of four 1D convolutional layers. After each convolutional operation, a batch normalization layer is connected first, followed by a max pooling layer and a LeakyReLU activation function in sequence. Finally, the feature vector is output through a fully connected layer.

[0014] The task-specific classification head adopts a linear mapping structure, inputting the dimensional feature vector output by the shared encoder into the classification head of the corresponding task and mapping it to the label space dimension of the current task; after normalization by the Softmax function, the class probability is output to realize the fault type identification of the current task.

[0015] Furthermore, the generator The process of synthesis based on input signals includes:

[0016] S311, Condition Embedding and Fusion Stage: The working condition vector is respectively processed through a multilayer perceptron. and fault labels Encode the two encoded vectors and then fuse them with the latent noise z to form a seed for generation;

[0017] S312, Adaptive Resonance Layer Stage: For seed generation, multi-layer 1D transposed convolution is used to generate the basic signal; after each 1D transposed convolution, a batch normalization layer is connected, and then the signal is processed through residual connections.

[0018] S313, Fault Modulation Module Stage: The basic signal is processed using a bandpass-enhanced convolutional kernel constructed based on fault characteristic frequencies to obtain a vibration signal containing fault-specific transient signals;

[0019] Finally, the output signal is normalized to the [-1,1] interval through a Conv1D layer with a tanh activation function to obtain the synthesized vibration signal, which is used as the input of the synthetic sample for subsequent federated training.

[0020] Furthermore, the bandpass-enhanced convolutional kernel constructed based on fault feature frequencies sets its center frequency as the target fault feature frequency. ,bandwidth A bandpass filter that covers the harmonic response range.

[0021] Furthermore, the server-side uses a composite loss function. For generator The training is performed using the following composite loss function:

[0022] ,

[0023] in, These are the loss weighting coefficients; The cross-entropy loss is obtained based on predictions from a global model.

[0024] For batch normalized alignment loss:

[0025] ,

[0026] in, The set of batch normalization layers in the model. and Representing batch normalization layers Mean and variance of activation values; This indicates that based on the normal distribution z and the working condition vector... Generate synthetic samples, This represents the actual signal sample in the client's local dataset, i.e., the original vibration signal sample;

[0027] For spectral consistency loss:

[0028] ,

[0029] in, The envelope spectrum energy at the fault characteristic frequency. For total envelope energy, Based on the working condition vector The calculated theoretical energy percentage;

[0030] For signal smoothing loss:

[0031] ,

[0032] In the formula, B is the batch size, K is the number of signal channels, and L is the signal length. The sampled value of the synthesized sample signal output by the generator corresponds to the signal amplitude of the synthesized vibration signal at the i-th sample, k-th channel, and l-th time-domain sampling point.

[0033] Furthermore, based on the working condition vector The calculated theoretical energy percentage It is obtained through the following steps:

[0034] First, Hilbert envelope is calculated for the time-domain vibration signal of the calibration sample, and then FFT is performed on the envelope signal to obtain the envelope. At each target fault frequency and its harmonics The squared amplitude value of the integral envelope spectrum over the interval is used to obtain the frequency band energy. And calculate the total envelope energy. Then, the observed proportion is calculated for the calibration sample. For each frequency band, log-linear regression was used to fit the relationship between the operating conditions and the proportion. ; The fitted linear regression function is then used to determine the appropriate function based on the given information. Obtain the prediction function Finally, the theoretical proportions under this operating condition are obtained by normalizing the predicted values ​​of each harmonic: ,in This is the set of fault frequency bands used for constraints, i.e., all frequency band indices related to the target fault; This represents the total number of all frequency bands under the current operating conditions.

[0035] Furthermore, the physical similarity as follows:

[0036] ,

[0037] In the formula, Similarity weights; These represent the global ranges of rotational speed and load across all tasks, respectively, and are used as normalization constants; , )and( , ( ) are historical tasks The corresponding current task The corresponding operating condition vector.

[0038] Furthermore, the playback threshold is set to 0.6.

