Power transmission and transformation equipment data filling method and system based on time series prediction

Abstract

The present application relates to the field of power systems and their digitization technology, and more particularly to a power transmission and transformation equipment data filling method and system based on time series prediction, which infers missing values through small least squares support vector machine and dynamic Bayesian network, and replaces missing data in complete time series curves with existing data rules; It shows strong robustness when dealing with long-time data missing or sudden abnormalities, and can effectively avoid model distortion caused by data blank; Through the continuity prediction of time series and the filling of blank data, the digital twin model will maintain its real-time and accurate reflection of the operation state of the power transmission and transformation equipment; This provides more reliable support for equipment fault diagnosis, state monitoring and predictive maintenance, thereby improving the operation efficiency and safety of the power transmission and transformation equipment.

Description

Technical Field

[0001] This invention relates to the field of power systems and their digital technology, and in particular to a method and system for filling data into power transmission and transformation equipment based on time series prediction. Background Technology

[0002] Currently, digital twin technology for power transmission and transformation equipment integrates information technologies such as physical sensing, numerical computation, and simulation. It establishes a virtual entity corresponding to the physical entity, enabling a digital description of the physical entity and using data analysis and modeling techniques to monitor, diagnose, and predict its performance. The application of this technology in power transmission and transformation equipment can establish a connection between the physical and information spaces, achieving interactive mapping between the physical equipment and its virtual twin. However, the application of digital twin technology in power transmission and transformation equipment is still in the theoretical research stage, but it provides a new technical path for the full lifecycle management of power transmission and transformation equipment. Areas for improvement include standard setting, model fusion, and data mining.

[0003] The application of existing time series forecasting digital twin technology in power transmission and transformation equipment faces several technical challenges, including insufficient understanding of the physical laws governing defects and faults, significant differences in the quality of sensing data leading to the inability to effectively integrate data, the need to improve the accuracy of existing power transmission and transformation equipment condition assessment models and their poor scalability, and the inability of the current level of intelligence to achieve auxiliary judgment functions. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention is proposed.

[0005] Therefore, the technical problem this invention aims to solve is: to address the issue of data gaps that may occur during the construction of digital twins for power transmission and transformation equipment due to sensor failures, data transmission interruptions, or data loss. A time-series forecasting method can fill these data gaps by analyzing the trends of equipment performance indicators over time, identifying periodic characteristics, and detecting anomalies, effectively preventing equipment failures and predicting maintenance needs. This method ensures that the digital twin model accurately reflects the state of the physical entity, thereby guaranteeing the continuity and integrity of the digital twin model data.

[0006] To address the aforementioned technical problems, this invention provides the following technical solution: a data filling method for power transmission and transformation equipment based on time series prediction, comprising: collecting and analyzing historical operating data of power transmission and transformation equipment to obtain a multivariate time series; performing missing value detection on the multivariate time series to determine the data filling region; filling the missing data; inferring the missing values; and optimizing the parameters of the filling algorithm based on the verification results.

[0007] As a preferred embodiment of the data filling method for power transmission and transformation equipment based on time series prediction described in this invention, the multivariate time series includes observations arriving in a time series manner, expressed as:

[0008] x i (t), (i=1, 2,..., m; t=1, 2,..., n)

[0009] Where i is the measured value of time point t[1]; when i = 1, it is a univariate time series, and when i ≥ 2, it is a multivariate time series.

[0010] As a preferred embodiment of the data filling method for power transmission and transformation equipment based on time series prediction described in this invention, the missing value detection includes: obtaining an item from an incomplete subset and comparing it with an item from a complete subset; replacing the missing value with the corresponding value in the complete item; calculating the dynamic time warping distance between the two time series curves; finding the minimum distance between the entire complete subset; and replacing the missing value with the corresponding value in the best sequence curve.

[0011] As a preferred embodiment of the data filling method for power transmission and transformation equipment based on time series prediction described in this invention, the method for determining the data filling region includes a multivariate filling method. If there is missing data in the i-th variable dimension of sequence S1, a similar sequence to S1 is searched centrally based on the multivariate time series dataset. If the search results are S1, S2, ..., S... n Then it is considered as the training set D = {(x k y k )};x k ∈R m-1 The input vector consists of (m-1) variables, excluding the i-th variable, with dimensions S2, S3, ..., S... n The data composition at a given time point; y k ∈R represents the output vector, consisting of S1, S2, ..., S n It consists of data from each time point of the i-th variable dimension.

