Multi-sensor signal expansion method and system based on graph constraint

Abstract

The invention provides a multi-sensor signal expansion method and system based on graph constraint. The method comprises the following steps: acquiring multi-sensor signal data, corresponding category labels and an adjacent matrix defining a topological relation among multiple sensors; constructing a graph condition variation adversarial network, wherein the network comprises a graph condition variation encoder, a generator and a graph discriminator; a joint loss function is adopted to train the graph condition variational adversarial network, and the joint loss function at least comprises loss related to a graph condition variational autoencoder and loss related to a generative adversarial network; and using the trained generator to generate extended signal data for a few categories of tags. According to the method, the generated expansion samples are ensured to accord with physical consistency, and efficient and condition-controllable generation is realized.

Description

Technical Field

[0001] This invention belongs to the field of mechanical equipment health monitoring technology, specifically relating to a multi-sensor signal augmentation method and system based on graph constraints. Background Technology

[0002] In safety-critical fields such as marine propulsion and industrial power generation, the reliable operation of complex rotating machinery such as gas turbines is crucial. Fault diagnosis of these devices (such as intermediate bearings) is a core technology for ensuring system safety and reducing operation and maintenance costs.

[0003] In recent years, data-driven intelligent diagnostic methods have made significant progress, but their performance is highly dependent on massive, balanced fault datasets. However, in real-world industrial scenarios, equipment typically operates under high reliability conditions, making destructive testing difficult and costly. This results in an extreme scarcity of fault samples (especially early-stage fault samples), leading to severe class imbalance in the training dataset. When deep learning models are trained on such imbalanced data, they become heavily biased towards the well-supplied normal class, resulting in extremely poor ability to identify the rare "fault" class and thus rendering them unusable for engineering applications.

[0004] To overcome the core technical challenges of small sample size and class imbalance, data augmentation has become a key research direction. However, existing data augmentation techniques have significant limitations:

[0005] First, traditional oversampling techniques (such as SMOTE) have limited effectiveness. These methods generate new samples based on simple interpolation principles. Although they can balance the class distribution, the generated samples often lack diversity and do not truly introduce new, valuable feature information, which can easily lead to model overfitting.

[0006] Secondly, existing deep generative models each have their own shortcomings.

[0007] Although variational autoencoders (VAEs) can learn the latent probability distribution of data and the training process is relatively stable, the samples they generate often lack fidelity and have fuzziness issues.

[0008] Generative Adversarial Networks (GANs) can generate high-quality, high-fidelity, and realistic samples, but their training process is extremely unstable and often carries the risk of pattern collapse (i.e., the generator can only produce a few types of samples). Therefore, there is a need in this field for a hybrid model that can combine the stable distributed learning capability of VAEs with the high-fidelity generation capability of GANs.

[0009] Secondly, and most critically, the existing generative models lack consideration for physical constraints. Mechanical equipment is a coupled system composed of multiple components, and its various sensors (nodes) are not independent but closely interconnected through the equipment's structure (topological relationships). The occurrence and propagation of faults follow explicit physical laws (such as causal relationships). Existing VAE or GAN models, when generating multi-sensor data, typically flatten the data into vectors, completely ignoring the topological structure between sensors. This leads to samples that may appear statistically plausible but are physically inconsistent or impossible (e.g., the generated data may violate the propagation direction or physical correlation of fault signals). Such false samples that do not conform to physical laws can seriously mislead subsequent diagnostic models.

[0010] Finally, existing technologies also have shortcomings in terms of expansion efficiency. For example, some methods can only expand for a single fault category of a single sensor. To complete the expansion task of multiple sensors and multiple categories, the model must be trained and run multiple times, which is inefficient. Summary of the Invention

[0011] The purpose of this invention is to address the shortcomings of the aforementioned background technology and provide a multi-sensor signal augmentation method and system based on graph constraints, which simultaneously possesses the stability of VAE and the high fidelity of GAN; it utilizes known sensor topological relationships as physical constraints to ensure that the generated augmented samples conform to physical consistency, thereby achieving efficient and conditionally controllable generation.

[0012] The technical solution adopted in this invention is: a multi-sensor signal augmentation method based on graph constraints, comprising the following steps:

[0013] Acquire multi-sensor signal data, corresponding category labels, and an adjacency matrix that defines the topological relationships between the multi-sensors;

[0014] Construct a graph conditional variational adversarial network, which includes a graph conditional variational encoder, a generator, and a graph discriminator.

[0015] The graph conditional variational encoder includes a graph convolutional layer for processing the signal data and category labels according to the adjacency matrix, and generating graph-level latent variables through a single graph average pooling operation.

[0016] The generator generates augmented signal data based on the latent variables at the graph level and the category labels;

[0017] The graph discriminator includes a graph convolutional layer, used to determine whether the augmented signal data is authentic under the topological constraints defined by the adjacency matrix.

[0018] The graph conditional variational adversarial network is trained using a joint loss function, wherein the joint loss function includes at least: a loss associated with the graph conditional variational autoencoder and a loss associated with the generative adversarial network;

[0019] Using the trained generator, augmented signal data is generated for labels in a few categories.