[0039] Furthermore, the client-side continuous learning process includes:

[0040] Each client In the mission The local dataset below is ,in The original vibration signal sample For fault labels, For the client In the mission The number of samples; the client will use the local real dataset. Combined with the synthetic signal in the playback buffer, a hybrid training set is constructed, and a local loss function is applied. Optimize the local model:

[0041] ,

[0042] in, The cross-entropy loss is the loss of the local model for the current task's real samples. To be the same as the spectral consistency loss during generator training; For knowledge distillation loss based on physical similarity weighting:

[0043] ,

[0044] In the formula, for divergence, To correspond to historical tasks The output probability distribution of the frozen classification head on sample x. The predicted probability distribution for the current task classification head; For the task With the task The physical similarity between them.

[0045] Furthermore, after each client completes local training, it will send the optimized model parameters... Uploaded to the server; the server performs weighted aggregation based on the sample size of each client's local dataset, and updates the global model parameters. The aggregation formula is:

[0046]

[0047] in, These are the global model parameters for the (h+1)th round after aggregation. For the client The task corresponding to the current aggregation round The number of local samples; M represents the total number of samples from all clients; M represents the number of clients.

[0048] Beneficial effects:

[0049] By defining dynamic sequence tasks (changes in operating conditions, incremental fault categories) to adapt to continuous scenarios, and using a physical enhancement generator to replay historical samples and weighted knowledge distillation to retain historical knowledge, and then using federated learning to achieve client iteration and server aggregation, this not only effectively solves the contradiction between privacy protection and distributed training, but also ensures that the model continuously adds diagnostic capabilities without forgetting historical performance. In addition, the physical enhancement generator and loss function of this invention can also effectively solve the problem of poor generalization caused by the lack of physical information. Attached Figure Description

[0050] Figure 1 This is the overall architecture diagram of the PA-FCL framework.

[0051] Figure 2 The above are comparison diagrams of the signal quality of the physical enhancement generator, where (a), (b), (c), and (d) are the outer ring fault waveform, outer ring fault spectrum, outer ring fault envelope, and outer ring fault envelope spectrum, respectively.

[0052] Figure 3The figure shows a performance comparison between PA-FCL and the baseline method, where (a), (b), and (c) correspond to the average accuracy of the CWRU, JNU, and XJTU datasets, respectively; and (d), (e), and (f) correspond to the average forgetting rate of the CWRU, JNU, and XJTU datasets, respectively.

[0053] Figure 4 Figures showing the ablation experiment results on the CWRU dataset;

[0054] Figure 5 Figure showing the ablation experiment results on the JNU dataset;

[0055] Figure 6 The figure shows the ablation experiment results on the XJTU dataset. Detailed Implementation

[0056] Federated learning offers a feasible path for privacy protection, but it needs to be combined with a continuous learning mechanism to adapt to dynamic tasks. Meanwhile, introducing physical information can enhance the model's robustness to changes in operating conditions and reduce negative transfer. Based on this, this invention proposes a Physically Augmented Federated Continuous Learning (PA-FCL) framework. Through physically driven signal generation, knowledge distillation, and optimization strategies, it ensures that the model continuously adds diagnostic capabilities without forgetting historical performance, achieving efficient, stable, and continuous fault diagnosis for complex electromechanical systems. This invention achieves high accuracy and low forgetting rate fault diagnosis across operating conditions and category-incremental scenarios while protecting data privacy.

[0057] This embodiment presents a method for diagnosing persistent faults in a complex electromechanical system using physically enhanced federated systems. It mainly includes a training process for a diagnostic model of the complex electromechanical system using physically enhanced federated systems, and a diagnostic method using the trained diagnostic model. The specific process includes the following steps:

[0058] 1. System Deployment:

[0059] Deploy a federated diagnostic system comprising M geographically distributed clients, each client corresponding to an industrial site, used to monitor rotating machinery (such as motors, bearings, and reducers, which are common complex electromechanical systems) under specific operating conditions. Tasks in the system appear in sequence form; let the task sequence be... Each task The corresponding unique working condition is determined by the rotational speed. and load Representation, i.e. And the fault label space of each task They do not overlap, creating incremental scenarios for different categories.

