Small sample time sequence modeling prediction method and device based on new information priority

Abstract

The invention discloses a small sample time sequence modeling prediction method and device based on new information priority, and relates to the field of data prediction. Historical data sequence samples are iterated based on a whale optimization algorithm to obtain unstructured parameter optimal values; a structured parameter estimation value vector is calculated through a least square method based on an unstructured parameter optimal value, a TVNDGM (1, 1) model is constructed, and a time variable item is introduced to extend a traditional homogeneous discrete grey prediction model to a non-homogeneous discrete grey prediction model to improve the model prediction effect. In information processing, a time-varying anti-forgetting function is designed by simulating a human forgetting process, and a target accumulation sequence based on new information priority is generated based on a collected original data sequence, so that the new information priority is effectively ensured. A target accumulation sequence with new information priority is input into a model, and a target prediction result is obtained based on model reduction processing, so that the problem that the new information priority of a fractional order gray model is insufficient is solved.

Description

Technical Field

[0001] This application relates to the field of data prediction technology, and in particular to a method and apparatus for small-sample time series modeling and prediction based on prioritizing new information. Background Technology

[0002] As global environmental problems become increasingly severe, solar power generation, with its clean and renewable characteristics, is playing an increasingly crucial role in the global energy structure and has become an important means of addressing climate change and reducing greenhouse gas emissions. Accurately predicting solar power generation is of great significance for promoting the development of new energy technologies, helping policymakers optimize resource allocation, improving energy efficiency, and promoting sustainable development.

[0003] In related technologies, grey prediction models have become an important tool for predicting solar power generation and other problems due to their effectiveness in handling information-limited systems. Among them, fractional grey models are widely used in the application of new information. When the fractional accumulation operator r is between [0,1], it can ensure the priority of new information. At the same time, researchers are constantly expanding and improving grey prediction models to enhance their accuracy and applicability. However, the applicant recognizes that, on the one hand, fractional grey models cannot guarantee the priority of new information when the fractional accumulation operator r is greater than 1, making it difficult to effectively cope with the dynamic changes in data in the field of solar power generation; on the other hand, solar power generation prediction faces problems such as the limited annual data samples available for actual prediction, the time lag between statistical data and socio-economic development, and the difficulty in accurately identifying many influencing factors. Therefore, existing grey prediction models have low accuracy and reliability in small-sample, dynamically changing solar power generation prediction scenarios, and cannot meet the demand for high-precision prediction in practical applications. Summary of the Invention

[0004] In view of this, this application provides a small-sample time series modeling and prediction method and apparatus based on new information priority. The main purpose is to solve the problem that the existing gray prediction model has low prediction accuracy and reliability in small-sample, dynamically changing solar power generation prediction scenarios, and cannot meet the needs of practical applications for high-precision prediction.

[0005] According to a first aspect of this application, a small-sample time series modeling and prediction method based on prioritizing new information is provided, the method comprising: Obtain historical data sequence samples corresponding to the prediction target; Based on the whale optimization algorithm, with the goal of minimizing the mean absolute percentage error, the historical data sequence samples are iteratively calculated to obtain the optimal values ​​of unstructured parameters. Based on the optimal value of the unstructured parameter, the estimated value vector of the structured parameter is calculated by the least squares method. The TVNDGM(1,1) model corresponding to the prediction target is constructed using the optimal value of the unstructured parameter and the estimated value vector of the structured parameter. The TVNDGM(1,1) model is a non-homogeneous discrete grey model that includes a time variable term. Based on the predicted target, the original data sequence is collected, and a time-varying anti-forgetting function is constructed to perform exponential weighting on the original data sequence to construct a target accumulation sequence based on new information priority. The target accumulation sequence with priority to the new information is input into the TVNDGM(1,1) model corresponding to the predicted target to obtain the target prediction value sequence, and the target prediction result is obtained by calculating the target prediction value sequence based on the model reduction formula.

[0006] According to a second aspect of this application, a small-sample time series modeling and prediction device based on prioritizing new information is provided, the device comprising: The acquisition module is used to acquire historical data sequence samples corresponding to the prediction target; The optimization module is used to perform iterative calculations on the historical data sequence samples based on the whale optimization algorithm, with the goal of minimizing the mean absolute percentage error, to obtain the optimal values ​​of unstructured parameters. The construction module is used to calculate the structured parameter estimation vector based on the optimal value of the unstructured parameter using the least squares method, and to construct the TVNDGM(1,1) model corresponding to the prediction target using the optimal value of the unstructured parameter and the structured parameter estimation vector. The TVNDGM(1,1) model is a non-homogeneous discrete grey model that includes a time variable term. The preprocessing module is used to collect the original data sequence according to the prediction target, construct a time-varying anti-forgetting function to perform exponential weighting on the original data sequence, and construct a target accumulation sequence based on new information priority; The prediction module is used to input the target accumulation sequence with priority to the new information into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence, and to calculate the target prediction value sequence based on the model reduction formula to obtain the target prediction result.

[0007] By employing the above technical solutions, the technical solutions provided in the embodiments of this application have at least the following advantages: This application provides a small-sample time series modeling and prediction method and apparatus based on prioritizing new information. This application obtains historical data sequence samples corresponding to the prediction target. Based on the whale optimization algorithm, with the minimization of the mean absolute percentage error as the optimization objective, it iterative calculations are performed on the historical data sequence samples to obtain the optimal values ​​of unstructured parameters. Compared with traditional parameter selection methods, this method can find the optimal solution in the parameter space more efficiently, providing strong support for model accuracy. Then, based on the optimal values ​​of the unstructured parameters, the estimated vector of structured parameters is calculated using the least squares method. The optimal values ​​of the unstructured parameters and the estimated vector of structured parameters are used to construct the TVNDGM(1,1) model corresponding to the prediction target, i.e., a time-varying non-homogeneous discrete grey prediction model. By introducing a time variable term, the traditional homogeneous discrete grey prediction model is extended to a non-homogeneous discrete grey prediction model. This not only expands the model's applicability but also effectively corrects the time lag effect between statistical data and economic and social development by adding a time-related correction term, thus improving the model's prediction performance. In information processing, a time-varying anti-forgetting function was innovatively designed by mimicking the human forgetting process. Based on the collected original data sequence, a target accumulation sequence prioritizing new information was generated. The time-varying anti-forgetting function is an anti-forgetting curve that changes over time, serving as a weight accumulation function when accumulating the initial data sequence. This effectively ensures the priority of new information, enabling the prediction system to more sensitively capture dynamic changes and update according to the latest market dynamics and environmental changes, thereby improving the accuracy and reliability of predictions to adapt to new development trends. The target accumulation sequence prioritizing new information is then input into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence. The target prediction result is then calculated based on the model's reduction formula. This approach specifically addresses issues such as insufficient priority of new information in fractional-order grey models and poor adaptation of existing models to small-sample dynamic scenarios, expanding the application scope of grey prediction models in small-sample, dynamically changing time series (such as new energy power generation and economic indicators).

