Power data virtual acquisition method based on stochastic differential equation

Abstract

The invention provides an electric power data virtual acquisition method based on a stochastic differential equation, and the method constructs a diffusion model network structure with a continuous time distribution modeling capability aiming at the problem that data missing is easy to occur in a new energy load data acquisition process. The method comprises the following steps: firstly, masking an input sequence through a random mask strategy in a training process so as to simulate a potential data missing scene, and carrying out supervised training on observed data; and then accurate virtual acquisition of missing values is realized through learning conditional probability distribution. On the basis, a stochastic differential equation (SDE) is adopted, noise is slowly injected, complex data distribution is smoothly converted into known prior distribution, and reverse time SDE of a time correlation gradient field which only depends on disturbance data distribution is adopted, and the prior distribution is converted into data distribution by slowly removing noise. Experimental verification on two real world data sets shows that the method is superior to an existing method in the aspect of virtual acquisition accuracy, and the superiority of the method is proved.

Description

Technical Field

[0001] This invention relates to a virtual acquisition method for power data based on stochastic differential equations, belonging to the field of deep learning technology in computer intelligent science. Background Technology

[0002] New energy sources are being integrated into my country's power system at an unprecedented speed and scale, becoming a key force in promoting green and low-carbon transformation. The installed capacity of new energy sources such as wind and solar power continues to grow rapidly, occupying an increasingly important position in the power supply system. However, real-world new energy load data is prone to gaps during collection, resulting in poor data quality. Therefore, a spatiotemporal graph interpolation method is urgently needed to virtually collect missing data and improve the quality of new energy load data.

[0003] Currently, existing research mainly employs attention-based Transformers and their variants, or generative methods such as diffusion models, for spatiotemporal graph interpolation. Attention-based methods focus on the global interaction of data patterns. Variants utilize multi-scale approaches to focus on data patterns at different scales, decompose data into more interpretable parts using seasonal trend decomposition, or perform attention calculations between different sites at the same time step. Diffusion model methods primarily focus on restoring real data patterns from noise. The main idea is to add multiple steps of noise to the real data and then restore it using a noise prediction module. These two types of methods have addressed the interpolation problem of new energy data to some extent. However, attention-based methods do not adequately utilize graph structure information, and the discrete-time-step noise addition used in diffusion model methods does not match the continuity of noise in the real world, limiting the model's generalization ability in complex interpolation scenarios. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a virtual acquisition method for power data based on stochastic differential equations. This method can utilize the capabilities of diffusion models to perform spatiotemporal graph interpolation in new energy data scenarios, and its accuracy is superior to existing methods.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for virtual acquisition of power data based on stochastic differential equations, the method comprising the following steps:

[0007] Step 1: Since the goal of the virtual data acquisition task is to generate missing values, this method treats it as an imputation task. Given a sample X containing missing values... 0 Through observed values The graph structure information A generates the interpolation target. The goal of the diffusion model is to use model distribution Predict the true conditional distribution In spatiotemporal graph tasks, this conditional distribution also includes graph structure information A, i.e., the model distribution. Predict the true conditional distribution The forward and reverse diffusion processes in the diffusion model used for spatiotemporal graph networks include the following sub-steps:

[0008] Step 1-1, the forward diffusion process of the diffusion model is defined by the following Markov process:

[0009]

[0010] Where β t It is a hyperparameter that controls the variance of added noise. It is a Gaussian distribution. Based on the properties of the Gaussian distribution, we can directly determine X... 0 Sample X t As shown in the following formula:

[0011]

[0012] in By introducing variables sampled from a standard Gaussian distribution You can directly use X t Represented as

[0013] Steps 1-2, the reverse process of the diffusion model, utilizes spatiotemporal correlation to recover missing values ​​from random noise. In the spatiotemporal graph interpolation task, the spatiotemporal graph data contains observed values. The reverse process of graph structure information A is defined by the following Markov process:

[0014]

[0015] Using reparameterization techniques, μ can be... θ and It is expressed as follows:

[0016]

[0017] Where ∈ θ It is a neural network parameterized by θ, using noise sampling X t Current diffusion step t, observed values Using graph structure information A as input, we predict the noise added to the interpolation target and recover the original value from the noise. and These are the mean and variance parameters in (4), respectively.

