A time series ensemble prediction method, system and storage medium

Abstract

The application provides a time series set prediction method, system and storage medium, and relates to the technical field of time series prediction; the method comprises the following steps: acquiring historical time series and real-time data of monitoring data of a monitoring system; constructing a plurality of time series prediction models of the monitoring data according to the historical time series; predicting the real-time data through each time series prediction model based on the real-time data to obtain a prediction result corresponding to each time series prediction model; and collecting all the prediction results and fusing the prediction results through a time series set prediction model to obtain a final prediction result of the monitoring data in a future preset time period. The application improves the prediction accuracy of the time series, enhances the stability and reliability of the prediction result, and improves the prediction performance of the time series prediction of the monitoring data.

Description

Technical Field

[0001] This invention relates to the field of time series forecasting technology, and more specifically, to a method, system, and storage medium for forecasting time series ensembles. Background Technology

[0002] In recent years, with the development of fields such as the Internet of Things, environmental monitoring, and industrial automation, time series forecasting is often used to better inform decision-making in these areas. For example, in agriculture, time series forecasting of temperature monitoring data is used to quickly understand local temperature changes, thereby providing more accurate agricultural planning.

[0003] In related technologies, traditional time series forecasting methods, such as autoregressive integral moving average models and autoregressive conditional heteroscedasticity models, can provide relatively accurate prediction results for monitoring data time series in steady-state scenarios. However, their predictive performance is limited in complex dynamic environments such as nonlinearity, non-stationarity, and mixed long- and short-term variations. Furthermore, time series forecasting using artificial intelligence models, such as long short-term memory networks and attention mechanism models, relies on only a single decomposition technique or model, resulting in limited prediction accuracy and consequently, larger prediction errors. Summary of the Invention

[0004] The problem addressed by this invention is how to improve the predictive performance of time series forecasting.

[0005] To address the above problems, this invention provides a method, system, and storage medium for predicting time series datasets.

[0006] In a first aspect, the present invention provides a time series ensemble prediction method, which is applied to a monitoring system. The method includes: acquiring historical time series and real-time data of monitoring data from the monitoring system; constructing multiple time series prediction models for the monitoring data based on the historical time series; predicting the real-time data using each of the time series prediction models based on the real-time data, obtaining a prediction result corresponding to each of the time series prediction models; summarizing all the prediction results and fusing them using the time series ensemble prediction models to obtain a final prediction result for the monitoring data in a future preset time period.

[0007] Optionally, constructing multiple time series prediction models for the monitoring data based on the historical time series includes: constructing a monitoring data time series based on the historical time series; performing spectral analysis on the monitoring data time series to obtain multi-scale typical time-varying features of the monitoring data; constructing basis functions corresponding to each of the multi-scale typical time-varying features based on the multi-scale typical time-varying features; decomposing the monitoring data time series using all the basis functions to obtain multi-scale time-varying component sequences; filtering the multi-scale time-varying component sequences based on the variance contribution rate of the multi-scale time-varying component sequences; constructing a time series prediction model corresponding to each of the filtered multi-scale time-varying component sequences based on a deep learning model; and constructing a time series prediction model for the monitoring data based on the time series prediction model corresponding to each of the multi-scale time-varying component sequences.

[0008] Optionally, the step of decomposing the monitoring data time series using all the basis functions to obtain multi-scale time-varying component sequences includes: determining an expression for the monitoring data time series based on the basis functions; substituting the monitoring data time series into the expression, and decomposing the monitoring data time series using the expression to obtain multiple multi-scale time-varying component sequences, wherein the multiple multi-scale time-varying component sequences include at least one component sequence with a periodicity and one component sequence without a periodicity; the expression for the monitoring data time series is: ; in, t For time variables, X ( t ) represents the time series of the monitoring data. x 0( t () refers to the component sequence that does not have a period of change. For the basis functions, ω k For the first k The characteristic frequencies of the basis functions φ k ( t ) is the first k The phase parameters of the basis functions. A k ( t ) is the first k The time-varying coefficients of the aforementioned basis functions change over time. K The number of basis functions. For the first k The expression for the multi-scale time-varying component sequence.

[0009] Optionally, the step of substituting the monitoring data time series into the expression and decomposing the monitoring data time series through the expression to obtain multiple multi-scale time-varying component sequences, wherein the multiple multi-scale time-varying component sequences include at least one component sequence with a periodicity and one component sequence without a periodicity, includes: determining the characteristic period of the monitoring data time series based on the typical time-varying characteristics, and determining the characteristic frequency based on the characteristic period; selecting multiple feature points from the monitoring data time series, and obtaining the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series; and determining the characteristic frequency based on the characteristic frequency and the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points in the monitoring data time series. By considering the relationship between the number and time-varying coefficients and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series, the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points are obtained using the least squares method. Based on the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points in the monitoring data time series and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series, and the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points, the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series are obtained. Based on the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series, at least one component sequence with a periodicity and one component sequence without a periodicity are obtained.

