Failure identification method under limited sample for generating vibration data based on frequency domain transformation

Abstract

The invention discloses a fault identification method for generating vibration data based on frequency domain transformation under a finite sample. The method comprises the following steps: collecting multiple types of fault vibration signals and extracting frequency domain spectrum characteristics; a forward diffusion stochastic differential equation based on mirror image Brownian motion is constructed, and original spectral distribution is converted into Gaussian prior distribution through progressive noise injection; training a gradient network by adopting a fractional matching criterion, and realizing spectrum feature reconstruction by combining a reverse stochastic differential equation and a Langevin dynamic sampling strategy; and the generated sample and original data are spliced and then input into a spectrum feature lexical element Transform model, local resonance frequency band feature extraction is enhanced through a multi-head attention mechanism, and finally fault identification is realized through coding, decoding and linear classification. According to the method, the problem of low fault identification precision of the rotating machinery in a data scarce scene is effectively solved, and a high-reliability data enhancement and feature decoupling scheme is provided for an industrial equipment intelligent diagnosis system.

Description

Technical Field

[0001] The present invention relates to rotating machinery fault and damage identification, and in particular to a fault identification method under finite samples based on frequency domain transformation to generate vibration data. Background Art

[0002] In the field of industrial machinery health monitoring, vibration signal analysis has become a cornerstone technology for early fault detection and diagnosis. As a core method of predictive maintenance strategies, this technology provides a key means for analyzing the dynamic behavior of rotating components such as bearings, gears, and shafting. By capturing subtle anomalies in vibration patterns, engineers can identify initial defects before catastrophic failures occur, effectively reducing downtime and repair costs. However, the effectiveness of data-driven fault identification methods is highly dependent on the availability of high-quality vibration data, a requirement that is often difficult to meet due to operational limitations, rare failure events, or high data acquisition costs.

[0003] The challenge of data scarcity is particularly prominent in specialized equipment or newly deployed machinery, where the vibration signatures of specific faults are often scarce or missing. Traditional machine learning models, represented by deep neural networks and support vector machines, typically require large amounts of labeled data to achieve effective generalization. Insufficient training data can easily lead to overfitting, decreased diagnostic accuracy, and insufficient adaptability to unknown fault conditions. In addition, conventional data enhancement techniques (such as noise injection and time domain transformation) often have difficulty generating physically meaningful vibration signals and cannot reflect the complex frequency domain characteristics of mechanical faults. Overcoming this limitation requires innovative methods to achieve vibration signal synthesis, which requires the inclusion of both random noise components and deterministic fault-related frequency modulation.

[0004] Recent advances in artificial intelligence generated content (AIGC) models offer new approaches to alleviating data scarcity in engineering. Generative adversarial networks (GANs) and variational autoencoders (VAEs) have been applied to time series data synthesis, including vibration signal generation. For example, the Wasserstein conditional GAN ​​was designed for bearing fault signal generation under limited sample conditions, while the conditional variational autoencoder was used to augment unbalanced datasets in gearbox diagnosis. However, GAN-based methods often suffer from mode collapse and training instability, particularly when modeling the inherent high-frequency components of vibration data. While more stable, VAEs often exhibit overly smoothed outputs and lack the transient impact characteristics characteristic of localized faults. Recently developed diffusion models, which progressively remove Gaussian noise through a learning process, demonstrate potential for generating high-fidelity data. Their hierarchical structure and progressive optimization mechanism are theoretically well-suited to capturing multi-scale vibration features, from low-frequency harmonics to high-frequency transients. However, existing diffusion-based fault diagnosis methods primarily focus on time-domain operations, neglecting the critical role of frequency-domain features in mechanical fault identification—a shortcoming that compromises the physical interpretability and diagnostic utility of the generated signals. Summary of the Invention

[0005] Purpose of the invention: In view of the above shortcomings, the present invention provides a high-precision fault identification method based on a finite sample of vibration data generated by frequency domain transformation.

