Data prediction method and system based on time sequence adaptive mode decomposition

Abstract

The invention relates to the technical field of data processing, in particular to a data prediction method and system based on time sequence adaptive modal decomposition, and the method comprises the steps: obtaining multi-scale original data which is distributed according to a time sequence, and recognizing and replacing a nonlinear mutation point in the original data, so as to obtain pre-decomposed data which is smoothly distributed; performing variational mode decomposition on the pre-decomposed data based on each mode number in a preset range to obtain a plurality of candidate mode function subsequences; calculating the sum of the sample entropies of the plurality of candidate modal function subsequences corresponding to each modal number, determining an optimal modal number, and obtaining a plurality of target modal function subsequences based on the optimal modal number; dividing the target modal function sub-sequence into a plurality of sub-sequence segments with distribution differences to obtain a sub-predicted value corresponding to each sub-sequence segment; and determining a corresponding weight based on the sample entropy of each sub-sequence segment, and performing weighted stacking on the sub-predicted values of the plurality of sub-sequence segments at the same time point to obtain a target predicted value.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a data prediction method and system based on time-series adaptive mode decomposition. Background Technology

[0002] The core logic of time series forecasting is to construct an ordered sequence from acquired data according to chronological order, and then, by deeply analyzing the trends and fluctuations in the data within the sequence, predict the levels that the data may reach in multiple future time periods. As a technology with wide-ranging applications, time series forecasting occupies an indispensable research position in many key areas such as financial market trend prediction, weather data reporting, medical and health monitoring, and industrial production scheduling. Accurate time series forecasting results can provide solid data support for decision-making in various fields, help optimize resource allocation schemes, and significantly improve the operational efficiency of various systems.

[0003] In practical applications, time series data generally exhibits non-stationary characteristics. Over time, the overall trend and local fluctuations of the data constantly change, typically encompassing multi-scale features such as long-term trends, seasonal periodic fluctuations, and short-term random fluctuations. Simultaneously, during data acquisition and transmission, data may be affected by external noise interference and measurement errors, all of which exacerbate the complexity of time series modeling. Especially when time series contain multiple periodic patterns, sudden event shocks, or interference from external factors, traditional forecasting methods often struggle to fully capture the complex patterns behind the data and cannot adequately adapt to its dynamic characteristics, thus limiting forecasting effectiveness. Therefore, improving the forecasting accuracy of non-stationary time series, particularly when the data contains measurement noise interference and complex long- and short-term dependencies, has become a core challenge in the development of current time series forecasting technology.

[0004] Traditional forecasting methods are mainly divided into two categories: statistical methods and machine learning methods. Statistical methods, typified by ARIMA models and grey prediction models, can achieve relatively stable forecasting results when dealing with stationary time series data, relying on a mature statistical theoretical framework. However, when faced with non-stationary time series with complex distributions and frequent dynamic changes, their strong dependence on data stationarity makes it difficult to adapt to the nonlinear changes and dynamic fluctuations of the data, often resulting in a significant drop in forecasting accuracy. Machine learning methods, such as artificial neural networks and support vector machines, while capable of capturing nonlinear correlations in data and adapting to complex data distributions to some extent, have significant limitations in processing non-stationary signals. Especially when dealing with complex time series signals containing multiple frequency components, the models are prone to underfitting due to insufficient learning of data features or overfitting due to overlearning local noise features, making it difficult to balance forecasting accuracy and model generalization ability.

[0005] In summary, when faced with complex time series data that simultaneously contain multi-scale features, nonlinear correlations, and non-stationary characteristics, how to further improve the accuracy of data prediction and meet the reliability requirements of prediction results in practical application scenarios has become an urgent problem to be solved. Summary of the Invention

[0006] To improve the accuracy of data prediction and meet the reliability requirements of prediction results in practical application scenarios, this application provides a data prediction method and system based on time-series adaptive mode decomposition.

[0007] Firstly, this application provides a data prediction method based on temporal adaptive mode decomposition, employing the following technical solution:

[0008] A data prediction method based on temporal adaptive mode decomposition, the method comprising:

[0009] Acquire raw data that is multi-scale and distributed over time, and identify and replace nonlinear abrupt changes in the raw data to obtain pre-decomposed data with a smooth distribution.

[0010] Variational mode decomposition is performed on the pre-decomposed data based on the number of modes within a preset range to obtain multiple candidate mode function subsequences;

[0011] Calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number;

[0012] The target mode function subsequence is divided into multiple subsequence segments with different distributions, and the subsequence segments are input into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment;

[0013] The corresponding weight is determined based on the sample entropy of each sub-sequence segment, and the sub-predicted values ​​of multiple sub-sequence segments at the same time point are weighted and superimposed to obtain the target predicted value.

[0014] In one possible implementation, nonlinear abrupt changes in the original data are identified and replaced to obtain smoothly distributed pre-decomposed data and noisy subsequences.

[0015] After calculating the sample entropy of each candidate mode function subsequence to determine the optimal number of modes, and obtaining the target mode function subsequence based on the optimal number of modes;

[0016] The target mode function subsequence and the noise subsequence are recombined to obtain the reconstructed time series sequence;

[0017] The difference between the reconstructed time series sequence and the pre-decomposed data is determined. When the difference is less than a preset threshold, the target modal function subsequence is divided into multiple subsequence segments with distribution differences according to the time dimension.

[0018] In one possible implementation, multi-scale and time-series distributed raw data is acquired, and nonlinear abrupt changes in the raw data are identified and replaced to obtain smoothly distributed pre-decomposed data and noisy subsequences, including:

[0019] Obtain raw data at multiple scales and distributed over time, and then filter to obtain valid data;

[0020] Based on the effective data, the preset adjacent data neighborhood radius, and the minimum number of samples, the nonlinear mutation point is obtained;

[0021] Obtain multiple normal and valid data adjacent to the nonlinear mutation point, calculate the mean, and then replace the nonlinear mutation point;

[0022] Pre-decomposed data and a noise subsequence are obtained. The pre-decomposed data is obtained by replacing the nonlinear mutation points in the valid data, and the noise subsequence is obtained by at least one nonlinear mutation point.

[0023] In one possible implementation, calculating the sum of the sample entropies of the multiple candidate mode function subsequences corresponding to each mode number includes:

[0024] Based on the preset vector dimension, the corresponding candidate modal function subsequence is split into multiple sequence vectors;

[0025] Determine the maximum distance between any two sequence vectors, and obtain the similarity vector pair ratio for each sequence vector based on the maximum distance, a similarity threshold, and the similarity vector pair ratio.

[0026] Calculate the average of the similarity vector pair ratios for all upgraded sequence vectors and all sequence vectors, respectively;

[0027] The sample entropy of the corresponding candidate mode function subsequence is calculated based on the ratio of the average values ​​of the proportions of two similar vector pairs.

[0028] Calculate the sum of sample entropies for multiple candidate mode function subsequences.

[0029] In one possible implementation, after calculating the sum of the sample entropies of the multiple candidate mode function subsequences, the process includes:

[0030] The optimal number of modes is determined by finding the minimum sum of the entropies of multiple samples for each mode number.

[0031] In one possible implementation, dividing the target mode function subsequence into multiple subsequence segments with different distributions includes:

[0032] Multiple subsequence segments are obtained by dividing the sequence into multiple subsequence segments based on the number of different subsequences.

[0033] The difference value is determined based on the number of corresponding subsequences and the KL divergence between any two subsequence segments;

[0034] Based on the number of subsequences corresponding to the largest difference value, multiple subsequence segments are obtained.

[0035] In one possible implementation, the step of splitting the data into multiple sub-sequence segments based on the number of different sub-sequence partitions includes:

[0036] The number of subsequences is within a preset range, and the length of the subsequence segments after division based on the number of subsequences is greater than the preset length.

