Incomplete time series data repairing method and system

Abstract

This invention relates to a method and system for repairing incomplete time series data, belonging to the field of photovoltaic power output data preprocessing technology. The method specifically includes: S1: For multidimensional photovoltaic power generation data and meteorological related factor data, firstly, outliers and missing values ​​are detected, and outliers are treated as missing data; S2: Low-rank approximation and feature extraction are performed on the processed data; S3: Similar daily matching data for missing data is obtained by constructing a cost matrix in DTW; S4: Missing data is filled in to complete data recovery. This solution significantly improves the accuracy and reliability of photovoltaic power output prediction by comprehensively considering the historical integrity of the data and multidimensional meteorological factors. Furthermore, the flexibility and adaptability of this solution make it applicable not only to the photovoltaic field but also extendable to other occasions requiring time series data repair.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic power output data preprocessing technology, and relates to a method and system for repairing incomplete time series data. Background Technology

[0002] With the increasing prominence of energy issues, countries are paying more attention to the photovoltaic (PV) industry, and global PV installed capacity is increasing year by year. However, PV power output is significantly volatile due to environmental factors such as solar irradiance, temperature, and seasonal variations, leading to rapid changes in power generation within short periods. Furthermore, PV power output is intermittent, primarily affected by solar cycles and seasonal variations, resulting in power outages at night and on cloudy days. These characteristics make PV power generation difficult to predict, potentially impacting grid stability when connected to the public grid. Considering the uncertainty of PV power output, current global energy policies tend to incentivize renewable energy participation in medium- and long-term electricity market regulation and trading to improve the overall economic efficiency and reliability of the power system. Within this framework, the accuracy of PV power output forecasting becomes crucial, directly impacting the stability of power supply and influencing energy trading decisions and future grid planning.

[0003] Because medium- and long-term forecasts require more accurate capture of long-term dependencies and seasonal patterns in time series, they demand higher data quality compared to short- and ultra-short-term forecasts. Medium- and long-term forecasting models must process and analyze data over longer time spans to ensure the identification and simulation of these patterns. However, during data collection, issues such as equipment malfunctions leading to data interruptions, inaccurate recording, and missing data segments due to oversights can negatively impact subsequent forecast results. To address this, most current data preprocessing research focuses on statistical techniques, such as mean imputation and outlier / outlier imputation. While simple to implement, these techniques often overlook the dynamic characteristics of the data and fail to recover the original trends and complex patterns. Some researchers use machine learning and deep learning to handle the complex relationship between photovoltaic data and meteorological factors, but this requires extensive feature engineering to improve accuracy. Although some researchers use historical data similarity for missing value imputation, they often fail to adequately consider the importance of time alignment. Time alignment is crucial for ensuring that the imputed data accurately reflects the dynamic characteristics of photovoltaic output. Without precise time alignment, even using historically similar data for imputation may not accurately reflect changes in photovoltaic output, thus affecting the accuracy and reliability of the forecasting model. Summary of the Invention

[0004] In view of this, and to address the aforementioned shortcomings in existing technologies, this invention proposes a method and system for repairing incomplete time series data. The aim is to enhance the historical integrity of photovoltaic power output data and improve the generalization performance of prediction models through similarity analysis and time series alignment. The method and system provided by this invention first identify and label outliers and missing values ​​in the dataset, and then intelligently fill in the missing values ​​using historical similar day data, ensuring that the incomplete dataset accurately reflects the long-term dynamics of photovoltaic power output.

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

[0006] An incomplete time series repair method, the method specifically includes:

[0007] S1: For multidimensional photovoltaic power generation data and meteorological related factor data, firstly, outlier and missing values ​​are detected, and outlier data is treated as missing data;

[0008] S2: Perform low-rank approximation and feature extraction on the processed data;

[0009] S3: Obtain similar day matching data for missing data by constructing a cost matrix in DTW;

[0010] S4: Fill in the missing data to complete data recovery.