[0006] Technical solution: To solve the above problems, the present invention adopts a fault identification method based on a finite sample of vibration data generated by frequency domain transformation, which includes the following steps:

[0007] (1) Obtain vibration signals of rotating machinery under different fault and damage categories and perform spectral feature extraction;

[0008] (2) Construct the stochastic differential equation of the forward diffusion process and introduce the mirror Brownian motion to perform forward diffusion on the spectral characteristics of the vibration signal;

[0009] Based on the forward diffusion process, by gradually adding Gaussian noise to the extracted spectral features, the extracted spectral features are transformed into an approximately processable noise distribution to obtain noise samples;

[0010] (3) Iteratively correcting the noise samples along the reverse diffusion process of the stochastic differential equation, wherein the drift term of the reverse diffusion process includes the gradient of the logarithmic probability density, and using the fractional matching method to train the fractional estimation network to estimate the gradient of the logarithmic probability density. Combined with the Langevin dynamics sampling strategy, the noise component is gradually stripped off, and finally the Gaussian prior is mapped to the spectral characteristics of the target data distribution in the continuous time domain;

[0011] (4) The generated spectral features of the target data distribution are concatenated with the extracted spectral features, and then input into the spectral feature-based word unit transformer to realize embedded feature extraction and obtain the embedded spectral features;

[0012] (5) Encoding and decoding calculations are performed on the embedded spectral features to capture the sensitive components in the spliced ​​spectral features, and finally classification and recognition under limited samples are achieved through the linear layer.

[0013] Furthermore, the spectral feature extraction in step (1) is performed by discrete Fourier transform The implementation is as follows:

[0014]

[0015] Where κ is the frequency component index in the frequency domain, which is an integer in the range of 0≤κ≤N-1. N is the total number of sampling points of the time domain signal, that is, the length of the input sequence x. τ Represents the signal value at index τ in the time domain, that is, the τth sampling point of the input sequence. i represents the imaginary unit, satisfying i 2 = -1, sometimes also denoted as j in engineering. τ represents the sample index in the time domain, which is an integer in the range of 0≤τ≤N-1, corresponding to the τth time point of the signal.

[0016] For all κ∈[N], in the field of signal processing, each κ corresponds to a frequency Harmonic components, discrete Fourier transform results It is regarded as the mathematical representation of the input sequence x in the frequency domain, and the result is in complex value form: For complex space.

[0017] Furthermore, the forward diffusion in the frequency domain in step (2) is to integrate the discrete Fourier transform operator into the forward diffusion process based on the fractional diffusion model, where Characterize the forward diffusion process solution after frequency domain transformation, as shown in the following formula:

[0018]

[0019] in is a frequency domain signal The deterministic drift function at diffusion step t, diffusion step t (usually expressed as a discrete time step t∈{1,2,…,T}, T is the total number of diffusion steps), and g(t) is the diffusion coefficient. U is defined as [U] κτ :=N -1 / 2 exp(-iω κ τ), yes Mirror Brownian motion on .

[0020] Furthermore, the reverse diffusion process in step (3) is specifically shown in the following formula:

[0021]

[0022] in, is the drift term, Indicates that the definition The time evolution direction of the mirror Brownian motion on is reversed from T to 0.

[0023] Furthermore, the drift term As shown in the following formula:

[0024]

[0025] in, represents a diagonal matrix, represents the state variable at time t The gradient of the logarithmic probability density function is This term is also called the score network and can be approximated by a neural network in the diffusion model.

[0026] Furthermore, in order to run the above-mentioned reverse diffusion process, a score matching method is required to train a score estimation network. In the diffusion model, the drift term of the reverse diffusion process contains the gradient of the logarithmic probability density, which determines how the sample gradually approaches the data distribution from noise during the sampling process. However, this density function cannot be obtained explicitly in practice, so it needs to be estimated through a neural network. Score Estimation Network That is, it is used to approximate this term. Its training quality directly determines the effectiveness and data quality of the back diffusion generation. Therefore, the iterative denoising process of back diffusion can be converted into solving the score estimation network in the following formula Hyperparameters:

[0027]

[0028] The loss function in the formula Used to train the score estimation network By minimizing the network The estimated score function and forward diffusion conditional probability density The difference between the true gradient and the real gradient is used to approximate the gradient field of the data distribution. represents the joint expectation (mathematical expectation) of all training samples and time points, Represents a variable The gradient (i.e., multidimensional partial derivative), λ(t) is the time function used to adjust the training weights at different time points, Λ 2is the diagonal diffusion matrix square term used in the diffusion process to maintain scale consistency.