[0037] In one possible implementation, a corresponding weight is determined based on the sample entropy of each sub-sequence segment, and the sub-predicted values ​​of multiple sub-sequence segments at the same time point are weighted and superimposed to obtain the target predicted value, including:

[0038] The weight of each subsequence segment is obtained based on the sample entropy of each subsequence segment and the sample entropy of all subsequence segments, where the sum of the weights of all subsequence segments is 1;

[0039] Based on the weight of each subsequence segment and the corresponding sub-prediction value, the weighted prediction value of each subsequence segment is obtained.

[0040] Multiple weighted prediction values ​​at the same time point are superimposed to obtain the target prediction value.

[0041] Secondly, this application provides a data prediction system based on temporal adaptive mode decomposition, which adopts the following technical solution:

[0042] A data prediction system based on temporal adaptive mode decomposition, the system comprising:

[0043] The data preprocessing module is used to acquire raw data that is multi-scale and distributed in time sequence, and to identify and replace nonlinear abrupt changes in the raw data to obtain pre-decomposed data with a smooth distribution.

[0044] The data decomposition module is used to perform variational mode decomposition on the pre-decomposed data based on the number of modes within a preset range, so as to obtain multiple candidate mode function subsequences;

[0045] The mode determination module is used to calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number;

[0046] The segmented prediction module is used to divide the target mode function subsequence into multiple subsequence segments with different distributions, and input the subsequence segments into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment;

[0047] The data processing module is used to determine the corresponding weight based on the sample entropy of each sub-sequence segment, and to weight and superimpose the sub-predicted values ​​of multiple sub-sequence segments at the same time point to obtain the target predicted value.

[0048] Thirdly, this application provides a data prediction device based on temporal adaptive mode decomposition, which adopts the following technical solution:

[0049] A data prediction device based on temporal adaptive mode decomposition includes: a memory and a processor;

[0050] The memory stores computer-executed instructions;

[0051] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0052] This application provides a data prediction method and system based on time-series adaptive mode decomposition. By identifying and replacing dislinear abrupt change points in the original data, noise and outliers are removed, ensuring the data quality of the pre-decomposed data. The optimal mode number is determined by summing the corresponding candidate mode sub-function sequences decomposed with different mode numbers and their corresponding sample entropies. The optimal mode number can improve the data fidelity after decomposition, reduce mode aliasing, and adapt to the multi-scale characteristics of the data. Furthermore, the target mode function sub-sequence segment is divided into multiple sub-sequence segments with different distributions for individual prediction, and weights are assigned based on the sample entropy of each sub-sequence segment. This achieves high accuracy in predicting complex time series data under multi-scale features, dislinear correlation, and stationary characteristics. Moreover, this method has strong generalization ability and can provide reliable support for result prediction in multiple scenarios and domains. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating a data prediction method based on temporal adaptive mode decomposition according to this application.

[0054] Figure 2 This is a flowchart illustrating a data prediction method based on temporal adaptive mode decomposition, provided as an embodiment of this application.

[0055] Figure 2a This is a flowchart of step S201 in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0056] Figure 2b This is a flowchart of step S203 in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0057] Figure 2c The image shows the VMD mode decomposition result in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0058] Figure 2d This is a comparison diagram of the original data and the VMD reconstructed time series in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0059] Figure 2e This is a flowchart of step S206 in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0060] like Figure 2f This is a comparison diagram of the prediction results of subsequence segments in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0061] Figure 2gThis is a flowchart of step S207 in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0062] Figure 2h This is a comparison chart of test machine prediction results in a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application.

[0063] Figure 3 This is a schematic diagram of the structure of a data prediction system based on temporal adaptive mode decomposition, provided in an embodiment of this application.

[0064] Figure 4 This is a schematic diagram of the structure of a data prediction device based on temporal adaptive mode decomposition, provided in an embodiment of this application. Detailed Implementation

[0065] To better understand the purpose, technical solutions, and advantages of this application, it has been described and illustrated below with reference to the accompanying drawings and embodiments. However, those skilled in the art should understand that this application can be implemented without these details. In some cases, to avoid obscuring various aspects of this application due to unnecessary description, well-known methods, processes, systems, components, and / or circuits already described at a higher level will not be elaborated upon. It will be apparent to those skilled in the art that various modifications can be made to the embodiments disclosed in this application, and the general principles defined in this application can be applied to other embodiments and application scenarios without departing from the principles and scope of this application. Therefore, this application is not limited to the illustrated embodiments, but conforms to the broadest scope consistent with the scope of protection claimed in this application.

[0066] It should be noted that the descriptions of these embodiments are for the purpose of aiding understanding the present invention, but do not constitute a limitation thereof. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0067] It should be understood that the embodiments described herein may be implemented in hardware, software, firmware, middleware, microcode, or any combination thereof. For hardware implementations, the processor may be implemented as one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, other electronic units designed to perform the functions described herein, or combinations thereof.

[0068] When an embodiment is implemented as software, firmware, middleware, or microcode, program code, or code segments, it may be stored in a machine-readable medium, such as a storage component. A code segment may represent a procedure, function, subroutine, program, routine, subroutine, module, software package, class, or any combination of instructions, data structures, or program statements. One code segment can be coupled to another code segment or hardware circuitry by passing and / or receiving information, data, arguments, parameters, or memory contents. Information, arguments, parameters, data, etc., can be passed, forwarded, or transmitted using any suitable means, including memory sharing, messaging, token passing, network transmission, etc.

[0069] For software implementations, the techniques described herein can be implemented using modules (e.g., programs, functions, etc.) that perform the functions described herein. The software code can be stored in memory units and executed by a processor. The memory units can be implemented within or outside the processor; in the latter case, the memory units can be communicatively coupled to the processor via various methods known in this art.

[0070] In the description of this application, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0071] In the description of this application, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples.

[0072] In existing technologies, time series generally exhibit non-stationarity, with overall trends and local fluctuations constantly changing. Furthermore, data acquisition and transmission are subject to external noise interference and data gaps. Directly inputting such data into a single learning model or traditional mode decomposition model is problematic because a single learning model struggles to adapt to multi-scale mixed features. Additionally, traditional mode decomposition models rely on manually set mode numbers K and penalty factors. Key parameters such as [specific parameters] are highly subjective and have poor adaptability, resulting in poor adaptive ability of the prediction results and an inability to dynamically match the complex fluctuations of the data, leading to low accuracy of the prediction results.

[0073] To address the aforementioned technical issues, this application improves the prediction accuracy of nonlinear and non-stationary data by smoothing and purifying the data, dynamically determining the number of modes, and splitting multi-scale feature data, thereby meeting the reliability requirements of prediction results in practical application scenarios.

[0074] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0075] Figure 1 This is a flowchart illustrating a data prediction method based on temporal adaptive mode decomposition according to this application. This application is applicable to various scenarios; in this embodiment, a clothing sales prediction scenario is used as an example. Figure 1 As shown in the figure, this application discloses a data prediction method based on temporal adaptive mode decomposition, the method comprising:

[0076] S101. Obtain the original data with multiple scales and time-series distribution, and identify and replace nonlinear abrupt change points in the original data to obtain pre-decomposed data with a smooth distribution.

[0077] Multi-scale raw data refers to raw data that needs to be used for time series prediction, which includes different levels of information, such as different time dimensions, different fluctuation frequencies, and different feature granularities. These levels of information together constitute the complex dynamic characteristics of the raw data.

[0078] For example, fluctuations in clothing sales data are not random, but rather generated by the superposition of driving factors at different frequencies, each frequency corresponding to a scale. Specifically, the raw data can include three scale types: high-frequency scale, mid-frequency scale, and low-frequency scale.

[0079] The frequency characteristics of high-frequency scales are short-term rapid fluctuations. For example, the period of the raw data is less than one week. This raw data represents the sudden changes in sales on a single day or within a week. The driving factors for this frequency may be temporary promotions during the week, sudden weather changes, stockouts being reinstated, or weekend consumption peaks.

[0080] The characteristic frequency of the mid-frequency scale is the medium-term periodic fluctuation. For example, the period of the raw data is 1 week to 3 months. This raw data represents the weekly / monthly sales pattern. The driving factors for this frequency may be weekly consumption habits, such as high sales on weekends, monthly new product launches, and holidays.