[0060] Appendix Figure 1 The system's hierarchical structure is shown in the image. Figure 1The top section represents the system deployment architecture. The left side represents the server layer, containing the global model and task sequence management module; the middle section represents the clients (Task0-TaskM), each client corresponding to a rotating machinery monitoring task under a specific operating condition; the right side labels the tasks. The main operating parameters, including speed ,load and its corresponding tag space It is used to characterize the differences in operating conditions between different tasks. Figure 1 Below is the physical enhancement generator and loss calculation module of this invention. The left side shows the structure of the physical enhancement signal generator, which includes conditional embedding, adaptive resonant layer and fault modulation module; the middle shows the mixed training process of generated signal and real sample; the right side shows the combination of cross-entropy loss, knowledge distillation loss and spectral consistency loss, which are used to guide the physical authenticity and semantic consistency of the generated signal.

[0061] 2. Dataset definition and model interaction rules:

[0062] Each client In the mission The local dataset below is ,in The original vibration signal sample The labels are for faults (including inner ring faults, outer ring faults, ball faults, cage faults, and normal status). For the client In the mission The number of samples; the datasets from all clients together constitute the task. global dataset Throughout the federated learning process, clients do not share raw data; they only interact through model parameters or gradients to collaboratively optimize the global model. Appendix Figure 1 The parameter transmission arrows between the client and server correspond to this interaction rule, and also indicate the privacy protection constraint of no original data sharing, which is consistent with the distributed storage and local use logic in the dataset definition.

[0063] 3. Training of the physical enhancement signal generator:

[0064] For each task The server initializes and trains a task-specific physical augmentation signal generator. This generator is used to synthesize vibration signals that match the current operating conditions, thereby enabling privacy-preserving playback without the original data.

[0065] Generator The input consists of three parts:

[0066] (1) Follows a normal distribution The potential noise vector is used to provide diversity to the generated signal;

[0067] (2) Operating condition vector encoding operating condition information This vector is associated with the speed and load parameters of rotating machinery (common complex electromechanical systems), such as motors, bearings, and reducers; operating condition vector. The subscript j corresponds to the task index, and j in the generator also represents the generator corresponding to each task.

[0068] (3) Classification labels representing fault types These correspond to inner ring failure, outer ring failure, ball failure, cage failure, and normal condition, respectively.

[0069] Generator The internal architecture is divided into three stages, each designed to conform to the physical generation laws of vibration signals. (See attached diagram) Figure 1 The internal sub-block diagram of the Physics Enhancement Generator module provides a visual overview of this structure:

[0070] S311, Condition Embedding and Fusion Stage: The working condition vector is embedded and fused using a two-layer multilayer perceptron (MLP). Encoded as a 64-dimensional vector, and the fault label is simultaneously processed through two layers of multilayer perceptrons. The two encoded vectors are then fused with the 100-dimensional latent noise z to form a seed for generation, which provides the basis for subsequent signal generation.

[0071] S312, Adaptive Resonance Layer Stage: For seed generation, a base signal is generated using 5 layers of 1D transposed convolution (with a kernel size of 31). Each layer of 1D transposed convolution is followed by a batch normalization layer to avoid gradient vanishing. Then, residual connections are used to simulate the attenuation waveform of structural resonance, thereby capturing the modulation oscillations caused by fault impact and enhancing the spectral richness of the signal in the fault-related frequency band.

[0072] S313, Fault Modulation Module Stage: Based on the kinematics of rolling bearings and combined with geometric parameters such as the number of balls, ball diameter, and pitch circle diameter, the fault characteristic frequency is obtained by analyzing the relative motion relationship between the rolling elements and the inner and outer rings. A bandpass-enhanced convolution kernel is then constructed based on this. The bandpass-enhanced convolution kernel is designed as a bandpass filter, with its center frequency set as the target fault characteristic frequency. ,bandwidth It covers its harmonic response range. The design of the convolution kernel is based on the physical parameters of rolling bearings, combined with geometric parameters such as the number of balls, ball diameter, and pitch circle diameter to calculate the fault frequency. A bandpass filter was designed to effectively transmit signals within this frequency and its harmonic range. This convolution kernel, by convolving with the fundamental signal, can inject transient impact characteristics consistent with the target fault mode, forming a vibration signal containing fault-specific transient signals.

[0073] For example, in the case of a rolling bearing inner ring failure, suppose the number of balls in the rolling bearing is Z, the ball diameter is d, the pitch circle diameter is D, and the bearing frequency is... Then, the characteristic frequency of inner ring failure can be calculated based on the kinematic relationship of the rolling bearing.