[0020] In the above technical solution, the process of generating graph-level latent variables includes:

[0021] The multi-sensor signal data is concatenated with the category label to form an encoder input matrix;

[0022] The graph conditional variational encoder processes the encoder input matrix through its graph convolutional layers to learn the mean and variance of the latent variables, wherein the mean and variance are at the node level.

[0023] The reparameterization technique is applied to the mean and variance at the node level to sample the latent variables at the node level;

[0024] The graph average pooling operation is performed on the node-level latent variables to generate the graph-level latent variables.

[0025] In the above technical solution, the process by which the image discriminator determines whether the signal data is genuine includes:

[0026] The real or augmented signal data is concatenated with the category label to form the discriminator input matrix;

[0027] The graph discriminator processes the discriminator input matrix through its graph convolutional layer, applying the topological constraints in a way that aggregates neighborhood information, and generates node-level feature representations.

[0028] Perform a graph global pooling operation on the node-level feature representation to generate a graph-level feature representation;

[0029] The graph-level feature representation is fed into at least one fully connected layer, and finally outputs a probability for distinguishing between real and fake.

[0030] In the above technical solution, the joint loss function includes at least a weighted sum of four losses: a Kerbeck-Leibler divergence loss, a reconstruction loss, a discriminator loss, and a generator adversarial loss.

[0031] In the above technical solution, the training adopts an alternating optimization strategy, including: fixing the parameters of the generator and encoder and updating the parameters of the discriminator; fixing the parameters of the discriminator and updating the parameters of the generator and encoder.

[0032] In the above technical solution, through the collaborative design of graph conditional variational encoder and graph discriminator both including graph convolutional layers, the generated augmented signal data can implicitly retain the main topological relationships defined by the adjacency matrix.

[0033] In the above technical solution, the multi-sensor signal data is the vibration signal of the mechanical equipment, the category label is the fault type of the mechanical equipment, and the signal amplification is used for fault diagnosis.

[0034] In the above technical solution, the adjacency matrix is ​​a sparse directed causal graph obtained through a spatiotemporal causal inference method.

[0035] The present invention also provides a multi-sensor signal processing system, comprising:

[0036] A graph conditional variational encoder is configured to process signal data and class labels based on an input adjacency matrix to generate latent variables;

[0037] A generator is configured to generate augmented signal data based on the latent variables and the category labels;

[0038] A graph discriminator is configured to determine whether the augmented signal data is genuine based on the adjacency matrix;

[0039] Both the graph conditional variational encoder and the graph discriminator contain graph convolutional layers.

[0040] In the above technical solution, the system further includes a graph convolutional network classifier for fault diagnosis of the augmented signal data; wherein the network architecture of the graph convolutional network classifier is consistent with the network architecture of the graph discriminator in the system.

[0041] The beneficial effects of this invention are: This invention aims to overcome the key defects of existing small-sample, class-imbalanced data augmentation methods (such as SMOTE, traditional VAE, or GAN) in the background art. The methods in the background art either suffer from insufficient sample diversity due to interpolation principles; or they struggle to balance model stability (such as VAE) with generation fidelity (such as GAN); more importantly, they completely ignore the inherent physical topological relationships between multi-sensor data, leading to generated samples that may violate physical laws, thereby reducing the reliability of the diagnostic model.

[0042] This invention no longer treats multi-sensor data as isolated vectors, but rather as a whole constrained by a graph structure. Through a specific Graph Conditional Variational Adversarial Network (GCVAN) architecture, this invention perfectly solves all the aforementioned technical challenges:

[0043] This invention ensures that the entire learning and discrimination process of the model must be carried out under the topological constraints defined by the adjacency matrix by forcing the use of graph convolutional layers (i.e., a dual GCN architecture) in both the encoder and discriminator. This is a fundamental improvement over the prior art's neglect of topological defects.

[0044] This invention successfully combines the advantages of both frameworks by explicitly using a joint loss function that combines CVAE-related loss and GAN-related loss: it obtains both stable training and structured latent space of CVAE and high-fidelity, high-realism samples of GAN, thus ensuring quality while avoiding mode collapse.

[0045] This invention achieves "train once, generate on demand" by introducing category labels as conditions, overcoming the inefficiency of some methods in the background technology that can only expand a single fault category at a time.

[0046] Furthermore, the entire process of encoder node-to-graph data dimensionality reduction provided by this invention, through splicing data and labels, learning the mean and variance and reparameterization at the node level, and finally performing graph average pooling to obtain graph-level latent variables, ensures that the encoder can intelligently compress the topological state of the entire graph into a single, holistic latent variable, rather than scattered node information, thus providing high-quality input for the generator to generate globally consistent samples.

[0047] Furthermore, this invention provides the entire discrimination process from the discriminator node to the graph, explicitly linking topological constraints and aggregated neighborhood information. It clarifies that the discriminator's GCN must apply topological constraints by aggregating neighbor information, and then make a final judgment on the physical rationality of the entire graph (rather than a single signal) through graph global pooling. This is a discrimination mechanism that is far more intelligent and more in line with physical reality than the standard GAN discriminator.

