Fault data generation method and system based on physical constraint double-domain diffusion model

Abstract

The invention discloses a fault data generation method and system based on a physical constraint double-domain diffusion model, relates to the technical field of predictive maintenance, and solves the technical problem that an existing data generation method is easy to generate data with similar statistics but violating a fault physical mechanism when generating industrial fault data and cannot meet actual application requirements. The method comprises the following steps: capturing complementary physical characteristics of real fault data in a time domain and a frequency domain; a diffusion model is constructed, the diffusion model comprises forward diffusion and reverse denoising, an FANS mechanism is introduced in the forward diffusion process, and physical characteristics are conditionally injected in the reverse denoising process; constructing a total loss function optimization diffusion model based on energy consistency and denoising reconstruction loss to obtain a fault data generation model; the fault data generation model generates simulated fault data; according to the method, the limitation that a uniform noise scheduling scheme is adopted in a traditional DDPM is broken through, and the problem that weak fault features are damaged too early in the diffusion process of a standard DDPM is fundamentally solved.

Description

Technical Field

[0001] This invention relates to the field of predictive maintenance technology, specifically to a method and system for generating fault data based on a physically constrained dual-domain diffusion model. Background Technology

[0002] Accurate and rapid fault diagnosis is crucial for ensuring the safe operation of complex electromechanical equipment systems and minimizing downtime. In recent years, deep learning methods have made significant progress in fault diagnosis, but they face a severe data imbalance problem in practical industrial applications. Under normal conditions, equipment can operate continuously and collect a large amount of data, while fault conditions often require immediate shutdown for maintenance, resulting in extremely scarce fault samples. This data imbalance makes it difficult for deep learning models to fully learn fault characteristics, severely impacting diagnostic accuracy.

[0003] To address the imbalanced data problem, researchers have attempted to expand fault samples using data generation techniques. Generative Adversarial Networks (GANs) generate new samples through adversarial training between the discriminator and generator, but they suffer from training instability, pattern collapse, and vanishing gradients, resulting in insufficient diversity of generated samples. Variational Autoencoders (VAEs) often encounter posterior collapse, leading to blurred samples that fail to retain the fine features of fault signals. More importantly, these methods generally lack explicit modeling of the physical properties of mechanical vibration signals, potentially causing the generated data to violate fundamental physical laws and degrading the performance of downstream diagnostic algorithms.

[0004] Denoising diffusion probability model (DDPM), as an emerging generative model, has demonstrated good performance and training stability in fields such as image generation by constructing a reversible noise diffusion process. However, its direct application to industrial fault diagnosis data generation faces some challenges. Mechanical vibration signals have a highly non-uniform frequency domain energy distribution, and fault features are usually concentrated in specific frequency bands. The globally uniform noise scheduling strategy adopted by standard DDPM can prematurely destroy these weak fault features during the forward diffusion process. For example, the generation of bearing faults follows strict physical mechanisms. Inner ring faults, outer ring faults, and rolling element faults correspond to different impact modes and characteristic frequencies. Existing DDPM lacks explicit modeling of these physical constraints and may generate signals that violate the physical mechanisms. Summary of the Invention

[0005] While standard diffusion models perform well in image generation, they face numerous challenges when directly applied to mechanical vibration signals. The frequency domain energy distribution of mechanical vibration signals is highly non-uniform, with fault features often concentrated in specific frequency bands. Standard diffusion models employ a globally uniform noise scheduling strategy, causing these weak fault features to be prematurely destroyed during forward diffusion, making accurate recovery difficult during reverse generation. More importantly, industrial faults follow strict physical laws; different fault types correspond to different impact modes and characteristic frequencies, but existing generation models generally lack explicit modeling of these physical constraints. Furthermore, when a generation model contains a dual-branch structure in both the time and frequency domains, the lack of explicit constraints allows each branch to independently optimize its reconstruction objective, leading to generated signals that violate the law of energy conservation and are physically unrealizable. To address these issues, this application proposes a fault data generation method and system based on a physically constrained dual-domain diffusion model.

[0006] A fault data generation method based on a physically constrained dual-domain diffusion model includes the following steps:

[0007] Step 1: Extract the complementary physical features of the target's real fault data in the time and frequency domains;

[0008] Step 2: Construct a diffusion model. The generation process of the diffusion model includes a forward diffusion process and a reverse denoising process. The forward diffusion process introduces the FANS mechanism, and the reverse denoising process injects conditional constraints containing the physical features. The FANS mechanism refers to adaptively adjusting the noise intensity based on the spectral energy distribution.

[0009] Step 3: Construct a total loss function by combining energy consistency loss and denoising reconstruction loss, and optimize the diffusion model based on the total loss function to obtain the fault data generation model; the fault data generation model generates target simulated fault data based on the target real fault data.