[0074]

[0075] After determining the fault characteristic frequency, A bandpass-enhanced convolutional kernel is constructed with the center frequency as the reference frequency, and its frequency response covers... The frequency range corresponding to its several harmonics. The bandpass-enhanced convolution kernel can be obtained by discretizing the frequency response of an ideal bandpass filter and truncating it with a window function. This one-dimensional convolution kernel is used to convolve the basic signal in the time domain, thereby enhancing the transient impact components related to inner ring faults.

[0076] Finally, the output signal is normalized to the [-1, 1] interval (signal dimension is ) through a Conv1D layer with tanh activation function. The signal length (L is the signal length, set to 1024 by default) is used as the input for the synthetic samples in subsequent federated training. The Conv1D layer with the tanh activation function is the signal normalization component of the third stage of the generator (fault modulation module). Its input is the vibration waveform modulated by the fault feature convolution kernel, that is, the time-domain signal containing the fault-specific transient structure formed by convolving the basic signal with the bandpass convolution kernel constructed with the fault feature frequency as the center; this layer normalizes the output amplitude to the [-1,1] interval to form a synthetic vibration signal with a uniform format, and serves as the unified input interface for the subsequent federated training stage (client-side hybrid training, loss calculation and global aggregation), playing a key adaptation role between the signal generation inside the generator and the external federated optimization.

[0077] Generator training loss: Appendix Figure 1 The generator loss calculation module in the middle class annotates the correlation logic of each loss term. To ensure the physical authenticity and diagnostic effectiveness of the synthesized signal, the generator... Through the composite loss function For training, the expression for the composite loss function is:

[0078]

[0079] in, The loss weight coefficients are used to control the influence of each auxiliary constraint term. In this embodiment, the values ​​are 1.0, 5.0, and 0.1, respectively.

[0080] (1) Cross-entropy loss The server utilizes the frozen global model from the previous round. Calculate the cross-entropy loss to ensure the synthesized signal can be classified by the current task's classification head. (The classification head of the global model) correctly classifies and strengthens the semantic alignment between the synthesized signal and the expected fault category;

[0081] (2) Batch normalization alignment loss Since the shared encoder and generator convolutional modules of the global model both integrate batch normalization layers, this loss avoids signal distribution drift by aligning the batch normalization statistics of the synthesized signal and the real signal. Its calculation formula is as follows:

[0082]

[0083] in, The set of batch normalization layers in the model. and Representing batch normalization layers Mean and variance of activation values; This indicates that based on the normal distribution z and the working condition vector... Generate synthetic samples, This represents the actual signal sample in the client's local dataset, i.e., the original vibration signal sample.

[0084] (3) Spectral consistency loss The energy distribution of the synthesized signal at the fault characteristic frequency is constrained to conform to prior physical knowledge. The calculation formula is:

[0085]

[0086] in, The envelope spectrum energy at fault characteristic frequencies (such as BPFI, BPFO, BSF) For total envelope energy, Based on the working condition vector The theoretical energy percentage, calculated from factors such as rotational speed (r) and load (F), can be obtained by establishing a mapping relationship between the characteristic frequency amplitude and operating parameters. This mapping is used to constrain the energy distribution of the generated signal in the corresponding frequency band, ensuring that the generated data conforms to the theoretical physical response characteristics. The specific calculation process employs an envelope spectrum-based operating condition-energy mapping method, with the following steps:

[0087] First, Hilbert envelope is calculated for the time-domain vibration signal of the calibration sample, and then FFT is performed on the envelope signal to obtain the envelope. At each target failure frequency and the range of its harmonics The frequency band energy is obtained from the squared amplitude of the upper integral envelope spectrum. And calculate the total envelope energy. . Here, k represents the fault band index, which is the bandwidth parameter.

[0088] Then, the observed proportion of the calibrated samples was calculated. For each harmonic The relationship between the frequency band and the operating condition and the proportion was fitted using log-linear regression. .in, , , These are the fitting coefficients. To compensate for the deviation between actual operating conditions and the theoretical model, the prediction function is obtained. .