[0018] Compared to traditional generation methods, the diffusion model generates data through forward and backward diffusion, which has stronger interpretability: the diffusion model learns the data distribution at each diffusion step and restores the data to be virtually collected from the noise step by step according to the data distribution characteristics, while traditional models often generate an end-to-end output with poor interpretability of intermediate steps.

[0019] Step 2: Incorporate stochastic differential equations to improve the diffusion process. The above diffusion model method uses a discrete approach for adding and removing noise, employing the SDE method to construct the diffusion process using continuous-time variables t∈[0,T] as an index. Make x(0) ~ p0, x(T) ~ p T Where p0 is the data distribution, p T This is the prior distribution. This diffusion process can be modeled using the following formula:

[0020] dx=f(x,t)dt+g(t)dw (5)

[0021] Where w is the standard Wiener process, and its inverse process can be given by the following equation:

[0022]

[0023] Where f(x,t) is the drift coefficient with respect to x, and g(t) is the diffusion coefficient with respect to x. This represents a standard Wiener process with time ranging from T to 0. The marginal distribution can be estimated using the score matching method.

[0024]

[0025] Where λ(t) is a positive weighting function, and t is obtained by uniform sampling over [0,T]. In the diffusion model, the diffusion step is set to uniformly sample from [0,T], and the noise is estimated by a noise estimation module.

[0026] Compared to existing diffusion models that rely on discrete diffusion steps, continuous diffusion with stochastic differential equations can generate more accurate noise addition and denoising results, breaking through the accuracy and speed problems caused by the step-by-step noise addition and denoising of previous models.

[0027] Step 3 introduces various masking mechanisms for training, including: point masking, block masking, and hybrid masking. The point masking strategy sets a percentage m within the range of [0, 100%], randomly selecting data points representing m percentages from the observed data for masking. The block masking strategy sets a length L and a probability within the range of [0, 15%]. Each point is used as the starting point for the block mask according to its probability, and a uniform sampling length of [L / 2, L] is applied for masking. The hybrid masking strategy uses both types of masks simultaneously: first, block masking is applied, and then point masking is performed on the unmasked data. These masking strategies allow for supervised training of the model on the observed data, thereby optimizing model parameters against real-world data.

[0028] By changing the training method from unsupervised training to supervised training, the model can verify its virtual collection results with real values ​​during the training process, thus enabling more effective training.

[0029] Step 4 involves capturing spatiotemporal graph information using attention mechanisms and graph convolution methods, and estimating the noise of the diffusion model, including the following sub-steps:

[0030] Step 4-1: For a directed graph, its graph propagation process has two directions, where the positive transition matrix is ​​P. f =A / rowsum(A), the reverse transition matrix is ​​P b =A / rowsum(A T Using the forward and backward transition matrices, the graph spread convolution calculation can be represented as follows:

[0031]

[0032] Among them, W k1 and W k2 These are learnable parameters.

[0033] Step 4-2, introduce the adaptive adjacency matrix End-to-end learning is performed using stochastic gradient descent. The matrix is ​​obtained by multiplying the embeddings of two nodes:

[0034]

[0035] Where E1, E2 ∈ R N×C These are two learnable node embeddings. By multiplying E1 and E2, the spatial dependency weights between the source and target nodes can be derived.

[0036] Step 4-3 combines graph spread convolution calculation and adaptive adjacency matrix. The graph convolutional layer is further rewritten as follows:

[0037]

[0038] Among them, W k1 W k2 and W k3 These are learnable parameters.

[0039] Step 4-4 employs an attention mechanism to capture the time-series relationships in the spatiotemporal graph data, allowing the model to learn the overall changing trends of missing data while incorporating geographical relationships between sites. The calculation of the fusion of the attention mechanism and graph convolution is as follows:

[0040] H temp =Conv(H l-1 (11)

[0041]

[0042] Where Attn(·) represents attention calculation, the subscripts spa and tem represent spatial attention and temporal attention respectively, MPNN(·) represents the graph convolutional layer in steps 4-3, Conv(·) represents a one-dimensional convolutional layer, MLP(·) represents a fully connected layer, and H l H represents the hidden representation of the output of the l-th layer of the model, where H 0 =X.