[0010] Specifically, the proposed Frequency Adaptive Noise Scheduling (FANS) mechanism overcomes the limitations of uniform noise scheduling in traditional DDPM, preserving weak fault characteristics for a longer period during the diffusion process. Combined with a dual-domain conditional injection module, the physical characteristics of the target domain are used as conditions to guide the generation process. This ensures the physical consistency between the generated samples and the actual fault evolution patterns, thus avoiding statistically valid but physically incompatible outputs. Finally, the Passevar Relative Difference (PRDT) term is proposed to enforce energy consistency of the denoised signal in both the time and frequency domains, thereby addressing the limitation of DDPM, which only fits the time-domain waveform without considering frequency-domain characteristics.

[0011] Further, step 1 includes:

[0012] A hierarchical convolutional architecture is used in the temporal branch to capture temporal features at different scales as temporal features;

[0013] Logarithmic power spectrum is calculated on the frequency domain branch to enhance weak fault harmonics, and then logarithmic power spectrum features are extracted as frequency domain features.

[0014] Finally, the time-domain and frequency-domain features are integrated and refined to obtain physical features based on physical mechanisms.

[0015] Furthermore, the hierarchical convolutional architecture includes two convolutional layers. The first convolutional layer is used to capture coarse temporal features, including fault periodicity and overall waveform structure. The second convolutional layer is used to extract fine temporal features, including the extraction of transient impulses and envelope modulation.

[0016] Furthermore, the logarithmic power spectrum features include characteristic frequencies, harmonic families, and resonance bands.

[0017] Further, step 2 includes: defining the forward diffusion process as a T-step Markov chain, in which frequency-adaptive noise determined by the FANS mechanism is introduced;

[0018] The reverse denoising process uses a denoising network based on the U-Net architecture for reverse generation. Through a multi-scale adaptive injection mechanism, physical features are explicitly integrated into each layer of the U-Net.

[0019] Furthermore, the FANS mechanism includes:

[0020] For the signal spectrum, frequency importance weights are defined to quantify the contribution of each frequency, with fault characteristic frequency band values ​​tending to 1 and background noise values ​​tending to 0.

[0021] Then, during the adaptive noise modulation process, the frequency selective mask is defined as a function that takes values ​​in the frequency domain. This function reduces the noise intensity of the high-energy fault band by controlling the protection strength and frequency importance weight.

[0022] The expression for the modulation noise in the frequency domain is obtained by using a frequency-selective mask, and finally, the expression is reversed back to the time domain to obtain the frequency-adaptive noise.

[0023] Furthermore, the multi-scale adaptive injection mechanism includes determining the region or frequency band that needs physical feature guidance based on the feature distribution of the currently generated signal through a gating term.

[0024] Furthermore, the construction energy consistency loss includes:

[0025] Collect the noise signal and predicted noise at each time step of the inverse denoising process of the diffusion model, and derive and estimate the predicted value of the initial signal in reverse.

[0026] The time-domain and frequency-domain energy of the initial signal prediction values ​​are calculated separately. Based on the calculation results, a relative difference loss function is constructed as the energy consistency loss to quantify the difference between the two. Finally, the denoising reconstruction loss and the energy consistency loss are weighted to obtain the total loss function to optimize the diffusion model.

[0027] A fault data generation system based on a physically constrained dual-domain diffusion model includes:

[0028] The first processing module is used to obtain the actual fault data of the target object;

[0029] The second processing module is used to input the target real fault data into the fault data generation model, and obtain the target simulated fault data output by the target fault data generation model. The fault data generation model is a diffusion model. First, the FANS mechanism is introduced in the forward diffusion process, and physical features are conditionally injected in the reverse denoising process. Finally, the total loss function is constructed and optimized based on energy consistency and denoising reconstruction loss. The FANS mechanism refers to adaptively adjusting the noise intensity based on the spectral energy distribution. The physical features are a combination of time-domain features and frequency-domain features extracted from the real fault data.

[0030] The beneficial effects of this invention include:

[0031] This invention proposes a data generation method for imbalanced data (PD-DDPM), which ensures that the generated samples maintain physical consistency with the actual fault evolution patterns, avoiding the generation of statistically similar data that violates the physical mechanisms of faults. It overcomes the limitations of traditional DDPM's uniform noise scheduling scheme, fundamentally solving the problem of standard DDPM prematurely destroying weak fault characteristics during the diffusion process. Furthermore, the introduction of a PRDT regularization term achieves energy conservation between the time and frequency domains. Extensive experiments based on three sets of bearing datasets fully validate the effectiveness and generalization ability of the PD-DDPM method, achieving classification accuracies of 97.64%, 98.91%, and 98.06%, respectively, significantly outperforming other methods and addressing the diagnostic problem of insufficient fault samples in industrial environments. Attached Figure Description

[0032] Figure 1 This is a framework diagram of the fault data generation method based on a physically constrained dual-domain diffusion model involved in the embodiments of this application.

[0033] Figure 2 This is a flowchart illustrating the specific process of fault data generation method based on a physically constrained dual-domain diffusion model, as described in the embodiments of this application.

[0034] Figure 3 This is the FANS frequency adaptive weighting graph involved in the embodiments of this application.

[0035] Figure 4 This is the CWRU bearing failure test bench involved in the embodiments of this application.

[0036] Figure 5 This is a real bearing failure test bench involved in the embodiments of this application.