[0029] The initial state of the vibration sequence is The evolution state is Represents the conditional probability distribution after given initial conditions, loss function The evaluation is carried out through the following steps: First, the spectral features of the vibration signal are obtained, and then sampling is performed based on forward diffusion. When the trained score estimation network is obtained Afterwards, through the reverse diffusion process The synergy of generating Sample. Used to evaluate the score estimation network The core purpose of approximating the true score function is to train the network through supervised learning to accurately estimate the logarithmic density gradient of the state variable during the diffusion process. Minimizing the objective function not only ensures the rationality and stability of the back-diffusion process but also directly affects the quality of the resulting data. Therefore, evaluating this loss is a core step in the training phase, used to guide the update of network parameters and determine the degree of convergence of model training.

[0030] Furthermore, the embedding feature extraction of the spectrum feature word unit Transformer in step (4) is to extract each spectrum feature sequence Complete embedding into word units, achieved through multi-layer perceptron:

[0031] h n =Multilayer(X T :,n )

[0032] Among them, L is the length of the spectrum feature, N′ is the number of variables that generate the spectrum feature, X T :,n It is represented as the transpose of the nth time series variable in all time steps, H = {h1,…h n …,h N} is the embedding feature expression of the word.

[0033] Furthermore, in the process of classification and recognition of spectral feature word units, the spectral feature word unit Transformer uses multi-head attention to calculate the correlation of spectral feature word units. Specifically, for the spectral feature variables generated by With the original spectrum characteristic variable Perform splicing operations to obtain expanded spectral features Input multi-head attention for calculation:

[0034] Q s =XW sq

[0035] K s =XW s k

[0036] V s =XW s v

[0037] Where W s q 、W s k and W s v Q is the parameter that needs to be trained and learned. s , K s and V s are the calculated query matrix, key matrix, and value matrix respectively;

[0038] Then Q s , K s and V s Perform matrix product and scale it through the softmax function, as shown in the following formula:

[0039]

[0040] Where d k It's Q s , K s and V s The dimension of the vector, introduced This is for numerical stability, to avoid excessively large dot product values ​​in high-dimensional spaces.

[0041] The above single-head attention A s Extended to h-head attention, as shown in the following formula:

[0042] A h (X)=concat(head1,…,head h )W0,where head i=A s (XW i q ,XW i k ,XW i v )

[0043] Among them, concat is the concatenation operator, and W0 is the linear mapping representing the connector.

[0044] The present invention also adopts a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0045] The present invention also adopts a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above method when executed by a processor.

[0046] Beneficial effects: Compared with the existing technology, the significant advantage of the present invention is that it proposes a new frequency diffusion vibration signal generation and recognition framework under data-limited conditions. The synthesized signal not only significantly reduces the distance from the original signal, but also overcomes the limitation of the existing AIGC technology in capturing local spectral features. This advantage makes it particularly suitable for generating typical vibration signals of rotating machinery; it effectively solves the problem of low fault identification accuracy of rotating machinery in data-scarce scenarios, and provides a highly reliable data enhancement and feature decoupling solution for the intelligent diagnosis system of industrial equipment. Focusing on two typical rotating machinery types, deep groove ball bearings (including inner and outer ring / rolling element faults) and centrifugal compressors (including blade crack damage), the proposed method successfully generates corresponding fault damage signals, achieving higher recognition accuracy than the existing methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the fault identification method in the present invention.

[0048] Figure 2 It is a schematic diagram of the process of generating vibration signals by frequency domain diffusion in the present invention.

[0049] Figure 3 is the bearing fault vibration signal generated in the present invention; wherein Figure 3 (a) is the vibration signal of the inner ring fault. Figure 3 (b) is the outer ring fault vibration signal, Figure 3 (c) in the figure is the vibration signal of the roller fault. Figure 3 (d) in the figure is the vibration signal of the inner and outer ring faults.

[0050] Figure 4 is the blade damage vibration signal generated in the present invention; wherein Figure 4 (a) is the vibration signal of a 5mm crack damage on the blade, where Figure 4 (b) is the vibration signal of the blade with 10mm crack damage, where Figure 4 (c) is the vibration signal of the blade with 15mm crack damage, where Figure 4 (d) in the figure is the vibration signal of a 20mm crack damage on the blade.

