Missing load recovery method based on similar block embedding and first-order polynomial interpolation

Abstract

The invention discloses a missing load recovery method based on similar block embedding and first-order polynomial interpolation. The method comprises the following steps: firstly, acquiring power consumer load data and constructing a third-order load tensor; according to the missing load position, a matched similar block offset is constructed, and the matched similar block offset is specifically the offset between the missing load position and the matched similar block position; matching similar blocks are optimized and selected through a spreading rule and irregular search, the sum of squares of errors of the matching similar blocks and missing load position data blocks serves as a selection standard, and initial recovery data are generated through the optimal similar blocks. And performing first-order polynomial interpolation on the missing position load data of the expansion tensor, and constructing auxiliary recovery data. And combining the preliminary recovery data with the auxiliary recovery data to obtain a final missing load recovery result. The method provided by the invention is helpful for fully mining the characteristics of the load data, and has certain practical significance for realizing the recovery of random missing of the user load data.

Description

Technical Field

[0001] The present invention relates to the field of electric power big data mining, and in particular to a missing load recovery method based on similar block embedding and first-order polynomial interpolation. Background Art

[0002] The continuous construction of smart grids and the increase in the number of electricity consumers have led to the integration of a large number of intelligent measurement and real-time monitoring devices into the power network, generating a huge amount of data. The huge data sets generated by these smart grids are widely used in power system planning, power equipment status assessment, anomaly detection, fault diagnosis and load forecasting. Accurate measurement data is the basis for information mining and application. However, missing data in power load data is a common problem. On the distribution network and power consumption side, due to the complexity of distribution lines and the large number of users, the collection, transmission, storage and processing of user load data may be interfered by various factors such as equipment failure, transmission interference, and external environment. These factors may cause load data loss or damage, thereby seriously damaging the integrity of load data. This will seriously affect the accuracy and effectiveness of user load data analysis, making it impossible to accurately perform a series of subsequent operations based on the analysis results, such as load forecasting, status estimation, operation planning, etc., which seriously affects the stable operation of the power system. Therefore, according to the characteristic relationship between the load characteristics of power users and the measurement data, it is crucial to effectively restore the missing load data to ensure the safety and stable operation of the power system. Summary of the invention

[0003] The purpose of the present invention is to address the deficiencies of the prior art and provide a missing load recovery method based on similar block embedding and first-order polynomial interpolation. The method utilizes the local similarity and continuity of user load data, embeds the missing position load by matching similar blocks, and integrates the first-order polynomial interpolation results, so as to comprehensively and efficiently recover and reconstruct the missing load data.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A missing load recovery method based on similar block embedding and first-order polynomial interpolation includes the following steps:

[0006] Step 1: Collect all user load data and construct a third-order load tensor based on sampling time, sampling date and user. Take the sampling time as the first mode, expand the third-order load tensor according to the first mode, and obtain the expanded tensor to highlight the change trend and characteristics of the load in time distribution;

[0007] Step 2: Based on the missing load position index, construct a matching similar block offset, wherein the matching similar block offset is specifically the offset between the missing load position and the matching similar block position; optimize the selection of matching similar blocks through multiple iterations based on the spreading rule and irregular search, and use the square sum of the errors between the matching similar blocks and the missing load position data block as the selection criterion for matching similar blocks; use the finally selected matching similar block as the optimal similar block, and use the optimal similar block as the preliminary recovery data of the missing load;

[0008] Step 3: construct auxiliary recovery data based on the missing position load data of the expanded tensor through first-order polynomial interpolation, and fuse the preliminary recovery data and the auxiliary recovery data to obtain the final missing load recovery results for all users.

[0009] In the above technical solution, further, in step 1, the third-order load tensor is expanded according to the first mode to obtain an expanded tensor, which is specifically:

[0010]

[0011] In the formula, is the load matrix of user sample m, a represents the total number of sampling moments, b represents the number of sampling days, and c represents the number of user samples; It represents the expanded tensor obtained by expanding the third-order load tensor according to the sampling time. Among them, the load matrix can highlight the changing trend and characteristics of the time information constructed according to the sampling time in these dimensions, and retain the interactive information and correlation influence with the other two modes, which is reflected in the column distribution of the load matrix.