[0012] As a preferred embodiment of the time-series prediction-based data imputation method for power transmission and transformation equipment described in this invention, the imputation of missing data includes training an LSSVM using a training set, where the function x in the original space... k →y k Convert to:

[0013]

[0014] in, J(ω, e) represents minimizing ω, b, and e, where ω represents the weight vector, b represents the bias term, e represents the error term, and J(ω, e) represents the objective function.T ω represents the regularization term, where ω T This represents the transpose of the weight vector ω. T ω represents the sum of squares of the weight vectors. This represents the sum of squares of the error terms. Let y represent the weight vector and y represent the regularization parameter. Represents the kernel space mapping function; e k ∈R represents error, and b represents deviation.

[0015] As a preferred embodiment of the time-series prediction-based data filling method for power transmission and transformation equipment described in this invention, the method for inferring missing values ​​includes using a dynamic Bayesian network to infer missing values. If two curves x and Y, x... i Represent a set of points on the curve x, y j Let X be a set of points representing curve Y. Then the Euclidean distance d(X, Y) is expressed as:

[0016]

[0017] The dynamic time-warped distance is calculated as follows: If time series curves x and Y, x = <x1,x2,...,x i , ..., x n >,Y= <y1,y2,...,y j , ..., y m >, where n represents the length of x and m represents the length of Y; the minimum dynamic time warp distance is expressed as:

[0018]

[0019] Where, d k This represents the distance between elements; the DTW distance is calculated using dynamic programming with the cumulative matrix, and is expressed as:

[0020]

[0021] Where r(i, j) represents the cumulative distance, d(x) i y j ) represents the distance between the i-th element of time series X and the j-th element of time series Y, p represents the penalty term, and min represents the function that takes the minimum value.

[0022] As a preferred embodiment of the data filling method for power transmission and transformation equipment based on time series prediction described in this invention, the parameters of the optimized filling algorithm include solving the optimization problem by constructing a Lagrange equation, expressed as:

[0023]

[0024] Where L(ω, b, e, α) represents the Lagrange function, α represents the Lagrange multiplier, and α k ∈R denotes the Lagrange multiplier, k denotes the data point, and J(ω,e) denotes the original objective function. The difference between the predicted and actual values;

[0025] If L reaches ω, b, e k α k The partial derivatives are equal to 0, and ω, e k Elimination, represented as:

[0026]

[0027] in, Let y = [y1, y2, ..., y3] be a v×v matrix. N ] T Let α = [α1, α2, ..., α3] be the regularization function. N ] T Denotes the Lagrange multiplier vector, 1 v = [1, 1, ..., 1] T Represents a column vector of dimensions v;

[0028] According to Mercer's condition, there exists a mapping function. The relationship between the kernel function K(·,·) and the kernel function K(·,·) is expressed as follows:

[0029]

[0030] The estimation function of the least squares support vector machine is expressed as:

[0031]

[0032] Another objective of this invention is to provide a data imputation system for power transmission and transformation equipment based on time series prediction. This system utilizes modules for data collection, missing value detection, data imputation, and imputation verification, along with time series prediction methods, to extract feature values ​​from past time series data. Based on the principle of curve similarity, the more similar the corresponding features of two curves, the more similar the two lines are. By leveraging the correlation between variables in a multivariate time series, incomplete time series curves are compared with all complete curves in the dataset. Then, a less-squares support vector machine and a dynamic Bayesian network are used to infer missing values ​​and replace the missing data in the complete time series curves.

[0033] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a data filling system for power transmission and transformation equipment based on time series prediction, comprising: a data collection module, a missing data detection module, a data filling module, and a filling verification module;

[0034] The data collection module obtains multivariate time series data by collecting and analyzing historical operating data of power transmission and transformation equipment;

[0035] The missing value detection module performs missing value detection on the multivariate time series to determine the data filling region;

[0036] The data filling module fills in the missing data;

[0037] The filling verification module verifies the filled data, evaluates the error between the filled data and the actual data, and optimizes the parameters of the filling algorithm based on the verification results.