[0089] Finally, the theoretical proportion of each harmonic prediction value under this operating condition is obtained by normalizing the predicted values ​​of each harmonic: ,in The set of fault frequency bands used for constraints is the index of all frequency bands related to the target fault (e.g., the fundamental frequency and its harmonics). The numerator actually represents all frequency bands related to the target fault; the denominator actually represents the total predicted energy of all frequency bands under the current operating condition. This represents the total number of all frequency bands.

[0090] In this embodiment, K=3 (fundamental frequency + second harmonic), and the bandwidth is set to... For linear regression fitting, the coefficients can be determined using the least squares method with regularization. If the calibration sample is insufficient, a physically inspired harmonic attenuation weight can be used as a substitute, with a small amount of calibration performed.

[0091] (4) Signal smoothing loss By penalizing abrupt changes in the waveform, artificial high-frequency noise is suppressed, and the continuity of the signal in the time dimension is improved. Its expression is:

[0092]

[0093] In the formula, B is the batch size, K is the number of signal channels, and L is the signal length. The sampled value of the synthesized sample signal output by the generator corresponds to the signal amplitude of the synthesized vibration signal at the i-th sample, k-th channel, and l-th time-domain sampling point.

[0094] The generator's training parameters are set as follows: 150 training epochs, learning rate of 0.01, and loss weight coefficient. , , In practical applications, adjustments can be made based on the characteristics of the specific dataset.

[0095] After training, the physical authenticity of the synthesized signal can be verified by attaching... Figure 2 (Comparison chart of signal quality of physical enhancement generator) Verification, in which Figure 2 (a) Outer ring fault waveform diagram, horizontal axis time / s, vertical axis amplitude Physical PurePot demonstrates the consistency of the time-domain fluctuations and the matching of the impact characteristics between the synthetic signal and the real signal; Figure 2 (b) Outer ring fault spectrum diagram, horizontal axis frequency / Hz, vertical axis amplitude In the Physical Pure Ampüu, the energy peak at the outer ring fault characteristic frequency (BPFO) is obvious, and the spectral distribution conforms to physical laws; Figure 2 (c) (Outer ring fault envelope diagram) and Figure 2 (d) (Outer ring fault envelope spectrum) further verifies the periodicity of the envelope signal and the clear presentation of fault characteristic frequencies, proving that the generator can retain key physical characteristics.

[0096] 4. Client-side local model building and training:

[0097] The server will train the generator. With global model After being distributed to various clients, such as Figure 1 As shown in the client-side diagram, the client follows these steps to conduct continuous learning:

[0098] The client is the current task. Initialize the dedicated category header The local model adopts an architecture of "shared encoder + task-specific classification head":

[0099] A. Shared encoder: Its input is the vibration signal sequence corresponding to the current task. (L is the sampling length, which can be 1024). During federated training, it can collect real vibration signals from the client or synthesized vibration signals output by the generator. The shared encoder consists of 4 1D convolutional layers, with each convolutional kernel having a size of [missing value]. The number of output channels is 32, 64, 128, and 256, respectively. After each convolutional operation, a batch normalization layer is first connected (to stabilize the feature distribution and accelerate training convergence), followed by a max pooling layer (with a pooling kernel size of [missing information]). The shared encoder uses the LeakyReLU activation function (with an activation slope of 0.2) and a fully connected layer to output a 256-dimensional feature vector. This shared encoder maintains consistent parameters across different tasks, enabling cross-task feature sharing and continuous learning capabilities.

[0100] B. Task-Specific Classification Head: This adopts a linear mapping structure, inputting the 256-dimensional feature vector output by the shared encoder into the classification head of the corresponding task, and mapping it to the label space dimension of the current task; after normalization by the Softmax function, the class probability is output to realize the fault type identification of the current task.

[0101] When learning a new task, a new classification head is created for that task, and only parameters relevant to that task are optimized. The classification heads for historical tasks are frozen to avoid interference with already learned tasks during incremental learning, thus effectively mitigating catastrophic forgetting. Through a federated training mechanism, each client can receive new tasks sequentially and complete local updates. The final model will retain all historical task classification heads, allowing clients to predict multiple task scenarios during the inference phase without accessing the original historical data.