[0012] Furthermore, the matching similar block offset in step 2 is specifically:

[0013]

[0014] In the formula, Indicates the offset of the matching similar block at the similar block (i, j), including the x and y directions; dx and dy are independent from [-p max ,p max ]A random variable sampled from a uniform distribution, p max Indicates the maximum allowed offset.

[0015] Furthermore, in step 2, the selection of matching similar blocks is optimized through multiple iterations based on the spreading rule and irregular search, and the sum of square errors between the matching similar blocks and the missing load position data blocks is used as the selection criterion for matching similar blocks, specifically:

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, err cur 、err left and err up They are the similarity errors of the current similar block, the similar block on its left, and the similar block above it based on the sum of squared errors; and are the missing load location data block and the current similarity block respectively. and They are Offset in x and y directions; and They are The offset in the x and y directions, and They are The offset in the x and y directions, and are the offsets of the similar block at (i, j) and its left similar block and the similar block above it. The above process borrows the preferred matching similar block offset from the adjacent similar blocks according to the spreading rule, O I (i, j) represents the matching similar block offset corresponding to the minimum square error sum between the similar block at (i, j) and the missing load position data block, which is the transfer optimization result of the current matching relationship.

[0021] In order to avoid local optimum, I The matching block position corresponding to (i, j) is taken as the center, and an irregular search is performed in the radius area with exponential decay until the search radius becomes a similar block:

[0022]

[0023] Where r represents the maximum search radius; β represents the specified attenuation coefficient in [0,1]; τ represents a random number that obeys a two-dimensional uniform distribution; k represents the number of irregular searches; O II (i, j) represents the offset of the matching similar block at (i, j) after k irregular searches;

[0024] If the error decreases, use O II (i,j) replaces O I (i,j), otherwise keep O I (i, j), continue iterative search until the search radius becomes a similar block;

[0025] The matching similar block corresponding to the matching similar block offset with the smallest square error sum in the entire iterative search process is taken as the optimal similar block; and the optimal similar block is taken as the preliminary recovery data of the missing load; the calculation formula of the preliminary recovery data of the missing load is:

[0026]

[0027] In the formula, represents the preliminary recovery data of the missing load at (i, j); is the offset of the matching similar block with the smallest sum of squared errors in the entire iterative search process, and They are The offset in the x and y directions.

[0028] Furthermore, the auxiliary recovery data is constructed based on the missing position load data of the expanded tensor based on the first-order polynomial interpolation described in step 3, specifically:

[0029]

[0030] Where w is the row index of the load missing location, ; v is the column index of the load missing position, ; p and q represent the row indices of the non-missing positions of the load, satisfying p <w<q; Auxiliary recovery data representing the load data at the missing position (w,v) of the unfolded tensor;

[0031] The preliminary recovery data and the auxiliary recovery data are integrated to obtain the final missing load recovery results of all users, which are specifically:

[0032]

[0033] In the formula, represents the final missing load recovery result, and They are the primary recovery data and auxiliary recovery data for all users respectively.

[0034] The present invention also provides a device for recovering missing load data of power users based on similar block embedding technology and first-order polynomial interpolation, which is used to implement the above method. The device comprises:

[0035] The expanded tensor acquisition module is used to collect all user load data and construct a third-order load tensor based on the sampling time, sampling date and user, and take the sampling time as the first mode, expand the third-order load tensor according to the first mode to obtain the expanded tensor;

[0036] The module for obtaining preliminary recovery data of missing load is used to construct a matching similar block offset based on the missing load position index, wherein the matching similar block offset is specifically the offset between the missing load position and the matching similar block position; optimize the selection of matching similar blocks through multiple iterations based on the spreading rule and irregular search, and use the square sum of the errors between the matching similar blocks and the missing load position data block as the selection criterion of the matching similar blocks; use the finally selected matching similar block as the optimal similar block, and use the optimal similar block as the preliminary recovery data of the missing load;

[0037] The missing load recovery module is used to construct auxiliary recovery data based on the missing position load data of the expanded tensor through first-order polynomial interpolation, and fuse the preliminary recovery data and the auxiliary recovery data to obtain the final missing load recovery results for all users.

