Multidimensional data completion method based on Bayesian inference

Abstract

The invention discloses a Bayesian inference-based multi-dimensional data completion method, which comprises the following steps of: calculating a posterior probability of missing data by combining a dual-scale Bayesian model with a naive Bayesian model and correction of feature correlation, and dynamically selecting a maximum posterior probability filling or probability distribution filling strategy according to the posterior probability, and the complementation requirements in scenes with different missing rates are met. In addition, low-rank matrix regularization is introduced into single transformer area load data, and efficient and low-distortion data completion is realized through an optimization algorithm; according to the method, a three-order tensor structure is expanded in multi-zone-area data, total variation regularization is introduced, solving is carried out through a block coordinate descent method, the multi-dimensional features of the data can be effectively processed, and the data complementation precision under the condition of a high missing rate is improved. Finally, the complemented single-zone-area and multi-zone-area data are integrated into a power system data set for load prediction and state monitoring, and the monitoring and prediction capability of the power system is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of power data completion, and in particular, relates to a multidimensional data completion method based on Bayesian inference. Background Art

[0002] In the power system, real-time monitoring and accurate prediction of load data play an important role in power dispatching and system stability. However, due to problems such as sensor failure and communication delay, load data is often missing, especially in multi-station load monitoring, the problem of missing data is more serious. Existing data completion methods mostly rely on simple interpolation or statistical methods. Although these methods can restore data to a certain extent, they do not fully consider the structural characteristics of complex time series load data, and it is difficult to accurately capture the random, oscillatory and trend characteristics in load data. In addition, power load data has a complex multidimensional structure in terms of time, station and feature dimensions. The completion effect of existing methods in high missing rate scenarios is often not ideal, which can easily lead to data distortion and affect subsequent load forecasting and status monitoring.

[0003] To address these issues, some methods attempt to decompose data through techniques such as empirical mode decomposition (EMD) to extract the main components of the signal, but these methods are sensitive to noise and the decomposition accuracy is easily affected by disturbances. On the other hand, probabilistic models based on Bayesian theory are also used to complete missing data, but the traditional naive Bayes model assumes that feature conditions are independent and fails to fully consider the correlation between features, resulting in insufficient accuracy of the completion results in complex scenarios.

[0004] In view of this, the present invention is proposed. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a multidimensional data completion method based on Bayesian inference, which solves the problems raised in the above-mentioned background technology.

[0006] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0007] A multidimensional data completion method based on Bayesian inference includes the following steps:

[0008] S1: Performing ensemble empirical mode decomposition on the power system load data, decomposing the load data into random component, oscillation component and trend component to extract the main features of the data;

[0009] S2: Using the extracted feature data, a dual-scale Bayesian model including a naive Bayesian model and a correction factor is constructed to calculate the posterior probability of missing data while comprehensively considering the correlation between data attributes;

[0010] S3: Based on the posterior probability of the dual-scale Bayesian model, select the corresponding completion strategy for data completion, including maximum posterior probability filling and probability distribution filling;

[0011] S4: Apply the completion strategy to the load data of a single substation, convert the completed data into a low-rank matrix form, and solve it through a regularized optimization algorithm to achieve efficient completion of missing values;

[0012] S5: For the load data of multiple stations, the completed data is expanded and reorganized into a third-order tensor structure, total variation regularization is introduced, and the block coordinate descent method is used for tensor solution to handle multi-dimensional and high missing rate data;

[0013] S6: Integrate the completed single-station area and multi-station area data back into the power system dataset and use it for load forecasting and status monitoring.

[0014] Optionally, the steps of performing collective empirical mode decomposition on the power system load data to decompose the load data into a random component, an oscillating component and a trend component to extract the main features of the data are:

[0015] S101: Collect the load time series data of the power system and preprocess the data to obtain the original load data. Then, generate a set of white noise sequences W i (t), and add it to the original load data to generate multiple disturbance signals X i (t), its expression is: X i (t) = X(t) + ∈ · W i (t), where ∈ is the noise amplitude factor and i is the index of the noise disturbance;