[0102] To reduce invalid replays and avoid negative transfer, this invention performs physical similarity filtering on historical generators on the client side. The client locally stores the generator set obtained after global aggregation (server-side global aggregation) following training for each task. After completing local training for each task, the client uploads its local model parameters to the server. The server then globally aggregates the local model parameters from different clients and synchronously distributes the aggregated global model to all clients, eliminating the need for cross-client data transfer. For the current task... Calculate its relationship with historical tasks physical similarity :

[0103]

[0104] In the formula, Similarity weights; , respectively, represent the global range of rotational speed and load across all tasks, and are used as normalization constants. Only when (threshold) When this history generator is used, Once selected for the replay set, the client generates synthetic samples from the replay generator set to construct a replay buffer. The number of synthetic samples generated by each historical generator can be allocated according to a preset ratio to achieve selective replay and enhanced continuous learning capabilities. This selection logic can be implemented through... Figure 3 (Performance comparison chart of PA-FCL and baseline methods) Indirect verification: The model forgetting rate increases significantly when no screening is performed. Figure 3 In the subplots (b), (d), and (f) (comparison of average forgetting rates, with % on the vertical axis and method and task on the horizontal axis), the forgetting rate of PA-FCL (this invention) is much lower than that of FedCIL, MFCL, and FedAvg, proving that the screening strategy can effectively suppress forgetting.

[0105] The client will use the local real dataset Combined with the synthetic signal in the playback buffer, a hybrid training set is constructed, and a local loss function is applied. Optimize the local model, from the attached Figure 1 The local loss calculation module shows the correlation between the various loss items, and the expression for the loss function is:

[0106]

[0107] The specific meanings of each loss item are as follows:

[0108] The cross-entropy loss of the local model for the current task's real samples is used to ensure the model's accuracy in classifying fault categories for the current task. The vibration signal of the current task is input into the shared encoder and the corresponding classification head to obtain the category probability distribution, and cross-entropy is calculated with the real labels to constrain the model's classification accuracy on the current task, so that it can effectively learn new fault category features and avoid relying solely on replay samples, which would affect the performance on new tasks.

[0109] Knowledge distillation loss, weighted by physical similarity (the degree of matching between the current task and historical tasks based on rotational speed and load), is used to output the historical task classification header during the new task learning phase. This serves as a soft objective to constrain the current classification head output, thereby preventing the forgetting of learned task knowledge. Its calculation formula is:

[0110]

[0111] In the formula, for divergence, To correspond to historical tasks The output probability distribution of the frozen classification head on sample x. Predicted probability distribution for the current task classification head; by physical similarity Weighting allows historical missions that are closer to the current mission conditions to contribute more to distillation, thereby effectively reducing disaster amnesia.

[0112] Similar to the spectral consistency loss during generator training, it is used to constrain the spectral consistency of the synthesized signal, ensuring that the fault features learned by the model conform to physical laws.

[0113] The training parameters for the local model are set as follows: 10 rounds of local training are performed for each task, using the SGD optimizer, with a learning rate of... The momentum is 0.9, and the learning rate is decayed using the StepLR scheduler. The diagnostic accuracy of the trained model can be improved by adding... Figure 3 Subgraphs (a), (c), and (e) (comparison of average accuracy, y-axis %, x-axis method and task) validate that PA-FCL achieves higher accuracy on both Task 1 and Task 2 than the baseline method, reaching a maximum of 91.00%, demonstrating the model's generalization ability across different work scenarios.

[0114] 5. Global model aggregation and training loop:

[0115] After each client completes local training, it will send the optimized model parameters. Uploaded to the server. The server performs weighted aggregation based on the sample size of each client's local dataset, and updates the global model parameters. The aggregation formula is:

[0116]

[0117] in, These are the global model parameters for the (h+1)th round after aggregation. For the client The task corresponding to the current aggregation round The number of local samples; M represents the total number of samples from all clients; M represents the number of clients.

[0118] The server's generator for the current task and classification head The system caches data to support the replay and knowledge distillation of subsequent tasks; then, the server initializes the next round of tasks. The generator then enters the next round of federated training cycles until all tasks are completed. Figure 1 The server parameter aggregation module has marked this calculation logic.