[0048] Furthermore, this invention provides a four-loss and alternating optimization strategy for implementing hybrid loss. Through this specific combination of losses and alternating training, this invention provides a specific implementation plan to ensure that such a complex hybrid model can converge stably and prevent mode collapse.

[0049] Furthermore, this invention defines a dual GCN collaborative design to implicitly preserve the main topological relationships; the samples generated by this invention are not only statistically "true" but also physically "reasonable," and the generated samples successfully preserve the main causal direction of the original data, which makes the expanded data extremely valuable for training downstream diagnostic models.

[0050] Furthermore, this invention possesses significant strategic value in application and system integration: it clearly demonstrates its direct application value in the field of mechanical equipment vibration signals and fault diagnosis, addressing the pain point of small sample sizes in industry. More importantly, this invention utilizes a causal graph obtained through a spatiotemporal causal inference method, ensuring the highest quality of the input graph.

[0051] Furthermore, this invention achieves an efficient collaborative design by ensuring that the network architecture of the downstream graph convolutional network classifier and the graph discriminator remains consistent: the discriminator has been shaped into an expert in judging physical rationality during adversarial training, so reusing its architecture as a classifier enables the final fault diagnosis model to naturally possess stronger topological awareness, thereby improving the accuracy of diagnosis. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0053] Figure 2 This is an example of a dual-rotor high-speed rolling bearing fault simulation test bench.

[0054] Figure 3 Diagrams showing different health states of the intermediate bearing in this embodiment;

[0055] Figure 4 The flowchart for constructing the G-PCMCI cause-effect graph in this embodiment is shown.

[0056] Figure 5 A comparison diagram of the pre-expansion confusion matrix for the example;

[0057] Figure 6 This is a comparison chart of the expanded confusion matrix of the embodiment;

[0058] Figure 7 This is a performance comparison chart of different graph structures in the embodiments;

[0059] Figure 8 This is a comparison chart of the causal strength of generated samples in an example. Detailed Implementation

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but these descriptions do not constitute a limitation on the present invention.

[0061] like Figure 1 As shown, this invention provides a multi-sensor signal augmentation method based on graph constraints, comprising the following steps:

[0062] Acquire multi-sensor signal data, corresponding category labels, and an adjacency matrix that defines the topological relationships between the multi-sensors;

[0063] Construct a graph conditional variational adversarial network, which includes a graph conditional variational encoder, a generator, and a graph discriminator.

[0064] The graph conditional variational encoder includes a graph convolutional layer for processing the signal data and category labels according to the adjacency matrix, and generating graph-level latent variables through a single graph average pooling operation.

[0065] The generator generates augmented signal data based on the latent variables at the graph level and the category labels;

[0066] The graph discriminator includes a graph convolutional layer, used to determine whether the augmented signal data is authentic under the topological constraints defined by the adjacency matrix.

[0067] The graph conditional variational adversarial network is trained using a joint loss function, wherein the joint loss function includes at least: a loss associated with the graph conditional variational autoencoder and a loss associated with the generative adversarial network;

[0068] Using the trained generator, augmented signal data is generated for labels in a few categories.

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description of a graph-constrained multi-sensor signal augmentation method of this invention, in conjunction with the accompanying drawings and specific embodiments, is provided. It should be noted that this embodiment is a preferred embodiment of this invention, intended to illustrate in detail how this invention solves the problem of fault diagnosis in mechanical equipment (especially safety-critical systems such as gas turbines) under scenarios with small sample sizes and imbalanced data.

[0070] This embodiment will fully demonstrate all the steps: starting from acquiring the original data and constructing the topological relationships (adjacency matrix), to constructing a graph conditional variational adversarial network (GCVAN), then training the network using a joint loss function, and finally using the trained network to generate augmented data and apply it to fault diagnosis.

[0071] It is worth noting that the adjacency matrix used in this invention is not a traditional graph structure based on correlation (such as fully connected graphs, K-nearest neighbor graphs, or radial graphs). Correlation graphs cannot distinguish between true causality and spurious correlations, leading to the model learning incorrect physical relationships when data is scarce. In contrast, this invention uses a "sparse directed causal graph" obtained through the spatiotemporal causal inference method (G-PCMCI) as the adjacency matrix. This causal graph can reflect the true physical propagation path of fault signals among multiple sensors. This invention designs graph convolutional layers in both the graph conditional variational encoder and the graph discriminator. This "co-design" uses the aforementioned physically meaningful causal graph as a topological constraint, forcing the generator to generate signal data that conforms to this physical constraint. This ensures that the generated augmented samples have "physical consistency" and "causal preservation," meaning that the simulated fault signals will propagate among sensors according to the true causal path, thus solving the fundamental problem that traditional generative models (VAE, GAN) may generate samples that violate the physical laws of the system.