[0038] The present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the missing load recovery method based on similar block fitting and first-order polynomial interpolation.

[0039] The present invention also provides a computer-readable storage medium on which computer instructions are stored, wherein the computer instructions are used to enable a computer to execute the missing load recovery method based on similar block embedding and first-order polynomial interpolation.

[0040] The beneficial effects of the present invention are:

[0041] The present invention aims at the missing completion and recovery of user load data with missing values, and proposes a missing load recovery method based on similar block mosaic and first-order polynomial interpolation. The present invention optimizes the selection through the spreading rule and irregular search, takes the error square sum as the optimization selection criterion, and generates preliminary recovery data with the optimal similar block average value. First-order polynomial interpolation is performed on the load data at the missing position of the expanded tensor, auxiliary recovery data is constructed, and the preliminary recovery data and auxiliary recovery data are weighted and combined to output the final missing load recovery result. Compared with relying solely on the first-order polynomial interpolation algorithm, this method introduces similar block mosaic technology, which can introduce more realistic texture details while maintaining the coherence of the load matrix structure; at the same time, similar block mosaic can provide better edge retention characteristics to compensate for the blurring effect produced by the first-order polynomial interpolation at the edge. This method can fully consider the inherent connection of user load data, such as local correlation, continuity and other characteristics, and has certain practical significance for realizing a more comprehensive and effective completion of missing values ​​of load data. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1The figure is a schematic diagram of the overall steps of the missing load recovery method based on similar block embedding and first-order polynomial interpolation of the present invention.

[0043] Figure 2 The load curve results of the method of the present invention and other methods for completing load data with different missing rates are compared. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is described in detail below in conjunction with the accompanying drawings and implementation examples. It should be understood that the specific implementation examples described herein are only used to explain the present invention and are not used to limit the invention.

[0045] The present invention proposes a missing load recovery method based on similar block embedding and first-order polynomial interpolation, such as Figure 1 As shown, according to a specific embodiment of the present invention, the implementation process of the method includes the following steps:

[0046] Step 1: Collect all user load data and construct a third-order load tensor based on sampling time, sampling date and user, and take the sampling time as the first mode, expand the third-order load tensor according to the first mode to obtain an expanded tensor, highlighting the change trend and characteristics of the load in time distribution. The specific implementation method of this step is as follows:

[0047]

[0048] In the formula, is the load matrix of user sample m, a represents the total number of sampling moments, b represents the number of sampling days, and c represents the number of user samples; Represents the expanded tensor obtained by expanding the third-order load tensor according to the sampling time.

[0049] Step 2: Based on the missing load position index, construct a matching similar block offset, wherein the matching similar block offset is specifically the offset between the missing load position and the matching similar block position; optimize the selection of matching similar blocks through multiple iterations based on the spreading rule and irregular search, and use the sum of squared errors between matching similar blocks and missing load position data blocks as the selection criterion for matching similar blocks; use the finally selected matching similar block as the optimal similar block, and use the optimal similar block as the preliminary recovery data of the missing load. Among them, the missing load position data block can specifically be composed of a total of 5 data including the missing load position and its upper, lower, left and right data. Then the optimal similar block finally selected will include 5 data. At this time, the preliminary recovery data of the missing load can be obtained by calculating the average value of the optimal similar block (optimal similar block / 5). The specific implementation method of this step is as follows:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] In the formula, Indicates the offset of the matching similar block at the similar block (i, j), including the x and y directions; dx and dy are independent from [-p max ,p max ]A random variable sampled from a uniform distribution, p max Indicates the maximum allowed offset; err cur 、err left and err up They are the similarity errors of the current similar block, the similar block on its left, and the similar block above it based on the sum of squared errors; and are the missing load location data block and the current similarity block respectively. and They are Offset in x and y directions; and They are The offset in the x and y directions, and They are The offset in the x and y directions, and are the offsets of the similar block at (i, j) from the similar block on its left and the similar block above; I (i, j) represents the matching similar block offset corresponding to the minimum sum of square errors between the similar block at (i, j) and the missing load position data block.

