Sample set reconstruction method and system

Abstract

The invention discloses a sample set reconstruction method and system. The method comprises the following steps: acquiring a data set; according to the data set, an interpolation function and an attractor are defined, the data set is interpolated in the interpolation function, and a function image passes through all interpolation points; selecting a vertical scale factor, and constructing a fractal dimension of an IFS system attractor; and substituting the data set into an affine IFS system with a convergence condition, continuously iterating until the IFS system converges to be near an attractor, and outputting an interpolation result, thereby completing reconstruction of a missing value. According to the method, a sample set reconstruction method is adopted, continuous missing fragments are reconstructed, the overall change trend of a wind power curve can be kept, local fluctuation characteristics of data can be reflected, and higher interpolation precision and goodness of fit are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of data reconstruction, and in particular to a method and system for reconstructing a sample set. Background Art

[0002] The power prediction accuracy of a wind farm is highly dependent on the quality of its historical operating data. However, due to factors such as measurement errors, sensor failures, and wind abandonment, there are a large number of abnormal data in the collected wind farm operating data. After the abnormal value identification and screening analysis of wind power historical data, the original data samples will inevitably have a large number of power data missing problems, and there will inevitably be normal data that is mistakenly excluded. On the one hand, it will reduce the abundance of data samples, and on the other hand, it will destroy the integrity of the wind power time series, which is not conducive to subsequent short-term wind power prediction research. Therefore, in order to ensure the validity of the original data sample and the integrity of the time series in the subsequent prediction analysis, it is necessary to fill the missing values ​​of the wind power time series after removing the abnormal data.

[0003] Missing value filling is of great significance to the adequacy of data samples and the integrity of wind power time series. According to the number of missing samples, missing value data can be divided into two categories: discrete missing points and continuous missing fragments. Common methods for filling missing values ​​after removing abnormal data include: linear interpolation, cubic spline method, Lagrange interpolation, Hermite interpolation and fractal interpolation.

[0004] In the process of researching and practicing this method, the inventors of the present invention found that the existing missing value filling methods have many shortcomings: Hermite interpolation and cubic spline interpolation are very suitable for interpolating smooth curves, but they are not effective for interpolating violently oscillating curves. Due to the strong fluctuation of wind power data, the traditional interpolation method cannot maintain the overall fluctuation characteristics and local characteristics of the wind power curve. It is suitable for simple missing value filling, but the effect is not ideal for strongly fluctuating curves. Summary of the invention

[0005] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0006] In view of the above existing problems, the present invention is proposed. Therefore, the present invention provides a method for reconstructing a sample set to solve the problem that the traditional interpolation method has poor effect when processing data with strong fluctuations.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] In a first aspect, the present invention provides a method for reconstructing a sample set, comprising:

[0009] Get the dataset;

[0010] According to the data set, an interpolation function and an attractor are defined, the data set is interpolated within the interpolation function and the function graph passes through all interpolation points;

[0011] Select the vertical scale factor to construct the fractal dimension of the attractor of the IFS system;

[0012] The data set is substituted into an affine IFS system with convergence conditions, and the iterative process is continued until the IFS system converges to the vicinity of the attractor, and the interpolation result is output, thereby completing the reconstruction of the missing values.

[0013] As a preferred solution of the sample set reconstruction method of the present invention, the data set includes:

[0014] The expression of the data set is:

[0015] {(x i ,y i )∈R 2 |i=0,1,…,N}

[0016] x0<x1<…<x N

[0017] Among them, (x i ,y i ) is the interpolation point, N is the number of interpolation points, and i represents the current interpolation point.

[0018] As a preferred solution of the sample set reconstruction method of the present invention, the interpolation function includes:

[0019] The interpolation function corresponding to the data set is a continuous function, and the interpolation function is expressed as:

[0020] F: [x0, x N ] → R

[0021] Where F represents the interpolation function, and x0 is the value in the data set;

[0022] By the interpolation function, the data set is interpolated within the interpolation function and the function graph passes through all interpolation points:

[0023] F(x i )=y i , i=0,1,2,…,N

[0024] Among them, (x i ,y i ) is the interpolation point, xi ∈[x0,x N ],y i ∈[y0,y N ].