[0081] Low-frequency scales are characterized by long-term trend changes. For example, the period of the raw data is more than 3 months. This raw data represents the sales trend of the quarter / year. The driving factors for this frequency may be seasonal changes, changes in annual consumption capacity, and the long-term accumulation of brand reputation.

[0082] The time-series distribution refers to the original data being recorded continuously in chronological order, such as by day, week, or month, forming a time series.

[0083] Nonlinear mutation points are outliers in the original data that suddenly deviate from the normal trend according to the time series distribution. Such data are generated without a fixed pattern and have nonlinear characteristics. Specifically, they may be caused by a sudden promotion at a specific time, such as a 3-fold increase in sales on the first day of the 618 promotion, or a sudden increase in sales on the day when supply is restored after a 10-day stockout, or a system failure that causes a daily error of 0 or an abnormally high value.

[0084] The raw data can be extracted from historical data in the ERP system of apparel companies and the back-end of e-commerce platforms. The time span can cover at least one full year, so that the raw data contains low-frequency features such as seasons and years.

[0085] When acquiring raw data, core fields such as transaction date, product category, and daily sales volume, which serve as time series benchmarks, can be retained, while irrelevant fields such as user ID and payment method can be removed to reduce the amount of data processing and improve data processing efficiency.

[0086] For example, the daily sales data of a certain brand of jeans from January 1, 2019 to October 31, 2023 were extracted, totaling 1765 records. After being sorted by date, a time series was formed. The data includes multi-scale features such as the sales peak before the Spring Festival (low frequency), weekend sales higher than weekday sales (medium frequency), and the Double 11 promotion explosion (high frequency).

[0087] These raw data are usually multi-feature superpositions and continuously distributed over time. By collecting, processing and analyzing these raw data, the accuracy of subsequent result predictions can be improved.

[0088] After the raw data is collected, nonlinear mutation points are identified using the density clustering algorithm (DBSCAN). The DBSCAN algorithm does not require a preset outlier threshold and can adaptively identify discrete nonlinear mutation points.

[0089] After identifying nonlinear mutation points using the DBSCAN algorithm, these mutation points can be replaced to maintain a smooth distribution of data in the time sequence. The original data after smoothing is the pre-decomposed data.

[0090] When replacing the data at this nonlinear abrupt change point, the following method can be used:

[0091] 1. Mean replacement method: By collecting data from multiple consecutive normal points before and after the nonlinear mutation point, calculating the mean, and then replacing the nonlinear mutation point.

[0092] For example, if the sales volume on November 11, 2022 is 120,000, and the sales volume of the five normal points before and after it is 52,000, 51,000, 53,000, 50,000, and 54,000, and the average of the sales volume of the five normal points before and after it is 52,000, then replace 120,000 with 52,000. After the replacement, the time sequence changes from "52,000, 51,000, 120,000, 53,000, 50,000, 54,000" to "52,000, 51,000, 52,000, 53,000, 50,000, 54,000".

[0093] 2. Linear interpolation method: If there is a linear change between adjacent normal data before and after the nonlinear mutation point, the equation of the straight line is determined by two points, and the fitted value of the nonlinear mutation point is calculated.

[0094] For example, suppose the nonlinear mutation point is x, with its preceding normal data point being (t1, y1) and its following normal data point being (t2, y2), such as (t1=2023-10-01, y1=50000), (t2=2023-10-07, y2=52000). The time interval between the two data points is Δt=t2-t1=6 days, and the sales change is Δy=y2-y1=2000. Then, the fitted value y of the nonlinear mutation point x is... x =y1+(t x -t1)*(Δy / Δt), that is, if x is 2023-10-4, y x =50000+3*(2000 / 6)=51000.

[0095] 3. Polynomial interpolation: When the data before and after the nonlinear abrupt change point shows a nonlinear trend, such as sales dropping rapidly first and then gradually after a promotion, a higher-order polynomial can be used to fit a more complex trend, such as a quadratic or cubic polynomial, to reduce the error of the linear assumption.

[0096] For example, select 2-3 normal data points before and after the mutation point, such as before the promotion: (t 1，y1) = (2023-11-09, 48000), (t2, y2) = (2023-11-10, 50000); After promotion: (t4, y4) = (2023-11-12, 35000), (t5, y5) = (2023-11-13, 32000)), the mutation point is (t3, y3) (2023-11-11, the original outlier is 120000), construct a quadratic polynomial y = at² + bt + c, substitute the 4 normal points to solve for the coefficients a, b, c, substitute t3 into the polynomial, and get the fitted value y3 = 42000.

[0097] 4. Historical similarity matching method: Assuming that the same product category has similar sales characteristics on the same dates of the year / month, such as December 25th of each year or the first weekend of each month, the average normal sales of the same period in the past 1-3 years is used as the replacement value for the non-linear mutation point.

[0098] 5. Construct a time window centered on the mutation point (e.g., 7 days before and after), find the matching window in historical data that is most similar to the sales trend of this window, and use the sales at the corresponding position of the matching window as the replacement value.

[0099] By identifying and replacing nonlinear abrupt changes in the original data, we can obtain pre-decomposed data with a smooth distribution. Subsequent predictions can then be made using this pre-decomposed data, thus improving the accuracy of the predictions.

[0100] S102. Perform variational mode decomposition on the pre-decomposed data based on the number of modes within a preset range to obtain multiple candidate mode function subsequences.

[0101] Variational Mode Decomposition (VMD) is an adaptive signal processing method. Its core is to adaptively decompose the original multi-scale time series signal into multiple independent mode function subsequences (IMFs) with different center frequencies through a variational optimization framework.

[0102] VMD can automatically identify different scale features such as low-frequency trends, mid-frequency cycles, and high-frequency fluctuations hidden in pre-decomposed data arranged in time sequence, and can decompose the pre-decomposed data into independent modal function subsequences.

[0103] For example, in the scenario of apparel sales forecasting, VMD can decompose the pre-decomposed data into:

[0104] Low-frequency IMF (IMF1-IMF5): corresponds to annual seasonal trends, such as peak sales of summer dresses and peak sales of down jackets.

[0105] Mid-frequency IMF (IMF6-IMF8): Corresponds to the weekly consumption cycle (weekend sales are higher than weekday sales) and monthly new product launches;

[0106] High-frequency IMF (IMF9-IMF11): corresponds to short-term promotional fluctuations (618 promotion, Double 11 promotion) and random noise.

[0107] S103. Calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number.

[0108] Sample entropy is a quantitative indicator of the irregularity of data in a modal function subsequence. It quantifies the feature purity of a modal function subsequence. The smaller the sample entropy value, the stronger the regularity of the modal function subsequence data, the more stable the features, and the more likely the modal function subsequence contains only single-scale features, such as only annual trends or only weekly cycles, without modal aliasing. Conversely, the larger the sample entropy value, the stronger the randomness of the modal function subsequence data, and the more drastic the fluctuations. For example, an IMF may contain both high-frequency fluctuations in promotions and medium-frequency monthly cycles, resulting in severe feature aliasing.

[0109] By traversing each modality number, the sum of sample entropy of all candidate modal function subsequences corresponding to each modality number is calculated. The modality number with the smallest sum of sample entropy and whose center frequencies of each candidate modal function subsequence do not overlap, as verified by Fourier transform, is selected as the optimal modality number. The optimal modality number reduces the subjectivity of manual parameter tuning.

[0110] S104. Divide the target mode function subsequence into multiple subsequence segments with different distributions, and input the subsequence segments into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment.

[0111] Since the target mode function subsequence has already undergone scale feature separation, there may still be differences in subscales within the same IMF. For example, the distribution patterns of "618 promotion fluctuations" and "daily small promotion fluctuations" in high-frequency IMFs are different. Therefore, by using the subsequence segment with the largest distribution difference, secondary refinement of the data in the target mode function subsequence can be achieved.