[0038] A computer device includes a memory and a processor, the memory storing a computer program, characterized in that the processor executes the computer program to implement the steps of the time-series prediction-based data filling method for power transmission and transformation equipment as described above.

[0039] A computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the time-series prediction-based data filling method for power transmission and transformation equipment as described above.

[0040] The beneficial effects of this invention are as follows: By filling in the gaps in power transmission and transformation equipment data using a time-series prediction method, the continuity and integrity of the digital twin model data are ensured. The use of least-squares support vector machines (LSSVM) and dynamic Bayesian networks for missing value inference enhances the model's robustness in handling long-term data gaps or sudden anomalies, avoiding model distortion caused by data gaps. Through the analysis of equipment performance index trends and anomaly detection, the digital twin model can more accurately reflect the physical entity's state, providing reliable support for equipment fault diagnosis and predictive maintenance, and optimizing the operating efficiency and safety of power transmission and transformation equipment. This method provides technical support for equipment condition monitoring, fault diagnosis, and predictive maintenance, promoting a new path for the full lifecycle management of power transmission and transformation equipment. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A flowchart of a data filling method for power transmission and transformation equipment based on time series prediction, provided as an embodiment of the present invention.

[0043] Figure 2 The flowchart illustrates the missing data filling algorithm for power transmission and transformation equipment based on time series prediction, as provided in one embodiment of the present invention. Detailed Implementation

[0044] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0045] Example 1, referring to Figures 1-2 This is one embodiment of the present invention, which provides a method for data filling of power transmission and transformation equipment based on time series prediction, including:

[0046] S1: By collecting and analyzing historical operating data of power transmission and transformation equipment, a multivariate time series is obtained.

[0047] It should be noted that, such as Figure 1 As shown in S1, the time series includes observations arriving in time, represented as:

[0048] x i (t), (i=1,2,…,m; t=1,2,…,n)

[0049] Where i represents the measured value at time point t[1]; when i = 1, it is a univariate time series, and when i ≥ 2, it is a multivariate time series.

[0050] Furthermore, due to various interference factors, data loss in multivariate time series is inevitable, which will affect data processing and analysis. Therefore, methods for imputing missing data in multivariate time series are needed.

[0051] Furthermore, the multivariate autoregressive model is a classic time series analysis method. The method based on functional relationships is used to fill in missing data. A dataset can be regarded as an information system, and the data in a set of data usually have the same pattern of change. The algorithm can mine reasonable values ​​by analyzing the inherent principle of the dataset. LSSVM introduces the least squares linear system into the vector machine, which transforms the quadratic programming problem into a linear equation. This helps LSSVM to effectively improve the computation speed and generalization ability.

[0052] S2: Perform missing value detection on multivariate time series data to determine the data regions to be filled.

[0053] It should be noted that, such as Figure 1As shown in S2, an item is obtained from the incomplete subset and compared with an item from the complete subset; missing values ​​are replaced with corresponding values ​​from the complete items, and the dynamic time-warped distance between the two time series curves is calculated. In this way, the minimum distance between the entire complete subset is found, and the missing values ​​are replaced with the corresponding values ​​from the best sequence curve. The algorithm flow is as follows: Figure 2 As shown.

[0054] Furthermore, there are correlations between variables in a multivariate time series, so missing data in one variable dimension can be filled with data from other related variables; without loss of generality, in this invention, it is assumed that there is missing data in the i-th variable dimension of sequence S1.

[0055] Furthermore, based on the multivariate time series dataset, search for similar sequences to S1. If the search results are S1, S2, ..., S... n Then it is considered as the training set D = {(x k ,y k )};x k ∈R m-1 The input vector consists of (m-1) variables, excluding the i-th variable, with dimensions S2, S3, ..., S... n The data composition at a given time point; y k ∈R represents the output vector, consisting of S1, S2, ..., S n It consists of data from each time point of the i-th variable dimension.

[0056] S3: Fill in the missing data.