[0008] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0009] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1This illustration shows a flowchart of a method for small-sample time series modeling and prediction based on prioritizing new information, according to an embodiment of this application. Figure 2A This paper illustrates a flowchart of another method for small-sample time series modeling and prediction based on prioritizing new information, provided by an embodiment of this application. Figure 2B The flowchart illustrates the operation of the small-sample time series modeling and prediction method based on prioritizing new information provided in this application embodiment. Figure 2C The diagram illustrates the non-structural parameter selection process provided in an embodiment of this application. Figure 2D A comparison chart showing the mean absolute percentage error of the prediction results of different prediction methods provided in the embodiments of this application is shown; Figure 3 This illustration shows a schematic diagram of the structure for small-sample time series modeling and prediction based on prioritizing new information, provided in an embodiment of this application. Detailed Implementation

[0010] In the description of this application, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are used only for the convenience of describing this application 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, and therefore should not be construed as a limitation of this application. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified.

[0011] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0012] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0013] This application proposes a small-sample time series modeling and prediction method based on prioritizing new information. First, historical data series samples of the prediction target are acquired. Then, the optimal values ​​of unstructured parameters are obtained iteratively using the whale optimization algorithm with the objective of minimizing the mean absolute percentage error. This is combined with the structured parameter estimation vector obtained by the least squares method to construct a TVNDGM(1,1) model. Next, the newly acquired original data series is processed using a designed time-varying anti-forgetting function to obtain a target cumulative sequence based on prioritizing new information. This sequence is then input into the model and the final prediction result is obtained through a reduction formula. The time-varying anti-forgetting function emphasizes the weight of new information, accurately capturing the dynamic trends of small-sample time series and solving the problem of lagging response to new information in traditional models. The whale optimization algorithm intelligently, efficiently, and accurately optimizes unstructured parameters, laying a solid foundation for model accuracy. Combining the inherent advantages of small-sample modeling in grey models, the method strengthens information extraction from limited data, significantly improving prediction reliability in small-sample scenarios. This approach ensures prediction accuracy while possessing good engineering feasibility due to its clear and easy-to-operate process. It can also adapt to scenarios with dynamic fluctuations and limited samples, such as new energy power generation, effectively expanding the application scope of grey prediction models. The implementing entity of this application can be a data prediction system. The data prediction system provides services to users by relying on the computing power of the server. The server can be an independent server or a server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDN), and big data and artificial intelligence platforms.

[0014] This application provides a small-sample time series modeling and prediction method based on prioritizing new information, such as... Figure 1 As shown, the method includes: 101. Obtain historical data sequence samples corresponding to the prediction target.

[0015] In this embodiment, the historical data sequence sample is a collection of historical observation data related to the prediction target (such as solar power generation, economic indicators, etc.), forming an ordered data sequence, which serves as the basic input for subsequent modeling and optimization. Historical data is the core basis for the model to learn the inherent laws. Obtaining historical data that matches the target ensures that the model works based on real and relevant information, laying a solid data foundation for the rationality and accuracy of subsequent predictions.

[0016] 102. Based on the whale optimization algorithm, with the goal of minimizing the mean absolute percentage error, iterative calculations are performed on historical data sequence samples to obtain the optimal values ​​of unstructured parameters.

[0017] In this embodiment, the Whale Optimization Algorithm, an intelligent optimization tool, is used to repeatedly iterate and calculate historical data with the goal of minimizing the mean absolute percentage error. Finally, the optimal value of the unstructured parameter is determined. Compared with traditional parameter selection methods, the Whale Optimization Algorithm has stronger global search and optimization efficiency and can find the unstructured parameter value that minimizes the prediction error more accurately. It ensures the model prediction accuracy from the parameter level and solves the problems of strong subjectivity and insufficient accuracy in traditional parameter selection.

[0018] 103. Based on the optimal values ​​of unstructured parameters, the estimated vector of structured parameters is calculated by the least squares method. The TVNDGM(1,1) model corresponding to the prediction target is constructed using the optimal values ​​of unstructured parameters and the estimated vector of structured parameters.

[0019] In this embodiment, based on the optimal values ​​of unstructured parameters, a structured parameter vector characterizing the sequence trend and constant terms is calculated using the least squares method. Then, combined with the optimal values ​​of the unstructured parameters, a TVNDGM(1,1) model is constructed for the prediction target. The least squares method can stably and efficiently estimate structured parameters, allowing the model to fit historical data more accurately. The model is then constructed by combining the optimal values ​​of the unstructured parameters. The TVNDGM(1,1) model is a non-homogeneous discrete grey model containing time-varying variables, possessing both the characteristic of prioritizing new information and the ability to accurately characterize the sequence change pattern, thus improving the predictive ability of small-sample, dynamic time series from the model structure level.

[0020] 104. Collect the original data sequence according to the prediction target, construct a time-varying anti-forgetting function to perform exponential weighting on the original data sequence, and construct a target cumulative sequence based on new information priority.

[0021] In this embodiment, the latest raw data sequence related to the prediction target is collected, and the raw data is weighted using a time-varying anti-forgetting function. Then, an accumulation operation is performed to generate a target accumulation sequence prioritizing new information. The time-varying anti-forgetting function designs weight coefficients based on the interval between the raw data collection time and the current time. The weights decrease exponentially with the interval, and the decay rate is related to the time density of the raw data sequence collection. This suppresses historical noise interference and prioritizes recent data change trends to construct a target accumulation sequence prioritizing new information. The time-varying anti-forgetting function is used for weighted preprocessing of the raw data sequence, specifically strengthening the weight of new information. This makes the accumulation sequence more closely reflect the dynamic change trends of the data, solving the problem of delayed response to new information in traditional methods. It is particularly suitable for small-sample, highly dynamic time series (such as solar power generation), providing a more closely following input basis for subsequent predictions.

[0022] 105. Input the target accumulation sequence with new information priority into the TVNDGM(1,1) model corresponding to the predicted target to obtain the target prediction value sequence, and calculate the target prediction value sequence based on the model reduction formula to obtain the target prediction result.

[0023] In this embodiment, the target cumulative sequence prioritizing new information is input into the TVNDGM(1,1) model to first obtain the predicted value sequence at the cumulative sequence scale; then, through model reduction, the predicted result of the cumulative sequence is restored to the original data scale, finally obtaining the target prediction result. The TVNDGM(1,1) model combines optimized unstructured parameters with accurately estimated structured parameters, exhibiting strong fitting ability for cumulative sequences; simultaneously, the process of prioritizing new information input and reduction output allows the model to keenly capture dynamic trends while ensuring that the prediction result falls back to the real data dimension, ultimately achieving high-precision, dynamic prediction under small sample sizes, meeting the demand for accurate prediction in scenarios such as solar power generation.