[0043] By constructing an adaptive adjacency matrix, the model can adaptively learn spatial relationships between nodes in addition to predefined graph structure information. Through bidirectional graph diffusion convolution, this method can simultaneously model the influence of a node on its surrounding nodes and the influence of surrounding nodes on the node during graph information propagation. Through an attention mechanism, the model can fuse spatial information between different nodes with temporal information within the same node, thereby providing a more reasonable and accurate estimate of noise.

[0044] Step 5: Combining the masking mechanism from Step 3, the mean squared error (MSE) loss function is used for model training.

[0045]

[0046] Where M represents the mask matrix, M tn =1 indicates that the position is masked, otherwise it indicates that it is not masked. tn and These represent the output data after model interpolation and the actual observation data, respectively.

[0047] After the model is trained, the trained model can be used to perform spatiotemporal graph interpolation tasks in different scenarios.

[0048] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0049] (1) A virtual acquisition method for power data based on stochastic differential equations is adopted, which transforms the discrete time step noise addition in the previous diffusion model into continuous time step noise addition, making the noise simulation in the diffusion model more in line with the real noise situation, thereby giving the model a stronger noise modeling ability and generalization ability; (2) Multiple masking methods are introduced to mask and generate the observed data, so that the model can be trained in a supervised manner on data with missing data, thereby improving the model performance; (3) Adaptive graph learning is introduced in the noise estimation module of the diffusion model, so that the model can adaptively construct topological graph information according to the current data pattern and the relationship between stations, thereby improving the model's ability to utilize spatial graph information; (4) Bidirectional graph diffusion convolution is adopted in the noise estimation module of the diffusion model to fully consider the data interaction between different stations, thereby improving the effectiveness of graph structure modeling; (5) When applied to virtual acquisition on real power datasets, this method can generate more accurate virtual acquisition results than other methods, and is less prone to abnormal phenomena such as jumps, exceeding limits, and dead values. Moreover, this method does not depend on specific scenarios or specific data, nor does it depend on prior knowledge. It can be transferred to virtual acquisition tasks of any number of stations and has strong generalization ability. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method of the present invention.

[0051] Figure 2 This is a schematic diagram of the virtual power data acquisition method based on stochastic differential equations provided by the present invention.

[0052] Figure 3 This is a schematic diagram of the virtual data acquisition performance experiment results of the present invention on a real power dataset. Figure 1 ,

[0053] Figure 4 This is a schematic diagram of the virtual data acquisition performance experiment results of the present invention on a real power dataset. Figure 2 . Detailed Implementation

[0054] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0055] Example: The present invention proposes a virtual power data acquisition method based on stochastic differential equations, as follows: Figure 1 and Figure 2 As shown, specifically, the present invention includes the following steps:

[0056] Step 1: Since the goal of the virtual data acquisition task is to generate missing values, this method treats it as an imputation task. Given a sample X containing missing values... 0 Through observed values The graph structure information A generates the interpolation target. The goal of the diffusion model is to use model distribution Predict the true conditional distribution In spatiotemporal graph tasks, this conditional distribution also includes graph structure information A, i.e., the model distribution. Predict the true conditional distribution The forward and reverse diffusion processes in the diffusion model used for spatiotemporal graph networks include the following sub-steps:

[0057] Step 1-1, the forward diffusion process of the diffusion model is defined by the following Markov process:

[0058]

[0059] Where β t It is a hyperparameter that controls the variance of added noise. It is a Gaussian distribution. Based on the properties of the Gaussian distribution, we can directly determine X... 0 Sample X t As shown in the following formula:

[0060]

[0061] in By introducing variables sampled from a standard Gaussian distribution You can directly use X t Represented as

[0062] Steps 1-2, the reverse process of the diffusion model, utilizes spatiotemporal correlation to recover missing values ​​from random noise. In the spatiotemporal graph interpolation task, the spatiotemporal graph data contains observed values. The reverse process of graph structure information A is defined by the following Markov process:

[0063]

[0064] Using reparameterization techniques, μ can be... θ and It is expressed as follows:

[0065]

[0066] Where ∈ θ It is a neural network parameterized by θ, using noise sampling X t Observed values Using graph structure information A as input, we predict the noise added to the interpolation target and recover the original value from the noise.