[0037] Figure 6 This is the KAt bearing failure test bench involved in the embodiments of this application.

[0038] Figure 7 This represents the maximum mean difference between the various methods described in the embodiments of this application applied to the CWRU bearing fault dataset.

[0039] Figure 8 This represents the maximum mean difference between the various methods described in the embodiments of this application applied to a real bearing fault dataset.

[0040] Figure 9 This represents the maximum mean difference between the various methods described in the embodiments of this application applied to the KAt bearing fault dataset.

[0041] Figure 10 These are the time-domain scores, frequency-domain scores, and self-similarity scores of the various methods involved in the embodiments of this application applied to the CWRU bearing fault dataset.

[0042] Figure 11 These are the time-domain scores, frequency-domain scores, and self-similarity scores of the various methods involved in the embodiments of this application applied to a real bearing fault dataset.

[0043] Figure 12 These are the time-domain scores, frequency-domain scores, and self-similarity scores of the various methods involved in the embodiments of this application applied to the KAt bearing fault dataset.

[0044] Figure 13 The accuracy of the various methods involved in the embodiments of this application on the unbalanced dataset of the CWRU bearing fault dataset.

[0045] Figure 14 The accuracy of the various methods involved in the embodiments of this application when applied to an unbalanced dataset of real bearing fault datasets.

[0046] Figure 15 The accuracy of the various methods involved in the embodiments of this application on the unbalanced dataset of the KAt bearing fault dataset. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0048] Example 1

[0049] The following is in conjunction with the appendix Figure 1 Specific embodiments of the present invention will be described in detail;

[0050] A fault data generation method based on a physically constrained dual-domain diffusion model includes the following steps:

[0051] Step 1: Dual-domain feature extraction

[0052] To address the lack of physical mechanism constraints in standard DDPM, a dual-domain extractor for extracting physical conditions was designed. This extractor can explicitly capture the complementary physical characteristics of real faults in the time and frequency domains. By transforming the original vibration signal into a physically meaningful condition vector, the diffusion process is guided. The specific process is as follows: Figure 2 As shown.

[0053] 1) Temporal feature extraction

[0054] The temporal branch employs a hierarchical convolutional architecture to capture temporal features at different scales:

[0055] Designed to capture transient characteristics and periodic patterns of impact responses, a multi-scale convolutional architecture is employed to capture fault features at different time scales: the first convolutional layer uses a 16×16 convolutional kernel with a stride of 4 to capture coarse time-domain features such as fault periodicity and overall waveform structure. The second layer uses an 8×8 convolutional kernel with a stride of 2 to refine the representation of the previous layer by extracting fine features such as transient impact and envelope modulation.

[0056]

[0057]

[0058] After hierarchical feature extraction, an adaptive pooling layer and a projection layer are used to aggregate multi-scale information.

[0059]

[0060]

[0061] in To refine the time-domain features, comprehensive time-domain physical information, including impact intensity, periodic patterns, and transient characteristics, was encoded. Representing the set of real numbers, meaning each value in the vector, and dc / 2 representing the dimension of the vector, this indicates that the time-domain features are compressed or mapped into a vector of length . One-dimensional array

[0062] 2) Frequency domain feature extraction

[0063] Calculate the logarithmic power spectrum of the frequency domain branch to enhance weak fault harmonics:

[0064]

[0065] A three-layer fully connected network is used to learn logarithmic power spectrum features, including characteristic frequencies, harmonic families, and resonance bands. Frequency embedding. The aforementioned logarithmic power spectrum features are encoded as frequency domain features. This indicates the original fault vibration signal. Perform a Fourier transform to convert it from the time domain to the frequency domain; It is a very small normal number used to prevent the occurrence of 0 in parentheses during logarithmic operations.

[0066] 3) Dual-domain fusion

[0067] Finally, by integrating and refining the time-domain and frequency-domain features, a conditional vector based on physical mechanisms is obtained:

[0068]

[0069] in, This serves as a comprehensive physical prior, guiding the subsequent diffusion process. Specifically, this physical condition vector... The data will be fed into each layer of the denoising network (U-Net) as a global constraint input for the reverse denoising process in step three. Through the gating mechanism described below, it is ensured that the generated data strictly follow the shock and resonance physical features extracted here.

[0070] Step 2: Frequency Adaptive Noise Scheduling Mechanism

[0071] During forward diffusion, the standard DDPM algorithm applies Gaussian noise uniformly to all frequency components, causing weak fault features to gradually degrade at the same rate as the background noise. This fundamentally conflicts with the frequency localization characteristic of real faults—diagnostic information is concentrated within specific features.

[0072] To address this limitation, a FANS mechanism is proposed, which adaptively adjusts noise intensity based on spectral energy distribution. The specific process is as follows: Figure 2 As shown. The visualization results of the noise-weighted result are shown below. Figure 3 .

[0073] For the signal spectrum Frequency importance weights are defined to quantify the contribution of each frequency, with fault characteristic frequency band values ​​close to 1 and background noise values ​​close to 0. The calculation formula is as follows:

[0074]

[0075] In adaptive noise modulation, the frequency-selective mask is defined as:

[0076]

[0077] in Control the protection intensity to reduce the noise intensity of high-energy fault zones to 50%.