[0024] This application provides a small-sample time series modeling and prediction method based on prioritizing new information. Compared with existing technologies, this application obtains historical data sequence samples corresponding to the prediction target, and uses the whale optimization algorithm to iteratively calculate the historical data sequence samples with the goal of minimizing the mean absolute percentage error. This yields the optimal values ​​of unstructured parameters, which, compared with traditional parameter selection methods, can find the optimal solution in the parameter space more efficiently, providing strong support for model accuracy. Then, based on the optimal values ​​of unstructured parameters, the estimated vector of structured parameters is calculated using the least squares method. The optimal values ​​of unstructured parameters and the estimated vector of structured parameters are used to construct the TVNDGM(1,1) model corresponding to the prediction target, i.e., a time-varying non-homogeneous discrete grey prediction model. By introducing a time variable term, the traditional homogeneous discrete grey prediction model is extended to a non-homogeneous discrete grey prediction model. This not only expands the model's applicability but also effectively corrects the time lag effect between statistical data and economic and social development by adding a time-related correction term, thus improving the model's prediction performance. In information processing, a time-varying anti-forgetting function was innovatively designed by mimicking the human forgetting process. Based on the collected original data sequence, a target accumulation sequence prioritizing new information was generated. The time-varying anti-forgetting function is an anti-forgetting curve that changes over time, serving as a weight accumulation function when accumulating the initial data sequence. This effectively ensures the priority of new information, enabling the prediction system to more sensitively capture dynamic changes and update according to the latest market dynamics and environmental changes, thereby improving the accuracy and reliability of predictions to adapt to new development trends. The target accumulation sequence prioritizing new information is then input into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence. The target prediction result is then calculated based on the model's reduction formula. This approach specifically addresses issues such as insufficient priority of new information in fractional-order grey models and poor adaptation of existing models to small-sample dynamic scenarios, expanding the application scope of grey prediction models in small-sample, dynamically changing time series (such as new energy power generation and economic indicators).

[0025] Furthermore, as a refinement and extension of the specific implementation methods of the above embodiments, and in order to fully illustrate the specific implementation process of this embodiment, this application provides another small-sample time series modeling and prediction method based on prioritizing new information, such as... Figure 2A As shown, the method includes: 201. Obtain historical data sequence samples corresponding to the prediction target.

[0026] In this embodiment, historical observation data directly related to the object to be predicted (i.e., the prediction target) and arranged in chronological order are collected to form an ordered time series set, which serves as the basic input for subsequent modeling and prediction. The prediction target is, for example, the annual solar power generation of a certain region.

[0027] 202. Set the hyperparameters of the whale optimization algorithm, and initialize the whale population state based on the search space of the whale population size and unstructured parameters in the hyperparameters.

[0028] In this embodiment, hyperparameters of the whale optimization algorithm are set, including whale population size, maximum number of iterations, and search space for unstructured parameters. By customizing hyperparameters such as whale population size, maximum number of iterations, and search space, the algorithm's search capability can be flexibly adjusted according to the characteristics of the prediction target, making the algorithm more adaptable to specific prediction scenarios. Next, the whale population state is initialized based on the whale population size and the search space for unstructured parameters. Each whale position in the whale population state represents a candidate value for an unstructured parameter. Multiple candidate values ​​for unstructured parameters are evenly distributed within the search space for unstructured parameters, allowing the algorithm to broadly cover the possible values ​​of the parameters in the initial stage. This avoids the local optimum problem caused by the local concentration of initial candidate values ​​and increases the likelihood of finding the globally optimal unstructured parameters.

[0029] Steps 203 to 210 below specifically illustrate how the fitness function and maximum number of iterations of the whale optimization algorithm are used to minimize the mean absolute percentage error as the optimization objective, where the optimization objective is expressed as: The detailed process of using whale population status and historical data sequence samples for iterative calculation to obtain the optimal values ​​of unstructured parameters.

[0030] 203. For each unstructured parameter candidate value in the current iteration, the historical data sequence samples are exponentially weighted using the time-varying anti-forgetting function and each unstructured parameter candidate value to construct an accumulated sequence based on new information priority for each unstructured parameter candidate value.

[0031] In this embodiment, for each unstructured parameter candidate value, the historical data sequence sample is processed using the designed time-varying anti-forgetting function and the unstructured parameter candidate value to construct an accumulated sequence based on new information priority corresponding to the unstructured parameter candidate value, as shown in Formula 1 below: Formula 1:

[0032]

[0033]

[0034]

[0035] in, This represents a non-negative historical data sequence sample. This represents the s-th historical observation in a historical data sequence sample. , where n represents the sequence length. Represents the time-varying anti-forgetting function. This is used to perform a weighted calculation on the s-th historical observation for the i-th unstructured parameter candidate value at the current iteration number j. This represents the anti-forgetting curve. This represents the i-th unstructured parameter candidate value at the current iteration number j. , This represents the w-th data point in the cumulative sequence based on new information priority, corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the accumulated sequence based on prioritizing new information, corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This application innovatively designs a time-varying anti-forgetting function by mimicking the human forgetting process, and uses it as a weight during the accumulation of the original sequence, effectively ensuring the priority of new information.

[0036] 204. Calculate the structured parameter estimate vector corresponding to each unstructured parameter candidate value using the cumulative sequence based on new information priority.

[0037] In this embodiment, for each unstructured parameter candidate value, a result matrix and a data matrix corresponding to the unstructured parameter candidate value are constructed using the cumulative sequence based on new information priority, as shown in Formula 2 below: Formula 2:

[0038]

[0039] in, This represents the result matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the data matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the nth data point in the cumulative sequence based on new information priority, corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the (n-1)th data point in the cumulative sequence based on new information priority, corresponding to the i-th unstructured parameter candidate value at the current iteration number j. Then, using the result matrix and data matrix corresponding to the unstructured parameter candidate values, the structured parameter estimate vector corresponding to the unstructured parameter candidate values ​​is calculated, as shown in Formula 3 below: Formula 3:

[0040] in, This represents the vector of structured parameter estimates corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the result matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the data matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the second structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. Let represent the third structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. The proof is as follows: let According to the TVNDGM(1,1) model The result matrix and data matrix can be obtained in the form of formula 4 below: Formula 4:

[0041]

[0042] in, It is The matrix, when There is no definitive solution at this time, and the error is assumed. ,So Therefore, based on the least squares estimation, we can obtain the following formula 5: Formula 5:

[0043] According to the conditions for the existence of extrema, we have ,therefore Satisfy regularization equation Therefore, the proof is complete. .

[0044] Traditional homogeneous discrete grey models are usually or Because of its uniform recurrence relation, the solutions of time series typically exhibit pure growth or decay patterns, making it difficult to fit time series with obvious linear trends or complex non-homogeneous changes well. Therefore, a time variable term is introduced. That is, a variable about time. By introducing a linear term, a TVNDGM(1,1) model, i.e., a non-homogeneous discrete grey model, is constructed, enabling the model to describe and predict linear trends in a sequence. By introducing a time variable term, the traditional homogeneous discrete grey prediction model is extended to a non-homogeneous discrete grey prediction model. This not only broadens the model's applicability but also effectively corrects the time lag between statistical data and economic and social development, improving the model's predictive performance.

[0045] 205. Using the time response formula, calculate the time response function value sequence corresponding to each unstructured parameter candidate value and the structured parameter estimate vector corresponding to each unstructured parameter candidate value.