[0016] S102: Add each disturbance signal X to the noise i (t) is decomposed into several intrinsic mode functions and a residual component r i (t), where each intrinsic mode function represents a different frequency component in the data. By repeatedly screening local extreme values, the different frequency components of the signal are gradually extracted;

[0017] S103: performing collective averaging on the same intrinsic mode function group obtained from all disturbance signals to reduce the influence of noise on the result and calculating the final kth intrinsic mode function by averaging the kth intrinsic mode function obtained from the ith disturbance signal, and the expression thereof is: Where M is the number of noise disturbances, IMF i，k (t) is the kth intrinsic mode function of the ith disturbance signal;

[0018] S104: removing all extracted intrinsic mode function groups from the original data to obtain a final residual component, and finally outputting all ensemble-averaged intrinsic mode function groups, and reconstructing the original signal by combining these intrinsic mode function groups with the final residual component.

[0019] Optionally, the steps of constructing a dual-scale Bayesian model including a naive Bayesian model and a correction factor using the extracted feature data to calculate the posterior probability of missing data while comprehensively considering the correlation between data attributes are:

[0020] S201: extracting feature data from the power load data, building a preliminary model based on the acquired feature data using the naive Bayes method, and then, based on the built naive Bayes model, identifying the dependency relationship between the data features by calculating the Pearson correlation coefficient between the features;

[0021] S202: According to the feature correlation obtained by analysis, a correction factor is introduced to adjust the conditional probability in the naive Bayes model. λ The value of is obtained by calculating the correlation between data, and its expression is: Among them, X i and X j Represents two related data attributes;

[0022] S203: Combine the preliminary calculation results of the naive Bayes model with the corrected conditional probability to calculate the final posterior probability. By weighted merging the outputs of the two, the final posterior probability is obtained, which is expressed as P(Y|X) DSB =α·P(Y|X) NB +(1-α)·P(Y|X) adjusted , where α is a balancing factor ranging from 0 to 1, which is used to adjust the ratio of the output of the naive Bayes model and the corrected model, P(Y|X) NB is the preliminary calculation result of the naive Bayes model, P(Y|X) adjusted is the corrected conditional probability;

[0023] S204: According to the posterior probabilities calculated in step S202, the category with the highest posterior probability is selected as the filling value of the missing data to complete the missing data.

[0024] Optionally, the steps of constructing a preliminary model using the naive Bayes method in S201 are:

[0025] S2011: Collect and organize the data set for training. The data set should include input features and corresponding category labels. The input features are the data obtained through the feature extraction process, including but not limited to the time series data of power load;

[0026] S2012: After the training data set is prepared, the prior probability of each category is calculated. The prior probability represents the probability of a category appearing without any feature information. Then, for each category, the conditional probability of each feature in the category is calculated. When calculating the conditional probability, it is first assumed that the features are conditionally independent. The conditional probability of each feature in a given category can be obtained by calculating the distribution of the feature in each category.

[0027] S2013: Through Bayes’ theorem, the prior probability of the category and the conditional probability of the feature are combined to construct a naive Bayes model to form a complete model.

[0028] Optionally, the steps for obtaining the preliminary calculation results of the naive Bayes model are:

[0029] S2031: The input feature data set for prediction is extracted from the trained naive Bayes model for each category’s prior probability, and then the conditional probability of each feature under a given category is extracted from the model;

[0030] S2032: Using the prior probability and conditional probability, calculate the posterior probability P(Y|X) that the sample belongs to each category NB , and then calculate the posterior probability P(Y|X) of each category NB Finally, the posterior probability is normalized so that its sum is 1, and finally the posterior probability of each category is output as the preliminary calculation result.

[0031] Optionally, based on the posterior probability of the dual-scale Bayesian model, a corresponding completion strategy is selected to complete the data. The completion strategy includes the steps of maximum posterior probability filling and probability distribution filling:

[0032] S301: using a dual-scale Bayesian model to calculate the preprocessed power load data to obtain the posterior probability distribution under each category, then sorting all categories according to the calculated posterior probabilities, and then selecting the category with the highest posterior probability in the sorting as the completion value of the missing data;

[0033] S303: When the data category distribution is uneven, a filling strategy based on the posterior probability distribution is adopted. The filling strategy of the posterior probability distribution is to randomly select according to the posterior probability value, and randomly select one from all possible categories as the completion value according to the posterior probability distribution of each category;

[0034] S303: Compare the completed data with the known data. If the verification result is not ideal, adjust the completion strategy for re-evaluation. Finally, evaluate the effects of different completion strategies based on the verification result. For example, if the maximum a posteriori probability filling effect is not good, the frequency of using the probability distribution-based filling strategy can be increased, or more feature information can be introduced into the calculation of the a posteriori probability.