[0072] Example 1

[0073] This embodiment is specifically applied to the diagnosis of small-sample faults in intermediate bearings of gas turbines, and includes the following steps:

[0074] Step 1: Acquire multi-sensor signal data, corresponding category labels, and an adjacency matrix defining topological relationships. This includes the following steps:

[0075] 1.1 Data Acquisition and Preprocessing

[0076] The mechanical equipment used in this embodiment is a dual-rotor system of a marine gas turbine. For example... Figure 2 As shown, a dual-rotor high-speed rolling bearing fault simulation test bench was built. At key locations on the test bench (such as...) Figure 2 (As shown in the red triangle in the middle) arranged One accelerometer is used to collect vibration signals from mechanical equipment. The data sampling frequency is set to [value missing]. .

[0077] The acquired 8-channel raw vibration signals were preprocessed. A sliding window was used for segmentation, with each sample having a signal length of 1024 data points. Therefore, each raw signal data sample... They are all one The matrix represents the signal data from eight sensors within the same time window.

[0078] This embodiment simulates five different health states, which serve as category labels or fault types. For example... Figure 3 As shown, these health states and their labels are defined as follows:

[0079] Tag 0: Normal (NC, NormalCondition);

[0080] Tag 1: Inner Ring Fault (IR);

[0081] Tag 2: Outer Ring Fault;

[0082] Tag 3: Ball Fault (BF);

[0083] Tag 4: Compound Fault (CF).

[0084] To simulate the difficulty of fault sample collection in real-world industrial scenarios, this embodiment constructs a class-imbalanced dataset. Taking dataset E as an example, the majority class (label 0, NC) has 200 samples, while each minority fault class (labels 1-4) has only 4 samples. This results in… The extreme imbalance ratio. The ultimate goal of this invention, namely "generating augmented signal data for a small number of categories of tags," is to solve this extreme imbalance problem.

[0085] 1.2 Construction of the Adjacency Matrix

[0086] This step aims to obtain the adjacency matrix that defines the topological relationships between the multiple sensors. .

[0087] As mentioned above, one of the core innovations of this invention lies in the definition of the adjacency matrix. In this embodiment, the adjacency matrix is ​​a sparse directed causal graph obtained through a spatiotemporal causal inference method.

[0088] like Figure 4 As shown, this embodiment uses a two-stage G-PCMCI method to construct this causal graph adjacency matrix:

[0089] Phase 1: Initial sparsity reduction based on grey relational analysis (GRA):

[0090] The goal of this stage is to use GRA to quickly screen for potential correlations between sensors, effectively reducing the computational complexity of subsequent causal inference.

[0091] For any two sensor sequences and The grey relational coefficient between them is calculated according to the following formula. The correlation coefficient is calculated as follows: in The resolution coefficient is usually set to 0.5.

[0092] Calculate the average correlation coefficient for each pair of sensors. :

[0093] Set a correlation coefficient threshold This embodiment aims to maximize connectivity and minimize structural complexity, selecting... .when At that time, it is considered that the sensor and There is a potential connection between them.

[0094] Phase Two: Causal Discovery and Directional Inference Based on PCMCI

[0095] The purpose of this stage is to eliminate spurious correlations (e.g., pseudo-correlations caused by common drivers) based on the potential associations identified by GRA through conditional independence tests, and to infer the true causal direction and time lag. This process consists of two steps.

[0096] First, the PC algorithm is used in time delay. The algorithm identifies the relevant parents for each variable. This step is an iterative simplification process: the algorithm starts by evaluating an initial set containing all potential time-delay parents. The parent set is defined as follows: .

[0097] Subsequently, the algorithm iteratively evaluates and removes those variables that, given other parent terms, are incompatible with the target variable. The variables are conditionally independent. In this way, the PC algorithm ultimately outputs a simplified set containing the most strongly correlated parent terms. This embodiment determines the optimal time delay using the causal intensity rate of change stabilization method. .

[0098] Then, the parent terms retained by the PC algorithm (which may still contain weakly correlated or indirect effects) will be finally verified through the transient conditional independence (MCI) test. The MCI test is more rigorous because it considers the parent terms of both the target variable and the candidate cause variable when assessing direct causal effects.

[0099] The algorithm calculates an I value representing the strength of causality and compares it to a threshold set based on a statistical significance level (e.g., 0.05). Only when I is greater than this threshold is the invention definitively confirmed to have a causal relationship. arrive The time delay is The causal relationship.

[0100] Using the G-PCMCI method described above, this embodiment obtained a sparse directed adjacency matrix The matrix This topological constraint has a clear physical meaning; its (directed) edges represent the actual physical propagation paths of fault signals between sensors. For example, sensors 5 and 6 exhibit a significant out-degree advantage, generating unidirectional causal drives to the remaining nodes (1, 2, 4, 7, 8) in the network, thus acting as the primary information source. This is the foundation upon which the subsequent GCVAN model can generate causal-preserving samples.

[0101] like Figure 7 As shown, this figure compares the G-PCMCI cause-effect graph used in this invention (…). Figure 7 The topological form of graph (d) in this paper is compared with that of the other three graph structures ((a) KNN graph, (b) Radius graph, and (c) Complete fully connected graph). As shown in the figure, the G-PCMCI graph (d) is a sparse directed graph obtained based on spatiotemporal causal inference, which is significantly different from the graph structures based on correlation or full connectivity in (a), (b), and (c). When data is scarce (e.g., 50:1), the diagnostic accuracy of the sparse causal graph structure (G-PCMCI) of this invention is significantly higher than that of other graph structures. This proves that the adjacency matrix used in this invention can provide accurate physical propagation paths, avoiding noise interference introduced by other graph structures when data is scarce due to their inability to distinguish between true causality and false associations.