[0046] In this embodiment of the application, for each unstructured parameter candidate value, the time response formula is used to calculate the vector of structured parameter estimates corresponding to the unstructured parameter candidate value, and the time response function value sequence corresponding to the unstructured parameter candidate value is obtained, as shown in Formula 6 below: Formula 6:

[0047] in, This represents the (r+1)th time response function value in the sequence of time response function values ​​corresponding to the i-th unstructured parameter candidate value at the current iteration number j. Let r be the power of the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the i-th unstructured parameter candidate value at the current iteration number j, where n represents the sequence length. This represents the first historical observation in the historical data sequence sample. This represents the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the second structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the third structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. Let represent the rt-th power of the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. The proof is as follows: The time response function of the TVNDGM(1,1) model is shown in Equation 7 below: Formula 7:

[0048] Based on the model's expression, we can obtain the following formula 8: Formula 8:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Therefore, it can be proven that the time response function of the TVNDGM(1,1) model can be obtained.

[0056] 206. Using the model reduction formula, the time response function value sequence corresponding to each candidate value of unstructured parameter is restored to the original data scale prediction value, thus obtaining the prediction value sequence corresponding to each candidate value of unstructured parameter.

[0057] In this embodiment, for each unstructured parameter candidate value, the time response function value sequence corresponding to the unstructured parameter candidate value is restored to the original data scale prediction value using the model reduction formula, resulting in the prediction value sequence corresponding to the unstructured parameter candidate value, as shown in Formula 9 below: Formula 9:

[0058] in, This represents the (r+1)th predicted value in the predicted value sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the i-th unstructured parameter candidate value at the current iteration number j. This represents the (r+1)th time response function value in the sequence of time response function values ​​corresponding to the i-th unstructured parameter candidate value at the current iteration number j. The predicted values ​​of the accumulated sequence are mapped back to the original data scale, ensuring that the predicted results are consistent with the units and magnitudes of the actual object to be predicted, thus guaranteeing practicality. Simultaneously, the restoration process uses the unstructured parameters to inversely eliminate weighting, accurately restoring the dynamic change characteristics of the original data and improving the accuracy of predictions for small sample scenarios.

[0059] 207. Substitute the predicted value sequence corresponding to each candidate value of unstructured parameter and the original data sequence into the fitness function to obtain the fitness value corresponding to each candidate value of unstructured parameter.

[0060] In this embodiment of the application, for each unstructured parameter candidate value, the predicted value sequence corresponding to the unstructured parameter candidate value and the original data sequence are substituted into the fitness function with the mean absolute percentage error as the metric to obtain the fitness value corresponding to the unstructured parameter candidate value, as shown in the following formula 10: Formula 10:

[0061] in, This represents the fitness value corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the l-th predicted value in the sequence of predicted values ​​corresponding to the i-th unstructured parameter candidate value at the current iteration number j. Let represent the l-th historical observation in the historical data sequence sample, and n represent the sequence length. The fitness function provides a quantitative standard for evaluating accuracy, which can objectively compare the prediction effects of different candidate values. This provides a basis for selecting the optimal parameters for the subsequent whale optimization algorithm. Moreover, compared with qualitative analysis, quantitative fitness values ​​make parameter optimization more accurate, ensuring that the final parameters minimize the prediction error of the model on small samples and dynamic sequences.

[0062] 208. Using the whale optimization algorithm, adjust multiple unstructured parameter candidate values ​​based on the fitness value corresponding to each unstructured parameter candidate value to obtain multiple unstructured parameter candidate values ​​for the next iteration number. If the current iteration number is less than the maximum iteration number, then execute step 209 below; if the current iteration number is equal to the maximum iteration number, then execute step 210 below.

[0063] In this embodiment, based on the whale optimization algorithm, multiple unstructured parameter candidate values ​​are adjusted according to the fitness value of each candidate value. For example, candidate values ​​(whale positions) are updated by simulating whale encirclement and hunting behavior to generate candidate values ​​for the next iteration. Then, by comparing the current iteration number with the maximum iteration number, if the current iteration number is less than the maximum iteration number, step 209 is executed; if the current iteration number is equal to the maximum iteration number, step 210 is executed. The intelligent iterative mechanism of the whale optimization algorithm can efficiently search for optimal unstructured parameters. It uses fitness values ​​to guide parameters to evolve towards regions with smaller prediction errors, avoiding the subjectivity of manual parameter selection. Moreover, combined with the termination condition of the maximum iteration number, it balances search accuracy and computational efficiency, ensuring that better parameters are found without wasting computational resources, and adapting to the high requirements for parameter accuracy in small sample scenarios.

[0064] 209. If the current iteration number is less than the maximum iteration number, then multiple unstructured parameter candidate values ​​for the next iteration number are used to enter the next round of iteration calculation.

[0065] In this embodiment, if the current iteration number is less than the maximum iteration number, multiple candidate values ​​of unstructured parameters for the next iteration number are used to enter the next round of iteration calculation, i.e., the calculation process of step 203 is repeated. By expanding the search range through multiple iterations, the algorithm avoids getting trapped in local optima and ensures the search accuracy of unstructured parameters.

[0066] 210. If the current iteration number is equal to the maximum iteration number, then select the unstructured parameter candidate value with the smallest fitness value from multiple unstructured parameter candidate values ​​as the optimal unstructured parameter value.

[0067] In this embodiment, if the current iteration number is equal to the maximum iteration number, the candidate unstructured parameter with the smallest fitness value is selected from multiple candidate unstructured parameter values ​​as the optimal unstructured parameter value. The maximum iteration number is used to balance search accuracy and efficiency, and the minimum fitness value is used to quantitatively screen the optimal parameter, providing core support for subsequent high-precision modeling.

[0068] 211. Based on the optimal values ​​of unstructured parameters, the estimated vector of structured parameters is calculated by the least squares method. The TVNDGM(1,1) model corresponding to the prediction target is constructed using the optimal values ​​of unstructured parameters and the estimated vector of structured parameters.

[0069] In this embodiment, based on the optimal values ​​of unstructured parameters, the estimated vector of structured parameters is calculated using the least squares method. The TVNDGM(1,1) model corresponding to the prediction target is then constructed using the optimal values ​​of unstructured parameters and the estimated vector of structured parameters. The least squares method stably and efficiently fits the structured parameters, and the model is then constructed by combining the optimal unstructured parameters. This results in a model that possesses both the characteristic of prioritizing new information and the ability to accurately characterize the changing patterns of small samples and dynamic time series.

[0070] 212. Collect the original data sequence according to the prediction target, construct a time-varying anti-forgetting function to perform exponential weighting on the original data sequence, and construct a target cumulative sequence based on new information priority.

[0071] In this embodiment, the original data sequence of the prediction target is collected, weighted using a time-varying anti-forgetting function to enhance the weight of new information, and then accumulated to obtain a target accumulation sequence based on the priority of new information. The time-varying anti-forgetting function addresses the problem of delayed response to new information in traditional models, and for small samples and dynamic sequences (such as new energy power generation data), it can keenly capture recent change characteristics, providing accurate input for prediction.