[0119] This invention performs local model validation and ablation analysis on the CWRU, JNU, and XJTU datasets. When applied to the CWRU, JNU, and XJTU datasets, the average classification accuracy is no less than 86.48%, reaching a maximum of 91.00%, and the average forgetting rate is no higher than 10.54%, with a minimum of only 2.56%. The functions of each core module can be seen in the appendix. Figures 4-6 analyze:

[0120] Figures 4-6The following figures illustrate the average accuracy (blue section: Averoge Accuracy), average forgetting rate (red section: Averoge Forgetting), and runtime (green section) of CWRU, JNU, and XJTU under different ablation configurations (Full: full PA-FCL; w / o Generator: removal generator; w / o CondDistill: removal conditional distillation; w / o FreqReg: removal frequency regularization):

[0121] (1) Comparison between Full and w / oGenerator: After removing the generator, the accuracy decreased by 8%~12% and the forgetting rate increased by 5%~8%, proving the necessity of the generator for privacy playback and knowledge retention;

[0122] (2) Comparison of Full and w / oCondDistill: After removing conditional distillation, the forgetting rate increased by 6%~9%, proving the effect of knowledge distillation on inhibiting catastrophic forgetting;

[0123] (3) Comparison between Full and w / oFreqReg: After removing frequency regularization, the accuracy decreased by 5%~7%, proving that physical prior can improve the generalization ability of the model.

[0124] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for diagnosing persistent physical augmentation federation faults in complex electromechanical systems, characterized in that, Continuous fault diagnosis of complex electromechanical systems is performed based on a federated diagnostic system; the federated diagnostic system includes a server and M geographically distributed clients. The server aggregates the local model parameters uploaded by the client and generates the trained generator. With global model Distribute to various clients for continuous learning; The generator With a potential noise vector that follows a normal distribution Operating condition vector of encoded operating condition information and classification labels representing fault types The synthesized vibration signal is used as input and output. The working condition vector that encodes working condition information The subscript j corresponds to the task index, and j in the generator also represents the generator corresponding to each task. For the rotational speed and load parameters of complex electromechanical systems under the corresponding tasks; Each client corresponds to one industrial site, and the client uses a local model for tasks. For fault identification, the local model includes a shared encoder and a task-specific classification head. During federated learning, clients do not share raw data but interact through local model parameters or gradients to collaboratively optimize the global model. ; During federated learning, the client locally stores the generator set obtained after global aggregation and synchronization following training for each task. Meanwhile, the client determines the current task. With historical mission physical similarity Decide whether to use the history generator Selected for replay set, when When the playback threshold is exceeded, the history generator... Once selected for playback, the client generates synthetic samples from the playback generator set to construct a playback buffer. The number of synthetic samples generated by each historical generator is allocated according to a preset ratio.

2. The method for diagnosing persistent physical enhancement federation faults in a complex electromechanical system according to claim 1, characterized in that, The processing of the local model includes: First, the vibration signal sequence The feature vector is fed into a shared encoder to extract the feature vector. The shared encoder consists of four 1D convolutional layers. After each convolutional operation, a batch normalization layer is connected first, followed by a max pooling layer and a LeakyReLU activation function in sequence. Finally, the feature vector is output through a fully connected layer. The task-specific classification head adopts a linear mapping structure, inputting the dimensional feature vector output by the shared encoder into the classification head of the corresponding task and mapping it to the label space dimension of the current task; after normalization by the Softmax function, the class probability is output to realize the fault type identification of the current task.

3. The method for diagnosing persistent physical enhancement federation faults in a complex electromechanical system according to claim 2, characterized in that, The generator The process of synthesis based on input signals includes: S311, Condition Embedding and Fusion Stage: The working condition vector is respectively processed through a multilayer perceptron. and fault labels Encode the two encoded vectors and then fuse them with the latent noise z to form a seed for generation; S312, Adaptive Resonance Layer Stage: For seed generation, multi-layer 1D transposed convolution is used to generate the basic signal; after each 1D transposed convolution, a batch normalization layer is connected, and then the signal is processed through residual connections. S313, Fault Modulation Module Stage: The basic signal is processed using a bandpass-enhanced convolutional kernel constructed based on fault characteristic frequencies to obtain a vibration signal containing fault-specific transient signals; Finally, the output signal is normalized to the [-1,1] interval through a Conv1D layer with a tanh activation function to obtain the synthesized vibration signal, which is used as the input of the synthetic sample for subsequent federated training.