[0057] It should be noted that, such as Figure 1 As shown in S3, imputing missing data includes training the LSSVM using the training set, and the function x in the original space. k →y k Convert to:

[0058]

[0059] in, J(ω,e) represents minimizing ω, b, and e, where ω represents the weight vector, b represents the bias term, e represents the error term, and J(ω,e) represents the objective function used to measure the model's performance and needs to be minimized. T ω represents the regularization term, where ω T This represents the transpose of the weight vector ω. T ω represents the sum of squares of the weight vectors. This represents the sum of squares of the error terms, used to control model complexity and avoid overfitting. Let y represent the weight vector and y represent the regularization parameter. Represents the kernel space mapping function; e k ∈R represents error, and b represents deviation.

[0060] S4: Infer the missing values ​​and optimize the parameters of the imputation algorithm based on the verification results.

[0061] It should be noted that, such as Figure 1 As shown in S4, missing value inference includes using a dynamic Bayesian network for missing value inference. If two curves X and Y, x... i Let y represent a set of points on curve X. j Let X be a set of points representing curve Y. Then the Euclidean distance d(X, Y) is expressed as:

[0062]

[0063] Dynamic Time Wrapping (DTW) is suitable for complex curves in similarity metrics. In DTW, it requires finding the nearest map path, allowing one-to-many correspondences in curve pairs, allowing curves to have different lengths, and inserting new points as needed to ensure order. The DTW calculation is expressed as: if time series curves X and Y, X = ... <x1,x2,...,x i , ..., x n >,Y= <y1,y2,...,y j , ..., y m >, where n represents the length of X and m represents the length of Y; construct an n×m matrix m, where the two curves have a point-to-point relationship, and this matrix can ensure that the wrapping path grows at any time; as can be seen from this invention, too many paths can meet the requirements, and how to select the minimum path is the key; the minimum dynamic time warping distance is expressed as:

[0064]

[0065] Where, d k d(x) i y j This refers to the distance between elements, which can be measured using different distance measures, such as Euclidean distance. The DTW distance is calculated using dynamic programming with the cumulative matrix and is expressed as:

[0066]

[0067] Where r(i, j) represents the cumulative distance, d(x) i y j) represents the distance or difference measure between the i-th element of time series X and the j-th element of time series Y. This distance can be Euclidean distance, absolute difference, or any other suitable measure. p represents a penalty term used to handle insertion or deletion operations in the time series. In the standard DTW algorithm, this penalty term is 0, but in some variants, a positive penalty value may be added to control the curvature of the time series. min represents a function that takes the minimum value and selects the smallest one from three cumulative distances to determine the cumulative distance of the current element pair.

[0068] Furthermore, optimizing the parameters of the filling algorithm involves solving the optimization problem by constructing the Lagrange equation, expressed as:

[0069]

[0070] Where L(ω, b, e, α) represents the Lagrange function, which is an extension of the original optimization problem, including α, which represents the Lagrange multiplier. k ∈R represents the constraint condition of the Lagrange multiplier for each data point k, where k represents the data point, and J(ω,e) represents the original objective function that needs to be minimized. The difference between the predicted and actual values; multiplied by the Lagrange multiplier α, it forms part of the Lagrange function;

[0071] If L reaches ω, b, e k α k The partial derivatives are equal to 0, and ω, e k Elimination, represented as:

[0072]

[0073] in, A v×v matrix, typically representing the similarity or kernel matrix between data points, y = [y1, y2, ..., y3]. N ] T This represents the regularization function, used to control the trade-off between model complexity and fitting error, α = [α1, α2, ..., α...]. N ] T Represents the Lagrange multiplier vector, corresponding to each data point, 1 v = [1, 1, ..., 1] T Represents a v-dimensional column vector, with all elements equal to 1;

[0074] According to Mercer's condition, any positive semi-definite function can be used as a kernel function, and a mapping function exists. The relationship between the kernel function K(·,·) and the kernel function K(·,·) is expressed as follows:

[0075]

[0076] The estimation function of the least squares support vector machine is expressed as:

[0077]

[0078] a and b can be obtained from the Lagrange multiplier matrix. Finally, this invention uses a trained LSSVM model to fill the missing data in S1. At each time point in S1, this invention takes the data of the other (m-1) variable dimensions as input values ​​and outputs the filled data of S1.