[0112] For low-frequency IMFs (such as annual trend IMF1), sub-series segments can be divided according to peak and off-peak seasons, such as the peak sales period for summer dresses and the trough period for winter dresses, to avoid the overlap of peak and off-peak trends, which could lead to subsequent forecasting errors.

[0113] For mid-frequency IMFs (such as the weekly cycle IMF6), the dynamic changes in weekly consumption patterns can be accurately captured by dividing them into weekdays / weekends and before and after monthly new product launches.

[0114] For high-frequency IMFs (such as promotional fluctuations IMF9), the fluctuation intensity is distinguished by large-scale promotions (618 promotion / Double 11 promotion) and small-scale promotions (weekend discounts).

[0115] Distributional dissimilarity refers to the degree of difference in the probability distribution patterns of different subsequence segments. If the data of two subsequence segments differ significantly in statistical characteristics such as mean, variance, fluctuation frequency, and peak position, it indicates that the distributional dissimilarity between the two subsequence segments is large; conversely, it indicates that the dissimilarity is small. The distributional dissimilarity between subsequence segments can be calculated using the KL divergence formula.

[0116] By dividing the objective function subsequence into multiple subsequence segments with different distributions, the features of each subsequence segment are made more accurate and clear.

[0117] Basic time series prediction models can include Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), and Long Short-Term Memory (LSTM).

[0118] When the basic time series prediction model is a CNN, the network structure is: a one-dimensional convolutional layer, a ReLU activation layer, a flattening layer, and two fully connected layers connected in sequence.

[0119] When the basic time series prediction model is an RNN, the network structure is: a single-layer SimpleRNN with 512 hidden units, followed by a fully connected output layer.

[0120] When the basic time series prediction model is LSTM, the network structure is: multi-layer LSTM, 256 hidden units, 4 layers, followed by a fully connected output layer.

[0121] Multiple subsequence segments can be predicted using one or more basic time series prediction models. The characteristics of each basic time series prediction model can be combined. For example, CNN is good at capturing local high-frequency features, such as local patterns of short-term promotional fluctuations; RNN / LSTM is good at capturing temporal dependencies, such as continuous changes in weekly cycles. By obtaining the sub-predicted values ​​corresponding to each subsequence segment through the basic time series prediction models, the model can focus on single feature patterns and reduce errors, while maximizing the predictive value of multi-scale features and improving prediction accuracy.

[0122] S105. Determine the corresponding weight based on the sample entropy of each subsequence segment, and weight and superimpose the sub-predicted values ​​of multiple subsequence segments at the same time point to obtain the target predicted value.

[0123] Since sample entropy represents the feature stability and information value of a subsequence segment, the weight of the subsequence segment can be determined by using sample entropy to further improve the accuracy of the target prediction value.

[0124] Among them, when the sample entropy of a subsequence segment is small, it indicates that the subsequence segment has strong regularity and gentle fluctuations, which means that the subsequence segment has high reference value for the target prediction value.

[0125] When the sample entropy of a subsequence segment is large, it indicates that the subsequence segment is highly random and fluctuates strongly, suggesting that the subsequence segment has low reference value for the target prediction value.

[0126] Because the pre-decomposed data contains multi-scale features, multiple sub-sequence segments at the same time point are weighted and superimposed to achieve the synergy between multi-scale features and single-scale features. This allows the final target prediction value to retain the stability of the long-term trend while also taking into account the accuracy of the medium-term cycle and short-term fluctuations.

[0127] This application provides a data prediction method based on temporal adaptive mode decomposition. It smooths and cleanses the multi-scale, time-series distributed raw data to eliminate the interference of nonlinear abrupt changes on subsequent predictions while preserving multi-dimensional temporal features. Then, it achieves accurate multi-scale splitting of the pre-decomposed data using the optimal number of modes, improving the feature purity of the target mode function subsequence. Furthermore, when obtaining the target mode function subsequence, it guides the selection of the optimal number of modes through sample entropy, achieving mode decomposition without manual intervention and ensuring the feature stability and independence of each target mode function subsequence. This reduces the subjectivity of active parameter tuning. Then, by dividing the target modal function subsequence into multiple subsequence segments according to distribution differences, a secondary refined representation of the subsequence segments is achieved, adapting to the feature patterns of different scales and avoiding sub-scale aliasing within a single modality. At this point, the subsequence segments are predicted using a basic time series prediction model, and the target prediction value at a unified time point can be obtained by combining the weights determined by the sample entropy of each subsequence segment. Through full-process adaptation and data-driven logical features, cross-scenario generalization and adaptation are achieved, maintaining high accuracy in multiple scenarios, reducing manual dependence and improving prediction efficiency.

[0128] Figure 2 A flowchart illustrating a data prediction method based on temporal adaptive mode decomposition provided in an embodiment of this application is shown below. Figure 2 As shown, based on the above embodiments, this embodiment includes the following method:

[0129] S201. Obtain the original data with multiple scales and time-series distribution, and identify and replace nonlinear abrupt change points in the original data to obtain smooth-distributed pre-decomposed data and noise subsequences.

[0130] For a detailed description of step S201, please refer to step S101. Based on step S101, the result of replacing the nonlinear mutation point is processed and collected to generate a noise subsequence.

[0131] like Figure 2a As shown, the specific operation is as follows:

[0132] S2011. Obtain raw data with multiple scales and time-series distribution, and filter to obtain valid data.

[0133] When acquiring raw data, filter to obtain valid data. When filtering valid data, core fields can be retained, such as transaction date, product category, and daily sales volume, which serve as time series benchmarks. Irrelevant fields, such as user ID and payment method, can be removed to reduce the amount of data processing and improve data processing efficiency.

[0134] S2012. Based on the valid data and the preset adjacent data neighborhood radius and minimum number of samples, obtain the nonlinear mutation point.

[0135] The domain radius is the distance range used to determine whether data belong to the same cluster. In clothing sales data, it is usually set at 10%-20% of the sales standard deviation. For example, if the sales standard deviation is 5000, the domain radius can be 800.

[0136] The minimum sample size is the minimum amount of data to form a dense cluster. It is set according to the density of time-series data. Daily sales data is usually set to 5-8. For example, if the minimum sample size is 6, that is, the sales of the 6 neighboring data around a certain point are all within the range of the neighborhood radius, it is considered a normal point.

[0137] S2013. Obtain multiple normal and valid data adjacent to the nonlinear mutation point, calculate the mean, and then replace the nonlinear mutation point.

[0138] The nonlinear mutation point is filled by replacing it with the mean of adjacent normal data, thus avoiding the introduction of new noise.

[0139] Specifically, the window size is determined based on the stability of the data around the mutation point. If the data trend before and after the mutation point is stable, such as during non-promotional periods, three normal points before and after the mutation point are taken out when there are a total of 6 points.

[0140] If there are slight fluctuations in the data before and after, such as when a promotion is approaching, the number of points can be increased from 10 to 5 normal points before and after to ensure that the data within the window represents a normal trend.

[0141] Replace the mutation points with the mean of the normal data within the window. The mean reflects the overall trend better than the median and is suitable for subsequent linear reconstruction.

[0142] S2014. Obtain pre-decomposed data and noise subsequence. The pre-decomposed data is obtained by replacing the nonlinear mutation points in the effective data, and the noise subsequence is obtained by at least one nonlinear mutation point.

[0143] Furthermore, the difference between the original nonlinear mutation point data value and the replaced data value is recorded to form an independent noise subsequence, and smooth pre-decomposed data and noise subsequence are output.

[0144] S202. Perform variational mode decomposition on the pre-decomposed data based on the number of modes within a preset range to obtain multiple candidate mode function subsequences.

[0145] For a detailed description of step S202, please refer to step S102. Furthermore, based on step S102, it should be further explained that the preset range of the number of modes can be adjusted according to the characteristics of the corresponding scenario. The number of modes can be represented by K.

[0146] For example, in the scenario of clothing prediction, the preset range of the modality number K can be set to [2, 15].