[0078] The expression for modulation noise in the frequency domain is:

[0079]

[0080] It is standard, random Gaussian white noise. In a typical diffused white noise model (DDPM), this noise would be uniformly distributed across all signals. Reversing the direction back to the time domain yields adaptive noise. This noise retains its fault characteristics during propagation. This generated frequency-adaptive noise... This will directly replace the Gaussian white noise in the standard diffusion model, used in the forward diffusion process described in step three. By pre-adjusting the noise distribution in this step, it ensures that the high-frequency resonance bands containing key fault information are not excessively submerged during the subsequent noise addition process in step three, laying the foundation for accurate reconstruction.

[0081] The dual-domain conditional and FANS mechanisms are integrated into a unified diffusion framework, including forward diffusion with FANS modulation and inverse denoising with conditional injection.

[0082] 1) The forward diffusion process of the FANS modulation is defined as a T-step Markov chain:

[0083]

[0084] in This represents the frequency-adaptive noise determined by the mask M(f).

[0085] 2) Denoising network using U-Net architecture Reverse generation is performed. The U-Net denoising network used in this embodiment mainly consists of an encoder (downsampling path), a bottleneck layer, and a decoder (upsampling path). Features are fused between layers through skip connections.

[0086] 1. Encoder Section (Downsampling): The input signal (1 channel) is first expanded to 64 channels through a convolutional layer. The encoder contains four downsampling stages, each consisting of two stacked 3×3 convolutional layers for feature extraction and a 2×2 downsampling operation to reduce the feature map size. As the network depth increases, the number of feature channels increases sequentially from 64 to 128, 256, and finally reaches 512 channels at the bottleneck layer to extract high-level features.

[0087] 2. Decoder Section (Upsampling): The decoder also contains four upsampling stages to restore the signal size. Each stage first upsamples the feature map through a 4×4 transposed convolutional layer, enlarging the feature map size and halving the number of channels. The upsampled feature map is then concatenated with the corresponding layer's feature map from the encoder via skip connections to fuse shallow detail features and deep semantic features. The fused features are then refined again through two 3×3 convolutional layers.

[0088] 3. Output and Conditional Injection: After progressive upsampling, the number of channels is restored from 512 to 64. Finally, a 1×1 convolutional layer maps the number of channels back to 1, outputting the predicted noise. During this process, the physical feature conditional vector is explicitly integrated into the intermediate layers of the network through the conditional concatenation module, and the features are physically corrected using the aforementioned gating mechanism. Figure 1 As shown in the illustration, the network also includes 1×1 convolutional layers for feature alignment and projection layers for changing feature dimensions.

[0089] To ensure that the generated fault data strictly follows the actual physical mechanism, this invention uses a multi-scale adaptive injection mechanism to inject the dual-domain physical condition vector extracted in step one, which includes time-domain impact characteristics and frequency-domain resonance features. It is explicitly integrated into every layer of U-Net.

[0090] Specifically, in each feature level l of U-Net, the physical condition vector Instead of being used as a simple concatenation input, the feature representation z of the current layer is dynamically modified through an adaptive gating mechanism. l The fusion formula is as follows:

[0091]

[0092] Where: z l These are the original intermediate features of the l-th layer of U-Net; This is the projection matrix, used to represent the global physical conditions. Mapped to the current layer feature z l Same dimensional space;

[0093] Gated items Based on the characteristic distribution of the currently generated signal, it automatically determines which time-domain or frequency-domain features require guidance from physical mechanisms. When the model identifies that the currently generated waveform features are ambiguous or lack physical regularity, the gating term is increased, forcibly introducing physical mechanisms. The physical prior information in the data allows for physical correction of features; this mechanism enables shallow networks to rely on... The temporal components in the data accurately reproduce local impact details, while deep networks can utilize... The frequency domain component constrains the global energy distribution structure, thereby ensuring that the final generated fault data conforms to the real physical fault evolution law in both the time and frequency domains.

[0094] Step 3: Regularize the loss function based on the Parseval theorem

[0095] After completing the physical condition-based inverse denoising and outputting the predicted signal x0 in step three, this step applies regularization constraints to the output of step three to further verify the consistency of the generated signal at the physical energy level. Standard DDPM training only optimizes the time-domain reconstruction and does not impose any constraints on the frequency-domain structure. This can lead to the generated signal potentially matching the time-domain waveform but violating the principle of physical energy conservation across different domains. To address this, regularization based on Parseval's theorem is introduced to enforce energy consistency. The detailed process is as follows... Figure 2 As shown.

[0096] 1) Energy conservation

[0097] According to Passevar's theorem, for a physically real vibration signal, its total energy in the time domain should be exactly equal to its total energy in the frequency domain. To apply this fundamental law of physical conservation to discrete signals, the energy conservation relation is defined as follows:

[0098]

[0099] Where x[n] is the discrete-time signal, X[k] is its corresponding discrete Fourier transform (DFT) frequency domain signal, and N is the signal length. The left side of the equation represents the total energy in the time domain, and the right side represents the normalized total energy in the frequency domain.