[0051] Figure 5 This is the architecture diagram of the inverse Transformer based on spectral features in the present invention.

[0052] Figure 6 It is the classification accuracy of the fault identification method in the present invention under different identification tasks.

[0053] Figure 7 It is the recognition accuracy and diffusion time of the fault recognition method in the present invention under different preset parameters T.

[0054] Figure 8 It is the recognition accuracy and sampling time of the fault recognition method in the present invention under different preset parameters n. DETAILED DESCRIPTION

[0055] like Figure 1 As shown, in this embodiment, a method for generating vibration data based on frequency domain transformation and identifying faults under finite samples includes the following steps:

[0056] Step S1: Use accelerometer to obtain vibration signals of rotating machinery under different fault and damage categories, where spectral feature extraction is achieved through discrete Fourier transform The specific formula is as follows:

[0057]

[0058] Where κ is the frequency component index in the frequency domain signal, which is an integer in the range of 0≤κ≤N-1. x is the input sequence of the vibration signal, and N is the total number of sampling points of the time domain signal, that is, the length of the input sequence x. τ Represents the signal value at index τ in the time domain signal, that is, the τth sampling point of the input sequence. i represents the imaginary unit, satisfying i 2 = -1, sometimes also denoted as j in engineering. τ represents the sample index in the time domain, which is an integer in the range of 0≤τ≤N-1, corresponding to the τth time point of the signal. For all κ∈[N], in the field of signal processing, each κ corresponds to a frequency Therefore, the discrete Fourier transform result is It can be regarded as the mathematical representation of the input sequence x in the frequency domain (as opposed to the time domain representation), and the result is in complex value form:

[0059] This example verifies the fault identification method for finite samples based on frequency domain transform-generated vibration data through deep groove ball bearing faults (inner race fault, outer race fault, rolling element fault, and combined inner and outer race fault) and centrifugal compressor blade crack damage experiments. The deep groove ball bearing fault test bench consists of a control module, a bearing test module, a drive and load module driven by a hydraulic cylinder, an oil pressure regulation system using a counterweight, and a data acquisition module. The relevant settings for the fault experiment are shown in Table 1. The blade crack damage experiment introduces four artificial damages of different depths (crack depths of 5mm, 10mm, 15mm, and 20mm) into the blade at a constant speed of 1200rpm, and collects their vibroacoustic signals at a sampling frequency of 25.6kHz. Based on the severity of the crack, the four crack types are assigned different labels: 1, 2, 3, and 4.

[0060] Table 1 Deep groove ball bearing fault experiment settings

[0061]

[0062] Step S2: Construct the stochastic differential equation of the forward diffusion process for the above bearing fault and blade damage data, introduce the mirror Brownian motion to perform forward diffusion on the spectral feature samples of the vibration signal, and integrate the discrete Fourier transform operator into the forward diffusion process of the fractional diffusion model, as shown in the following example: Figure 2 As shown. Characterize the forward diffusion process solution after frequency domain transformation. The spectral characteristics of the original vibration signal are gradually added to the noise process, and finally a noise distribution is formed that is independent of the original data distribution, as shown in the following formula:

[0063]

[0064] in, is the spectral feature The deterministic drift function at diffusion step t, diffusion step t (usually expressed as a discrete time step t∈{1,2,…,T}, T is the total number of diffusion steps), and g(t) is the diffusion coefficient. It can be defined as [U] κτ :=N -1 / 2 exp(-iω κ τ). yes The total number of diffusion steps T is a key parameter in forward diffusion, which is obtained here by grid search. The details can be seen in the subsequent analysis and discussion.

[0065] Step S3: Iteratively correct the noise samples along the reverse stochastic differential equation, and combine the Langevin dynamics sampling strategy to gradually remove the noise components, as shown in the following formula:

[0066]

[0067] The drift term is represents a diagonal matrix, Indicates that it is defined in complex space The time evolution direction of the mirror Brownian motion on is reversed from T to 0. Represents the spectral characteristics of the state variable at time t The gradient of the logarithmic probability density function is This term, also known as a fractional estimation network, can be approximated by a neural network in the diffusion model. Ultimately, the Gaussian prior is mapped into spectral feature samples of the target data distribution (bearing faults and blade damage) in the continuous time domain. The number of generated samples, n, serves as a key parameter in back diffusion and is determined here using a grid search. See the subsequent analysis and discussion for details.