[0147] Lower limit K=2: Ensure that at least two core scales, low-frequency trend and high-frequency fluctuation, are separated to avoid missing key features;

[0148] Upper limit K=15: Covers most possible subdivision scales of clothing data, such as five time dimensions: annual, quarterly, monthly, weekly, and daily. Each category is further subdivided into 2-3 fluctuation frequencies, while avoiding excessive decomposition that leads to computational redundancy.

[0149] If the K value is too small, features at different scales will be forcibly merged into a single candidate modality function subsequence. For example, monthly promotional fluctuations (high frequency) and weekly consumption cycles (medium frequency) may overlap, and the subsequent model will be unable to distinguish the contribution of the two types of features, leading to an increase in prediction error.

[0150] If the value of K is too large, features at the same scale will be split into multiple redundant candidate mode function subsequences. For example, daily random noise will be split into 3 candidate mode function subsequences, which will not only increase the computational cost of model training, but also introduce meaningless noise features and interfere with the prediction results.

[0151] S203. Calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number.

[0152] For a detailed description of step S203, please refer to the detailed description of step S103. Based on step S103, such as Figure 2b As shown, the specific implementation method is as follows:

[0153] S2031. Based on the preset vector dimension, split the corresponding candidate modal function subsequence into multiple sequence vectors.

[0154] The dimension of a vector can be represented by m.

[0155] First, construct an m-dimensional vector:

[0156] ;

[0157] in, The length of the current candidate mode function subsequence. Represents the k-th candidate mode function subsequence. The specific value of each data point This represents the first subsequence of the k-th candidate mode function. Starting from a data point, an m-dimensional feature vector is formed by m consecutive data points.

[0158] For example, in jeans sales forecasting, u3(5) represents the sales data value on the 5th day of the 3rd candidate modal function subsequence (which may correspond to quarterly cyclical fluctuations).

[0159] If m=2, k=3, i=5, then X(5)=[u3(5),u3(6)], which is a 2-dimensional vector composed of the sales data of the 5th and 6th days in the 3rd candidate modal function subsequence.

[0160] Each candidate modal function subsequence is transformed into an m-dimensional time window vector, where m is usually 2, to balance computational cost and accuracy.

[0161] S2032. Determine the maximum distance between any two sequence vectors, and obtain the similarity vector pair ratio for each sequence vector based on the maximum distance, the similarity threshold, and the similarity vector pair ratio.

[0162] Any two sequence vectors can be used and This means that the maximum distance between any two sequence vectors can be expressed as... This means that the similarity threshold can be used... It can be expressed that the similarity vectors can be compared using... If it means:

[0163] ;

[0164] ;

[0165] ;

[0166] in, It is the standard deviation of the candidate mode function subsequence.

[0167] Calculate the maximum distance between any two sequence vectors to measure their similarity; the smaller the distance, the more similar their features.

[0168] Set a similarity threshold to ensure that the threshold is appropriate for the range of data fluctuations.

[0169] Similar vector pairs Output a set of vector-level scale values, the number of which is the same as the total number of m-dimensional vectors, i.e., -m+1, reflecting the similarity of a single sequence vector to all other sequence vectors.

[0170] S2033. Calculate the average of the similarity ratios of all upgraded sequence vectors and all sequence vectors.

[0171] The average similarity is the ratio of the proportions of similar vector pairs of sequence vectors. The average similarity of sequence vectors can be represented by B. m (r) means that:

[0172] ;

[0173] The average similarity of all upgraded sequence vectors is B. m+1 (r).

[0174] S2034. Based on the ratio of the average values ​​of the two similar vector pairs, the sample entropy of the corresponding candidate mode function subsequence is calculated.

[0175] Sample entropy can be used This means, that is:

[0176] ;

[0177] S2035. Calculate the sum of sample entropy of multiple candidate modal function subsequences.

[0178] The sample entropy of multiple candidate mode function subsequences under the corresponding mode number K is added together to obtain the total sample entropy corresponding to K.

[0179] S2036. Determine the optimal number of modes based on the minimum sum of the entropies of multiple samples for each mode number.

[0180] Iterate through the sum of sample entropies corresponding to each mode number K, and take the mode number corresponding to the minimum value of the sum of sample entropies as the optimal mode number.

[0181] S2037. Based on the optimal number of modes, obtain multiple target mode function subsequences.

[0182] Based on the optimal number of modes, multiple target mode function subsequences are obtained through VMD decomposition.

[0183] For example, based on the optimal mode number K decomposition, multiple target mode function subsequences are obtained, and the set of multiple target mode function subsequences is {IMF1, IMF2, ..., IMF...}. K}, where IMF1-IMF5 are low-frequency components containing annual trends and seasonal cycles, and IMF6-IMF 11 It contains high-frequency components that include promotional fluctuations and random noise.

[0184] S204. Reconstruct the target mode function subsequence and the noise subsequence to obtain the reconstructed time series sequence.

[0185] By reconstructing the time series, the guarantee degree of VMD decomposition can be verified, ensuring that key features in the original data are not lost during the decomposition process and that no additional errors are introduced, thus providing a reliable decomposition basis for subsequent predictions.

[0186] Reconstructing time series sequences can be done using F recon This means, that is:

[0187] ;

[0188] IMF k Let {IMF1, IMF2, ..., IMF} be the set of multiple target mode function subsequences obtained based on the optimal mode number K decomposition. K};

[0189] Noise represents the noise subsequence.

[0190] Reconstructing the time series ensures that the reconstructed data retains the complete characteristics of the original data.

[0191] S205. Determine the difference between the reconstructed time series and the pre-decomposed data.

[0192] When calculating the difference between the reconstructed time series and the pre-decomposed data, the reconstructed time series F is calculated. recon With pre-decomposed data F pre The mean squared error (MSE) and normalized mean absolute error (MAE) are calculated.

[0193] When MSE and Normalized MAE are less than the corresponding preset thresholds, for example, MSE≤0.0001 and NormalizedMAE≤0.005, the decomposition result is deemed valid. The pre-decomposed data almost completely overlaps with the VMD reconstructed time series sequence, proving that the reconstructed time series sequence can completely retain the original data features and has not lost key information. Proceed to step S206.

[0194] like Figure 2cThe VMD mode decomposition result diagram shown is based on the optimal number of modes K=11 determined by minimizing sample entropy, combined with the parameters calculated by sample entropy (m=2) and r=0.3×std(u k The decomposition results are generated together with the decomposition validity verification parameters (MSE≤0.0001, Normalized MAE≤0.005) to ensure that the decomposition results can separate the multi-scale features of clothing sales while fully preserving the original data information.

[0195] like Figure 2d The chart shown compares the original data with the VMD reconstructed time series, based on the optimal VMD parameters (K=11, m=2, r=0.3×std(u)). k The pre-decomposed data is decomposed to obtain the target mode function subsequence and noise subsequence. Finally, the validity of the reconstructed sequence is confirmed by the error verification parameters (MSE≤0.0001, Normalized MAE≤0.005). Finally, a comparison chart of the pre-decomposed data and the VMD reconstructed sequence is generated to intuitively verify that the VMD decomposition did not lose the original data features.

[0196] When the MSE exceeds the corresponding preset threshold, the process returns to step S202 to re-perform VMD decomposition. Since the VMD decomposition result is determined by multiple key parameters, such as the number of modes K, penalty factor α, and noise tolerance τ, among which...

[0197] The number of modes K has a preset range. The parameter can be adjusted by changing the range of values ​​for the number of modes K. Changes in the value of K directly change the number and scale of candidate mode function subsequences: when K increases, the decomposition is more refined; when K decreases, candidate mode function subsequences of similar scales are merged to avoid over-decomposition.