[0102] Step 2: Construct a Graph Conditional Variational Adversarial Network (GCVAN).

[0103] The Graph Conditional Variational Adversarial Network (GCVAN) constructed in this embodiment, namely the multi-sensor signal processing system, consists of three core components: a graph conditional variational encoder, a generator, and a graph discriminator.

[0104] The specific network architecture parameters of the three components of GCVAN are shown in Table 1. This table defines in detail the type, parameters, and output dimensions of each layer.

[0105] Table 1: GCVAN Model Network Architecture Details

[0106] (Note: Input dimensions) ; Generator input dimension Generator output dimension )

[0107] The function of an encoder is to convert input graphical data (signals) into graphical representations. ) and conditions (tags) ), in the adjacency matrix Under constraints, latent variables are encoded as graph-level variables. The execution process is as follows:

[0108] 1. Input splicing: This involves combining the multi-sensor signal data... Concatenate with the category label (e.g., the 5D one-hot code of "inner ring fault") to form The "encoder input matrix" .

[0109] 2. Graph Convolution and Latent Variable Learning: The graph conditional variational encoder, through its graph convolutional layer (GCN-conv1 in Table 1), learns the causal adjacency matrix obtained in step 1.2. To handle The graph convolution operation, as shown in the following equation, aggregates neighborhood information through message passing.

[0110] The formula for calculating graph convolutional layers (GCNs) is as follows:

[0111] Where H (l) This represents the node feature matrix of the l-th layer of the graph encoder. To concatenate input features and conditional labels, U (l) γ is the graph filter parameter matrix for each layer of the graph encoder, where γ represents the activation function.

[0112] Normalized adjacency matrix

[0113] The calculation is as follows:

[0114] Here, A represents the adjacency matrix of the graph, indicating whether there are connections between nodes. If a connection exists, the corresponding element is 1; otherwise, it is 0. As a unit array, yes The degree matrix.

[0115] Subsequently, the mean of the latent variables is learned through two parallel graph convolutional layers (GCN-conv2, GCN-conv3). and variance

[0116] The formula is:

[0117] According to Table 1, these means and variances are at the "node level". .

[0118] Reparameterization: Apply reparameterization techniques to the mean and variance at the node level, as shown in the following equation:

[0119] Where ε follows a standard multivariate normal distribution, from Random sampling is used to obtain latent variables at the node level. .

[0120] Graph average pooling: for the latent variables at the node level Perform the graph average pooling operation, z i For the latent features of the i-th sensor, aggregate them into a graph-level latent variable. The calculation formula is:

[0121] The generator's function is to generate graph-level latent variables based on those generated by the encoder. and the category label This generates expanded signal data.

[0122] Specifically, and spliced ​​as The input vector. This embodiment uses a two-layer fully connected neural network (FNN) (FCLayer1, Layer2 in Table 1). Its calculation process is shown in the following formula:

[0123]

[0124] In the formula and It is a fully connected layer.

[0125] The final output is The vector, reshaped into The matrix is ​​the augmented signal data, which has the same dimensions as the original signal data.

[0126] The graph discriminator (its function is to "distinguish between the adjacency matrices") Under the defined topological constraints, determine whether the augmented signal data is genuine. The implementation process is as follows:

[0127] 1. Input splicing: This involves combining real or augmented signal data. Combined with the category label (5-dimensional one-hot) to form The discriminator input matrix.

[0128] Graph Convolution: The graph discriminator includes graph convolutional layers (GCN-conv4, GCN-conv5 in Table 1). These layers are based on the causal adjacency matrix obtained in step 1.2. The topological constraints are applied by aggregating neighborhood information to process the input matrix and generate node-level feature representations. The graph convolution calculation process is as follows:

[0129] In the formula, This represents the node feature matrix of the l-th layer of the graph discriminator. This involves concatenating real or generated samples with conditional labels. It is the graph filter parameter matrix for each layer of the graph discriminator.

[0130] 2. Pooling and Output: Perform a graph global pooling (GAP) operation on the node-level feature representation to generate a graph-level feature representation.

[0131] The graph-level feature representation is fed into at least one fully connected layer (FC Layer3, Layer4 in this embodiment), ultimately outputting a probability for distinguishing between real and fake data. The calculation process is shown in the following formula:

[0132] In the formula, GAP represents graph-level average pooling, and L... D The number of convolutional layers represents the number of layers in the graph; FC3 and FC4 are fully connected layers. The structural details of the GCVAN model are shown in Table 1. Parameter settings are defined with a sample length of 1024 and the number of classes c=5.