[0068] At the same time, in order to run the above-mentioned reverse diffusion process, a score matching method is needed to train a score estimation network to accurately fit the data distribution gradient under different noise scales. In the diffusion model, the drift term of the reverse diffusion process contains the gradient of the logarithmic probability density, which determines how the sample gradually approaches the data distribution from the noise during the sampling process. However, this density function cannot be obtained explicitly in practice, so it needs to be estimated through a neural network. Score Estimation Network That is, it is used to approximate this term. Its training quality directly determines the effectiveness and data quality of the back diffusion generation. Therefore, the iterative denoising process of back diffusion can be converted into solving the score estimation network in the following formula Hyperparameters:

[0069]

[0070] The loss function in the formula Used to train the score estimation network By minimizing the network The estimated score function and forward diffusion conditional probability density The difference between the true gradient and the real gradient is used to approximate the gradient field of the data distribution. represents the joint expectation (mathematical expectation) of all training samples and time points, Represents a variable The gradient (i.e., multidimensional partial derivative), λ(t) is the time function used to adjust the training weights at different time points, Λ 2is the diagonal diffusion matrix square term used in the diffusion process to maintain scale consistency.

[0071] The initial state of the vibration sequence is The evolution state is Represents the conditional probability distribution loss function after given initial conditions The evaluation is performed through the following steps: first, the spectral features of the vibration signal input sequence are obtained, and then sampling is performed based on forward diffusion. The forward diffusion process not only constructs the evolution path from data to noise, but also provides the supervision information required for training the score estimation network. Specifically, by generating noisy samples and their conditional density functions at different time points An explicit score function expression can be constructed to guide the supervised training of the score network. Afterwards, through the reverse diffusion process The synergistic effect can generate a target distribution Sample. Used to evaluate the score estimation network The core purpose of approximating the true score function is to train the network through supervised learning to accurately estimate the logarithmic density gradient of the state variable during the diffusion process. Minimizing the objective function not only ensures the rationality and stability of the back-diffusion process but also directly affects the quality of the resulting data. Therefore, evaluating this loss is a core step in the training phase, used to guide the update of network parameters and determine the degree of convergence of model training.

[0072] In the bearing fault experiments, individual samples were constructed by extracting 0.5-second segments of the vibration signals corresponding to inner race, outer race, rolling element, and combined (inner and outer race) faults. In the blade crack damage experiments, the blade crack samples were segmented into 0.2-second intervals. Figure 3-4 The waveforms of fault and damage samples generated in the time domain and frequency domain are shown. In the figure, the first row of each sub-graph represents real signal samples, the second row of each sub-graph represents signal samples generated by the method of this embodiment, and the third row of each sub-graph represents signal samples synthesized using the traditional time-domain fractional-based diffusion method. Regardless of the experimental object (bearing / blade) or defect type (including composite faults and different crack lengths), the signal generated by the traditional fractional-based diffusion method shows disordered and incoherent characteristics in the spectrum, and there is a significant deviation from the original signal. In contrast, the proposed frequency domain method can accurately capture the local transient characteristics in the fault spectrum. This also indirectly proves the synergistic effect of Fourier transform on transient signal generation in the diffusion model.

[0073] The deep learning software and hardware settings for the vibration data generation and subsequent classification and recognition stages are shown in Table 2:

[0074] Table 2 Software and hardware settings for verification calculation

[0075] parameter value parameter value operating system Ubuntu 20.04 programming language Python 3.8.18 CPU Intel-i9-13900KF GPU RTX 4090 Memory 64G Deep Learning Libraries PyTorch 2.1 Cudnn version 8.9.7 CUDA version 11.8

[0076] Step S4: Splice the generated samples with the spectral feature samples of faults and damages in the original training set to expand the limited training sample volume, and then input them into the constructed spectral feature word unit Transformer to realize embedded feature extraction. The recognition network structure and hyperparameter settings are as follows: Figure 5 As shown in Table 3. The embedding feature extraction of the spectral feature word unit Transformer is to transform each spectral feature sequence The complete embedding into word units can be achieved through multi-layer perceptron:

[0077] h n =Multilayer(X T :,n )

[0078] Among them, L is the length of the spectrum feature, N′ is the number of variables that generate the spectrum feature, X T :,n Represented as the transpose of the nth time series variable at all time steps, is the embedding feature expression of the word, d embedding is the word embedding dimension.