[0056] In order to avoid local optimum, I The matching similar block position corresponding to (i, j) is taken as the center, and an irregular search is performed in the exponentially decaying radius area until the search radius becomes a similar block:

[0057]

[0058] Where r represents the maximum search radius; β represents the specified attenuation coefficient in [0,1]; τ represents a random number that obeys a two-dimensional uniform distribution; k represents the number of irregular searches; O II(i, j) represents the offset of the matching similar block at (i, j) after k irregular searches;

[0059] If the error decreases, use O II (i,j) replaces O I (i,j), otherwise keep O I (i, j), continue iterative search until the search radius becomes a similar block;

[0060] The matching similar block corresponding to the matching similar block offset with the smallest square error sum in the entire iterative search process is taken as the optimal similar block; and the optimal similar block is taken as the preliminary recovery data of the missing load; the calculation formula of the preliminary recovery data of the missing load is:

[0061]

[0062] In the formula, represents the preliminary recovery data of the missing load at (i, j); is the offset of the matching similar block with the smallest sum of squared errors in the entire iterative search process, and They are The offset in the x and y directions.

[0063] Step 3: construct auxiliary recovery data based on the missing position load data of the expanded tensor through first-order polynomial interpolation, and fuse the preliminary recovery data and the auxiliary recovery data to obtain the final missing load recovery results for all users. The specific implementation method of this step is as follows:

[0064] The construction of auxiliary recovery data based on the missing position load data of the expanded tensor based on first-order polynomial interpolation is specifically:

[0065]

[0066] Where w is the row index of the load missing location, ; v is the column index of the load missing position, ; p and q represent the row indices of the non-missing positions of the load, satisfying p <w<q; Auxiliary recovery data representing the load data at the missing position (w,v) of the unfolded tensor;

[0067] The preliminary recovery data and the auxiliary recovery data are integrated to obtain the final missing load recovery results of all users, which are specifically:

[0068]

[0069] In the formula, represents the final missing load recovery result, and They are the primary recovery data and auxiliary recovery data for all users respectively.

[0070] The following uses the user load data of a certain area as an example to illustrate:

[0071] In order to verify the effectiveness and superiority of the proposed missing load recovery method based on similar block fitting and first-order polynomial interpolation, the load voltage data of users in a certain area from March 1 to 28 for a total of 28 days were selected as the complete original data samples. The data was sampled at an interval of 15 minutes, and there were 96 sampling points every day. For the complete original load data, 5%, 10%, 15%, 20%, 25%, 30%, 35%, and 40% of the load data were randomly missing, and load data analysis samples with different missing rates were established.

[0072] The missing user load data with different missing rates are used as input samples, and the load data completion results of the present invention are compared with those of the first-order polynomial interpolation method and the cubic spline interpolation method. The first-order polynomial interpolation is to connect two known points and use the straight line equation to estimate the value of any position between the two points; the cubic spline interpolation is to construct a cubic polynomial curve between multiple known points to ensure that the curve is continuous and smooth at these points to estimate the value of any position.

[0073] Table 1 shows the root mean square error of the completion results of three different methods for load data with different missing rates and the complete load data, Table 2 shows the determination coefficient of the completion results of three different methods for load data with different missing rates and the complete load data, and Table 3 shows the mean absolute percentage error of the completion results of three different methods for load data with different missing rates and the complete load data. It can be seen that the present invention has the best performance in the three error analysis indicators. The load data curve results before and after the missing data is restored are shown in Figure 1. Figure 2 As shown, Figure 2 (a), (b) and (c) are the load comparison effects of the method proposed in the present invention, first-order polynomial interpolation and cubic spline interpolation after the same missing load data is restored. It can be seen that the method proposed in the present invention is closer to the original load data curve in the overall trend, and the load data completion effect is better.