[0133] It is worth noting that both the encoder and discriminator incorporate a collaborative design of graph convolutional layers. The principle and beneficial effects of this collaborative design are as follows:

[0134] The encoder learns how to convert causal graphs into their corresponding structures through its GCN layers (GCN-conv1,2,3). The true signal is compressed into a structured graph-level latent space. middle.

[0135] The discriminator learns, through its GCN layers (GCN-conv4,5), how to determine whether an input signal conforms to a causal graph. The defined physical constraints.

[0136] This collaborative design creates a strong constraint bottleneck: the generator is a... It does not directly receive images. As input. But in order to deceive the discriminator, it must learn how to exploit...

[0137] (It has been encoded) The topological information is used to decode and generate an exact causal graph. Constraint signals .

[0138] Therefore, this co-design allows the generated augmented signal data to implicitly retain the main topological relationships defined by the adjacency matrix (i.e., the causal graph). This ensures the physical consistency of the generated samples. For example, based on By establishing causal relationships, the generator learns to produce a corresponding response on sensor 1 that conforms to physical time delay and propagation intensity when simulating a fault in sensor 5, instead of randomly generating artifacts on unrelated sensors.

[0139] like Figure 8 As shown in the figure, this graph compares the causal strength between the original samples and the augmented samples generated by GCVAN in this invention using the G-PCMCI method. Figure 8 As shown, although the causal strength of the generated samples fluctuates slightly compared to the original samples, the main causal directions and key strong causal relationships are accurately preserved without introducing spurious causal relationships. This demonstrates that the present invention, through a collaborative design in which both the encoder and discriminator contain graph convolutional layers, can ensure that the generated augmented data implicitly retains the main topological relationships defined by the adjacency matrix A, thus guaranteeing the physical consistency of the generated samples.

[0140] Step 3: Train the graph conditional variational adversarial network using a joint loss function.

[0141] This embodiment uses a joint loss function to train GCVAN, as shown in the following formula:

[0142]

[0143] The KL divergence loss of the encoder ensures the learned posterior distribution. It approximates the predefined prior distribution p(z|c). Assume the prior distribution is a standard normal distribution. , It can be expressed as follows:

[0144]

[0145] Used to measure the degree of difference between two probability distributions. It is the mean of the j-th dimension of the latent variables. is the variance of the j-th dimension of the latent variable, and the constant 1 represents the contribution of each dimension. The total contribution is the sum of the dimensions, dz. This regularization ensures that the latent space has a good structure, facilitating the sampling of new fault samples. This term represents the loss of CVAE. As a regularization term, it ensures that the encoder learns the posterior distribution.

[0146] Approximately a predefined prior distribution (e.g., a standard normal distribution). This gives the latent space a good structure, making it easy to sample from it to generate new samples.

[0147] Discriminator loss measures the error of the discriminator in distinguishing between real and generated samples. Discriminator loss is based on binary cross-entropy and can be expressed as follows:

[0148]

[0149] This term represents the loss of the GAN. It is used to train the discriminator D to maximize its ability to correctly distinguish between real samples x and generated samples.

[0150] L G The reconstruction loss between the generator's samples and the real samples, ensuring their similarity in the feature space, can be expressed by the following formula:

[0151]

[0152] This is also the loss of CVAE. In this embodiment, mean squared error (MSE) is used to measure the similarity between generated samples and real samples in the feature space, ensuring that the generator (when acting as a decoder for CVAE) can reconstruct the original input.

[0153] L GD The generator's adversarial loss, which enables generated samples to deceive the discriminator, can be expressed by the following formula:

[0154]

[0155] This model achieves high-quality sample generation and implicit preservation of causal relationships through the collaborative optimization of four loss functions. Specifically, the encoder effectively encodes the causal graph structure into the latent space and maintains key directional features using the adjacency matrix. Simultaneously, the reconstruction loss function ensures that the generated data strictly follows the original causal distribution. Furthermore, the discriminator can accurately identify data patterns that conform to the causal structure. Notably, although this model does not explicitly introduce causal constraints, the generated samples can effectively preserve the underlying causal structure through the synergistic effect of the aforementioned multi-level mechanisms.

[0156] To rigorously evaluate the contribution of each key module in the proposed framework to the final diagnostic performance, a systematic ablation experiment was conducted. Under an extreme imbalance condition of 50:1:

[0157] If only CVAE loss (L) is used KL +L G The model's accuracy plummeted to 31.20%.

[0158] If only GAN loss (L) is used D +L GDThe model (CGAN) achieved an accuracy of 54.00%.

[0159] The present invention (GCVAN) using all four loss terms achieved an accuracy of 62.60%. This indicates that while the adversarial loss of GAN (claims 3 and 4 in claim 4) is the main driver of improved generation quality and diagnostic performance, the loss of CVAE provides more stable training and a more structured latent space, further improving performance from 54.00% to 62.60%. Therefore, the weighted sum of the four losses is necessary to achieve optimal results.

[0160] To balance the stable training of CVAEs and the adversarial game of GANs, this embodiment adopts an alternating optimization strategy, as shown in Table 2 below:

[0161] Table 2: Pseudocode for GCVAN Training Process

[0162]

[0163] As shown in the pseudocode, this training process strictly follows an alternating optimization strategy:

[0164] 1. Fix the parameters of the discriminator and update the parameters of the generator and encoder: This step corresponds to lines 9 and 10 in the pseudocode. Fix the discriminator. The parameters are updated by minimizing the CVAE loss and the generator adversarial loss. and generator The parameters.