[0100] At each time step t of the backdiffusion, in order to assess whether the current generated quality conforms to physical laws, it is necessary to first consider the noise signal x at the current moment. t and network prediction noise The initial signal prediction value is derived and estimated in reverse. The calculation formula is as follows:

[0101]

[0102] Based on the above-estimated signal Calculate its time-domain energy respectively and frequency domain energy To quantify the degree of physical violation between the two, a relative difference loss function is constructed. :

[0103]

[0104] 2) Complete training objectives

[0105] To balance the statistical distribution fidelity of the generated signal with the consistency of the physical mechanism, the final total loss function... It consists of a weighted sum of denoising reconstruction loss and energy conservation regularization term:

[0106]

[0107] The first term is the standard mean square error loss, i.e., the denoising and reconstruction loss, used to ensure the accuracy of the generated time-domain waveform; the second term... For physical constraints, This is the balance coefficient. By jointly optimizing this objective function, the data generated by the neural network is forced to maintain a high degree of consistency in both statistical realism and physical energy structure.

[0108] Using bearing failure as the target, a corresponding bearing dataset was selected for experimental verification, as follows:

[0109] I. Selecting the experimental dataset:

[0110] This invention has been extensively validated on three bearing datasets (CWRU, self-built test bench, and KAT). Experimental results show that the PD-DDPM method has significantly better fault diagnosis performance than existing methods in data imbalance scenarios.

[0111] Experiment 1: Case Western Reserve University Public Dataset

[0112] Experimental validation was conducted using a publicly available bearing dataset from Case Western Reserve University (CWRU). Data was collected from a motor drive system, and the test bearing was an SKF 6205-2RS deep groove ball bearing. Different degrees of single-point faults were introduced into the inner ring, outer ring, and rolling elements, with fault diameters of 7 / 14 / 21 mils. The experiment selected data from the drive-end bearing, including one normal state and nine fault states. Figure 4The CWRU test bench is shown. This platform mainly consists of an induction motor, fan-end bearing, drive-end bearing, torque sensor and encoder, and dynamometer. Table 1 shows detailed information on the data used in this example.

[0113] Table 1 CWRU Data Details

[0114]

[0115] The original time series was divided into 256 data segments using a sliding window method with a sliding step size of 128. Z-score normalization was used for preprocessing. The dataset partitioning simulated a real-world industrial scenario, with ample normal data and scarce fault data. The normal category maintained 500 samples across all imbalance ratios. For each fault category, a generative model was trained using 3 real samples, and the training set was then expanded with generated samples. The test set had a fixed 100 real samples per class to ensure the objectivity of the evaluation. Table 2 summarizes the dataset configurations under different imbalance ratios.

[0116] Table 2 Introduction to Imbalanced Datasets

[0117]

[0118] Experiment 2: Building a custom bearing fault dataset

[0119] This dataset is in Figure 5 Real vibration data collected on a real bearing test bench (shown in the image) were used for experimental verification. This test bench consists of a drive motor, bearings, and a magnetic powder brake. The test bench uses a UPH206 rolling bearing with an inner diameter of 30 mm. The sampling frequency was set to 10 kHz. The experimental platform's fault types were designed to cover outer ring faults, inner ring faults, rolling element faults, and combined inner and outer ring faults. Vibration sensors were radially mounted on replaceable bearing housings, and vibration signals were continuously collected for each operating condition, with a sampling time of approximately 60 seconds. The unbalanced dataset followed a CWRU configuration, and Table 3 summarizes the detailed configuration of this dataset.

[0120] Table 3. Details of data for self-built test benches

[0121]

[0122] Experiment 3: Paderborn University KAT Dataset

[0123] This experiment was conducted using the publicly available bearing dataset from Paderborn University's KAt-DataCenter, such as... Figure 6As shown, the corresponding KAT bearing fault test bench consists of a drive motor, a torque measuring shaft, a rolling bearing test module, a flywheel, and a load motor. The original sampling frequency was 64 kHz, which was downsampled to 10 kHz to maintain consistency with the previous experiments and improve computational efficiency. Data was selected under the conditions of 1500 rpm, 0.7 N·m torque, and 1000 N radial load. Each type of actual damage was divided into initial and severe stages according to the degree of degradation: inner ring (IR-1 / 2), outer ring (OR-1 / 2), and combined inner and outer ring (IOR-1 / 2). The downsampled vibration signal was segmented into data segments of length 256 using the sliding window method, with a sliding step size of 128. Z-score normalization was performed. The dataset configuration followed the unbalanced ratio design of Experiment 1. 500 samples were reserved for classifier training under normal conditions; the sample configuration strategy for the 6 types of fault conditions was consistent with the previous experiments. Table 4 shows the detailed information of the data used in this experiment.

[0124] Table 4. Details of KAt Data

[0125]

[0126] II. Selection of control method:

[0127] 2.1 To fully verify the performance advantages of PD-DDPM, this invention selects five representative deep generative models as comparison methods:

[0128] The basic DDPM (DDPM) method employs a standard model architecture and a linear noise scheduling strategy. This method serves as a benchmark for ablation experiments to evaluate the overall contribution of the three innovative aspects proposed in this paper.