[0079] Furthermore, in the LSSVM model, a kernel function is used to project the samples into a high-dimensional space, transforming the nonlinear problem into a linear one. Since the Radial Basis Function (RBF) has good performance and only has one shape parameter, this invention uses RBF as the kernel function. The LSSVM model includes two parameters: a regularization parameter y and a shape parameter σ. y represents the weight of the fitting error; the larger y is, the closer the fitting function is to the sampling point. σ affects the smoothness of the fitting curve; the larger σ is, the smoother the fitting curve, but the fitting effect may be poor. To obtain better filling effect, parameters should be reasonably selected during the use of this invention to ensure a smooth fitting curve and small fitting error.

[0080] The above is an illustrative scheme of a data filling method for power transmission and transformation equipment based on time series prediction according to this embodiment. It should be noted that the technical solution of this system for data filling of power transmission and transformation equipment based on time series prediction belongs to the same concept as the technical solution of the aforementioned data filling method for power transmission and transformation equipment based on time series prediction. Details not described in detail in the technical solution of the system for data filling of power transmission and transformation equipment based on time series prediction in this embodiment can be found in the description of the technical solution of the aforementioned data filling method for power transmission and transformation equipment based on time series prediction.

[0081] Example 2 is an embodiment of the present invention, which provides a data filling method for power transmission and transformation equipment based on time series prediction. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiment.

[0082] Data from 680 patients was collected for this test. First, we artificially created an incomplete dataset by removing some elements. The dataset was then divided into a complete subset (Sc) and an incomplete subset (Si), and experiments were conducted using mean distance, pattern distance, and our method. Our experimental environment consisted of a Dell 760 with a Core 2 dual-core E8500 CPU and 2GB of RAM. MATLAB V7.5 was used. We programmed and conducted experiments, using three methods to impute missing values. The imputed data was then compared to the actual values ​​to assess the imputation effectiveness of different methods, using the mean relative error (e) as the comparison criterion. The error calculation formula is as follows:

[0083]

[0084] e represents the normalization error, which is a metric measuring the difference between predicted and actual values. Here, n is the number of missing data points, and S... t ,r t Let represent the t-th filled data and the actual data, respectively. As can be seen from the table, the method proposed in this invention demonstrates the best filling results. To further verify the robustness of the algorithm, some values ​​were removed from the dataset given in the power grid system section, making it an incomplete dataset. After each filling, this incomplete dataset was compared with the actual data. The algorithm is effective when the size of the incomplete dataset does not exceed the size of the complete dataset.

[0085] The results are shown in Table 1 below:

[0086] Table 1 Data Results

[0087] Least squares method Bayesian traditional methods The method proposed in the patent All data 100 100 100 Correct data 36 32 68 Correct proportions 36％ 32％ 68％ deviation 47.40％ 52.32％ 25.64％

[0088] Example 3, an embodiment of the present invention, provides a data filling system for power transmission and transformation equipment based on time series prediction, including: a data collection module, a missing data detection module, a data filling module, and a filling verification module;

[0089] The data collection module obtains a multivariate time series by collecting and analyzing historical operating data of power transmission and transformation equipment;

[0090] The missing value detection module performs missing value detection on the multivariate time series to determine the data filling region;

[0091] The data filling module fills in the missing data;

[0092] The filling verification module verifies the filled data, evaluates the error between the filled data and the actual data, and optimizes the parameters of the filling algorithm based on the verification results.

[0093] This embodiment also provides a computing device applicable to data filling methods for power transmission and transformation equipment based on time series prediction, including:

[0094] The system includes a memory and a processor. The memory stores computer-executable instructions, and the processor executes these instructions to implement the data filling method for power transmission and transformation equipment based on time series prediction, as proposed in the above embodiments.

[0095] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the data filling method for power transmission and transformation equipment based on time series prediction as proposed in the above embodiments.