[0035] Optionally, the completion strategy is applied to the load data of a single substation, the completed data is converted into a low-rank matrix form, and the regularized optimization algorithm is used to solve the problem, so as to achieve efficient completion of missing values. The steps are as follows:

[0036] S401: Use posterior probability filling to complete the missing values ​​in the load data of a single substation area, and select the missing data with the maximum posterior probability to complete the corresponding value, so as to obtain a preliminary complete data set;

[0037] S402: reorganizing the completed data into a matrix form, wherein the rows of the matrix represent different time points and the columns represent different load data features. Then, a low-rank constraint is introduced into the completed matrix. The low-rank constraint is to assume that the completed data matrix has a lower rank, and the matrix is ​​optimized by a regularization method to ensure that the low-rank structure of the matrix is ​​maintained.

[0038] S403: Define the objective function used for matrix completion, and introduce the nuclear norm as a regularization term in the objective function to control the rank of the matrix. Then, use the alternating direction multiplication method to alternately update each part of the matrix. In each iteration, minimize the objective function to gradually restore the missing data in the matrix while maintaining the low rank property. Finally, the low rank matrix obtained by the optimization algorithm will be used as the completed data set in the single substation load data.

[0039] Optionally, for the load data of multiple stations, the completed data is expanded and reorganized into a third-order tensor structure, total variation regularization is introduced, and the block coordinate descent method is used for tensor solution. The steps for processing multi-dimensional and high missing rate data are as follows:

[0040] S501: Fill missing values ​​in the load data of multiple substations by posterior probability filling, and convert the completed load data of multiple substations into a three-order tensor structure, in which the first dimension represents time (for example, divided by hours or days), the second dimension represents different substations, and the third dimension represents different characteristics of the load (such as current, power, etc.);

[0041] S502: In the tensor completion process, a total variation regularization term is added to reduce high-frequency noise in the completion process;

[0042] S503: Measure the difference between the completed tensor and the known data to obtain the completion error, then construct an optimization objective function and combine the completion error and total variation regularization, where the optimization goal is to minimize the weighted sum of the two parts;

[0043] S504: By fixing the other dimensions of the tensor, gradually update the tensor blocks of each dimension to perform the optimization solution of tensor completion. After the solution is completed, the tensor completion is completed. After the tensor completion is completed, the final completed data set of the load data of multiple stations can be obtained. During the solution process, monitor the change of the objective function value of each iteration to determine whether the convergence condition is met. If the change of the objective function is less than the preset threshold, or the update change of the tensor is very small, it is considered that the optimization process has converged, and the iteration can be stopped to obtain the final completion result.

[0044] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art. Of course, any product implementing the present invention does not necessarily need to achieve all the advantages described below at the same time:

[0045] The present invention combines a dual-scale Bayesian model with a naive Bayesian model and corrections to feature correlation to calculate the posterior probability of missing data, and dynamically selects the maximum posterior probability filling or probability distribution filling strategy based on the posterior probability to adapt to the completion requirements in different missing rate scenarios. In addition, the present invention introduces low-rank matrix regularization in single-station load data, and achieves efficient and low-distortion data completion through an optimization algorithm; it is expanded to a third-order tensor structure in multi-station data, introduces total variation regularization and solves it through the block coordinate descent method, which can effectively process the multi-dimensional characteristics of the data and improve the data completion accuracy under high missing rate conditions. Finally, the present invention integrates the completed single-station and multi-station data into the power system data set for load forecasting and status monitoring, significantly improving the monitoring and prediction capabilities of the power system.

[0046] The specific implementation modes of the present invention are further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The drawings described below are only some embodiments. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0048] Figure 1 Flowchart of the multidimensional data completion method.