[0079] Table 3 Spectral feature word unit Transformer hyperparameter settings

[0080] parameter value parameter value Number of encoding and decoding layers 4 Batch size 16 Optimizer Adam Embedding Dimension 128 Number of iterations 10000 Deep Learning Libraries PyTorch 2.1 Cudnn version 8.9.7 Number of attention heads 3

[0081] Step S5: Encode and decode the embedded spectral features, capture the sensitive components in the expanded spectral features through multi-head attention mechanism, normalization operator, etc., and finally realize classification and recognition under limited samples through linear layer. In the process of classification and recognition of spectral feature word unit Transformer, multi-head attention is used to calculate the correlation of spectral feature word units. Specifically, for the generated spectral feature variables With the original spectrum characteristic variable Perform splicing operations to obtain expanded spectral features Input multi-head attention for calculation:

[0082] Q s =X′ s W s q

[0083] K s =X′ s W s k

[0084] V s =X′ s W s v

[0085] Where X′ s represents the embedded representation of X after position encoding, where W s q ,W s k and W s v Q is the parameter that needs to be trained and learned. s , K s and V s are the calculated query matrix, key matrix and value matrix. s , K s and V s Perform matrix product and scale it through the softmax function, as shown in the following formula:

[0086]

[0087] Where d k It's Q s , K s and V s The dimension of the vector, introduced This is for numerical stability, to avoid excessively large dot product values ​​in high-dimensional spaces.

[0088] The above single-head attention A s Extended to h-head attention, as shown below

[0089] A h (X)=concat(head1,…,head h )W0,where headi=A s (XW i q ,XW i k ,XW i v ) where concat is the concatenation operator, is a linear map representing the connector.

[0090] The generated spectrum data of the fault and damage samples and the original real signal are input into the constructed spectrum feature word unit Transformer. Through the encoder-decoder architecture, the embedded feature representation is extracted and then classified through the linear output layer to determine the specific fault category, such as Figure 6As shown in Figure 3, the framework proposed in Section 3 can provide higher classification results for both bearing fault and blade crack damage identification, with an accuracy improvement of about 3%.

[0091] The diffusion model consists of a forward process and a backward process. The hyperparameter T represents the number of time steps in the diffusion process, reflecting the current noise level of the data and the stage of denoising evolution. Therefore, six different levels of T were designed through grid search, ranging from 3000 to 500, decreasing by 500, as shown in the following example: Figure 7 Figure 2 compares the impact of noise intensity on the quality of generated samples and final diagnostic performance. It can be observed that longer diffusion steps increase generation time but do not necessarily improve the quality of generated samples, ultimately leading to a decrease in recognition accuracy. During the noise addition and denoising process, excessively long time steps can weaken the fidelity of the generated signal to some extent, resulting in the loss of fault and damage components. The number of generated samples, n, is another key ablation variable, determining the amount of additional data introduced into the recognition task. This is also determined using a grid search method. Figure 8 This figure shows the relationship between sampling time, recognition accuracy, and the number of generated samples. While generating 2000 samples improves recognition accuracy compared to 500 samples, it also significantly increases computational time. In practical applications, an appropriate trade-off should be made based on available computing resources and accuracy requirements.

[0092] In addition to the aforementioned ablation experiments, we further compared the performance of other generative models in terms of the quality of rotational vibration fault data generation and the final recognition and diagnosis accuracy. Three representative models are as follows:

[0093] (1) Generative Adversarial Network (GAN): GAN consists of a generator and a discriminator, which compete in a zero-sum game. The generator creates real data, while the discriminator distinguishes between real and fake data. Adversarial training is used to improve the performance of both. The generator and discriminator are composed of convolutional layers and fully connected layers, using the Adam gradient optimization algorithm and the ReLU activation function.