[0067] Step 2: Incorporate stochastic differential equations to improve the diffusion process. The above diffusion model method uses a discrete approach for adding and removing noise, employing the SDE method to construct the diffusion process using continuous-time variables t∈[0,T] as an index. Make x(0) ~ p0, x(T) ~ p T Where p0 is the data distribution, p T This is the prior distribution. This diffusion process can be modeled using the following formula:

[0068] dx=f(x,t)gt+g(t)dw (5)

[0069] Where w is the standard Wiener process, and its inverse process can be given by the following equation:

[0070]

[0071] Where f(x,t) is the drift coefficient with respect to x, and g(t) is the diffusion coefficient with respect to x. This represents a standard Wiener process with time ranging from T to 0. The marginal distribution can be estimated using the score matching method.

[0072]

[0073] Where λ(t) is a positive weighting function, and t is obtained by uniform sampling over [0,T]. In the diffusion model, the diffusion step is set to uniformly sample from [0,T], and the noise is estimated by a noise estimation module.

[0074] Step 3 introduces various masking mechanisms for training, including: point masking, block masking, and hybrid masking. The point masking strategy sets a percentage m within the range of [0, 100%], randomly selecting data points representing m percentages from the observed data for masking. The block masking strategy sets a length L and a probability within the range of [0, 15%]. Each point is used as the starting point for the block mask according to its probability, and a uniform sampling length of [L / 2, L] is applied for masking. The hybrid masking strategy uses both types of masks simultaneously: first, block masking is applied, and then point masking is performed on the unmasked data. These masking strategies allow for supervised training of the model on the observed data, thereby optimizing model parameters against real-world data.

[0075] Step 4 involves capturing spatiotemporal graph information using attention mechanisms and graph convolution methods, and estimating the noise of the diffusion model, including the following sub-steps:

[0076] Step 4-1: For a directed graph, its graph propagation process has two directions, where the positive transition matrix is ​​P. f =A / rowsum(A), the reverse transition matrix is ​​Pb =A / rowsum(A T Using the forward and backward transition matrices, the graph spread convolution calculation can be represented as follows:

[0077]

[0078] Among them, W k1 and W k2 These are learnable parameters.

[0079] Step 4-2, introduce the adaptive adjacency matrix End-to-end learning is performed using stochastic gradient descent. The matrix is ​​obtained by multiplying the embeddings of two nodes:

[0080]

[0081] Where E1, E2 ∈ R N×C These are two learnable node embeddings. By multiplying E1 and E2, the spatial dependency weights between the source and target nodes can be derived.

[0082] Step 4-3 combines graph spread convolution calculation and adaptive adjacency matrix. The graph convolutional layer is further rewritten as follows:

[0083]

[0084] Among them, W k1 W k2 and W k3 These are learnable parameters.

[0085] Step 4-4 employs an attention mechanism to capture the time-series relationships in the spatiotemporal graph data, allowing the model to learn the overall changing trends of missing data while incorporating geographical relationships between sites. The calculation of the fusion of the attention mechanism and graph convolution is as follows:

[0086] H temp =Conv(H l-1 (11)

[0087]

[0088] Where Attn(·) represents attention computation, the subscripts spa and tem represent spatial attention and temporal attention respectively, MPNN(·) represents the graph convolutional layer in steps 4-3, Conv(·) represents the one-dimensional convolutional layer, MLP(·) represents the fully connected layer, and Hl represents the hidden representation output by the l-th layer of the model, where H 0 =X.

[0089] Step 5: Combining the masking mechanism from Step 3, the mean squared error (MSE) loss function is used for model training.