[0165] 2. Fix the parameters of the generator and encoder, and update the parameters of the discriminator: This step corresponds to line 11 in the pseudocode.

[0166] fixed and The parameters are updated by minimizing the discriminator loss. The parameters.

[0167] The alternating optimization strategy ensures that the discriminator and generator / encoder maintain a dynamic balance during training, effectively avoiding the pattern collapse problem common in GAN training and making the training process more stable.

[0168] Step 4: Using the trained generator, generate augmented signal data for labels in a few categories.

[0169] After completing the training of GCVAN in step three, fix the generator. The parameters.

[0170] For the few categories that need to be expanded (e.g., tags) ), perform the following operations:

[0171] 1. Randomly sample a graphical level latent variable from a prior distribution (e.g., the standard normal distribution). .

[0172] 2. Provide corresponding minority category tags (For example ).

[0173] 3. The concatenated data is then input into the trained generator. In, that is .

[0174] 4. Generator Output "Extended signal data" .

[0175] Repeat this process until the number of minority class samples reaches the target (e.g., equals the number of majority class samples), forming a class-balanced training dataset.

[0176] This embodiment uses a Graph Convolutional Network (GCN) classifier trained on a generated class-balanced training dataset to perform the final fault diagnosis. This GCN classifier also uses the constructed causal adjacency matrix... As a topological constraint.

[0177] In this embodiment, the GCN classifier used for fault diagnosis has a network architecture consistent with that of the graph discriminator in the system. During the adversarial training process in step three, the discriminator's task is to analyze the causal graph... Under the constraints, it learns to distinguish between "real" and "fake" (signal-label) pairs. To accomplish this challenging task, the discriminator's GCN architecture (GCN-conv4,5 and subsequent layers in Table 1) must have evolved (trained) to be extremely adept at distinguishing between causal graphs. An expert network for extracting high-level fault characteristics.

[0178] Therefore, when a classifier is needed to perform nearly identical feature extraction tasks (i.e., distinguishing different fault labels on a causal graph), reusing this proven and efficient discriminator architecture is the most efficient and logical design choice. This ensures tight coupling between the diagnostic and generative modules. After the GCN classifier is trained using the augmented balanced dataset, the trained model will be deployed for actual fault diagnosis.

[0179] In real-time fault diagnosis, the model is configured to receive real-time multi-sensor signal data from mechanical equipment and utilize a constructed causal adjacency matrix as topological constraints. The GCN classifier processes the input signal data and ultimately outputs the corresponding "fault category" (e.g., label 0-4) and its "confidence level." This output provides reliable technical support for the operation and maintenance decisions of the mechanical equipment.

[0180] To quantitatively analyze the fault diagnosis performance of the proposed method, three indicators—accuracy, F1 score, and mean G—were used for comprehensive evaluation. Table 3 shows the classification results before and after the expansion of the graph sample. All results are the mean and standard deviation of the 5-fold cross-validation experiment. To rigorously evaluate the statistical significance of the performance improvement, paired t-tests were performed on the classification accuracy of the five validation folds before and after expansion. Given that paired t-tests are sensitive to the ranking of accuracy pairings, all 120 possible pairing combinations were calculated, and the mean t-value, p-value, and the proportion of statistically significant comparisons (p < 0.05) were calculated.

[0181] Experimental results show that an increase in the class imbalance ratio leads to a significant decrease in model classification performance. Statistical analysis reveals that when the imbalance ratio is ≥10:1, all configurations exhibit significant results with p<0.05. Furthermore, the increasing standard deviation with decreasing faulty samples reflects the intensified instability of the data distribution. The proposed GCVAN augmentation method effectively alleviates this problem, particularly under extreme imbalance conditions, achieving an approximately 39.2% improvement in classification accuracy when the imbalance ratio reaches 50:1.

[0182] Table 3. Classification results before and after sample augmentation under different imbalance ratios.

[0183]

[0184] like Figure 5 As shown in the figure, this is the confusion matrix for fault diagnosis before GCVAN augmentation under an extreme imbalance of 50:1, according to an embodiment of the present invention. The horizontal axis of the confusion matrix represents the predicted class, and the vertical axis represents the actual class. As shown in the figure, the model's prediction results are severely biased towards the majority class (label 0: normal), while the recognition rate for all minority fault classes (labels 1 to 4) is extremely low, with almost all fault samples being misclassified as normal. This intuitively demonstrates the technical problem that the present invention aims to solve: under imbalanced data, the standard GCN classifier model completely fails due to overfitting to the majority class features.

[0185] like Figure 6 As shown in the figure, this is the confusion matrix for training a GCN classifier using the balanced dataset augmented with the GCVAN of this invention. Figure 5 In stark contrast, Figure 6The values ​​on the main diagonal (i.e., the correct recognition rate of each category) are significantly increased, and the degree of confusion between categories is greatly reduced. This intuitively demonstrates that the method of the present invention effectively solves the class imbalance problem by generating high-quality augmented samples, enabling the diagnostic model to learn all fault features in a balanced manner, and significantly improving the overall accuracy and reliability of fault diagnosis.