[0096] The storage medium proposed in this embodiment and the data filling method for power transmission and transformation equipment based on time series prediction proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0097] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0098] The logic and / or steps otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0099] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0100] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A power transmission and transformation equipment data filling method based on time series prediction, characterized in that: The application relates to a time series prediction-based power transmission and transformation equipment data filling method and device. The method comprises the following steps: A multi-element time sequence is obtained by collecting and analyzing historical operation data of power transmission and transformation equipment; Missing value detection is performed on the multi-element time sequence to determine a data filling area; Missing data is filled in; Parameters of a filling algorithm are optimized according to a verification result after missing values are inferred; ； wherein, index time point measurement value; when is a univariate time series, when is a multivariate time series; The multi-element time sequence comprises observation values arriving in time sequence and is expressed as: The determining the filling data region comprises a multivariate filling method, if there is missing data in the variable dimension of the sequence , the first variable dimension is searched for similar sequences in the multivariate time series data set, and if the search result is , , , , the training set ; represents an input vector, which is composed of data from time points of variable dimensions except the first variable; , , represents an output vector, which is composed of data from each time point of variable dimensions , , , .​ The filling in the missing data includes training the LSSVM using the training set, the function in the original space is converted to: ； ； wherein represents a weight vector, minimizes, represents a weight vector, represents a bias term, represents an error term, represents an objective function, represents a regularization term, wherein represents a weight vector transpose of, represents a sum of squares of the weight vector, represents a sum of squares of the error term, wherein, , represents a weight vector, represents a regularization parameter, represents a kernel space mapping function; represents an error, represents a bias.

2. The power transmission and transformation equipment data filling method based on time series prediction according to claim 1, characterized in that: The inferring of the missing values includes inferring missing values using a dynamic Bayesian network, wherein if two curves and , represent a set of points of a curve , represent a set of points of a curve , then the Euclidean distance is represented as: ； The dynamic time warping distance is calculated as follows: If the time series curves and , , , represent the length of , represent the length of ; and the minimum dynamic time warping distance is calculated as follows: ； wherein, denotes the distance between elements; the DTW distance is computed by dynamic programming of the cumulative matrix, denoted as: ； wherein, denotes the accumulated distance, denotes the time series the distance between the element of the time series the element of the time series denotes the penalty term, denotes the function that takes the minimum value.

3. The power transmission and transformation equipment data filling method based on time series prediction according to claim 2, characterized in that: The missing value detection comprises the following steps: an item is obtained from an incomplete subset and compared with an item from a complete subset; the missing value is replaced by a corresponding value in the complete item, a dynamic time warping distance of two time sequence curves is calculated, a minimum distance between the whole complete subset is found, and the missing value is replaced by a corresponding value in the optimal sequence curve; ； wherein, denotes a Lagrangian function, denotes a Lagrange multiplier, denotes a Lagrange multiplier, denotes a data point, denotes an original objective function, denotes a difference between a predicted value of the type and an actual value. If to the partial derivative of and eliminate, expressed as: ； wherein denotes a matrix, denotes a regularization function, denotes a Lagrange multiplier vector, denotes a column vector of dimension According to the Mercer condition, there exists a mapping function and a kernel function The relationship is expressed as: ； The optimization of the parameters of the filling algorithm comprises solving an optimization problem by constructing a Lagrange equation and is expressed as: 。 4. A system for power transmission and transformation equipment data filling based on time series prediction according to any one of claims 1-3, characterized in that: An estimation function of the least squares support vector machine is expressed as: The application relates to a time series prediction-based power transmission and transformation equipment data filling method and device. The method comprises the following steps: A data collection module, a missing value detection module, a data filling module and a filling verification module are provided; The data collection module obtains a multi-element time sequence by collecting and analyzing historical operation data of power transmission and transformation equipment; The missing value detection module performs missing value detection on the multi-element time sequence to determine a data filling area; 5.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-4 when the computer program is executed by the processor. The data filling module fills in missing data; 6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The filling verification module verifies the filled data, evaluates an error between the filled data and actual data, and optimizes parameters of a filling algorithm according to a verification result. The processor executes the computer program to realize the steps of the time series prediction-based power transmission and transformation equipment data filling method in any one of claims 1 to 3. The computer program is executed by the processor to realize the steps of the time series prediction-based power transmission and transformation equipment data filling method in any one of claims 1 to 3.

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