[0198] The penalty factor α is an adjustable parameter in the VMD algorithm. It is initially set to a default value. If the original α causes the decomposition to be too smooth or undersmooth and retains noise, the size of α is adjusted. For example, if α is increased, the constraint is stronger and the candidate mode function subsequence is smoother; if α is decreased, the constraint is weakened and the candidate mode function subsequence retains more fluctuations. α directly affects the smoothness of the candidate mode function subsequence. After α is adjusted, the numerical characteristics of the candidate mode function subsequence under the same K will change.

[0199] The noise tolerance τ is a parameter in the VMD algorithm that controls the intensity of noise filtering. It is initially set to a default value. If the reconstruction error is due to incomplete noise separation, such as missing outliers in the noise subsequence, τ is adjusted. Decreasing τ makes it more sensitive to noise identification, while increasing τ reduces the filtering of small fluctuations. τ affects the composition of the noise subsequence, thereby changing the purity of the candidate mode function subsequence. After τ is adjusted, the amount of residual noise in the candidate mode function subsequence changes, and the reconstruction error changes accordingly.

[0200] S206. Divide the target mode function subsequence into multiple subsequence segments with different distributions, and input the subsequence segments into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment.

[0201] For a detailed description of step S206, please refer to step S104, and based on step S104, such as Figure 2e As shown, the specific steps include the following:

[0202] S2061. Multiple subsequence segments are obtained by splitting the data based on the number of different subsequences.

[0203] Let S be the number of subsequences. The target modal function subsequence is split into multiple subsequence segments according to the number of subsequences S.

[0204] The number of subsequences can be set according to the requirements of different scenarios. For example, the maximum number of subsequences S0=30 can be set, and the time length of each subsequence segment is not less than 7 days to ensure that the weekly cycle features are covered and to avoid feature fragmentation due to overly fine division.

[0205] The number of subsequences is within a preset range, and the length of the subsequence segments after division based on the number of subsequences is greater than the preset length.

[0206] S2062. Determine the difference value based on the number of corresponding subsequence divisions and the KL divergence between any two subsequence segments.

[0207] Construct the objective function:

[0208] The objective function is defined to maximize the distribution difference between subsequence segments:

[0209] ;

[0210] Where S is the number of subsequence partitions, Ω i Ω j For the i-th and j-th subsequence segments, d(Ω) i ,Ω j ) is the KL divergence, used to measure the difference in probability distribution between two subsequence segments.

[0211] S2063. Based on the number of subsequences corresponding to the maximum difference value, obtain multiple corresponding subsequence segments.

[0212] Press S ∗ Subdivide multiple target mode function subsequences into S ∗ The subsequence segment with the largest distribution difference.

[0213] Traverse S within the range [1, S0] to find the optimal number of partitions S. ∗=argmax0≤S≤S0f(S), which is the value of S when the difference in the average distribution between subsequence segments is the greatest, and finally determines S. ∗。

[0214] S2064. Input the subsequence segments into the basic time series prediction model to obtain the sub-prediction value corresponding to each subsequence segment.

[0215] Basic time series prediction models can include Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), and Long Short-Term Memory (LSTM).

[0216] When the basic time series prediction model is a CNN, the network structure is: a one-dimensional convolutional layer, a ReLU activation layer, a flattening layer, and two fully connected layers connected in sequence.

[0217] When the basic time series prediction model is an RNN, the network structure is: a single-layer SimpleRNN with 512 hidden units, followed by a fully connected output layer.

[0218] When the basic time series prediction model is LSTM, the network structure is: multi-layer LSTM, 256 hidden units, 4 layers, followed by a fully connected output layer.

[0219] Overall objective function construction: Integrating distributed distance loss L d L2 regularization loss L r The formula is:

[0220] ;

[0221] Where λ=0.005, R(Ω) i ) is the subsequence segment Ω i The corresponding model parameter, L2 norm, is used to control model complexity.

[0222] Model training strategy: A discontinuous random subsequence combination strategy is adopted, in which discontinuous segments are randomly selected from all subsequence segments to form training samples, minimizing the overall objective function J.

[0223] Prediction results output: Perform predictions separately for each subsequence segment and output the prediction results for each segment. (M is the total number of subsequence segments).

[0224] Ultimately, the validation set MAE=0.0036.

[0225] Multiple subsequence segments can be predicted using one or more basic time series prediction models. The characteristics of each basic time series prediction model can be combined. For example, CNN is good at capturing local high-frequency features, such as local patterns of short-term promotional fluctuations; RNN / LSTM is good at capturing temporal dependencies, such as continuous changes in weekly cycles. By obtaining the sub-predicted values ​​corresponding to each subsequence segment through the basic time series prediction models, the model can focus on single feature patterns and reduce errors, while maximizing the predictive value of multi-scale features and improving prediction accuracy.

[0226] like Figure 2f The comparison chart showing the prediction results of the subsequence segments is first obtained by using the maximum entropy subsequence partitioning parameter (S). * =12, segment length ≥7 days), the subsequence segments are input into the basic time series prediction model to obtain sub-predicted values. Finally, the model is optimized by the total objective function parameters (λ=0.005) and training strategy parameters (Batch Size=32, early stopping strategy) to ensure that the predicted values ​​accurately match the real values. Finally, a comparison chart of the subsequence segment prediction results under different basic models is generated to intuitively demonstrate the effectiveness of the method in multi-scale subsequence prediction.

[0227] S207. Determine the corresponding weight based on the sample entropy of each subsequence segment, and weight and superimpose the sub-predicted values ​​of multiple subsequence segments at the same time point to obtain the target predicted value.

[0228] A detailed description of step S207 can be found in the detailed description of step S105, and based on step S105, such as... Figure 2g As shown, the specific implementation methods include:

[0229] S2071. The weight of each subsequence segment is obtained based on the sample entropy of each subsequence segment and the sample entropy of all subsequence segments, wherein the sum of the weights of all subsequence segments is 1.

[0230] The weight w of the subsequence segment i The sample entropy is inversely proportional to the sample entropy of the subsequence segment; the sample entropy of the low-frequency target mode function subsequence segment is smaller, while the sample entropy of the high-frequency segment is larger.

[0231] The formula for calculating the weight is:

[0232] ;

[0233] in, For the first The sample entropy of each subsequence segment.

[0234] After the weights are calculated, they need to be normalized to ensure... .

[0235] S2072. Based on the weight of each sub-sequence segment and the corresponding sub-prediction value, obtain the weighted prediction value of each sub-sequence segment.

[0236] The weighted predicted value for each subsequence segment is the product of its weight and the corresponding sub-predicted value.

[0237] S2073. Multiple weighted predicted values ​​at the same time point are superimposed to obtain the target predicted value.

[0238] The final sales forecast at the same point in time is the weighted sum of the forecasts for all sub-series, as shown in the formula:

[0239] ;

[0240] Furthermore, after obtaining the target predicted value, evaluation indicators such as mean absolute error (MAE), mean square error (MSE), mean absolute percentage error (MAPE), consistency index (IA), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), directional accuracy (DA), and correlation coefficient (R) between the actual value and the predicted value can be calculated to generate a comparison chart of "actual value vs. predicted value" and provide intuitive reference for enterprise decision-making.

[0241] To verify the effectiveness of this application in the task of predicting clothing sales, a comparative experiment was conducted with existing methods such as single models (CNN, etc.), traditional mode decomposition models (VMD-CNN, etc.), and adaptive improvement models (ADA-CNN, etc.). A self-built Taobao clothing dataset was used as the experimental benchmark. This dataset contains four categories of data: dresses, jeans, sweatshirts, and sweaters, with 1765 samples in each category, covering the period from January 2019 to October 2023. It is suitable for e-commerce platforms, offline chain stores, and other retail scenarios. The results on the jeans dataset test set are shown in Table 1.