[0025] As a preferred solution of the method for reconstructing a sample set according to the present invention, the attractor includes:

[0026] The attractor is the interpolation function in the interval [x0, x N ], the expression of the attractor is:

[0027] G={(x,F(x))|x∈[x0,x N ]}

[0028] Among them, G is the attractor and F(x) is the interpolation function.

[0029] As a preferred solution of the sample set reconstruction method of the present invention, the vertical scale factor is selected including:

[0030] The method for selecting the vertical scale factor is expressed as:

[0031] e i =f1(y i )

[0032] e=f2(y i )

[0033] d i =e i / e

[0034] in, f2(y i )=max{|e i |}+1,y i represents the measured value of the interpolation node, where i = 0, 1, ..., N Indicates that the regression line for a given interpolation node is at x i The interpolation function value at .

[0035] As a preferred solution of the sample set reconstruction method of the present invention, the fractal dimension of the attractor includes:

[0036] Assumptions And the interpolation point {(x i ,y i )|i=0,1,2,…,N} are not collinear, then the fractal dimension of the attractor of the IFS system satisfies the following relationship:

[0037] f(d i , D)=1

[0038] Among them, di is the vertical scale factor and D is the fractal dimension.

[0039] As a preferred solution of the sample set reconstruction method of the present invention, wherein: substituting all known data sets into an affine IFS system with convergence conditions includes:

[0040] The parameters of the affine transformation are solved by the IFS equation with convergence conditions, expressed as:

[0041] a i =f3(x i )

[0042] e i =f4(x i )

[0043] c i =f5(y i )

[0044] f i =f6(y i )

[0045] Among them, a i , e i , c i , f i is the parameter of affine transformation, {x i ∈R 2 |i=0,1,...,N},{y i ∈R 2 |i=0,1,…,N}.

[0046] In a second aspect, the present invention provides a system for reconstructing a sample set, comprising:

[0047] A data acquisition module, used to acquire a data set;

[0048] A function definition module, used for defining an interpolation function and an attractor according to the data set, wherein the interpolation function interpolates the data set and the function graph passes through all interpolation points;

[0049] The parameter acquisition module is used to select the vertical scale factor and construct the fractal dimension of the attractor of the IFS system;

[0050] The reconstruction module is used to substitute the data set into an affine IFS system with convergence conditions, iterate continuously until the IFS system converges to the vicinity of the attractor, and output the interpolation result, thereby completing the reconstruction of the missing values.

[0051] In a third aspect, the present invention provides a computing device, comprising:

[0052] Memory and processor;

[0053] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, the steps of the sample set reconstruction method are implemented.

[0054] In a fourth aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the steps of the sample set reconstruction method.

[0055] Compared with the prior art, the present invention has the following beneficial effects: the present invention adopts a sample set reconstruction method to reconstruct continuous missing segments, which can not only maintain the overall change trend of the wind power curve, but also reflect the local fluctuation characteristics of the data, and has higher interpolation accuracy and consistency. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0057] Figure 1 A schematic diagram of the overall flow of a method for reconstructing a sample set according to an embodiment of the present invention;

[0058] Figure 2 A schematic diagram of a simulated power timing curve containing missing values ​​of a method for reconstructing a sample set according to an embodiment of the present invention;

[0059] Figure 3 A schematic diagram of the reconstruction results of a power time series curve containing missing values ​​using different interpolation methods of a method for reconstructing a sample set according to an embodiment of the present invention;

[0060] Figure 4 A schematic diagram of a framework process of wind power time series data missing value reconstruction of a sample set reconstruction method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0062] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0063] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0064] The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0065] At the same time, in the description of the present invention, it should be noted that the orientations or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the system or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0066] In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0067] Example 1