[0072] 213. Input the target accumulation sequence with priority to new information into the TVNDGM(1,1) model corresponding to the predicted target to obtain the target prediction value sequence, and calculate the target prediction value sequence based on the model reduction formula to obtain the target prediction result.

[0073] In this embodiment, the target accumulation sequence with new information priority is input into the TVNDGM(1,1) model corresponding to the predicted target to obtain the target prediction value sequence, as shown in Formula 11 below: Formula 11:

[0074] in, This represents the first structured parameter in the structured parameter estimate vector. This represents the second structured parameter in the structured parameter estimate vector. This represents the third structured parameter in the structured parameter estimate vector. This represents the p-th data point in the target accumulation sequence prioritizing new information. This represents the (p+1)th predicted value in the target predicted value sequence. This represents the optimal value of the unstructured parameters of the TVNDGM(1,1) model. This represents the time variable term of the TVNDGM(1,1) model. Next, the target prediction value sequence is restored to the original data-scaled prediction value using the model reduction formula, yielding the target prediction result, as shown in Formula 12 below: Formula 12:

[0075] in, This represents the (p+1)th predicted value in the target prediction results. This represents the optimal value of the unstructured parameters of the TVNDGM(1,1) model. This represents the (p+1)th predicted value in the target predicted value sequence, where n represents the sequence length. The TVNDGM(1,1) model combines optimal parameter fitting capabilities and, through the process of accumulating sequence predictions and restoring output, captures dynamic trends while allowing the results to fall back to the dimension of real data, achieving high-precision dynamic prediction with small samples.

[0076] To demonstrate that this application achieves better prediction results, the prediction of North American solar power generation is used as the research object. The novel grey prediction model proposed in this application is compared with seven other models to analyze the advantages of small-sample time series modeling based on prioritizing new information. Total North American solar power generation data from 2013 to 2023 is selected as sample data, with data from 2013 to 2021 used as the fitting set and data from 2022 to 2023 used as the test set. The model is constructed using the fitted data, and the predictive performance of the model is verified using the test set data. The total North American solar power generation shows an overall growth trend, while the growth rate exhibits a fluctuating trend. The TVNDGM(1,1) model in this application fully considers the priority of new information and presents it in a non-uniform form, making it very suitable for solving this type of nonlinear prediction problem.

[0077] According to such Figure 2B The diagram shows the operation flowchart of a small-sample time series modeling and prediction method based on prioritizing new information. The method obtains the original data sequence according to the prediction target. By processing the data, a cumulative sequence based on prioritizing new information is constructed, and the optimal unstructured parameter m is found using the whale optimization algorithm. Figure 2C The diagram showing the unstructured parameter selection process ultimately determines the optimal unstructured parameter to be 0.0231. The whale optimization algorithm includes setting the hyperparameters, initializing the whale's state, updating the current whale's state, calculating the fitness of each whale using the fitness function, selecting the optimal whale, and using the optimal whale as the best unstructured parameter after reaching the maximum number of iterations. Then, the estimated structured parameters are calculated using the least squares method. Then, the time response function of the model is calculated as follows: The data was fitted and predicted based on the model's regression equation, and the results were as follows: Finally, the model's fitting and prediction errors were calculated to determine its effectiveness. The fitting error was 2.28, and the prediction error was 1.65.

[0078] To better demonstrate the advantages of this application, the error performance of several classic grey models and time series models is compared with that of the TVNDGM(1,1) model, including GM(1,1), DCM(1,1), ROGM(1,1), FGM(1,1), TMA, TSQES, and TEP.

[0079] Table 1

[0080] Table 1 summarizes the fitting results of power generation data from 2013 to 2021 and the test results from 2022 to 2023, including eight methods. It is worth noting that the TVNDGM(1,1) method fits the actual data very well.

[0081] Figure 2DThe mean absolute percentage error (MAPE) values ​​derived from various methods are presented, providing an overall assessment of the fitting accuracy. The TVNDGM(1,1) model achieves a fitting error of only 2.28%, significantly outperforming the other seven methods and demonstrating its superior ability to capture sample fluctuations. Its test error of 1.65% further highlights its predictive advantage. While the GM(1,1), DCM(1,1), ROGM(1,1), FGM(1,1), TSQES, and TEP models all show fitting errors below 10%, indicating good data fitting ability, the prediction errors of DCM(1,1), ROGM(1,1), and TSQES exceed 10%, suggesting potential overfitting issues. In contrast, TMA shows a fitting error of 21.93% and a prediction error of 4.80%, reflecting its instability in predicting North American solar power generation. Time series methods can improve accuracy with a wider dataset, while grey prediction methods require only a smaller sample size. The improvement of TVNDGM(1,1) over DGM(1,1) in MAPE is attributed to its extension to a non-homogeneous model and the construction of a time-varying anti-forgetting curve as the accumulation function, ensuring that new information is prioritized. Similarly, the reduction in MAPE compared to FGM(1,1) indicates that the new weighting function is more suitable for predicting North American solar power generation. Overall, TVNDGM(1,1) demonstrates a significant advantage in MAPE comparisons with other methods. Therefore, the TVNDGM(1,1) method surpasses other models in prediction accuracy and closely matches the actual data trajectory. These findings highlight its ability to accurately capture and predict the characteristics of total solar power generation in North America. Furthermore, the use of the whale optimization algorithm for parameter tuning effectively reduces computational costs.

[0082] This application provides a small-sample time series modeling and prediction method based on prioritizing new information. Compared with existing technologies, this application obtains historical data sequence samples corresponding to the prediction target, and uses the whale optimization algorithm to iteratively calculate the historical data sequence samples with the goal of minimizing the mean absolute percentage error. This yields the optimal values ​​of unstructured parameters, which, compared with traditional parameter selection methods, can find the optimal solution in the parameter space more efficiently, providing strong support for model accuracy. Then, based on the optimal values ​​of unstructured parameters, the estimated vector of structured parameters is calculated using the least squares method. The optimal values ​​of unstructured parameters and the estimated vector of structured parameters are used to construct the TVNDGM(1,1) model corresponding to the prediction target, i.e., a time-varying non-homogeneous discrete grey prediction model. By introducing a time variable term, the traditional homogeneous discrete grey prediction model is extended to a non-homogeneous discrete grey prediction model. This not only expands the model's applicability but also effectively corrects the time lag effect between statistical data and economic and social development by adding a time-related correction term, thus improving the model's prediction performance. In information processing, a time-varying anti-forgetting function was innovatively designed by mimicking the human forgetting process. Based on the collected original data sequence, a target accumulation sequence prioritizing new information was generated. The time-varying anti-forgetting function is an anti-forgetting curve that changes over time, serving as a weight accumulation function when accumulating the initial data sequence. This effectively ensures the priority of new information, enabling the prediction system to more sensitively capture dynamic changes and update according to the latest market dynamics and environmental changes, thereby improving the accuracy and reliability of predictions to adapt to new development trends. The target accumulation sequence prioritizing new information is then input into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence. The target prediction result is then calculated based on the model's reduction formula. This approach specifically addresses issues such as insufficient priority of new information in fractional-order grey models and poor adaptation of existing models to small-sample dynamic scenarios, expanding the application scope of grey prediction models in small-sample, dynamically changing time series (such as new energy power generation and economic indicators).