[0242] Table 1: Comparison Results of the Jeans Dataset Test Set

[0243] Model MAE MSE MAPE RMSE SMAPE DA IA R CNN 0.0193 0.0006 0.0219 0.0244 0.0219 0.5900 0.7728 0.7511 RNN 0.0211 0.0008 0.0241 0.0277 0.0238 0.6500 0.7653 0.6440 LSTM 0.0186 0.0006 0.0212 0.0248 0.0211 0.5500 0.7599 0.7354 DEEPAR 0.0225 0.0009 0.0255 0.0298 0.0256 0.6200 0.7982 0.6502 DEPTS 0.0206 0.0008 0.0237 0.0277 0.0233 0.6400 0.7793 0.6684 VMD-CNN 0.0044 0.0000 0.0049 0.0068 0.0050 0.8400 0.9891 0.9847 VMD-RNN 0.0079 0.0001 0.0088 0.0118 0.0089 0.8100 0.9682 0.9545 VMD-LSTM 0.0090 0.0001 0.0101 0.1096 0.0101 0.7300 0.9720 0.9739 ADA-CNN 0.0169 0.0006 0.0194 0.0237 0.0192 0.6000 0.8104 0.7401 ADA-RNN 0.0196 0.0007 0.0225 0.0258 0.0223 0.5500 0.7194 0.7084 ADA-LSTM 0.0187 0.0007 0.0214 0.0262 0.0212 0.5700 0.7630 0.6570 The method of this invention (based on the CNN model) 0.0034 0.0000 0.0038 0.0062 0.0039 0.8600 0.9915 0.9863 The method of this invention (based on the RNN model) 0.0037 0.0000 0.0042 0.0065 0.0042 0.8500 0.9906 0.9853 The method of this invention (based on the LSTM model) 0.0043 0.0000 0.0049 0.0072 0.0049 0.8000 0.9886 0.9827

[0244] The results are shown in Table 5 and Figure 2hAs shown in the comparison chart of the test machine prediction results, the series of models in this scheme have the best performance. Taking the CNN as the base model as an example: MAE=0.0034, MSE=0.0000, MAPE=0.0038, IA=0.9915, DA=0.8600. Among them, MAE is improved by about 22.7% compared with VMD-CNN (0.0044) and by about 81.7% compared with the single LSTM model (0.0186). At the same time, MAPE is reduced by about 22.4% compared with VMD-CNN (0.0049), and IA is improved by about 0.24% compared with VMD-CNN (0.9891). The trend consistency between the predicted value and the true value and the numerical accuracy are both at the best level.

[0245] In another scenario, the ETTH oil temperature dataset was selected as the experimental dataset. The ETTH dataset is two years of transformer oil temperature monitoring data released by the State Grid Corporation of China. It has the characteristics of short-term drastic fluctuations and rapid periodic changes, which is suitable for the generalization verification of this application in high-fluctuation time series scenarios.

[0246] To address the short-term high volatility of the data, the optimal number of VMD modes K was adjusted to 11, and the optimal number of partitions S for the maximum entropy subsequence was adjusted accordingly. ∗ =10, ensuring that the model captures high-frequency fluctuation features. The comparison results of the ETTH oil temperature dataset test set are shown in Table 2.

[0247] Table 2: Comparison Results of ETTH Oil Temperature Dataset Test Set

[0248] Model MAE MSE MAPE RMSE SMAPE DA IA R CNN 0.166 0.041 0.633 0.203 0.422 0.52 0.414 0.055 RNN 0.041 0.003 0.134 0.057 0.137 0.8 0.955 0.957 LSTM 0.129 0.027 0.438 0.163 0.371 0.46 0.576 0.323 DEEPAR 0.119 0.026 0.335 0.161 0.388 0.61 0.587 0.423 DEPTS 0.089 0.016 0.301 0.125 0.275 0.67 0.701 0.583 VMD-CNN 0.028 0.002 0.082 0.049 0.085 0.88 0.968 0.96 VMD-RNN 0.047 0.005 0.138 0.071 0.146 0.79 0.942 0.891 VMD-LSTM 0.028 0.002 0.084 0.05 0.087 0.881 0.968 0.961 ADA-CNN 0.096 0.016 0.328 0.128 0.291 0.66 0.696 0.562 ADA-RNN 0.09 0.015 0.305 0.123 0.276 0.62 0.713 0.602 ADA-LSTM 0.091 0.016 0.315 0.127 0.28 0.63 0.688 0.569 The method of this invention (based on the CNN model) 0.029 0.003 0.086 0.051 0.089 0.85 0.965 0.958 The method of this invention (based on the RNN model) 0.031 0.003 0.091 0.052 0.095 0.88 0.964 0.957 The method of this invention (based on the LSTM model) 0.043 0.004 0.135 0.063 0.141 0.84 0.943 0.929

[0249] As shown in the table, the series of models of this invention perform excellently. Taking the basic model as RNN as an example, MAE=0.031, IA=0.964, DA=0.880. MAE is 65.6% lower than ADA-RNN (0.090), and IA is 2.3% higher than VMD-RNN (0.942).

[0250] As can be seen, this application can effectively balance volatility capture and prediction stability on short-term, highly volatile time series data, and its generalization ability is better than the ADA improved model and most single models.

[0251] In another scenario, the US dollar exchange rate dataset was selected as the experimental dataset. The US dollar exchange rate dataset is 26 years of exchange rate tracking data released by the International Monetary Fund (IMF), which has the characteristics of long-term stable trend and mild fluctuations. It is used to verify the adaptability of the present invention in long-term time series scenarios.

[0252] To address the long-term stationary nature of the data, the optimal number of VMD modes K is adjusted to 6, and the optimal number of partitions S for the maximum entropy subsequence is adjusted accordingly. ∗=8, ensuring the model captures high-frequency fluctuation characteristics. The comparison results of the test set of the US dollar exchange rate dataset are shown in Table 3:

[0253] Table 3: Comparison Results of the Test Set and the US Dollar Exchange Rate Dataset

[0254] Model MAE MSE MAPE RMSE SMAPE DA IA R CNN 0.067 0.006 0.193 0.075 0.218 0.490 0.598 0.834 RNN 0.018 0.000 0.053 0.021 0.052 0.470 0.965 0.961 LSTM 0.067 0.006 0.193 0.075 0.218 0.490 0.598 0.834 DEEPAR 0.020 0.001 0.066 0.035 0.076 0.470 0.912 0.860 DEPTS 0.019 0.001 0.055 0.024 0.058 0.480 0.951 0.961 VMD-CNN 0.012 0.000 0.035 0.013 0.035 0.590 0.985 0.995 VMD-RNN 0.024 0.002 0.086 0.047 0.104 0.570 0.862 0.823 VMD-LSTM 0.048 0.003 0.153 0.056 0.142 0.490 0.765 0.718 ADA-CNN 0.011 0.000 0.033 0.016 0.033 0.480 0.979 0.960 ADA-RNN 0.010 0.000 0.031 0.015 0.031 0.470 0.981 0.962 ADA-LSTM 0.010 0.000 0.031 0.016 0.032 0.470 0.978 0.962 The method of this invention (based on the CNN model) 0.003 0.000 0.010 0.006 0.010 0.770 0.997 0.995 The method of this invention (based on the RNN model) 0.003 0.000 0.010 0.006 0.010 0.780 0.997 0.995 The method of this invention (based on the LSTM model) 0.005 0.000 0.015 0.007 0.015 0.720 0.996 0.994

[0255] As can be seen, this application can accurately extract long-term trend features from long-term stationary time series data, and its prediction accuracy and stability far exceed those of existing mainstream models, and its generalization ability has been fully verified.

[0256] This application provides a data prediction method based on temporal adaptive mode decomposition (VMD). It employs the DBSCAN algorithm to accurately identify nonlinear abrupt changes, and combines mean replacement to generate smooth pre-decomposed data and independent noise subsequences. This method eliminates abnormal interference while fully preserving multi-scale temporal features, solving the problem of noise and effective feature aliasing in traditional methods. Furthermore, it achieves adaptive parameter selection for VMD decomposition by traversing a preset range of modes and minimizing the sum of sample entropy. This avoids the subjectivity of manual parameter tuning, reduces mode aliasing, and ensures that each target mode function subsequence corresponds to only a single-scale feature, significantly improving feature purity. Then, it reconstructs the temporal sequence by recombining the target mode function subsequence and the noise subsequence. The effectiveness of the decomposition is verified using both MSE and Normalized MAE error indices. When the error exceeds a threshold, the VMD parameters are dynamically adjusted for re-decomposition, ensuring that the decomposition results do not lose the key features of the original data. Finally, based on the KL divergence maximization principle, the target mode function subsequence is divided into subsequence segments with significantly different distributions, adapted for individual prediction by different basic temporal prediction models, and then weighted according to the inverse proportion of sample entropy to complete the superposition. This application allows the model to focus on single-scale features, reducing the learning difficulty, while integrating multi-scale prediction results, thus balancing long-term trend stability and short-term fluctuation accuracy.