[0129] Generative Adversarial Networks (GANs): Employ the standard GAN framework. The generator uses a fully connected network, while the discriminator uses a multilayer perceptron structure.

[0130] Deep Convolutional Generative Adversarial Network (DCGAN): Based on GAN, a convolutional structure is introduced. The generator uses transposed convolution for upsampling, and the discriminator uses standard convolution for feature extraction.

[0131] Adversarial Autoencoders (AAEs): Combining the advantages of variational autoencoders and adversarial training, they use discriminators to constrain the latent spatial distribution.

[0132] Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP): This network uses Wasserstein distance as the optimization objective and enhances training stability through a gradient penalty term.

[0133] All control methods were trained on the same dataset configuration. To ensure fair comparison, the training steps for each method were set to 2000 steps, and the batch size was 16.

[0134] III. Generative Model Training and Evaluation

[0135] In the model training and quality evaluation section, the three experiments are summarized together. All experiments used only 20 real samples per fault type as training data and followed the same training procedure: first, a physics-aligned dual-domain condition extractor was trained to extract and store physical feature vectors related to each fault type; then, a diffusion model was trained to complete the generation task. All comparison methods were trained under the same 20-sample condition, following their respective standard procedures.

[0136] For data generation quality assessment, a unified four-dimensional comprehensive evaluation was adopted: Statistical Consistency (MMD), Temporal Similarity (DTW), Frequency Domain Fidelity (SpecScore), and Sample Diversity (SelfSim). The comparison results of each method are detailed in Table 5-7, where "↑" indicates greater similarity and "↓" indicates even greater similarity. The results of this method are marked in bold. Figure 7-12 The specific results of each comparison method under each type of fault are summarized. Among them, Figure 7 The maximum mean difference between the various methods involved in the embodiments of this application on the CWRU bearing fault dataset; Figure 8 This represents the maximum mean difference between the various methods involved in the embodiments of this application on a real bearing failure dataset; Figure 9 The maximum mean difference between the various methods involved in the embodiments of this application on the KAt bearing fault dataset; Figure 10 The time-domain score, frequency-domain score, and self-similarity score of the various methods involved in the embodiments of this application on the CWRU bearing fault dataset; Figure 11 The time-domain score, frequency-domain score, and self-similarity score of the various methods involved in the embodiments of this application on a real bearing fault dataset; Figure 12 These are the time-domain scores, frequency-domain scores, and self-similarity scores of the various methods involved in the embodiments of this application on the KAt bearing fault dataset.

[0137] Specifically, Figure 7-12The values ​​represent the index values ​​for each type of fault. Table 5-7 lists the average index values ​​for all categories. As can be seen, across multiple datasets, the PD-DDPM method performs best across all fault categories, significantly outperforming mainstream GAN-based methods. On the CWRU dataset, PD-DDPM achieves an MMD score of 0.1698, far lower than the basic DDPM's 0.2347 and GAN's 0.4177. This indicates that the generated simulated fault data is statistically closest to the real data. On the KAT dataset, PD-DDPM achieves the highest score of 0.9814, significantly outperforming GAN (0.8795) and DDPM (0.8858), demonstrating its highly accurate reconstruction of temporal features such as transient shocks. PD-DDPM maintains the highest self-similarity scores across all three datasets, indicating that while improving fidelity, the generated samples possess good diversity and generation stability. PD-DDPM achieves higher quality generation results in terms of distribution fitting, time-frequency consistency, and frequency domain structure preservation. At the same time, it maintains high fidelity without sacrificing sample diversity, demonstrating good generation stability and generalization ability.

[0138] Table 5 Evaluation Indicators for Each CWRU Model

[0139]

[0140] Table 6 Evaluation Indicators for Each Model of the Self-Built Test Rig

[0141]

[0142] Table 7 Evaluation Indicators for Each KAt Model

[0143]

[0144] IV. Classifier Training and Diagnosis

[0145] In the imbalanced classification experiments, to eliminate the influence of differences in classifier structure on the results, all methods uniformly used the same 1D convolutional neural network for classification. This network consists of three convolutional blocks, each followed by batch normalization, ReLU activation, and max pooling operations in sequence. Ten independent experiments were conducted for each imbalance ratio, with the test set fixed at 100 real samples per class to ensure the comparability and stability of the experimental results.

[0146] In the imbalanced classification experiment, 500 real samples from the normal state and 3 real samples from each fault type were used as the training set. The number of generated samples for each fault type gradually increased from 2 to 497, causing the imbalance ratio to gradually decrease from 1:100 to 1:1. Specific details are shown in Table 2. Experimental results are as follows: Figure 13-15 As shown, where Figure 13 The accuracy of the various methods involved in the embodiments of this application on the imbalanced dataset of the CWRU bearing fault dataset; Figure 14 The accuracy of the various methods involved in the embodiments of this application on an imbalanced dataset of real bearing failure datasets; Figure 15 The accuracy of the various methods involved in the embodiments of this application on the unbalanced dataset of the KAt bearing fault dataset.