[0094] (2) Denoised Diffusion Probability Model (DDPM): The denoised diffusion probability model (DDPM) is also a classic diffusion model. It approximates the true data distribution through a Markov chain, minimizes the variational lower bound during training, and gradually denoises to generate clear data during sampling. DDPM optimizes noise predictions through variational inference at discrete time steps, while this embodiment guides continuous-time Langevin dynamics sampling generation by matching the data distribution gradient (score).

[0095] (3) Score-based diffusion: This is a classic continuous-time diffusion modeling method, while DDPM is discrete. The score-based diffusion method generates data by learning the score function (gradient) of the data distribution. The biggest difference between this embodiment and existing methods lies in its operating domain: traditional methods perform diffusion and backdiffusion processes within the time domain framework (such as the standard score-based diffusion model), while this embodiment focuses on the spectral feature space and uses frequency domain transformation to enhance the fidelity and diagnostic accuracy of the generated signal.

[0096] To ensure a fair comparison, all models use the same hyperparameter settings (e.g., m, n) and the same size of original training samples. Therefore, two sets of experiments were compared in step S5, covering a total of eight fault and damage identification tasks. Evaluation was conducted along two dimensions: the quality of the generated samples and the final recognition accuracy. The former evaluates the quality of the generated vibration fault signals by measuring the slice Wasserstein distance (SWD) between the generated and original vibration fault signals. This distance is a computationally efficient approximation of the Wasserstein distance. It projects the high-dimensional distribution onto a low-dimensional subspace (typically 1D) along random directions, calculates the Wasserstein distance for each projection, and averages the results. Specifically, for 2000 generated samples (n=2000), the slice Wasserstein distance (SWD) is calculated for each sample, and the mean and standard deviation of the SWD across different recognition tasks are calculated. Detailed results are shown in Table 4. The proposed frequency-domain diffusion-based vibration data generation method achieves the lowest SWD value, achieving an average reduction of approximately 43% compared to GAN, DDPM, and traditional score-based diffusion methods. This indirectly indicates that frequency domain transformation has a positive impact on vibration signal generation.

[0097] Table 4 SWD distance comparison

[0098]

[0099]

[0100] Subsequently, the samples generated by the above-mentioned comparison methods were input into a unified diagnostic model for identification, and their average diagnostic accuracy is shown in Table 5 below. The baseline method refers to the fault and damage identification without using a generative model to expand the training dataset. It is observed that only GAN has a lower recognition accuracy than the baseline method. Although the samples generated by GAN expand the training set, the final recognition accuracy decreases. This indicates that the quality of the generated data fails to fully capture the dynamic characteristics of the vibration signal (which can also be seen from the SWD comparison), which ultimately leads to a decrease in the recognition rate. Other diffusion-based methods all achieved results that are better than the baseline method. In addition, the proposed method is more effective in generating vibration signals containing fault and damage characteristics, improving the recognition rate by 7%. This advantage is reflected not only in the SWD value, but also in the final recognition accuracy.

[0101] Table 5 Comparison of average recognition accuracy

[0102] Benchmark Method GAN DDPM Score based diffusion The present invention Bearing failure experiment 93.25％ 92.43％ 98.34％ 97.54％ 99.25％ Leaf damage experiment 92.52％ 93.23％ 97.34％ 98.34％ 99.36％

[0103] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A fault identification method based on finite sample generation of vibration data using frequency domain transformation, characterized in that: The following steps are involved: (1) Obtain vibration signals of rotating machinery under different fault and damage categories and perform spectral feature extraction; (2) Construct the stochastic differential equation of the forward diffusion process and introduce the mirror Brownian motion to perform forward diffusion on the spectral characteristics of the vibration signal; Based on the forward diffusion process, the extracted spectral features are converted into noise distribution by gradually adding Gaussian noise to the extracted spectral features to obtain noise samples; (3) Iteratively correcting the noise samples along the reverse diffusion process of the stochastic differential equation, wherein the drift term of the reverse diffusion process includes the gradient of the logarithmic probability density, and using the fractional matching method to train the fractional estimation network to estimate the gradient of the logarithmic probability density. Combined with the Langevin dynamics sampling strategy, the noise component is gradually stripped off, and finally the Gaussian prior is mapped to the spectral characteristics of the target data distribution in the continuous time domain; (4) The generated spectral features of the target data distribution are concatenated with the extracted spectral features, and then input into the spectral feature-based word unit transformer to realize embedded feature extraction and obtain the embedded spectral features; (5) Encoding and decoding calculations are performed on the embedded spectral features to capture the sensitive components in the spliced ​​spectral features, and finally classification and recognition under limited samples are achieved through the linear layer.