[0068] Reference Figure 1 , as an embodiment of the present invention, provides a method for reconstructing a sample set, comprising:

[0069] S100: Obtain a data set;

[0070] In the embodiment of the present application, the expression of the data set is:

[0071] {(x i ,y i )∈R 2|i=0,1,…,N}

[0072] x0<x1<…<x N

[0073] Among them, (x i ,y i ) is the interpolation point, N is the number of interpolation points, and i represents the current interpolation point;

[0074] In an optional embodiment, the data set may be wind power data, environmental monitoring data, or financial time series data;

[0075] It should be noted that in the embodiments of the present application, wind power data is selected as an example for subsequent operations.

[0076] S102: According to the data set, define an interpolation function and an attractor, interpolate the data set within the interpolation function and the function graph passes through all interpolation points;

[0077] Preferably, the interpolation function corresponding to the data set is a continuous function, and the interpolation function is expressed as:

[0078] F: [x0, x N ] → R

[0079] Where F represents the interpolation function, and x0 is the value in the data set;

[0080] Preferably, the data set is interpolated by an interpolation function, and the function graph passes through all interpolation points:

[0081] F(x i )=y i , i=0,1,2,…,N

[0082] Among them, (x i ,y i ) is the interpolation point, x i ∈[x0,x N ],y i ∈[y0,y N ].

[0083] Preferably, the attractor is an interpolation function in the interval [x0, x N ], the expression of the attractor is:

[0084] G={(x,F(x))|x∈[x0,x N ]}

[0085] Among them, G is the attractor and F(x) is the interpolation function.

[0086] It should be noted that the interpolation function can effectively handle continuous missing segments in the data set and accurately reflect the local fluctuation characteristics of the data, thereby improving the accuracy and reliability of data reconstruction, especially when processing complex time series data such as wind power data.

[0087] S104: Select the vertical scale factor and construct the fractal dimension of the attractor of the IFS system;

[0088] It should be noted that IFS is an iterated function system (IFS). Fractal dimension is the most important concept and content in fractal geometry theory and application. It is the most important indicator for measuring the complexity and irregularity of physical or fractal bodies, and is a parameter that quantitatively describes the degree of fractal self-similarity. The size of the fractal dimension is related to the vertical scale factor;

[0089] Preferably, the method for selecting the vertical scale factor is expressed as:

[0090] e i =f1(y i )

[0091] e=f2(y i )

[0092] d i =e i / e

[0093] in, f2(y i )=max{|e i |}+1,y i represents the measured value of the interpolation node, where i = 0, 1, ..., N Indicates that the regression line for a given interpolation node is at x i The interpolation function value at ;

[0094] Preferably, assuming And the interpolation point {(x i ,y i )|i=0,1,2,…,N} are not collinear, then the fractal dimension of the attractor of the IFS system satisfies the following relationship:

[0095] f(d i , D)=1

[0096] or

[0097]

[0098] Among them, d i is the vertical scale factor, D is the fractal dimension, a i are the parameters of the affine transformation;

[0099] It can be obtained that the vertical scale factor d i It can determine the shape of the fractal interpolation curve, thus affecting the result of fractal interpolation. Therefore, it is necessary to adopt a reasonable selection of d i Method to construct IFS, the selection method is as follows:

[0100]

[0101] in, e=max{|e i |}+1,y i represents the measured value of the interpolation node, Indicates that the regression line for a given interpolation node is at x i The function value at ;

[0102] It should be noted that the vertical scale factor d i It represents the multiple of the large-scale data change characteristics being reduced in a small range, and the regression line of a given interpolation node reflects the overall change trend of the interpolation node to a certain extent. Therefore, d i =e i / e means comparing the local characteristics of a small range with the overall trend, thus more realistically reflecting the spatial variation characteristics of the data.