[0049] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but are intended to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0050] The present invention will now be described in further detail with reference to the accompanying drawings.

[0051] See also Figure 1 As shown, in this embodiment, a multidimensional data completion method based on Bayesian inference is provided, including the following steps:

[0052] S1: Performing ensemble empirical mode decomposition on the power system load data, decomposing the load data into random component, oscillation component and trend component to extract the main features of the data;

[0053] S2: Using the extracted feature data, a dual-scale Bayesian model including a naive Bayesian model and a correction factor is constructed to calculate the posterior probability of missing data while comprehensively considering the correlation between data attributes;

[0054] S3: Based on the posterior probability of the dual-scale Bayesian model, select the corresponding completion strategy for data completion, including maximum posterior probability filling and probability distribution filling;

[0055] S4: Apply the completion strategy to the load data of a single substation, convert the completed data into a low-rank matrix form, and solve it through a regularized optimization algorithm to achieve efficient completion of missing values;

[0056] S5: For the load data of multiple stations, the completed data is expanded and reorganized into a third-order tensor structure, total variation regularization is introduced, and the block coordinate descent method is used for tensor solution to handle multi-dimensional and high missing rate data;

[0057] S6: Integrate the completed single-station area and multi-station area data back into the power system dataset and use it for load forecasting and status monitoring.

[0058] In this embodiment, the steps of performing collective empirical mode decomposition on the load data of the power system and decomposing the load data into a random component, an oscillating component and a trend component to extract the main features of the data are as follows:

[0059] S101: Collect the load time series data of the power system and preprocess the data to obtain the original load data. Then, generate a set of white noise sequences W i (t), and add it to the original load data to generate multiple disturbance signals X i (t), its expression is: i (t) = X(t) + ∈ · W i (t), where ∈ is the noise amplitude factor and i is the index of the noise disturbance;

[0060] S102: Add each disturbance signal X to the noise i(t) is decomposed into several intrinsic mode functions and a residual component r i (t), where each intrinsic mode function represents a different frequency component in the data. By repeatedly screening local extreme values, the different frequency components of the signal are gradually extracted;

[0061] S103: performing collective averaging on the same intrinsic mode function group obtained from all disturbance signals to reduce the influence of noise on the result and calculating the final kth intrinsic mode function by averaging the kth intrinsic mode function obtained from the ith disturbance signal, and the expression thereof is: Where M is the number of noise disturbances, IMF i，k (t) is the kth intrinsic mode function of the ith disturbance signal;

[0062] S104: Remove all extracted intrinsic modal function groups from the original data to obtain the final residual component. Finally, output all the ensemble-averaged intrinsic modal function groups, and reconstruct the original signal by combining these intrinsic modal function groups with the final residual component. By adding white noise disturbance to the load time series data of the power system, and decomposing and ensemble-averaging multiple disturbance signals, different frequency components in the signal are gradually extracted to obtain a stable intrinsic modal function group and a final residual component. Through multiple disturbances and ensemble averaging, the influence of noise on the decomposition results is reduced, and the robustness and accuracy of signal decomposition are improved. This method can clearly separate the random, oscillatory and trend components of the load data, providing an accurate and complete feature data basis for further load forecasting and condition monitoring.

[0063] In this embodiment, the extracted feature data is used to construct a dual-scale Bayesian model including a naive Bayesian model and a correction factor to calculate the posterior probability of missing data, while comprehensively considering the correlation between data attributes. The steps are:

[0064] S201: extracting feature data from the power load data, building a preliminary model based on the acquired feature data using the naive Bayes method, and then, based on the built naive Bayes model, identifying the dependency relationship between the data features by calculating the Pearson correlation coefficient between the features;

[0065] S202: According to the feature correlation obtained by analysis, a correction factor is introduced to adjust the conditional probability in the naive Bayes model. The value of the correction factor λ is calculated by the correlation between the data, and its expression is: Among them, X i and X j Represents two related data attributes;