[0147] It can be seen that the proposed method achieves optimal performance in all imbalanced scenarios. Figure 13 For example, in a 1:10 scenario, only 47 generated samples are needed to achieve an accuracy of 94.08%, which is 7.5% higher than DDPM; in a near-balanced 1:1 scenario, the accuracy reaches 97.64%, significantly outperforming other methods. It is evident that the model (Ours) proposed in this embodiment exhibits superior performance under all test conditions. Although these three sets of experiments are based on different datasets, they collectively validate the classification accuracy of each generative model when handling imbalanced data. At imbalance ratios of 1:50 and above, it not only surpasses traditional GAN, DCGAN, and WGAN-GP models but also outperforms the basic DDPM and AAE models. As the dataset gradually becomes balanced (e.g., at a 1:1 ratio), the accuracy approaches the ideal level. This indicates that the proposed method can effectively capture the key features of the data when generating samples. Furthermore, the consistent performance across different datasets demonstrates its good generalization ability. Whether on datasets with large differences in data distribution or in scenarios with complex variations in sample features, this method maintains stable performance, which is particularly important in practical applications.

[0148] V. Ablation Experiment

[0149] Compared to traditional DDPM, the PD-DDPM proposed in this embodiment incorporates three key improvement strategies: Frequency Adaptive Noise Scheduling (FANS), a physically constrained dual-domain conditional injection module, and a Parseval theorem-based regularization term (PRDT). To further investigate the importance of each component and its independent contribution to fault diagnosis performance, ablation studies were conducted on four configurations:

[0150] (1) DDPM: Adopts the standard diffusion probability model. Uses a linear noise scheduling strategy and standard MSE loss. Does not include any special design for mechanical vibration signals.

[0151] (2) PC-DDPM (Physics-Constrained Dual-domain DDPM): A dual-domain condition injection module that integrates physical constraints on the basis of DDPM. By extracting impact interval features in the time domain branch and resonance peak features in the frequency domain branch, the physical mechanism of bearing failure is explicitly injected into the generation process.

[0152] (3) FPC-DDPM (FANS-enabled Physics-Constrained Dual-domain DDPM): Based on PD-DDPM, a FANS mechanism is further introduced. The noise intensity is adaptively adjusted according to the energy distribution of the signal spectrum to selectively protect the fault characteristic frequency band.

[0153] (4) PD-DDPM (Physics-Contrained Dual-Domain Denoising Diffusion Probabilistic Model): The complete proposed method. It integrates all three innovations. It introduces an additional PRDT regularization term on top of FPC-DDPM. It forces the network to learn a physically consistent generation process, ensuring energy conservation in the time and frequency domains.

[0154] Ablation experiments were conducted on the CWRU dataset. The same 1:10 imbalanced dataset configuration as the main experiment was used. To eliminate the influence of randomness, each configuration was run five times independently.

[0155] Table 8 compares the four configurations in terms of both generation quality and diagnostic performance. Fault data generated by the four data generation algorithms were used to expand the original training set to obtain different simulated training sets. Then, the same standard 1D convolutional neural network (1D CNN) was trained on each of these simulated training sets to obtain the final classification model corresponding to each data generation algorithm. Finally, classification tests were conducted on a real test set to obtain diagnostic accuracy. PD-DDPM achieved a classification accuracy 6.2% higher than DDPM, while all generation metrics were improved. These results indicate that explicitly modeling the physical characteristics of bearing faults allows the generated samples to better capture real fault evolution patterns. Integrating FANS into PC-DDPM further improved the accuracy of FPC-DDPM by 0.62%. FANS, through a frequency importance weighting mechanism, applies lower noise intensity to high-energy frequencies, preventing weak features from being prematurely destroyed during forward diffusion. The complete PD-DDPM model achieved a classification accuracy of 94.08%, an improvement of 0.72% and 7.54% compared to FPC-DDPM and the baseline DDPM, respectively.

[0156] To verify the effectiveness of the PRDT regularization term, Table 9 compares the time-frequency energy consistency of FPC-DDPM (without PRDT) and PD-DDPM (with PRDT) in nine types of CWRU faults using the Band Energy Conservation Error (BECE) index. This index divides the spectrum into five uniform frequency bands, calculates the time and frequency domain energy of each band, and measures the distribution consistency through relative error. A lower BECE value indicates a better fit to physical principles. The BECE value range for real vibration data is 10⁻. 6 Up to 10⁻ 7 This confirms that it conforms to Passevar's theorem. In contrast, the FPC-DDPM without PRDT produces a BECE value of 0.4715, indicating a severe time-frequency energy imbalance and a physically unrealizable signal. After introducing PRDT, PD-DDPM reduces BECE to 0.0019, achieving a reduction of 99.58%, which is close to the level of real data, fully validating the effectiveness of PRDT.

[0157] Tables 8 and 9 together demonstrate that the three innovations enable PD-DDPM to achieve optimal performance across all evaluation dimensions.