[0011] Furthermore, in step S1, the detection of outliers and missing values ​​specifically includes:

[0012] S11: Outliers typically fall into two categories: spikes and extreme values. Spikes refer to data values ​​at a specific point in time that deviate significantly from the actual ringing time, causing the data curve to exhibit a spike-like shape. Extreme values ​​refer to data points where the load data at a non-peak or non-trough time of a day is significantly higher than the peak value or lower than the trough value. Using these values ​​as input for subsequent model training will result in larger errors in the machine learning process. To detect outliers, the standard deviation method is first used to measure the degree of deviation of an individual data point from the mean. Therefore, the standard deviation... It is necessary to ensure that z| < 3, at which point the initial labeling of outliers is completed;

[0013] S12: Since IQR is more adaptable to the distribution of data, the time series is further labeled based on S11, selecting a smaller portion of boundary points Q1 and a larger portion of boundary points Q3 in the time series. At this point, there is a lower boundary limit L. l =Q1 - 1.5 × IQR and upper bound L u =Q3 + 1.5 × IQR, when the value of the data point x t Satisfy xt <L l Or x t >L u When a data point satisfies both S11 and S12, it is considered an outlier and is treated as a missing value.

[0014] S13: For all missing values ​​x t Statistical methods were used to identify missing values ​​and perform preliminary missing value imputation. First, the backward non-missing values ​​x were identified. t-1 and forward non-missing value x t+1 The mean of the missing values ​​is used to initially fill in the missing values, i.e.

[0015] Furthermore, in step S2, the low-rank approximation and feature extraction specifically include:

[0016] S21: Normalize the input data. In the photovoltaic output data, a daily value of 0 indicates that the equipment has no output or is shut down. To ensure that this key information is not lost in subsequent analysis, the input time series needs to be further normalized, corresponding to each data point x. t Its normalization result is

[0017] S22: Create an n×p dimensional data matrix Z and construct a covariance matrix to express the linear relationship between meteorological factors and photovoltaic output data in the dataset. The covariance matrix is ​​a p×p matrix, and each element c ij This represents the covariance between features;

[0018] S23: Perform eigenvalue decomposition on the covariance matrix C, i.e., |λI-C|, to obtain the eigenvalues ​​λ1,λ2,...,λ p After sorting the eigenvalues ​​in descending order, solve for the corresponding eigenvectors c1, c2, ..., c. p ;

[0019] S24: Select the eigenvectors corresponding to the k largest eigenvalues ​​according to the required information content, and calculate the contribution rate of each component. and its cumulative contribution rate The values ​​for each component are calculated as follows:

[0020]

[0021] For each sample, calculate its comprehensive meteorological coefficient F = η1z1 + η2z2 + ... + η i z i +...+ηm z m .

[0022] Furthermore, in step S3, the similarity date matching specifically includes:

[0023] S31: Outliers have been marked using S1. These marked data x... sign Using the date as the center, and selecting period T as a time window, at this time... If the missing dates are close to the beginning or end of the dataset, the time window needs to be adjusted to fit the data boundaries;

[0024] S32: Enumerate all time windows with a time interval of T in the dataset, ensuring that the data within each time window is complete and without missing values; for each time window, use the DTW algorithm to calculate the similarity score with the reference time window; the DTW algorithm finds the best alignment by minimizing the overall distance between time series, and arranges similar time series in ascending order according to the DTW score. The lower the score, the smaller the difference between the series, thus obtaining several series with high similarity; for the target time series X containing missing values ​​and the candidate time series T, construct the distance matrix D[i,j]=(X[i]-T[j]). 2 The DTW matrix is ​​initialized by setting DTW[0,0] = D[0,0], and the remaining DTW[0,j] and DTW[i,0] are initialized to infinity. Then, the entire matrix is ​​gradually filled in.