[0066] S203: Combine the preliminary calculation results of the naive Bayes model with the corrected conditional probability to calculate the final posterior probability. By weighted merging the outputs of the two, the final posterior probability is obtained, which is expressed as P(Y|X) DSB =αβ·P(Y|X) NB +(1-α)·P(Y|X) adjusted , where α is a balancing factor ranging from 0 to 1, which is used to adjust the ratio of the output of the naive Bayes model and the corrected model, P(Y|X) NB is the preliminary calculation result of the naive Bayes model, P(Y|X) adjusted is the corrected conditional probability;

[0067] S204: According to the posterior probability calculated in step S202, the category with the highest posterior probability is selected as the filling value of the missing data to complete the missing data. The dependency between the data is identified by calculating the Pearson correlation coefficient between the features, and the correction factor is introduced to adjust the conditional probability, thereby overcoming the limitations of the conditional independence assumption of the naive Bayes model. By weighted merging the preliminary calculation results of the naive Bayes model and the corrected conditional probability, a more accurate posterior probability is obtained, and the optimal category is selected to fill the missing data based on the probability. This scheme maintains the advantages of the naive Bayes model with high computational efficiency and simple structure.

[0068] In this embodiment, the steps of constructing a preliminary model using the naive Bayes method in S201 are:

[0069] S2011: Collect and organize the data set for training. The data set should include input features and corresponding category labels. The input features are the data obtained through the feature extraction process, including but not limited to the time series data of power load;

[0070] S2012: After the training data set is prepared, the prior probability of each category is calculated. The prior probability represents the probability of a category appearing without any feature information. Then, for each category, the conditional probability of each feature in the category is calculated. When calculating the conditional probability, it is first assumed that the features are conditionally independent. The conditional probability of each feature in a given category can be obtained by calculating the distribution of the feature in each category.

[0071] S2013: Through Bayes’ theorem, the prior probability of the category and the conditional probability of the feature are combined to construct a naive Bayes model to form a complete model.

[0072] In this embodiment, the steps for obtaining the preliminary calculation results of the naive Bayes model are:

[0073] S2031: The input feature data set for prediction is extracted from the trained naive Bayes model for each category’s prior probability, and then the conditional probability of each feature under a given category is extracted from the model;

[0074] S2032: Using the prior probability and conditional probability, calculate the posterior probability P(Y|X) that the sample belongs to each category NB , and then calculate the posterior probability P(Y|X) of each category NB Finally, the posterior probability is normalized so that its sum is 1, and the posterior probability of each category is finally output as the preliminary calculation result. By constructing a naive Bayes model, the posterior probability of the sample is calculated by combining the prior probability and the conditional probability, and the posterior probability is normalized to form a clear and structured preliminary calculation result. This model is concise and efficient. By assuming conditional independence between features, it can quickly infer the probability of each category and reduce the computational complexity. At the same time, the normalized posterior probability provides a reliable probability distribution for subsequent classification or data completion, making data analysis more accurate and easy to interpret.

[0075] In this embodiment, based on the posterior probability of the dual-scale Bayesian model, a corresponding completion strategy is selected to complete the data. The completion strategy includes the steps of maximum posterior probability filling and probability distribution filling:

[0076] S301: using a dual-scale Bayesian model to calculate the preprocessed power load data to obtain the posterior probability distribution under each category, then sorting all categories according to the calculated posterior probabilities, and then selecting the category with the highest posterior probability in the sorting as the completion value of the missing data;

[0077] S303: When the data category distribution is uneven, a filling strategy based on the posterior probability distribution is adopted. The filling strategy of the posterior probability distribution is to randomly select according to the posterior probability value, and randomly select one from all possible categories as the completion value according to the posterior probability distribution of each category;

[0078] S303: Compare the completed data with the known data. If the verification result is not ideal, adjust the completion strategy for re-evaluation. Finally, evaluate the effects of different completion strategies based on the verification results. For example, if the maximum a posteriori probability filling effect is not good, the frequency of use of the filling strategy based on probability distribution can be increased, or more feature information can be introduced into the calculation of the posterior probability. The posterior probability of the data is calculated by the dual-scale Bayesian model, and the maximum a posteriori probability filling and the random filling strategy based on the posterior probability distribution are flexibly selected to cope with the missing data filling problem of different category distributions. When the category distribution is uniform, the use of the maximum a posteriori probability filling ensures the accuracy of data completion; in the case of uneven category distribution, the random filling strategy based on probability distribution introduces randomness, avoids bias towards a single category, and increases the diversity of data. In addition, by verifying and adjusting the completion results, the solution can flexibly optimize the filling strategy and improve the overall effect of data completion.