[0103] S106: Substitute the data set into an affine IFS system with convergence conditions, iterate continuously until the IFS system converges to the vicinity of the attractor, and output the interpolation result, thereby completing the reconstruction of the missing values;

[0104] Preferably, the parameters of the affine transformation are solved by an IFS equation with convergence conditions, expressed as:

[0105] a i =f3(x i )

[0106] e i =f4(x i )

[0107] c i =f5(y i )

[0108] f i =f6(y i )

[0109] Among them, a i , e i , c i , f i is the parameter of affine transformation, {x i ∈R 2|i=0,1,…,N},{y i ∈R 2 |i=0,1,…,N}.

[0110] Specifically, assuming that w i is an affine transformation of the form:

[0111]

[0112] Among them, a i , e i , c i , f i is the parameter of affine transformation, d i is the vertical scale factor,

[0113] ω i : [x0, x N ]×R→R, i=0, 1, 2,...,N;

[0114] And the following endpoint conditions are met:

[0115]

[0116] Then the IFS {R 2 |ω i , i = 0, 1, 2, ..., N} is called affine IFS, d i is the vertical scale factor of the affine IFS, when |d i When |≤1, the IFS equation meets the convergence condition and can be solved as:

[0117]

[0118] All known data sets {(x i ,y i )∈R 2 |i=0,1,…,N} is substituted into the above formula and iterated continuously until the system converges to the vicinity of the constructed attractor G, thus completing the reconstruction of the missing values;

[0119] It should be noted that the present invention provides an efficient and accurate sample set reconstruction method, which is particularly suitable for processing complex time series data sets such as wind power data, environmental monitoring data or financial time series data; the present invention first obtains the data set and gives a detailed description of the wind power data, and by defining a continuous interpolation function and an attractor, it ensures that the interpolation result not only passes through all interpolation points, but also can effectively process the continuous missing fragments in the data set, while accurately reflecting the local fluctuation characteristics of the data; further, by selecting a reasonable vertical scale factor, the fractal dimension of the IFS system attractor is constructed. This step uses fractal geometry theory to improve the accuracy and reliability of data reconstruction; finally, the data set is substituted into an affine IFS system with convergence conditions, and the interpolation result is output through continuous iteration until the system converges to the vicinity of the attractor, thereby completing the reconstruction of the missing values; this process not only improves the efficiency of data reconstruction, but also ensures the accuracy and stability of the reconstruction results.

[0120] The above is a schematic scheme of a method for sample set reconstruction in this embodiment. It should be noted that the technical scheme of the system for sample set reconstruction and the technical scheme of the method for sample set reconstruction described above belong to the same concept, and the details of the technical scheme of the system for sample set reconstruction in this embodiment that are not described in detail can all be referred to the description of the technical scheme of the method for sample set reconstruction described above.

[0121] The system for reconstructing a sample set in this embodiment includes:

[0122] A data acquisition module, used to acquire a data set;

[0123] A function definition module is used to define an interpolation function and an attractor according to a data set, wherein the interpolation function interpolates the data set and the function graph passes through all interpolation points;

[0124] The parameter acquisition module is used to select the vertical scale factor and construct the fractal dimension of the attractor of the IFS system;

[0125] The reconstruction module is used to substitute the data set into an affine IFS system with convergence conditions, and continuously iterate until the IFS system converges to the vicinity of the attractor, output the interpolation result, and thus complete the reconstruction of the missing values.

[0126] This embodiment further provides a computing device, which is applicable to the case of sample set reconstruction, and includes:

[0127] A memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute computer executable instructions to implement the method for reconstructing a sample set as proposed in the above embodiment.

[0128] This embodiment further provides a storage medium on which a computer program is stored. When the program is executed by a processor, the method for reconstructing a sample set proposed in the above embodiment is implemented.

[0129] The storage medium proposed in this embodiment and the method for implementing sample set reconstruction proposed in the above embodiment belong to the same inventive concept. For technical details not fully described in this embodiment, reference can be made to the above embodiment. This embodiment has the same beneficial effects as the above embodiment.