[0025] DTW[i,j]=D[i,j]+min(DTW[i-1,j],DTW[i,j-1],DTW[i-1,j-1]);

[0026] S33: When the time series has sufficiently high requirements for the fineness of the sequence, the sequence selected in S32 is further matched, the similarity between the day and the day with the missing data is compared, and the day with the lowest DTW score is selected as the most similar date. If the missing data involves an entire day or multiple consecutive data points, the corresponding data of the similar day of the selected date is used to completely replace the missing value.

[0027] Furthermore, in step S4, the data recovery specifically includes: in S24, the corresponding principal component coefficients are obtained, and therefore, the inverse PCA transform is used on the newly obtained sequence to complete the final data recovery. i =c i1 x1+c i2 x2 + ... + c ij x j +…+c ip x p

[0028] The beneficial effects of this invention are as follows:

[0029] The technical solution provided by this invention significantly improves the accuracy and reliability of photovoltaic power output prediction by comprehensively considering the historical integrity of data and multidimensional meteorological factors. Furthermore, the flexibility and adaptability of this solution make it applicable not only to the photovoltaic field but also to other applications requiring time-series data repair.

[0030] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0032] Figure 1 This is a system architecture diagram as described in this invention;

[0033] Figure 2 The hash tree structure diagram designed for this invention. Detailed Implementation

[0034] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0035] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0036] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0037] Please see Figures 1-2 This paper presents a method for incomplete time series data restoration. To reduce the volatility and randomness of prediction results, it first detects outliers and treats them as missing data. After simple imputation of the missing data, the location of the missing points is recorded, and the data is standardized. Then, PCA is used to perform low-rank approximation on the data, while simultaneously obtaining the main direction of variation of the dataset. For the dimensionality-reduced data, DTW is used for similar day matching to complete the dataset imputation. Finally, the imputed data is restored to multidimensional data, realizing data reconstruction and enhancing the accuracy of subsequent predictions. To achieve the above objectives...

[0038] In this embodiment, the technical solution provided by the present invention is as follows:

[0039] This invention proposes a strategy for repairing incomplete time series data. Considering that current data preprocessing can be divided into two stages: outlier detection and correction, missing values ​​are directly statistically analyzed, while outliers are identified using threshold detection. Once the location of outliers is identified and statistically determined, correction is necessary. In this method, outliers and missing values ​​are detected and their locations are marked; if a value is an outlier, it is declared missing. When processing outliers, the Z-score method or the Interquartile Range (IQR) method is commonly used. The Z-score measures the deviation of a single data point from the mean. When the dataset approximates a normal distribution, it can be used to identify values ​​that differ significantly from the mean. Furthermore, when the photovoltaic power output dataset has a sufficiently large sample size, the data can be considered to follow a normal distribution (demonstrated in the simulation analysis section). The box plot method is a graphical method for displaying data distribution characteristics. Considering its robustness to outliers, it is applicable to data of any distribution type.

[0040] In photovoltaic (PV) output datasets, extreme Z-Score values ​​often indicate equipment failure, sudden environmental changes, or data recording errors. However, the applicability of Z-Score is limited for biased datasets containing a large number of extreme values, as it cannot distinguish between true outliers and extreme but normal values ​​in the dataset. IQR (Independent Quality Reduction) can help identify data points that deviate from seasonal patterns or from the normal range due to equipment failure during PV data analysis. Single outlier detection methods, whether based on Z-Score or IQR, may be overly sensitive to specific patterns or noise in the data. For example, Z-Score may perform well under the assumption of a Gaussian distribution but may fail with data exhibiting a heavy-tailed distribution. Similarly, IQR may fail to accurately capture outliers when multiple patterns or seasonal variations exist in the dataset. Therefore, combining multiple detection methods can provide a more comprehensive outlier identification capability. This paper adopts a combined detection strategy of Z-Score and IQR, based on the synergistic application of both methods. The theoretical basis of this strategy lies in the respective advantages and applicable scenarios of Z-Score and IQR in outlier detection. Z-Score performs well when the data is assumed to be Gaussian distributed, while IQR is more adaptable to different data distribution patterns. Combining these two methods achieves comprehensive outlier identification while reducing reliance on a single detection algorithm. First, Z-Score is used for initial outlier screening to identify points that deviate significantly from the mean. Then, IQR is used to further refine the outlier identification, ensuring that points that do not conform to the distribution characteristics of the dataset are accurately marked.