[0083] Furthermore, as Figure 1 In a specific implementation of the method, this application provides a small-sample time series modeling and prediction device based on prioritizing new information, such as... Figure 3 As shown, the device includes: an acquisition module 301, an optimization module 302, a construction module 303, a preprocessing module 304, and a prediction module 305.

[0084] The acquisition module 301 is used to acquire historical data sequence samples corresponding to the prediction target; Optimization module 302 is used to perform iterative calculations on the historical data sequence samples based on the whale optimization algorithm, with the goal of minimizing the mean absolute percentage error, to obtain the optimal values ​​of unstructured parameters; The construction module 303 is used to calculate the structured parameter estimation vector based on the optimal value of the unstructured parameter using the least squares method, and to construct the TVNDGM(1,1) model corresponding to the prediction target using the optimal value of the unstructured parameter and the structured parameter estimation vector. The TVNDGM(1,1) model is a non-homogeneous discrete grey model that includes a time variable term. Preprocessing module 304 is used to collect the original data sequence according to the prediction target, construct a time-varying anti-forgetting function to perform exponential weighting processing on the original data sequence, and construct a target accumulation sequence based on new information priority; The prediction module 305 is used to input the target accumulation sequence with priority to the new information into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence, and to calculate the target prediction value sequence based on the model reduction formula to obtain the target prediction result.

[0085] In a specific application scenario, the optimization module 302 is used to set the hyperparameters of the whale optimization algorithm, including the whale population size, the maximum number of iterations, and the search space for unstructured parameters; initialize the whale population state based on the whale population size and the search space for unstructured parameters, where each whale position in the whale population state represents a candidate value for an unstructured parameter, and multiple candidate values ​​for unstructured parameters are evenly distributed within the search space for unstructured parameters; and obtain the optimal value for the unstructured parameters by iteratively calculating using the fitness function of the whale optimization algorithm and the maximum number of iterations, based on the whale population state and the historical data sequence samples.

[0086] In a specific application scenario, the optimization module 302 is used to, for each unstructured parameter candidate value in the current iteration, perform exponential weighting on the historical data sequence sample using a time-varying anti-forgetting function and each unstructured parameter candidate value to construct an accumulated sequence based on new information priority for each unstructured parameter candidate value; calculate the structured parameter estimate vector corresponding to each unstructured parameter candidate value using the accumulated sequence based on new information priority for each unstructured parameter candidate value; calculate the time response function value sequence corresponding to each unstructured parameter candidate value and the structured parameter estimate vector corresponding to each unstructured parameter candidate value using the time response formula to obtain the time response function value sequence corresponding to each unstructured parameter candidate value; and use the model reduction formula to convert the time response function value sequence corresponding to each unstructured parameter candidate value into a time response function value sequence. The predicted values ​​are restored to the original data scale to obtain the predicted value sequence corresponding to each unstructured parameter candidate value; the predicted value sequence corresponding to each unstructured parameter candidate value and the original data sequence are substituted into the fitness function to obtain the fitness value corresponding to each unstructured parameter candidate value; the whale optimization algorithm is used to adjust the multiple unstructured parameter candidate values ​​according to the fitness value corresponding to each unstructured parameter candidate value to obtain multiple unstructured parameter candidate values ​​for the next iteration number; if the current iteration number is less than the maximum iteration number, the multiple unstructured parameter candidate values ​​for the next iteration number are used to enter the next round of iteration calculation; if the current iteration number is equal to the maximum iteration number, the unstructured parameter candidate value with the smallest fitness value is selected from the multiple unstructured parameter candidate values ​​as the optimal value of the unstructured parameter.

[0087] In specific application scenarios, the optimization module 302 is used to perform exponential weighting processing on the historical data sequence samples for each unstructured parameter candidate value using the time-varying anti-forgetting function and the unstructured parameter candidate value, thereby constructing an accumulated sequence based on new information priority corresponding to the unstructured parameter candidate value.

[0088]

[0089]

[0090]

[0091] in, This represents the historical data sequence sample. This represents the s-th historical observation in the historical data sequence sample, where n represents the sequence length. This represents the time-varying anti-forgetting function. This is used to perform a weighted calculation on the s-th historical observation for the i-th unstructured parameter candidate value at the current iteration number j. This represents the i-th unstructured parameter candidate value at the current iteration number j. This represents the w-th data point in the cumulative sequence based on new information priority, corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the cumulative sequence based on prioritizing new information, corresponding to the i-th unstructured parameter candidate value under the current iteration number j.

[0092] In specific application scenarios, the optimization module 302 is used to construct a result matrix and a data matrix corresponding to each unstructured parameter candidate value using the cumulative sequence based on new information priority.

[0093]

[0094] in, This represents the result matrix corresponding to the i-th unstructured parameter candidate value under the current iteration number j. This represents the data matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the nth data point in the cumulative sequence based on new information priority, corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the (n-1)th data point in the cumulative sequence based on new information priority, corresponding to the i-th unstructured parameter candidate value at the current iteration number j; the structured parameter estimate vector corresponding to the unstructured parameter candidate value is calculated using the result matrix and data matrix.

[0095] in, This represents the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the result matrix corresponding to the i-th unstructured parameter candidate value under the current iteration number j. This represents the data matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the second structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the third structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j.

[0096] In specific application scenarios, the optimization module 302 is used to calculate, for each unstructured parameter candidate value, the unstructured parameter candidate value and the corresponding structured parameter estimate vector using the time response formula, to obtain a sequence of time response function values ​​corresponding to the unstructured parameter candidate value.

[0097] in, This represents the (r+1)th time response function value in the sequence of time response function values ​​corresponding to the i-th unstructured parameter candidate value at the current iteration number j. Let r represent the power of the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the i-th unstructured parameter candidate value at the current iteration number j, where n represents the sequence length. This represents the first historical observation in the historical data sequence sample. This represents the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the second structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the third structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j. It represents the rt power of the first structured parameter estimate in the structured parameter estimate vector corresponding to the i-th unstructured parameter candidate value under the current iteration number j.

[0098] In specific application scenarios, the optimization module 302 is used to, for each unstructured parameter candidate value, use the model reduction formula to restore the time response function value sequence corresponding to the unstructured parameter candidate value to the original data-scale predicted value, thereby obtaining the predicted value sequence corresponding to the unstructured parameter candidate value.

[0099] in, This represents the (r+1)th predicted value in the predicted value sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the i-th unstructured parameter candidate value at the current iteration number j. This represents the (r+1)th time response function value in the sequence of time response function values ​​corresponding to the i-th unstructured parameter candidate value under the current iteration number j.

[0100] In a specific application scenario, the optimization module 302 is used to, for each unstructured parameter candidate value, substitute the predicted value sequence corresponding to the unstructured parameter candidate value and the original data sequence into the fitness function to obtain the fitness value corresponding to the unstructured parameter candidate value.

[0101] in, This represents the fitness value corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the l-th predicted value in the predicted value sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j. This represents the l-th historical observation in the historical data sequence sample, and n represents the sequence length.