[0079] In this embodiment, the completion strategy is applied to the load data of a single substation, the completed data is converted into a low-rank matrix form, and the regularized optimization algorithm is used to solve the problem, so as to achieve efficient completion of missing values. The steps are as follows:

[0080] S401: Use posterior probability filling to complete the missing values ​​in the load data of a single substation area, and select the missing data with the maximum posterior probability to complete the corresponding value, so as to obtain a preliminary complete data set;

[0081] S402: reorganizing the completed data into a matrix form, wherein the rows of the matrix represent different time points and the columns represent different load data features. Then, a low-rank constraint is introduced into the completed matrix. The low-rank constraint is to assume that the completed data matrix has a lower rank, and the matrix is ​​optimized by a regularization method to ensure that the low-rank structure of the matrix is ​​maintained.

[0082] S403: Define the objective function used for matrix completion, and introduce the nuclear norm as a regularization term in the objective function to control the rank of the matrix. Then, use the alternating direction multiplication method to alternately update each part of the matrix. Minimize the objective function in each iteration to gradually restore the missing data in the matrix while maintaining the low rank property. Finally, the low rank matrix obtained by the optimization algorithm will be used as the completed data set in the single-station load data. By filling the missing values ​​in the single-station load data with posterior probabilities and converting the completed data into a low-rank matrix form, regularized optimization and alternating direction multiplication method (ADMM) are used to solve the problem, effectively achieving efficient data completion. The low rank constraint ensures that the completed matrix maintains a simple structure. At the same time, the introduction of the nuclear norm regularization term can control the rank of the matrix, thereby avoiding overfitting. The ADMM method gradually optimizes each part of the matrix to ensure convergence and improve computational efficiency.

[0083] In this embodiment, for the load data of multiple stations, the completed data is expanded and reorganized into a third-order tensor structure, total variation regularization is introduced, and the block coordinate descent method is used for tensor solution to process multi-dimensional and high missing rate data. The steps are as follows:

[0084] S501: Fill missing values ​​in the load data of multiple substations by posterior probability filling, and convert the completed load data of multiple substations into a three-order tensor structure, in which the first dimension represents time (for example, divided by hours or days), the second dimension represents different substations, and the third dimension represents different characteristics of the load (such as current, power, etc.);

[0085] S502: In the tensor completion process, a total variation regularization term is added to reduce high-frequency noise in the completion process;

[0086] S503: Measure the difference between the completed tensor and the known data to obtain the completion error, then construct an optimization objective function and combine the completion error and total variation regularization, where the optimization goal is to minimize the weighted sum of the two parts;

[0087] S504: By fixing the other dimensions of the tensor, the tensor blocks of each dimension are gradually updated to optimize the solution of tensor completion. After the solution is completed, the tensor completion is completed. After the tensor completion is completed, the final completed data set of the load data of multiple stations can be obtained. During the solution process, the change of the objective function value of each iteration is monitored to determine whether the convergence condition is met. If the change of the objective function is less than the preset threshold, or the update change of the tensor is very small, it is considered that the optimization process has converged, and the iteration can be stopped to obtain the final completion result. By reorganizing the load data of multiple stations into a third-order tensor structure after completion, and combining total variation regularization and block coordinate descent method for optimization and solution, the multi-dimensional characteristics of the data and the high missing rate problem are effectively handled. Total variation regularization can suppress high-frequency noise and maintain the smoothness of the data, while the block coordinate descent method gradually optimizes each dimension in the tensor to ensure the accuracy and convergence of the completion result.

[0088] The present invention is not limited to the above-mentioned embodiments. Anyone should be aware that any structural changes made under the enlightenment of the present invention, and any technical solutions that are the same or similar to the present invention, fall within the protection scope of the present invention. The technology, shape, and structural parts not described in detail in the present invention are all well-known technologies.