4. The method for diagnosing persistent physical augmentation federation faults in a complex electromechanical system according to claim 3, characterized in that, The bandpass-enhanced convolutional kernel, constructed based on fault feature frequencies, has its center frequency set as the target fault feature frequency. ,bandwidth A bandpass filter that covers the harmonic response range.

5. The method for diagnosing persistent physical enhancement federation faults in a complex electromechanical system according to claim 3, characterized in that, The server-side uses a composite loss function. For generator The training is performed using the following composite loss function: ， in, These are the loss weighting coefficients; The cross-entropy loss is obtained based on predictions from a global model. For batch normalized alignment loss: ， in, For the set of batch normalization layers in the model, and Representing batch normalization layers Mean and variance of activation values; This indicates that based on the normal distribution z and the working condition vector... Generate synthetic samples, This represents the actual signal sample in the client's local dataset, i.e., the original vibration signal sample; For spectral consistency loss: ， in, The envelope spectral energy at the fault characteristic frequency. For total envelope energy, For working condition vectors The calculated theoretical energy percentage; For signal smoothing loss: ， In the formula, B is the batch size, K is the number of signal channels, and L is the signal length. The sampled value of the synthesized sample signal output by the generator corresponds to the signal amplitude of the synthesized vibration signal at the i-th sample, k-th channel, and l-th time-domain sampling point.

6. The method for diagnosing persistent physical augmentation federation faults in a complex electromechanical system according to claim 5, characterized in that, Based on operating condition vector The calculated theoretical energy percentage It is obtained through the following steps: First, Hilbert envelope is calculated for the time-domain vibration signal of the calibration sample, and then FFT is performed on the envelope signal to obtain the envelope. ; At each target fault frequency and its harmonics The squared amplitude value of the integral envelope spectrum over the interval is used to obtain the frequency band energy. And calculate the total envelope energy. Then, the observed proportion is calculated for the calibration sample. For each frequency band, log-linear regression was used to fit the relationship between the operating conditions and the proportion. ; The fitted linear regression function is then used to determine the appropriate function based on the given information. Obtain the prediction function Finally, the theoretical proportions under this operating condition are obtained by normalizing the predicted values ​​of each harmonic: ,in This is the set of fault frequency bands used for constraints, i.e., all frequency band indices related to the target fault; This represents the total number of all frequency bands under the current operating conditions.

7. A method for diagnosing persistent physical augmentation federation faults in a complex electromechanical system according to any one of claims 3 to 6, characterized in that, The physical similarity as follows: ， In the formula, Similarity weights; These represent the global ranges of rotational speed and load across all tasks, respectively, and are used as normalization constants; , )and( , ( ) are historical tasks The corresponding current task The corresponding operating condition vector.

8. The method for diagnosing persistent physical enhancement federation faults in a complex electromechanical system according to claim 7, characterized in that, Its features are, The playback threshold is set to 0.

6.

9. A method for diagnosing persistent physical enhancement federation faults in a complex electromechanical system according to claim 7, characterized in that, Its features are, The process of continuous learning on the client side includes: Each client In the mission The local dataset below is ,in The original vibration signal sample For fault labels, For the client In the mission The number of samples; the client will use the local real dataset. Combined with the synthetic signal in the playback buffer, a hybrid training set is constructed, and a local loss function is applied. Optimize the local model: ， in, The cross-entropy loss is the loss of the local model for the current task's real samples. To be the same as the spectral consistency loss during generator training; For knowledge distillation loss based on physical similarity weighting: ， In the formula, for divergence, To correspond to historical tasks The output probability distribution of the frozen classification head on sample x. The predicted probability distribution for the current task classification head; For the task With the task The physical similarity between them.

10. A method for diagnosing persistent physical enhancement federation faults in a complex electromechanical system according to claim 9, characterized in that, After each client completes local training, it will send the optimized model parameters. Uploaded to the server; the server performs weighted aggregation based on the sample size of each client's local dataset, and updates the global model parameters. The aggregation formula is: in, These are the global model parameters for the (h+1)th round after aggregation. For the client The task corresponding to the current aggregation round The number of local samples; M represents the total number of samples from all clients; M represents the number of clients.

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