[0102] In specific application scenarios, the prediction module 305 is used to input the target accumulation sequence with priority to the new information into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence.

[0103] in, This represents the first structured parameter in the structured parameter estimate vector. This represents the second structured parameter in the structured parameter estimate vector. This represents the third structured parameter in the structured parameter estimate vector. This represents the p-th data point in the target accumulation sequence prioritizing the new information. This represents the (p+1)th predicted value in the target predicted value sequence. This represents the optimal value of the unstructured parameters of the TVNDGM(1,1) model. This represents the time variable term of the TVNDGM(1,1) model; the target prediction value sequence is restored to the original data-scaled prediction value using the model's reduction formula to obtain the target prediction result.

[0104] in, This represents the (p+1)th predicted value in the target prediction result. This represents the optimal value of the unstructured parameters of the TVNDGM(1,1) model. This represents the (p+1)th predicted value in the target predicted value sequence, where n represents the sequence length.

[0105] This application provides an apparatus that, compared with the prior art, obtains historical data sequence samples corresponding to the prediction target. Based on the whale optimization algorithm, with the minimization of the mean absolute percentage error as the optimization objective, it iteratively calculates the historical data sequence samples to obtain the optimal values ​​of unstructured parameters. Compared with traditional parameter selection methods, this method can find the optimal solution in the parameter space more efficiently, providing strong support for model accuracy. Then, based on the optimal values ​​of the unstructured parameters, the estimated vector of structured parameters is calculated using the least squares method. The TVNDGM(1,1) model corresponding to the prediction target is constructed using the optimal values ​​of the unstructured parameters and the estimated vector of structured parameters; that is, a time-varying non-homogeneous discrete grey prediction model. By introducing a time variable term, the traditional homogeneous discrete grey prediction model is extended to a non-homogeneous discrete grey prediction model. This not only expands the scope of application of the model but also effectively corrects the time lag effect between statistical data and economic and social development by adding a time-related correction term, thereby improving the model's prediction performance. In information processing, a time-varying anti-forgetting function was innovatively designed by mimicking the human forgetting process. Based on the collected original data sequence, a target accumulation sequence prioritizing new information was generated. The time-varying anti-forgetting function is an anti-forgetting curve that changes over time, serving as a weight accumulation function when accumulating the initial data sequence. This effectively ensures the priority of new information, enabling the prediction system to more sensitively capture dynamic changes and update according to the latest market dynamics and environmental changes, thereby improving the accuracy and reliability of predictions to adapt to new development trends. The target accumulation sequence prioritizing new information is then input into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence. The target prediction result is then calculated based on the model's reduction formula. This approach specifically addresses issues such as insufficient priority of new information in fractional-order grey models and poor adaptation of existing models to small-sample dynamic scenarios, expanding the application scope of grey prediction models in small-sample, dynamically changing time series (such as new energy power generation and economic indicators).

[0106] It should be noted that other corresponding descriptions of the functional units involved in the small-sample time series modeling and prediction device based on prioritizing new information provided in this application embodiment can be found in the following references. Figure 1 and Figure 2A The corresponding descriptions in [the document] will not be repeated here.

[0107] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0108] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0109] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

[0110] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented in hardware or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) and includes several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0111] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application.

[0112] Those skilled in the art will understand that the modules in the apparatus of the implementation scenario can be distributed within the apparatus of the implementation scenario as described, or they can be located in one or more apparatuses different from this implementation scenario, with corresponding changes. The modules of the above-described implementation scenario can be combined into one module, or they can be further divided into multiple sub-modules.

[0113] The serial numbers in this application are for descriptive purposes only and do not represent the superiority or inferiority of the implementation scenario.

[0114] The above disclosures are only a few specific implementation scenarios of this application. However, this application is not limited to these. Any variations that can be conceived by those skilled in the art should fall within the protection scope of this application.

Claims

1. A small sample time series modeling and forecasting method based on new information priority, characterized in that, The method comprises the following steps: obtaining historical data sequence samples corresponding to a prediction target; based on the whale optimization algorithm, taking the minimization of the mean absolute percentage error as the optimization goal, iteratively calculating the historical data sequence samples to obtain the optimal value of the unstructured parameter; based on the optimal value of the unstructured parameter, calculating the estimated value vector of the structured parameter by the least squares method, and constructing the TVNDGM(1,1) model corresponding to the prediction target using the optimal value of the unstructured parameter and the estimated value vector of the structured parameter, wherein the TVNDGM(1,1) model is a non-homogeneous discrete grey model containing time variable terms; According to the original data sequence of the prediction target, the time-varying anti-forgetting function is constructed to perform exponential weighting processing on the original data sequence, and the target cumulative sequence based on new information priority is constructed; input the target cumulative sequence based on new information priority into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence, and calculate the target prediction value sequence based on the model restoration formula to obtain the target prediction result.

2. The method of claim 1, wherein, The method comprises the following steps: setting the hyperparameters of the whale optimization algorithm, wherein the hyperparameters include the whale population size, the maximum number of iterations, and the search space of the unstructured parameter; initializing the whale population state based on the whale population size and the search space of the unstructured parameter, wherein each whale position in the whale population state represents an unstructured parameter candidate value, and multiple unstructured parameter candidate values are uniformly distributed in the search space of the unstructured parameter; using the whale population state and the historical data sequence samples to perform iterative calculation through the fitness function of the whale optimization algorithm and the maximum number of iterations to obtain the optimal value of the unstructured parameter.

3. The method of claim 2, wherein, The method comprises the following steps: for each unstructured parameter candidate value of the current iteration number, the historical data sequence samples are exponentially weighted processed using the time-varying anti-forgetting function and each unstructured parameter candidate value to construct the cumulative sequence based on new information priority corresponding to each unstructured parameter candidate value; calculating the estimated value vector of the structured parameter corresponding to each unstructured parameter candidate value using the cumulative sequence based on new information priority corresponding to each unstructured parameter candidate value; using the time response formula to calculate each unstructured parameter candidate value and the estimated value vector of the structured parameter corresponding to each unstructured parameter candidate value to obtain the time response function value sequence corresponding to each unstructured parameter candidate value; restoring the time response function value sequence corresponding to each non-structured parameter candidate value to original data scale predicted value by using the model restoration formula, to obtain a predicted value sequence corresponding to each non-structured parameter candidate value; substituting the predicted value sequence corresponding to each non-structured parameter candidate value into the fitness function, to obtain a fitness value corresponding to each non-structured parameter candidate value; adjusting the multiple non-structured parameter candidate values according to the fitness value corresponding to each non-structured parameter candidate value by using the whale optimization algorithm, to obtain multiple non-structured parameter candidate values in the next iteration; if the current iteration number is less than the maximum iteration number, then entering the next round of iteration calculation by using the multiple non-structured parameter candidate values in the next iteration; if the current iteration number is equal to the maximum iteration number, then selecting a non-structured parameter candidate value with the minimum fitness value from the multiple non-structured parameter candidate values as the optimal non-structured parameter value.