Claims

1. A multidimensional data completion method based on Bayesian inference, characterized in that: The following steps are involved: S1: Performing ensemble empirical mode decomposition on the power system load data, decomposing the load data into random component, oscillation component and trend component to extract the main features of the data; S2: Using the extracted feature data, a dual-scale Bayesian model including a naive Bayesian model and a correction factor is constructed to calculate the posterior probability of missing data while comprehensively considering the correlation between data attributes; S3: Based on the posterior probability of the dual-scale Bayesian model, select the corresponding completion strategy for data completion, including maximum posterior probability filling and probability distribution filling; S4: Apply the completion strategy to the load data of a single substation, convert the completed data into a low-rank matrix form, and solve it through a regularized optimization algorithm to achieve efficient completion of missing values; S5: For the load data of multiple stations, the completed data is expanded and reorganized into a third-order tensor structure, total variation regularization is introduced, and the block coordinate descent method is used for tensor solution to handle multi-dimensional and high missing rate data; S6: Integrate the completed single-station area and multi-station area data back into the power system dataset and use it for load forecasting and status monitoring.

2. A multidimensional data completion method based on Bayesian inference according to claim 1, characterized in that: The steps of performing ensemble empirical mode decomposition on the load data of the power system and decomposing the load data into random components, oscillation components and trend components to extract the main features of the data are as follows: S101: Collect the load time series data of the power system and preprocess the data to obtain the original load data. Then, generate a set of white noise sequences W i (t), and add it to the original load data to generate multiple disturbance signals X i (t), its expression is: i (t) = X(t) + ∈ · W i (t), where ∈ is the noise amplitude factor and i is the index of the noise disturbance; S102: Add each disturbance signal X to the noise i (t) is decomposed into several intrinsic mode functions and a residual component r i (t), where each intrinsic mode function represents a different frequency component in the data. By repeatedly screening local extreme values, the different frequency components of the signal are gradually extracted; S103: performing collective averaging on the same intrinsic mode function group obtained from all disturbance signals to reduce the influence of noise on the result and calculating the final kth intrinsic mode function by averaging the kth intrinsic mode function obtained from the ith disturbance signal, and the expression thereof is: Where M is the number of noise disturbances, IMF i，k (t) is the kth intrinsic mode function of the ith disturbance signal; S104: removing all extracted intrinsic mode function groups from the original data to obtain a final residual component, and finally outputting all ensemble-averaged intrinsic mode function groups, and reconstructing the original signal by combining these intrinsic mode function groups with the final residual component.

3. The multidimensional data completion method based on Bayesian inference according to claim 1, characterized in that: Using the extracted feature data, a dual-scale Bayesian model including a naive Bayesian model and a correction factor is constructed to calculate the posterior probability of missing data. The steps of comprehensively considering the correlation between data attributes are as follows: S201: extracting feature data from the power load data, building a preliminary model based on the acquired feature data using the naive Bayes method, and then, based on the built naive Bayes model, identifying the dependency relationship between the data features by calculating the Pearson correlation coefficient between the features; S202: According to the feature correlation obtained by analysis, a correction factor is introduced to adjust the conditional probability in the naive Bayes model. λ The value of is obtained by calculating the correlation between data, and its expression is: Among them, X i and X j Represents two related data attributes; S203: Combine the preliminary calculation results of the naive Bayes model with the corrected conditional probability to calculate the final posterior probability. By weighted merging the outputs of the two, the final posterior probability is obtained, which is expressed as P(Y|X) DSB =α·P(Y|X) NB +(1-α)·P(Y|X) adjusted , where α is a balancing factor ranging from 0 to 1, which is used to adjust the ratio of the output of the naive Bayes model and the corrected model, P(Y|X) NB is the preliminary calculation result of the naive Bayes model, P(Y|X) adjusted is the corrected conditional probability; S204: According to the posterior probabilities calculated in step S202, the category with the highest posterior probability is selected as the filling value of the missing data to complete the missing data.