[0186] Example 2

[0187] The present invention also provides a multi-sensor signal processing system that can be deployed in an embedded controller of an industrial server, edge computing device, or mechanical device. This system is configured to perform all the method steps described in Embodiment 1 above.

[0188] The system includes at least:

[0189] A graph conditional variational encoder module: configured to operate based on an input adjacency matrix (preferably the causal graph). It processes signal data and category labels to generate latent variables.

[0190] A generator module is configured to generate augmented signal data based on the latent variables and the category labels.

[0191] A graph discriminator module: configured to discriminate based on the adjacency matrix (causal graph) Determine whether the augmented signal data is authentic.

[0192] The graph conditional variational encoder module and the graph discriminator module both include graph convolutional layers to achieve the aforementioned collaborative design.

[0193] In a preferred embodiment, the system further includes:

[0194] A graph convolutional network classifier module: used for fault diagnosis of the (raw or augmented) signal data.

[0195] The network architecture of the graph convolutional network classifier module is consistent with that of the graph discriminator module in the system, so as to achieve efficient and coupled feature extraction and classification.

[0196] Those skilled in the art should understand that the above embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0197] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A multi-sensor signal augmentation method based on graph constraints, characterized in that, Includes the following steps: Acquire multi-sensor signal data, corresponding category labels, and an adjacency matrix that defines the topological relationships between the multi-sensors; Construct a graph conditional variational adversarial network, which includes a graph conditional variational encoder, a generator, and a graph discriminator. The graph conditional variational encoder includes a graph convolutional layer for processing the signal data and category labels according to the adjacency matrix, and generating graph-level latent variables through a single graph average pooling operation. The generator generates augmented signal data based on the latent variables at the graph level and the category labels; The graph discriminator includes a graph convolutional layer, used to determine whether the augmented signal data is authentic under the topological constraints defined by the adjacency matrix. The graph conditional variational adversarial network is trained using a joint loss function, wherein the joint loss function includes at least: a loss associated with the graph conditional variational autoencoder and a loss associated with the generative adversarial network; Using the trained generator, augmented signal data is generated for labels in a few categories.

2. The method according to claim 1, characterized in that, The process of generating latent variables at the graph level includes: The multi-sensor signal data is concatenated with the category label to form an encoder input matrix; The graph conditional variational encoder processes the encoder input matrix through its graph convolutional layers to learn the mean and variance of the latent variables, wherein the mean and variance are at the node level. The reparameterization technique is applied to the mean and variance at the node level to sample the latent variables at the node level; The graph average pooling operation is performed on the node-level latent variables to generate the graph-level latent variables.

3. The method according to claim 1, characterized in that, The process by which the image discriminator determines whether the signal data is genuine includes: The real or augmented signal data is concatenated with the category label to form the discriminator input matrix; The graph discriminator processes the discriminator input matrix through its graph convolutional layer, applying the topological constraints in a way that aggregates neighborhood information, and generates node-level feature representations. Perform a graph global pooling operation on the node-level feature representation to generate a graph-level feature representation; The graph-level feature representation is fed into at least one fully connected layer, and finally outputs a probability for distinguishing between real and fake.

4. The method according to claim 1, characterized in that, The joint loss function includes at least a weighted sum of four losses: a Kerbeck-Leibler divergence loss, a reconstruction loss, a discriminator loss, and a generator adversarial loss.

5. The method according to claim 1 or 4, characterized in that, The training employs an alternating optimization strategy, including: fixing the parameters of the generator and encoder while updating the parameters of the discriminator; and fixing the parameters of the discriminator while updating the parameters of the generator and encoder.

6. The method according to claim 1, characterized in that, Through the collaborative design of graph conditional variational encoder and graph discriminator, both of which include graph convolutional layers, the generated augmented signal data can implicitly retain the main topological relationships defined by the adjacency matrix.

7. The method according to claim 1, characterized in that, The multi-sensor signal data is the vibration signal of the mechanical equipment, the category label is the fault type of the mechanical equipment, and the signal augmentation is used for fault diagnosis.

8. The method according to claim 1, characterized in that, The adjacency matrix is ​​a sparse directed causal graph obtained through a spatiotemporal causal inference method.

9. A multi-sensor signal processing system, characterized in that, include: A graph conditional variational encoder is configured to process signal data and class labels based on an input adjacency matrix to generate latent variables; A generator is configured to generate augmented signal data based on the latent variables and the category labels; A graph discriminator is configured to determine whether the augmented signal data is genuine based on the adjacency matrix; Both the graph conditional variational encoder and the graph discriminator contain graph convolutional layers.

10. The system according to claim 9, characterized in that, The system also includes a graph convolutional network classifier for fault diagnosis of the augmented signal data; wherein the network architecture of the graph convolutional network classifier is consistent with the network architecture of the graph discriminator in the system.

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