4. The method of claim 3, wherein, the exponential weighting processing of the historical data sequence sample by using the time-varying anti-forgetting function and each non-structured parameter candidate value, to obtain a new information priority-based accumulation sequence corresponding to each non-structured parameter candidate value, includes: for each non-structured parameter candidate value, the exponential weighting processing of the historical data sequence sample by using the time-varying anti-forgetting function and the non-structured parameter candidate value, to obtain a new information priority-based accumulation sequence corresponding to the non-structured parameter candidate value, wherein, denotes the history data sequence sample, denotes the s-th history observation in the history data sequence sample, n denotes the sequence length, denotes the time-varying anti-forgetting function, for the s-th history observation, for the i-th unstructured parameter candidate value at the current iteration number j, denotes the i-th unstructured parameter candidate value at the current iteration number j, denotes the w-th data point in the new-information-priority-based accumulated sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the new-information-priority-based accumulated sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j.

5. The method of claim 3, wherein, the calculation of the structured parameter estimation value vector corresponding to each non-structured parameter candidate value by using the new information priority-based accumulation sequence corresponding to each non-structured parameter candidate value, includes: for each non-structured parameter candidate value, constructing a result matrix and a data matrix corresponding to the non-structured parameter candidate value by using the new information priority-based accumulation sequence corresponding to the non-structured parameter candidate value, wherein, represents the result matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j, represents the data matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j, represents the n-th data point in the new information first based accumulation sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j, represents the n-1-th data point in the new information first based accumulation sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j, calculating the structured parameter estimation value vector corresponding to the non-structured parameter candidate value by using the result matrix and the data matrix corresponding to the non-structured parameter candidate value, wherein, denotes the structured parameter estimation vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the result matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the data matrix corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the first structured parameter estimation value in the structured parameter estimation vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the second structured parameter estimation value in the structured parameter estimation vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the third structured parameter estimation value in the structured parameter estimation vector corresponding to the i-th unstructured parameter candidate value at the current iteration number j.

6. The method of claim 3, wherein, the calculation of the time response function value sequence corresponding to each non-structured parameter candidate value by using the time response formula and the structured parameter estimation value vector corresponding to each non-structured parameter candidate value, includes: for each non-structured parameter candidate value, the calculation of the time response function value sequence corresponding to the non-structured parameter candidate value by using the time response formula and the structured parameter estimation value vector corresponding to the non-structured parameter candidate value, wherein, denotes the r+1th time response function value in the sequence of time response function values corresponding to the ith unstructured parameter candidate value at the current iteration number j, denotes the rth power of the first structured parameter estimate in the vector of structured parameter estimates corresponding to the ith unstructured parameter candidate value at the current iteration number j, denotes the ith unstructured parameter candidate value at the current iteration number j, n denotes the sequence length, denotes the 1st historical observation in the sequence of historical data samples, denotes the first structured parameter estimate in the vector of structured parameter estimates corresponding to the ith unstructured parameter candidate value at the current iteration number j, denotes the second structured parameter estimate in the vector of structured parameter estimates corresponding to the ith unstructured parameter candidate value at the current iteration number j, denotes the third structured parameter estimate in the vector of structured parameter estimates corresponding to the ith unstructured parameter candidate value at the current iteration number j, denotes the r-tth power of the first structured parameter estimate in the vector of structured parameter estimates corresponding to the ith unstructured parameter candidate value at the current iteration number j.

7. The method of claim 3, wherein, the restoration of the time response function value sequence corresponding to each non-structured parameter candidate value to original data scale predicted value by using the model restoration formula, to obtain a predicted value sequence corresponding to each non-structured parameter candidate value, includes: for each non-structured parameter candidate value, the time response function value sequence corresponding to the non-structured parameter candidate value is reduced to original data scale prediction values by using the model reduction formula, to obtain a prediction value sequence corresponding to the non-structured parameter candidate value, wherein, denotes the (r+1)-th predicted value in the sequence of predicted values corresponding to the i-th candidate value of the unstructured parameter at the current iteration number j, denotes the i-th candidate value of the unstructured parameter at the current iteration number j, denotes the (r+1)-th time response function value in the sequence of time response function values corresponding to the i-th candidate value of the unstructured parameter at the current iteration number j.

8. The method of claim 3, wherein, the prediction value sequence corresponding to each non-structured parameter candidate value is substituted into the fitness function to obtain a fitness value corresponding to each non-structured parameter candidate value, comprising: for each non-structured parameter candidate value, the prediction value sequence corresponding to the non-structured parameter candidate value is substituted into the fitness function to obtain a fitness value corresponding to the non-structured parameter candidate value, wherein, denotes the fitness value corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the l-th predicted value in the predicted value sequence corresponding to the i-th unstructured parameter candidate value at the current iteration number j, denotes the l-th historical observation in the historical data sequence sample, and n denotes the sequence length.

9. The method of claim 1, wherein, the new information priority target accumulation sequence is input into the TVNDGM(1,1) model corresponding to the prediction target to obtain a target prediction value sequence, and the target prediction value sequence is calculated based on a model reduction formula to obtain a target prediction result, comprising: the new information priority target accumulation sequence is input into the TVNDGM(1,1) model corresponding to the prediction target to obtain the target prediction value sequence, wherein, denotes a first structured parameter in the structured parameter estimate vector, denotes a second structured parameter in the structured parameter estimate vector, denotes a third structured parameter in the structured parameter estimate vector, denotes a pth data point in the target cumulative sequence of new information preference, denotes a (p+1)th prediction value in the target prediction value sequence, denotes an unstructured parameter optimum value of the TVNDGM(1,1) model, denotes a time variable term of the TVNDGM(1,1) model; the target prediction value sequence is reduced to original data scale prediction values by using the model reduction formula to obtain the target prediction result, wherein, represents the (p+1)th prediction value in the target prediction result, represents the unstructured parameter optimal value of the TVNDGM(1,1) model, represents the (p+1)th prediction value in the target prediction value sequence, and n represents the sequence length.

10. A device for modeling and predicting small sample time series based on new information priority, characterized in that, comprising: an acquisition module configured to acquire a historical data sequence sample corresponding to a prediction target; an optimization module configured to perform iterative calculation on the historical data sequence sample based on a whale optimization algorithm, with minimization of mean absolute percentage error as an optimization target, to obtain a non-structured parameter optimal value; a construction module configured to calculate a structured parameter estimation value vector by least squares method based on the non-structured parameter optimal value, and construct a TVNDGM(1,1) model corresponding to the prediction target by using the non-structured parameter optimal value and the structured parameter estimation value vector, the TVNDGM(1,1) model being a non-homogeneous discrete grey model containing a time variable term; a preprocessing module configured to acquire an original data sequence according to the prediction target, construct a time-varying anti-forgetting function, and perform exponential weighting processing on the original data sequence to construct a new information priority target accumulation sequence; a prediction module configured to input the new information priority target accumulation sequence into the TVNDGM(1,1) model corresponding to the prediction target to obtain a target prediction value sequence, and calculate the target prediction value sequence based on a model reduction formula to obtain a target prediction result.

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