[0257] Figure 3 A schematic diagram of the structure of a data prediction system based on temporal adaptive mode decomposition provided in an embodiment of this application is shown below. Figure 3 As shown, the data prediction system 30 based on temporal adaptive mode decomposition provided in this embodiment includes:

[0258] The data preprocessing module 301 is used to acquire multi-scale and time-series distributed raw data, and to identify and replace nonlinear abrupt change points in the raw data to obtain smoothly distributed pre-decomposed data.

[0259] The data decomposition module 302 is used to perform variational mode decomposition on the pre-decomposed data based on the number of modes within a preset range, so as to obtain multiple candidate mode function subsequences;

[0260] The mode determination module 303 is used to calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number;

[0261] The segmented prediction module 304 is used to divide the target mode function subsequence into multiple subsequence segments with different distributions, and input the subsequence segments into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment;

[0262] The data processing module 305 is used to determine the corresponding weight based on the sample entropy of each subsequence segment, and to weightedly sum the sub-predicted values ​​of multiple subsequence segments at the same time point to obtain the target predicted value.

[0263] This embodiment provides a data prediction system based on temporal adaptive mode decomposition, which can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0264] Figure 4 A schematic diagram of the structure of a data prediction device based on temporal adaptive mode decomposition provided in an embodiment of this application is shown below. Figure 4 As shown, the data prediction device 40 based on temporal adaptive mode decomposition provided in this embodiment includes:

[0265] The device 40 includes at least one processor 401 and a memory 402. Optionally, the device 40 also includes a communication component 403. The processor 401, memory 402, and communication component 403 are connected via a bus 404.

[0266] In a specific implementation, at least one processor 401 executes computer execution instructions stored in memory 402, causing at least one processor 401 to perform the above-described method.

[0267] The specific implementation process of processor 401 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0268] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0269] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0270] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0271] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0272] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0273] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0274] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0275] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0276] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0277] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0278] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0279] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0280] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A data prediction method based on temporal adaptive mode decomposition, characterized in that, The method includes: Acquire raw data that is multi-scale and distributed over time, and identify and replace nonlinear abrupt changes in the raw data to obtain pre-decomposed data with a smooth distribution. Variational mode decomposition is performed on the pre-decomposed data based on the number of modes within a preset range to obtain multiple candidate mode function subsequences; Calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number; The target mode function subsequence is divided into multiple subsequence segments with different distributions, and the subsequence segments are input into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment; The corresponding weight is determined based on the sample entropy of each sub-sequence segment, and the sub-predicted values ​​of multiple sub-sequence segments at the same time point are weighted and superimposed to obtain the target predicted value.

2. The method according to claim 1, characterized in that, include: Identify and replace nonlinear abrupt changes in the original data to obtain smoothly distributed pre-decomposed data and noisy subsequences. After calculating the sample entropy of each candidate mode function subsequence to determine the optimal number of modes, and obtaining the target mode function subsequence based on the optimal number of modes; The target mode function subsequence and the noise subsequence are recombined to obtain the reconstructed time series sequence; The difference between the reconstructed time series sequence and the pre-decomposed data is determined. When the difference is less than a preset threshold, the target modal function subsequence is divided into multiple subsequence segments with distribution differences according to the time dimension.

3. The method according to claim 2, characterized in that, Acquire raw data at multiple scales and distributed over time, and identify and replace nonlinear abrupt changes in the raw data to obtain smoothly distributed pre-decomposed data and noisy subsequences, including: Obtain raw data at multiple scales and distributed over time, and then filter to obtain valid data; Based on the effective data, the preset adjacent data neighborhood radius, and the minimum number of samples, the nonlinear mutation point is obtained; Obtain multiple normal and valid data adjacent to the nonlinear mutation point, calculate the mean, and then replace the nonlinear mutation point; Pre-decomposed data and a noise subsequence are obtained. The pre-decomposed data is obtained by replacing the nonlinear mutation points in the valid data, and the noise subsequence is obtained by at least one nonlinear mutation point.

4. The method according to claim 1, characterized in that, The calculation of the sum of sample entropies of multiple candidate mode function subsequences corresponding to each mode number includes: Based on the preset vector dimension, the corresponding candidate modal function subsequence is split into multiple sequence vectors; Determine the maximum distance between any two sequence vectors, and obtain the similarity vector pair ratio for each sequence vector based on the maximum distance, a similarity threshold, and the similarity vector pair ratio. Calculate the average of the similarity vector pair ratios for all upgraded sequence vectors and all sequence vectors, respectively; The sample entropy of the corresponding candidate mode function subsequence is calculated based on the ratio of the average values ​​of the proportions of two similar vector pairs. Calculate the sum of sample entropies for multiple candidate mode function subsequences.

5. The method according to claim 4, characterized in that, After calculating the sum of the sample entropies of multiple candidate mode function subsequences, the process includes: The optimal number of modes is determined by finding the minimum sum of the entropies of multiple samples for each mode number.

6. The method according to claim 1, characterized in that, The step of dividing the target mode function subsequence into multiple subsequence segments with different distributions includes: Multiple subsequence segments are obtained by dividing the sequence into multiple subsequence segments based on the number of different subsequences. The difference value is determined based on the number of corresponding subsequences and the KL divergence between any two subsequence segments; Based on the number of subsequences corresponding to the largest difference value, multiple subsequence segments are obtained.

7. The method according to claim 6, characterized in that, The process of splitting the data based on the number of different subsequences to obtain multiple subsequence segments includes: The number of subsequences is within a preset range, and the length of the subsequence segments after division based on the number of subsequences is greater than the preset length.

8. The method according to claim 1, characterized in that, The corresponding weight is determined based on the sample entropy of each sub-sequence segment, and the sub-predicted values ​​of multiple sub-sequence segments at the same time point are weighted and superimposed to obtain the target predicted value, including: The weight of each subsequence segment is obtained based on the sample entropy of each subsequence segment and the sample entropy of all subsequence segments, where the sum of the weights of all subsequence segments is 1; Based on the weight of each subsequence segment and the corresponding sub-prediction value, the weighted prediction value of each subsequence segment is obtained. Multiple weighted prediction values ​​at the same time point are superimposed to obtain the target prediction value.

9. A data prediction system based on temporal adaptive mode decomposition, characterized in that, The system includes: The data preprocessing module is used to acquire raw data that is multi-scale and distributed over time, and to identify and replace nonlinear abrupt changes in the raw data to obtain pre-decomposed data with a smooth distribution. The data decomposition module is used to perform variational mode decomposition on the pre-decomposed data based on the number of modes within a preset range, so as to obtain multiple candidate mode function subsequences; The mode determination module is used to calculate the sum of the sample entropy of multiple candidate mode function subsequences corresponding to each mode number, determine the optimal mode number, and obtain multiple target mode function subsequences based on the optimal mode number; The segmented prediction module is used to divide the target mode function subsequence into multiple subsequence segments with different distributions, and input the subsequence segments into the basic time series prediction model to obtain the sub-predicted value corresponding to each subsequence segment; The data processing module is used to determine the corresponding weight based on the sample entropy of each sub-sequence segment, and to weight and superimpose the sub-predicted values ​​of multiple sub-sequence segments at the same time point to obtain the target predicted value.

10. A data prediction device based on temporal adaptive mode decomposition, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-8.

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