[0074] Table 1

[0075] Load data missing rate First-order polynomial interpolation Cubic spline interpolation The method of the present invention 5% 0.7078 1.1517 0.7015 10% 0.7223 1.3378 0.7152 15% 0.7318 4.6441 0.7241 20% 0.7233 2.4270 0.7161 25% 0.7330 1.8353 0.7257 30% 0.7698 3.2275 0.7603 35% 0.7792 3.4881 0.7690 40% 0.7800 6.6110 0.7700

[0076] Table 2

[0077] Load data missing rate First-order polynomial interpolation Cubic spline interpolation The method of the present invention 5% 0.8774 0.7264 0.8784 10% 0.8711 0.6583 0.8722 15% 0.8682 0.1408 0.8692 20% 0.8711 0.3660 0.8722 25% 0.8672 0.5019 0.8682 30% 0.8554 0.2447 0.8569 35% 0.8523 0.2143 0.8539 40% 0.8516 0.0721 0.8531

[0078] Table 3

[0079] Load data missing rate <![CDATA[First-order polynomial interpolation (×10 -3 )]]> <![CDATA[Cubic Spline Interpolation (×10 -3 )]]> <![CDATA[The method proposed by the present invention (×10 -3 )]]> 5% 2.043 2.758 2.041 10% 2.080 2.860 2.072 15% 2.104 3.202 2.097 20% 2.091 3.176 2.085 25% 2.123 3.174 2.116 30% 2.185 3.582 2.176 35% 2.212 3.789 2.203 40% 2.232 4.016 2.222

[0080] The embodiment of the present invention further provides a device for recovering missing load data of power users based on similar block embedding technology and first-order polynomial interpolation, which is used to implement the above method. The device includes:

[0081] The expanded tensor acquisition module is used to collect all user load data and construct a third-order load tensor based on the sampling time, sampling date and user, and take the sampling time as the first mode, expand the third-order load tensor according to the first mode to obtain the expanded tensor;

[0082] The module for obtaining preliminary recovery data of missing load is used to construct a matching similar block offset based on the missing load position index, wherein the matching similar block offset is specifically the offset between the missing load position and the matching similar block position; optimize the selection of matching similar blocks through multiple iterations based on the spreading rule and irregular search, and use the square sum of the errors between the matching similar blocks and the missing load position data block as the selection criterion of the matching similar blocks; use the finally selected matching similar block as the optimal similar block, and use the optimal similar block as the preliminary recovery data of the missing load;

[0083] The missing load recovery module is used to construct auxiliary recovery data based on the missing position load data of the expanded tensor through first-order polynomial interpolation, and fuse the preliminary recovery data and the auxiliary recovery data to obtain the final missing load recovery results for all users.

[0084] An embodiment of the present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the missing load recovery method based on similar block fitting and first-order polynomial interpolation.

[0085] An embodiment of the present invention further provides a computer-readable storage medium having computer instructions stored thereon, wherein the computer instructions are used to enable a computer to execute the missing load recovery method based on similar block embedding and first-order polynomial interpolation.

[0086] The above is a detailed introduction to the missing load recovery method based on similar block embedding and first-order polynomial interpolation provided by the present invention. In the present invention, specific examples are used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A missing load recovery method based on similar block embedding and first-order polynomial interpolation, characterized in that: The following steps are involved: Step 1: Collect all user load data and construct a third-order load tensor based on sampling time, sampling date and user, and take the sampling time as the first mode, expand the third-order load tensor according to the first mode to obtain the expanded tensor; Step 2: Based on the missing load position index, construct a matching similar block offset, wherein the matching similar block offset is specifically the offset between the missing load position and the matching similar block position; optimize the selection of matching similar blocks through multiple iterations based on the spreading rule and irregular search, and use the square sum of the errors between the matching similar blocks and the missing load position data block as the selection criterion for matching similar blocks; use the finally selected matching similar block as the optimal similar block, and use the optimal similar block as the preliminary recovery data of the missing load; Step 3: construct auxiliary recovery data based on the missing position load data of the expanded tensor through first-order polynomial interpolation, and fuse the preliminary recovery data and the auxiliary recovery data to obtain the final missing load recovery results for all users.

2. The missing load recovery method based on similar block embedding and first-order polynomial interpolation according to claim 1 is characterized in that: In step 1, the third-order load tensor is expanded according to the first mode to obtain an expanded tensor, which is specifically: ； In the formula, is the load matrix of user sample m, a represents the total number of sampling moments, b represents the number of sampling days, and c represents the number of user samples; Represents the expanded tensor obtained by expanding the third-order load tensor according to the sampling time.