[0041]

[0042] Where x t Let μ represent the value at time t, μ be the mean of the series, and z be the standard deviation. Q1 and Q3 represent the first and third quartiles, respectively. Q1 represents the boundary point of the smaller portion of the dataset, indicating that 25% of the data points are less than this value. Q3 represents the boundary point of the larger portion of the dataset, indicating that 75% of the data points are less than this value. L l and L u These represent the lower and upper limits of the box plot method.

[0043] For all data points x t Perform the check: when x t <L l Or x t >L uIf a data point is marked as an outlier by the Z-Score method, its status is reconfirmed; otherwise, its marking is removed. Finally, all marked data points are made missing, and initial imputation is performed on the missing data. Indicates the missing values ​​that need to be filled, x t-1 and x t+1 These represent backward non-missing values ​​and forward non-missing values, respectively.

[0044] When analyzing photovoltaic (PV) power output datasets, the inherent high dimensionality and complex correlations between features make direct application of predictive models both time-consuming and potentially lead to the curse of dimensionality. To address this issue, Principal Component Analysis (PCA) can project data into a low-dimensional space composed of principal components that maximize variance through linear transformation. This process not only reduces the dimensionality of the data but also preserves the most important variable information—those features that contribute the most to the data variance. These principal components not only represent the key features of the original data but also ensure data integrity in large-scale time series analysis, guaranteeing accurate restoration of the original data after dimensionality reduction. Compared to other dimensionality reduction techniques, PCA's mathematical principles and algorithm implementation are relatively simple and computationally efficient, making it particularly effective for large-scale datasets. Furthermore, PCA does not rely on distribution assumptions, allowing it to maintain good performance even with non-normally distributed data. When considering multi-factor photovoltaic (PV) output prediction, different feature factors have different dimensions. PV output data often has a larger range than other feature factors, causing it to dominate the model algorithm during prediction, while other features with smaller values ​​are overwhelmed, preventing the model from effectively learning the patterns within these features. Therefore, input data normalization is necessary. Commonly used normalization methods include Min-Max normalization, decimal scaling normalization, logarithmic transformation, and square root transformation. In PV output data, a daily value of 0 indicates no output or equipment shutdown. To ensure this crucial information is not lost in subsequent analysis, and considering that Min-Max normalization not only preserves the original distribution shape and relative relationships of the data but also has a simple calculation process, offering simplicity, speed, and preservation of the original data distribution compared to other methods, the Min-Max normalization method is used. This method scales the original data to a specified range, making the model more adaptable to handling data of different dimensions and magnitudes, and improving the model's generalization ability to different input features. Where x max and x min and represent the maximum and minimum values ​​in the data sequence, respectively, and x is the value after normalization.

[0045] Based on the normalized results, an n×p dimensional data matrix Z is created, and a covariance matrix C is constructed to express the linear relationship between meteorological factors and photovoltaic output data in the dataset. Z T Let represent the transpose of matrix Z. The covariance matrix is ​​a p×p matrix, where each element c ij Let represent the covariance between feature i and feature j. Since the magnitude of the eigenvalues ​​in the constructed covariance matrix reflects the importance of the corresponding eigenvectors in the data and their ability to explain data variance, factors with larger eigenvalues ​​can be used as the main direction of variation in subsequent medium- and long-term photovoltaic power output prediction. Therefore, eigenvalue decomposition is performed on the covariance matrix C, i.e., |λI-C|, yielding eigenvalues ​​λ1, λ2, ..., λj. p After sorting the eigenvalues ​​in descending order, solve for the corresponding eigenvectors c1, c2, ..., c. p .