[0158] Table 8. Results of Ablation Experiment Accuracy and Evaluation Indicators

[0159]

[0160] Table 9. Validation of the effectiveness of PRDT in ablation experiments.

[0161]

[0162] Example 2

[0163] A fault data generation system based on a physically constrained dual-domain diffusion model includes a first processing module for acquiring the target real fault data corresponding to the target object.

[0164] The second processing module is used to input the target real fault data into the fault data generation model, and obtain the target simulated fault data output by the target fault data generation model, wherein;

[0165] The fault data generation model is a diffusion model. First, the FANS mechanism is introduced in the forward diffusion process. Then, physical features are conditionally injected in the reverse denoising process. Finally, the total loss function is constructed and optimized based on energy consistency and denoising reconstruction loss. The FANS mechanism refers to adaptively adjusting the noise intensity based on the spectral energy distribution. The physical features are a combination of time-domain features and frequency-domain features extracted from real fault data.

[0166] The embodiments described above merely illustrate specific implementation methods of this application, and while the descriptions are detailed and specific, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the technical solution of this application, and these modifications and improvements all fall within the scope of protection of this application.

Claims

1. A fault data generation method based on a physically constrained dual-domain diffusion model, characterized in that, Includes the following steps: Step 1: Extract the complementary physical features of the target's real fault data in the time and frequency domains; Step 2: Construct a diffusion model. The generation process of the diffusion model includes a forward diffusion process and a reverse denoising process. The forward diffusion process introduces the FANS mechanism, and the reverse denoising process injects conditional constraints containing the physical features. The FANS mechanism refers to adaptively adjusting the noise intensity based on the spectral energy distribution. Step 3: Construct a total loss function by combining energy consistency loss and denoising reconstruction loss, and optimize the diffusion model based on the total loss function to obtain the fault data generation model; the fault data generation model generates target simulated fault data based on the target real fault data.

2. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 1, characterized in that, Step 1 includes: A hierarchical convolutional architecture is used in the temporal branch to capture temporal features at different scales as temporal features; Logarithmic power spectrum is calculated on the frequency domain branch to enhance weak fault harmonics, and then logarithmic power spectrum features are extracted as frequency domain features. Finally, the time-domain and frequency-domain features are integrated and refined to obtain physical features based on physical mechanisms.

3. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 2, characterized in that, The hierarchical convolutional architecture includes two convolutional layers. The first convolutional layer is used to capture coarse temporal features, including fault periodicity and overall waveform structure. The second convolutional layer is used to extract fine temporal features, including the extraction of transient impulses and envelope modulation.

4. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 2, characterized in that, The logarithmic power spectrum features include characteristic frequencies, harmonic families, and resonance bands.

5. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 1, characterized in that, Step 2 includes: defining the forward diffusion process as a T-step Markov chain, in which frequency-adaptive noise determined by the FANS mechanism is introduced; The reverse denoising process uses a denoising network based on the U-Net architecture for reverse generation. Through a multi-scale adaptive injection mechanism, physical features are explicitly integrated into each layer of the U-Net.

6. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 1, characterized in that, The FANS mechanism includes: For the signal spectrum, frequency importance weights are defined to quantify the contribution of each frequency, with fault characteristic frequency band values ​​tending to 1 and background noise values ​​tending to 0. Then, adaptive noise modulation is performed, and the frequency selective mask is defined as a function that takes values ​​in the frequency domain. This function reduces the noise intensity of the high-energy fault band by controlling the protection strength and frequency importance weight. The expression for the modulation noise in the frequency domain is obtained by using a frequency-selective mask, and finally, the expression is reversed back to the time domain to obtain the frequency-adaptive noise.

7. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 5, characterized in that, The multi-scale adaptive injection mechanism includes determining the region or frequency band that needs physical feature guidance based on the feature distribution of the currently generated signal through a gating term.

8. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 1, characterized in that, The energy consistency loss during construction includes: Collect the noise signal and predicted noise at each time step of the inverse denoising process of the diffusion model, and derive and estimate the predicted value of the initial signal in reverse. The time-domain energy and frequency-domain energy of the initial signal prediction value are calculated separately. Based on the calculation results, a relative difference loss function is constructed as the energy consistency loss to quantify the difference between the two.

9. The fault data generation method based on a physically constrained dual-domain diffusion model according to claim 1, characterized in that, The diffusion model is the Denoising Diffusion Probability Model (DDPM).

10. A fault data generation system based on a physically constrained dual-domain diffusion model, characterized in that, include: The first processing module is used to obtain the actual fault data of the target object; The second processing module is used to input the target real fault data into the fault data generation model, and obtain the target simulated fault data output by the target fault data generation model. The fault data generation model is a diffusion model. First, the FANS mechanism is introduced in the forward diffusion process, and physical features are conditionally injected in the reverse denoising process. Finally, the total loss function is constructed and optimized based on energy consistency and denoising reconstruction loss. The FANS mechanism refers to adaptively adjusting the noise intensity based on the spectral energy distribution. The physical features are a combination of time-domain features and frequency-domain features extracted from the real fault data.

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