4. The multidimensional data completion method based on Bayesian inference according to claim 3 is characterized in that: The steps in S201 to build a preliminary model using the naive Bayes method are: S2011: Collect and organize the data set for training. The data set should include input features and corresponding category labels. The input features are the data obtained through the feature extraction process, including but not limited to the time series data of power load; S2012: After the training data set is prepared, the prior probability of each category is calculated. The prior probability represents the probability of a category appearing without any feature information. Then, for each category, the conditional probability of each feature in the category is calculated. When calculating the conditional probability, it is first assumed that the features are conditionally independent. The conditional probability of each feature in a given category can be obtained by calculating the distribution of the feature in each category. S2013: Through Bayes’ theorem, the prior probability of the category and the conditional probability of the feature are combined to construct a naive Bayes model to form a complete model.

5. The multidimensional data completion method based on Bayesian inference according to claim 3 is characterized in that: The steps to obtain the preliminary calculation results of the naive Bayes model are: S2031: The input feature data set for prediction is extracted from the trained naive Bayes model for each category’s prior probability, and then the conditional probability of each feature under a given category is extracted from the model; S2032: Using the prior probability and conditional probability, calculate the posterior probability P(Y|X) that the sample belongs to each category NB , and then calculate the posterior probability P(Y|X) of each category NB Finally, the posterior probability is normalized so that its sum is 1, and finally the posterior probability of each category is output as the preliminary calculation result.

6. The multidimensional data completion method based on Bayesian inference according to claim 1, characterized in that: Based on the posterior probability of the dual-scale Bayesian model, the corresponding completion strategy is selected for data completion. The completion strategy includes the steps of maximum posterior probability filling and probability distribution filling: S301: using a dual-scale Bayesian model to calculate the preprocessed power load data to obtain the posterior probability distribution under each category, then sorting all categories according to the calculated posterior probabilities, and then selecting the category with the highest posterior probability in the sorting as the completion value of the missing data; S303: When the data category distribution is uneven, a filling strategy based on the posterior probability distribution is adopted. The filling strategy of the posterior probability distribution is to randomly select according to the posterior probability value, and randomly select one from all categories as the completion value according to the posterior probability distribution of each category; S303: Compare the completed data with the known data. If the verification result is not ideal, adjust the completion strategy for re-evaluation. Finally, based on the verification result, evaluate the effects of different completion strategies.

7. The multidimensional data completion method based on Bayesian inference according to claim 1, characterized in that: The completion strategy is applied to the load data of a single substation, the completed data is converted into a low-rank matrix form, and the regularized optimization algorithm is used to solve it, so as to achieve efficient completion of missing values. The steps are as follows: S401: Use posterior probability filling to complete the missing values ​​in the load data of a single substation area, and select the missing data with the maximum posterior probability to complete the corresponding value, so as to obtain a preliminary complete data set; S402: reorganizing the completed data into a matrix form, wherein the rows of the matrix represent different time points and the columns represent different load data features, and then introducing a low-rank constraint into the completed matrix; S403: Define the objective function used for matrix completion, and introduce the nuclear norm as a regularization term in the objective function to control the rank of the matrix. Then, use the alternating direction multiplication method to alternately update each part of the matrix. In each iteration, minimize the objective function to gradually restore the missing data in the matrix while maintaining the low rank property. Finally, the low rank matrix obtained by the optimization algorithm will be used as the completed data set in the single substation load data.

8. The multidimensional data completion method based on Bayesian inference according to claim 1, characterized in that: For the load data of multiple stations, the completed data is expanded and reorganized into a third-order tensor structure. Total variation regularization is introduced, and the block coordinate descent method is used to solve the tensor. The steps to process multi-dimensional and high missing rate data are as follows: S501: filling missing values ​​in the load data of multiple substations by posterior probability filling, and converting the completed load data of multiple substations into a three-order tensor structure, in which the first dimension represents time, the second dimension represents different substations, and the third dimension represents different characteristics of the load; S502: In the tensor completion process, a total variation regularization term is added to reduce high-frequency noise in the completion process; S503: Measure the difference between the completed tensor and the known data to obtain the completion error, then construct an optimization objective function and combine the completion error and total variation regularization, where the optimization goal is to minimize the weighted sum of the two parts; S504: By fixing other dimensions of the tensor, the tensor blocks of each dimension are gradually updated to perform an optimized solution for tensor completion. After the solution is completed, the tensor completion is completed. After the tensor completion is completed, the final completed data set of the load data of multiple stations can be obtained.

Images