2. The method for fault identification under finite samples according to claim 1, characterized in that: The vibration signal in step (1) includes frequency domain signal and time domain signal, and the spectrum feature extraction is performed by discrete Fourier transform. The implementation is as follows: Among them, κ is the frequency component index in the frequency domain signal, N is the total number of sampling points of the time domain signal, x is the input sequence of the vibration signal, and x τ Represents the signal value at index τ in the time domain signal, and i represents the imaginary unit; For all κ∈[N], in the field of signal processing, each κ corresponds to a frequency Harmonic components, discrete Fourier transform results It is regarded as the mathematical representation of the input sequence x in the frequency domain, and the result is in complex value form: For complex space.

3. The method for fault identification under limited samples according to claim 2, characterized in that: Step (2) is to integrate the discrete Fourier transform operator into the forward diffusion process of the fractional diffusion model in the frequency domain, where Characterize the forward diffusion process solution after frequency domain transformation, as shown in the following formula: in, is the spectral feature The deterministic drift function at time t, g(t) is the diffusion coefficient, Indicates that it is defined in complex space Mirror Brownian motion on .

4. The method for fault identification under limited samples according to claim 3, characterized in that: The reverse diffusion process in step (3) is specifically shown in the following formula: in, is the drift term, Indicates that it is defined in complex space The time evolution direction of the mirror Brownian motion on is reversed from T to 0.

5. The method for fault identification under limited samples according to claim 4, characterized in that: The drift term As shown in the following formula: Where Λ represents a diagonal matrix, Represents the spectral characteristics at time t The gradient of the log probability density function of , also known as the fractional estimation network.

6. The method for fault identification under finite samples according to claim 5, characterized in that: At the same time, in order to run the above-mentioned reverse diffusion process, the score matching method is required to train the score estimation network. The iterative denoising process of reverse diffusion is converted to solving the score estimation network in the following formula Hyperparameters: in, For the score estimation network The loss function is is the forward diffusion conditional probability density, represents the joint expectation of all training samples and time points, Represents the spectrum characteristics The gradient of , λ(t) is the time function used to adjust the training weights at different time points; The initial state of the input sequence of the vibration signal is The evolution state is Represents the conditional probability distribution after given initial conditions, loss function The evaluation is carried out through the following steps: first, the spectral features of the vibration signal are obtained, and then sampling is performed based on forward diffusion. When the trained score function is obtained Afterwards, through the reverse diffusion process The synergy of generating Sample.

7. The method for fault identification under limited samples according to claim 6, characterized in that: The embedding feature extraction of the spectral feature word unit Transformer in step (4) is to transform each spectral feature sequence Complete embedding into word units, achieved through multi-layer perceptron: h n =Multilayer(X T :,n ) Among them, L is the length of the spectrum feature, N′ is the number of variables that generate the spectrum feature, X T :,n It is represented as the transpose of the nth time series variable in all time steps, H = {h1,…h n …,h N } is the embedding feature expression of the word.

8. The method for fault identification under finite samples according to claim 7, characterized in that: In the process of classification and recognition of spectral feature word units, the multi-head attention is used to calculate the correlation of spectral feature word units. Specifically, the generated spectral feature variable X′ is concatenated with the original spectral feature variable X″ to obtain the expanded spectral feature X, which is then input into the multi-head attention for calculation: Q s =XW s q K s =XW s k V s =XW s v Among them, W s q 、W s k and W s v Q is the parameter that needs to be trained and learned. s , K s and V s are the calculated query matrix, key matrix, and value matrix respectively; Then Q s , K s and V s Perform matrix product and scale it through the softmax function, as shown in the following formula: Where d k It's Q s , K s and V s The dimension of the vector; The above single-head attention A s Extended to h-head attention, as shown in the following formula: A h (X)=concat(head1,…,head h )W0,where head i=A s (XW i q ,XW i k ,XW i V ) Where concat is the concatenation operator and W0 is the linear mapping representing the connector.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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