[0046] Select the eigenvectors corresponding to the k largest eigenvalues ​​based on the required information content. The principal component contribution rate formula is as follows: Cumulative contribution rate Where m is the number of principal components. Characteristic values ​​with a cumulative contribution rate of 80%–95% are typically selected as principal components. The values ​​of each principal component are calculated using the following formula.

[0047]

[0048] In the formula c ij The elements of the eigenvector matrix, z i Principal component values. For each sample, calculate its comprehensive meteorological coefficient F = η1z1 + η2z2 + ... + η i z i +...+η m z m , where η i Contribution rate represents the weight percentage of each output component.

[0049] Given that the Dynamic Time Warping (DTW) algorithm is robust to noise and outliers in time series and can handle time series scaling and skew, it can provide reliable matching of similar days even with incomplete data. Photovoltaic output data is affected by various meteorological factors, resulting in significant fluctuations. The DTW algorithm not only exhibits good robustness to noise and outliers in the time series but also handles time series scaling and skew caused by changes in meteorological conditions. This means that even with data fluctuations caused by meteorological factors such as solar radiation intensity and cloud cover, the DTW algorithm can still accurately identify the date most similar to the target time series in history. The specific steps and process are as follows:

[0050] Selecting a time window: During outlier preprocessing, all outliers and missing values ​​have been marked. These marked data x sign Using the date as the center, a period T is selected as a time window. There are... If the missing dates are close to the beginning or end of the dataset, the time window needs to be adjusted to fit the data boundaries.

[0051] Preliminary DTW matching: Enumerate all time windows with a time interval of T in the dataset. Ensure that the data within each time window is complete and without missing data. For each time window, use the DTW algorithm to calculate the similarity score with the reference time window. The DTW algorithm finds the optimal alignment by minimizing the overall distance between time series. Based on the DTW score, similar time series are sorted in ascending order; the lower the score, the smaller the difference between the series, thus obtaining several series with high similarity.

[0052] For the target time series X containing missing values ​​and the candidate time series T, construct a distance matrix between them.

[0053] D[i,j]=(X[i]-T[j]) 2 Where and j represent the indices of time series X and T, respectively. The DTW matrix is ​​initialized by setting DTW[0,0] = D[0,0], and the remaining DTW[0,j] and DTW[i,0] are initialized to infinity. Then the entire matrix is ​​gradually filled: DTW[i,j] = D[i,j] + min(DTW[i-1,j],DTW[i,j-1],DTW[i-1,j-1]).

[0054] Daily DTW matching: Within the months selected in the previous step, perform a separate DTW analysis for each day. The cumulative distance matrix is ​​calculated using the same method as the initial DTW matching. Compare the similarity between this day and the day with the missing data, selecting the day with the lowest DTW score as the most similar date. If the missing data involves an entire day or multiple consecutive data points, the corresponding data from similar days of the selected date are used to completely replace the missing values, i.e., x... sign =x t .

[0055] For missing time-series data, this invention considers not only the overall pattern of similar days but also fluctuations at smaller time scales. It fills in the missing points more smoothly by interpolating similar day data with existing data points. This interpolation strategy considers the granularity of the data, i.e., the temporal distance and frequency of data points, ensuring that the filled data maintains consistency with adjacent data points in terms of statistical characteristics and time series properties. In this way, the time series of photovoltaic power output can be reconstructed more accurately, ensuring accuracy and smoothness even with fine-grained data.

[0056] Data Restoration: To reduce the impact on subsequent predictions, data restoration is necessary. This is because each data point contains a principal component coefficient (z) during the low-rank PCA approximation. i =c i1 x1+c i2 x2 + ... + c ij x j +…+c ip x p .

[0057] Finally, 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 can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications should be covered within the scope of the claims of the present invention.