3. The missing load recovery method based on similar block embedding and first-order polynomial interpolation according to claim 2 is characterized in that: The matching similar block offset in step 2 is specifically: ； In the formula, Indicates the offset of the matching similar block at the similar block (i, j), including the x and y directions; dx and dy are independent from [-p max ,p max ]A random variable sampled from a uniform distribution, p max Indicates the maximum allowed offset.

4. The missing load recovery method based on similar block embedding and first-order polynomial interpolation according to claim 3 is characterized in that: In step 2, the selection of matching similar blocks is optimized through multiple iterations based on the spreading rule and irregular search, and the sum of square errors between the matching similar blocks and the missing load position data blocks is used as the selection criterion for matching similar blocks, specifically: ； ； ； ； In the formula, err cur 、err left and err up They are the similarity errors of the current similar block, the similar block on its left, and the similar block above it based on the sum of squared errors; and are the missing load location data block and the current similarity block respectively. and They are Offset in x and y directions; and They are The offset in the x and y directions, and They are The offset in the x and y directions, and are the offsets of the similar block at (i, j) from the similar block on its left and the similar block above; I (i, j) represents the offset of the matching similar block corresponding to the minimum sum of square errors between the similar block at (i, j) and the missing load position data block; In order to avoid local optimum, I The matching similar block position corresponding to (i, j) is taken as the center, and an irregular search is performed in the exponentially decaying radius area until the search radius becomes a similar block: ； Where r represents the maximum search radius; β represents the specified attenuation coefficient in [0,1]; τ represents a random number that obeys a two-dimensional uniform distribution; k represents the number of irregular searches; O II (i, j) represents the offset of the matching similar block at (i, j) after k irregular searches; If the error decreases, use O II (i,j) replaces O I (i,j), otherwise keep O I (i, j), continue iterative search until the search radius becomes a similar block; The matching similar block corresponding to the matching similar block offset with the smallest square error sum in the entire iterative search process is taken as the optimal similar block; and the optimal similar block is taken as the preliminary recovery data of the missing load; the calculation formula of the preliminary recovery data of the missing load is: ； In the formula, represents the preliminary recovery data of the missing load at (i, j); is the offset of the matching similar block with the smallest sum of squared errors in the entire iterative search process, and They are The offset in the x and y directions.

5. The missing load recovery method based on similar block embedding and first-order polynomial interpolation according to claim 4 is characterized in that: In step 3, the construction of auxiliary recovery data based on the missing position load data of the expanded tensor based on first-order polynomial interpolation is specifically as follows: ； Where w is the row index of the load missing location, ; v is the column index of the load missing position, ; p and q represent the row indices of the non-missing positions of the load, satisfying p <w<q; Auxiliary recovery data representing the load data at the missing position (w,v) of the unfolded tensor; The preliminary recovery data and the auxiliary recovery data are integrated to obtain the final missing load recovery results of all users, which are specifically: ； In the formula, represents the final missing load recovery result, and They are the primary recovery data and auxiliary recovery data for all users respectively.

6. A device for recovering missing load data of power users based on similar block embedding technology and first-order polynomial interpolation, characterized in that: For implementing the method according to any one of claims 1 to 5, the device comprises: The expanded tensor acquisition module is used to collect all user load data and construct a third-order load tensor based on the sampling time, sampling date and user, and take the sampling time as the first mode, expand the third-order load tensor according to the first mode to obtain the expanded tensor; The module for obtaining preliminary recovery data of missing load is used to construct a matching similar block offset based on the missing load position index, wherein the matching similar block offset is specifically the offset between the missing load position and the matching similar block position; optimize the selection of matching similar blocks through multiple iterations based on the spreading rule and irregular search, and use the square sum of the errors between the matching similar blocks and the missing load position data block as the selection criterion of the matching similar blocks; use the finally selected matching similar block as the optimal similar block, and use the optimal similar block as the preliminary recovery data of the missing load; The missing load recovery module is used to construct auxiliary recovery data based on the missing position load data of the expanded tensor through first-order polynomial interpolation, and fuse the preliminary recovery data and the auxiliary recovery data to obtain the final missing load recovery results for all users.

7. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: Computer instructions are stored thereon, wherein the computer instructions are used to enable a computer to execute the steps of the method as described in any one of claims 1 to 5.

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