[0090]

[0091] Where M represents the mask matrix, M tn =1 indicates that the position is masked, otherwise it indicates that it is not masked. tn and These represent the output data after model interpolation and the actual observation data, respectively.

[0092] After the model is trained, the trained model can be used to perform spatiotemporal graph interpolation tasks in different scenarios.

[0093] The prediction errors of the virtual power data acquisition method based on stochastic differential equations provided by this invention and other comparative methods in experiments with real datasets are shown in Table 1. The bolded parts in the table indicate the smallest error, i.e. the best performance.

[0094] Table 1. Comparison Experiment of Spatiotemporal Map Interpolation

[0095]

[0096] As shown in Table 1, the model of this invention achieved the lowest values ​​for both mean absolute error (MAE) and mean squared error (MSE) across all datasets, demonstrating its stability and effectiveness in non-stationary scenarios. Compared with mainstream models, this method achieves higher imputation accuracy, indicating that the model can capture key patterns and invariant features from historical sequences and flexibly adapt to different data distributions.

[0097] like Figure 3 As shown, during testing on a real power dataset, a data segment was simulated missing at a certain power station, and the model was required to virtually collect data from it. Experiments demonstrate that the data generated by this method is more stable and closely approximates the actual values ​​compared to other methods.

[0098] like Figure 4 As shown, in a real power dataset, during the test, a data segment was simulated missing at a certain power station, and the actual value of this segment varied significantly over time. The model was required to virtually collect this data. Experiments show that the interpolation results of this method better match the changes and trends of the actual values.

[0099] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A method for virtual acquisition of power data based on stochastic differential equations, characterized in that, The method includes the following steps: Step 1: Since the goal of the virtual acquisition task is to generate missing values, this method treats it as an imputation task, given a sample X containing missing values. 0 Observed values Graph structure information A defines the forward and reverse diffusion processes for the diffusion model used in spatiotemporal graph networks. Step 2: Based on Step 1, a stochastic differential equation is added to improve the diffusion process. Step 3: Introduce multiple masking mechanisms to generate training data through random masks for supervised training of the model. Step 4: Use attention mechanisms and graph convolution methods to capture spatiotemporal graph information and estimate the noise of the diffusion model. Step 5: Combining the masking mechanism of Step 3, the mean squared error (MSE) loss function is used to train the model on a real power dataset. The trained model can be used to virtually collect power data that has not been collected during the power grid signal transmission process.

2. The method for virtual acquisition of power data based on stochastic differential equations according to claim 1, characterized in that, In step 1, the data processing procedure is as follows: Given a sample X containing missing values 0 Through observed values The graph structure information A generates the interpolation target. The goal of the diffusion model is to use model distribution Predict the true conditional distribution In spatiotemporal graph tasks, this conditional distribution also includes graph structure information A, i.e., the model distribution. Predict the true conditional distribution The forward and reverse diffusion processes for the diffusion model used in spatiotemporal graph networks are defined as follows: Step 1-1, the forward diffusion process of the diffusion model is defined by the following Markov process: Where β t It is a hyperparameter that controls the variance of added noise. It is a Gaussian distribution. Based on the properties of the Gaussian distribution, we can directly determine the distribution from X. 0 Sample X t As shown in the following formula: in By introducing variables sampled from a standard Gaussian distribution Directly X t Represented as Steps 1-2, the reverse process of the diffusion model, utilizes spatiotemporal correlation to recover missing values ​​from random noise. In the spatiotemporal graph interpolation task, the spatiotemporal graph data includes observed values. The reverse process of graph structure information A is defined by the following Markov process: Using reparameterization techniques, μ θ and It is expressed as follows: Where ∈ θ It is a neural network parameterized by θ, using noise sampling X t Current diffusion step t, observed values Using graph structure information A as input, we predict the noise added to the interpolation target and recover the original value from the noise. and These are the mean and variance parameters in (4), respectively.