Claims

1. A method for repairing incomplete time series data, characterized in that, The method specifically includes: S1: For multidimensional photovoltaic power generation data and meteorological related factor data, firstly, outlier and missing values ​​are detected, and outlier data is treated as missing data; S2: Perform low-rank approximation and feature extraction on the processed data; S3: Obtain similar day matching data for missing data by constructing a cost matrix in DTW; S4: Fill in the missing data to complete data recovery; In step S2, the low-rank approximation and feature extraction specifically include: S21: Normalize the input data. In the photovoltaic output data, a value of 0 for each day indicates that the equipment has no output or is shut down. This corresponds to the data point at each location. Its normalization result is ; S22: Creation 3D data matrix And construct the covariance matrix To express the linear relationship between meteorological factors and photovoltaic power output data in the dataset. covariance matrix for An dimensional matrix, each element of which Representation of features and characteristics Covariance between them; S23: For the covariance matrix Perform eigenvalue decomposition, i.e. The obtained eigenvalues After sorting the eigenvalues ​​in descending order, the corresponding eigenvectors are calculated. ; S24: Select before based on the required amount of information. The eigenvectors corresponding to the largest eigenvalues ​​are calculated, and the contribution rate of each component is also calculated. and its cumulative contribution rate The values ​​of each component are calculated as follows: For each sample, calculate its comprehensive meteorological coefficient. ; In step S3, the similarity date matching specifically includes: S31: Outlier marking has been completed through S1. These marked data... Choose the period based on the date as the center. As a time window, at this time If the missing date is close to the beginning or end of the dataset, the time window needs to be adjusted to fit the data boundaries. S32: Enumerate all time intervals in the dataset. The time windows are defined to ensure that the data within each time window is complete and without missing values. For each time window, the DTW algorithm is used to calculate the similarity score with the reference time window. The DTW algorithm finds the optimal alignment by minimizing the overall distance between time series. Similar time series are sorted in ascending order according to their DTW scores; the lower the score, the smaller the difference between the series, thus obtaining several series with higher similarity. For target time series containing missing values... and candidate time series Construct a distance matrix for it. Initialize the DTW matrix, that is, let ,the remaining and Initialize to infinity, then gradually fill the entire matrix: ； S33: When the time series has sufficiently high requirements for the fineness of the sequence, the sequence selected in S32 is further matched, the similarity between the day and the day with the missing data is compared, and the day with the lowest DTW score is selected as the most similar date. If the missing data involves an entire day or multiple consecutive data points, the corresponding data of the similar day of the selected date is used to completely replace the missing value.

2. The incomplete time series repair method according to claim 1, characterized in that: In step S1, the detection of outliers and missing values ​​specifically includes: S11: Outliers typically include two types: spikes and extreme values. Spikes refer to a significant deviation between the data value at a given point in time and the time of the ringing bell, causing the data curve to exhibit a spike-like shape. Extreme values ​​refer to outliers where the load data value at a non-peak or non-trough time of a given day is significantly higher than the peak value or lower than the trough value. To detect outliers, the standard deviation method is first used to measure the degree of deviation of an individual data point from the mean. Therefore, for the standard deviation... It is necessary to ensure At this point, the initial labeling of overall outliers is completed; S12: Since IQR is more adaptable to the distribution of data, the time series is further labeled based on S11, selecting a smaller portion of the boundary points in the time series. and most of the boundary points At this point, there is a lower bound. and boundary upper limit When the value of the data point satisfy or When a data point satisfies both S11 and S12, it is considered an outlier and is treated as a missing value. S13: For all missing values Statistical methods were used to identify missing values ​​and perform preliminary missing value imputation, starting by identifying backward non-missing values. and forward non-missing values The mean of the missing values ​​is used to initially fill in the missing values, i.e. .

3. The incomplete time series repair method according to claim 1, characterized in that: In step S4, the data recovery specifically includes: in S24, the corresponding principal component coefficients are obtained, and therefore, the inverse PCA transform is used on the newly obtained sequence to complete the final data recovery. .

4. An incomplete time series repair system, characterized in that: The system employs the method described in any one of claims 1 to 3.

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