[0130] Through the above description of the implementation methods, the technicians in the relevant field can clearly understand that the present invention can be implemented by means of software and necessary general hardware, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ReadOnly, Memory, ROM), random access memory (RandomAccess Memory, RAM), flash memory (FLASH), hard disk or optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform the methods of various embodiments of the present invention.

[0131] Example 2

[0132] Reference Figure 2-4 Table 1 and Table 1 are an embodiment of the present invention, which provides a method for reconstructing a sample set. In order to verify its beneficial effects, comparison results of several solutions are provided.

[0133] In order to verify the superiority of the fractal interpolation method of the present invention in processing continuous missing segments, this example uses the quartile method and DBSCAN clustering outlier screening method to screen the samples of wind farm operation data for one year, and selects 96 power time series segments from 00:00 to 23:45 on February 16, 2022 as the research object. All data points in the test sample were not identified as abnormal data. At the same time, the test sample was randomly sampled to simulate the situation of missing time series data. There are 9 discrete missing points and 2 continuous missing segments. The test power time series curve obtained is as follows Figure 2 shown.

[0134] In order to verify the effect of fractal interpolation on the reconstruction of continuous missing segments of wind farms, four interpolation methods, namely cubic spline interpolation, linear interpolation, multi-point cubic spline interpolation and fractal interpolation, were used to fill the above test samples. The reconstruction results of missing data points or segments of the wind farm output power time series were obtained as shown in the following figure. Figure 3 shown.

[0135] pass Figure 3 It can be seen that the fractal interpolation method can better reflect the fluctuation trend of the original time series data in processing continuous missing fragments than other interpolation methods. For example, in the continuous missing fragments 1 and 2 in the figure, the power curve after fractal interpolation can follow the original power curve well, and the multi-point cubic spline interpolation can also reflect certain power fluctuation characteristics, but it cannot follow the situation where the power fluctuation is large in a short period of time. At the same time, the power curves of cubic spline interpolation and linear interpolation cannot reflect the fluctuation characteristics of the original power curve at all. However, since the interpolation effect of fractal interpolation depends on the vertical scale factor, without further optimization calculation, the fractal interpolation method is not as effective as cubic spline interpolation and linear interpolation in processing some discrete missing points, which is reflected in the interpolation curve in the above figure, where many irregular burrs will appear.

[0136] In order to more objectively compare the reconstruction effects of various interpolation methods on power time series data with missing values, this paper repeatedly selects power time series segments that are not identified as outliers, and randomly samples the segments to simulate the situation of missing time series data. Four interpolation methods, namely cubic spline interpolation, linear interpolation, multi-point cubic spline interpolation and fractal interpolation, are used to reconstruct missing values. Finally, the errors of each method in processing discrete missing points and continuous missing segments are calculated. The error comparison results are shown in Table 1.

[0137] Table 1 Reconstruction error of different interpolation methods for power time series data with missing values

[0138]

[0139] It can be seen from the above table that when reconstructing the missing data of wind power time series, for discrete missing points, the reconstruction effect of multi-point cubic spline interpolation is the best, with a maximum absolute error of less than 700kW and an average absolute error of less than 100kW; the reconstruction effects of cubic spline interpolation and multi-point cubic spline interpolation are close, and the average absolute errors are both within 100kW; while the average error of fractal interpolation is the largest, and its reconstruction effect for discrete missing points is not as good as linear interpolation. For continuous missing segments, the maximum absolute error and average absolute error of fractal interpolation are both the smallest, indicating that its reconstruction effect is better than the other three interpolation methods. This result also verifies that the fractal interpolation method can better reflect the fluctuation trend of the original time series data when dealing with continuous missing segments than other interpolation methods.

[0140] In summary, considering the computational speed and model complexity, this paper intends to use cubic spline interpolation to reconstruct missing values ​​when processing wind power time series data with discrete missing points; when processing wind power time series data with continuous missing segments, this paper intends to use fractal interpolation to reconstruct missing values. The overall wind power time series data missing value reconstruction process is as follows: Figure 4 shown.