3. The method for virtual acquisition of power data based on stochastic differential equations according to claim 1, characterized in that, In step 2, stochastic differential equations are added to improve the diffusion process. The above diffusion model method uses a discrete approach for adding and removing noise, and the SDE method is used to construct the diffusion process by indexing the continuous time variable t∈[0,T]. Make x(0) ~ p0, x(T) ~ p T Where p0 is the data distribution, p T The prior distribution is used to model this diffusion process using the following formula: dx=f(x,t)gt+g(t)dw (5) Where w is the standard Wiener process, and its inverse process is given by the following equation: Where f(x,t) is the drift coefficient with respect to x, and g(t) is the diffusion coefficient with respect to x. The marginal distribution of a standard Wiener process representing time from T to 0 is estimated using a score matching method. Where λ(t) is a positive weighting function, and t is uniformly sampled on [0,T]. In the diffusion model, the diffusion step is set to uniformly sample from [0,T], and the noise is estimated by the noise estimation module.

4. The method for virtual acquisition of power data based on stochastic differential equations according to claim 1, characterized in that, In step 3, multiple masking mechanisms are introduced for training, including: point masking, block masking, and hybrid masking. The point masking strategy sets a percentage m of [0, 100%] and randomly selects data points of percentage m from the observed data for masking. The block masking strategy sets a length L and a probability within the range of [0, 15%]. Each point is used as the starting point for the block mask according to its probability, and a uniform sampling length of [L / 2, L] is used for masking. The hybrid masking strategy employs both types of masking simultaneously: first, block masking is used, and then point masking is applied to the unmasked data. These masking strategies allow the model to undergo supervised training on the observed data, thereby optimizing the model parameters with real data as the target.

5. The method for virtual acquisition of power data based on stochastic differential equations according to claim 1, characterized in that, In step 4, attention mechanisms and graph convolution methods are used to capture spatiotemporal graph information and estimate the noise of the diffusion model, including the following sub-steps: Step 4-1: For a directed graph, its graph diffusion process has two directions, where the positive transition matrix is ​​P. f =A / rowsum(A), the reverse transition matrix is ​​P b =A / rowsum(A T Using the forward and backward transition matrices, the graph spread convolution calculation is represented as follows: Among them, W k1 and W k2 For learnable parameters, Step 4-2, introduce the adaptive adjacency matrix End-to-end learning is performed using stochastic gradient descent, and the matrix is ​​obtained by multiplying the embeddings of two nodes: Where E1, E2 ∈ R N×C These are two learnable node embeddings. By multiplying E1 and E2, the spatial dependency weights between the source and target nodes are derived. Step 4-3 combines graph spread convolution calculation and adaptive adjacency matrix. The graph convolutional layer is further rewritten as follows: Among them, W k1 W k2 and W k3 For learnable parameters, Step 4-4 employs an attention mechanism to capture the time-series relationships in the spatiotemporal graph data. This allows the model to learn the overall trend of missing data while incorporating geographical relationships between sites. The calculation of the attention mechanism combined with graph convolution is as follows: H temp =Conv(H l-1 ) (11) Where Attn(·) represents attention calculation, the subscripts spa and tem represent spatial attention and temporal attention respectively, MPNN(·) represents the graph convolutional layer in steps 4-3, Conv(·) represents a one-dimensional convolutional layer, MLP(·) represents a fully connected layer, and H l H represents the hidden representation of the output of the l-th layer of the model, where H 0 =X.

6. The method for virtual acquisition of power data based on stochastic differential equations according to claim 1, characterized in that, In step 5, combining the masking mechanism from step 3, the mean squared error (MSE) loss function is used for model training: Where M represents the mask matrix, M tn =1 indicates that the position is masked, otherwise it indicates that it is not masked. tn and These represent the output data after model interpolation and the actual observation data, respectively.

7. A computer-readable storage medium storing computer instructions thereon, characterized in that: When executed by a processor, the computer instructions implement the steps of the power data virtual acquisition method based on stochastic differential equations as described in any one of claims 1-6.

8. An electronic device, characterized in that, include: processor; Memory used to store the processor's executable instructions; The processor is configured to execute the instructions to implement the virtual acquisition method for power data based on stochastic differential equations as described in any one of claims 1 to 6.

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