[0141] 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 the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for reconstructing a sample set, characterized in that: include: Get the dataset; According to the data set, an interpolation function and an attractor are defined, the data set is interpolated within the interpolation function and the function graph passes through all interpolation points; Select the vertical scale factor to construct the fractal dimension of the attractor of the IFS system; The data set is substituted into an affine IFS system with convergence conditions, and the iterative process is continued until the IFS system converges to the vicinity of the attractor, and the interpolation result is output, thereby completing the reconstruction of the missing values.

2. The method for reconstructing a sample set according to claim 1, characterized in that: The dataset includes, The expression of the data set is: {(x i ,y i )∈R 2 |i=0,1,…,N} x0<x1<...<x N Among them, (x i ,y i ) is the interpolation point, N is the number of interpolation points, and i represents the current interpolation point.

3. The method for reconstructing a sample set according to claim 1 or 2, characterized in that: Interpolation functions include, The interpolation function corresponding to the data set is a continuous function, and the interpolation function is expressed as: F:[x0,x N ]→R Where F represents the interpolation function, and x0 is the value in the data set; By the interpolation function, the data set is interpolated within the interpolation function and the function graph passes through all interpolation points: F(x i )=y i ,i=0,1,2,…,N Among them, (x i ,y i ) is the interpolation point, x i ∈[x0,x N ],y i ∈[y0,y N ].

4. The method for reconstructing a sample set according to claim 3, characterized in that: Attractors include, The attractor is the interpolation function in the interval [x0,x N ], the expression of the attractor is: G={(x,F(x))x∈[x0,x N ]} Among them, G is the attractor and F(x) is the interpolation function.

5. The method for reconstructing a sample set according to claim 4, characterized in that: Select the vertical scale factor including, The method for selecting the vertical scale factor is expressed as: e i =f1(y i ) e=f2(y i ) d i =and i / And in, f2(y i )=max{e i |}+1,y i represents the measured value of the interpolation node, where i = 0, 1, ..., N, Indicates that the regression line for a given interpolation node is at x i The interpolation function value at .

6. The method for reconstructing a sample set according to claim 5, characterized in that: The fractal dimensions of attractors include, Assumptions And the interpolation point {(x i ,y i )|i=0,1,2,…,N} are not collinear, then the fractal dimension of the attractor of the IFS system satisfies the following relationship: f(d i ,D)=1 Among them, d i is the vertical scale factor and D is the fractal dimension.

7. The method for reconstructing a sample set according to claim 6, characterized in that: Substituting all known data sets into the affine IFS system with convergence conditions includes, The parameters of the affine transformation are solved by the IFS equation with convergence conditions, expressed as: a i =f3(x i ) e i =f4(x i ) c i =f5(y i ) f i =f6(y i ) Among them, a i ,e i ,c i ,f i are the parameters of the affine transformation, {x i ∈R 2 | i=0,1,…,N},{y i ∈R 2 | i=0,1,…,N} 。 8. A system for reconstructing a sample set, characterized in that: include, A data acquisition module, used to acquire a data set; A function definition module, used for defining an interpolation function and an attractor according to the data set, wherein the interpolation function interpolates the data set and the function graph passes through all interpolation points; The parameter acquisition module is used to select the vertical scale factor and construct the fractal dimension of the attractor of the IFS system; The reconstruction module is used to substitute the data set into an affine IFS system with convergence conditions, continuously iterate until the IFS system converges to the vicinity of the attractor, and output the interpolation result, thereby completing the reconstruction of the missing values.

9. An electronic device, comprising: Memory and processor; The memory is used to store computer executable instructions, and the processor is used to execute the computer executable instructions. When the computer executable instructions are executed by the processor, the steps of the method for reconstructing a sample set according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions, when executed by a processor, implement the steps of the method for reconstructing a sample set according to any one of claims 1 to 7.

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