[0010] Optionally, the step of filtering the multi-scale time-varying component sequences based on the variance contribution rate of the multi-scale time-varying component sequences includes: calculating the variance contribution rate of all the multi-scale time-varying component sequences obtained from the decomposition; sequentially superimposing the multi-scale time-varying component sequences in order from low frequency to high frequency, and summing the variance contribution rates to obtain the cumulative variance contribution rate; determining whether the cumulative variance contribution rate exceeds a preset given threshold; if the cumulative variance contribution rate exceeds the preset given threshold, then using the currently sequentially superimposed multi-scale time-varying component sequences as the filtered multi-scale time-varying component sequences.

[0011] Optionally, constructing multiple time series prediction models for the monitoring data based on the historical time series includes: constructing a monitoring data time series based on the historical time series; performing endpoint extremum extension preprocessing on the monitoring data time series, and then performing layer-by-layer decomposition on the extended preprocessed monitoring data time series using the empirical mode decomposition method to obtain multiple intrinsic mode functions and trend terms; after the intrinsic mode functions and trend terms are decomposed, deleting the pseudo data in the extension part of the intrinsic mode functions and trend terms; based on the intrinsic mode functions and trend terms after deleting the pseudo data in the extension part, constructing a time series prediction model corresponding to each intrinsic mode function and trend term based on a deep learning model; and constructing a time series prediction model for the monitoring data based on the time series prediction model corresponding to each intrinsic mode function and trend term.

[0012] Optionally, constructing multiple time series prediction models for the monitoring data based on the historical time series includes: constructing a monitoring data time series based on the historical time series; decomposing the monitoring data time series using a variational mode decomposition method to obtain multiple variational mode functions; constructing a time series prediction model corresponding to each variational mode function based on a deep learning model for each variational mode function; and constructing a time series prediction model for the monitoring data based on the time series prediction model corresponding to each variational mode function.

[0013] Optionally, the step of summarizing all the prediction results and fusing them through a time series ensemble prediction model to obtain the final prediction result of the monitoring data in the future preset time period includes: summarizing all the prediction results and performing normalization processing to obtain a standardized prediction matrix. The standardized prediction matrix is ​​used as input data to the time series ensemble prediction model for prediction, thereby obtaining the future value and prediction interval of the monitored data. The time series ensemble prediction model includes a multi-channel convolutional neural network, a stacked bidirectional gated recurrent unit network, and an attention fusion module. Multiple parallel one-dimensional convolutional sub-modules of the multi-channel convolutional neural network extract features from the standardized prediction matrix to obtain local temporal feature representations at different scales. At least two layers of forward-gated recurrent unit networks and two layers of backward-gated recurrent unit networks of the stacked bidirectional gated recurrent unit network capture the long-term dependencies of the time series of the standardized prediction matrix, obtaining temporal feature representations. The attention fusion module uses dynamic weighting to fuse the local temporal feature representations and the temporal feature representations to obtain a fused feature representation. A fully connected layer outputs the final prediction result based on the fused feature representation.

[0014] In a second aspect, the present invention provides a time series ensemble prediction system, comprising: a processor and a memory, wherein the memory is used to store a computer program; when the computer program is loaded by the processor, the processor causes the processor to execute the time series ensemble prediction method as described above.

[0015] Thirdly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the time series set prediction method as described above.

[0016] The time series ensemble prediction method, system, and storage medium of this invention first acquire historical time series and real-time data of the monitoring system, providing a comprehensive and accurate data foundation for subsequent prediction model construction, ensuring the accuracy and timeliness of model training. Next, based on the historical time series, multiple time series prediction models for the monitoring data are constructed. By utilizing historical time series data to construct multiple prediction models, the rich information contained in the data can be fully explored and utilized, including trends, periodicity, and random fluctuations within different time periods, thus providing a more solid foundation for subsequent predictions. Secondly, constructing multiple prediction models can capture the changing characteristics of basis functions with different characteristic periods at different times, thereby more accurately decomposing the data and improving the stability and predictability of the decomposed data. This effectively avoids the limitations and biases that may exist in a single model, and the mutual complementarity of multiple models helps to more comprehensively reflect the complex dynamic characteristics of the monitoring data. Furthermore, the existence of multiple prediction models provides the possibility and flexibility for subsequent prediction result fusion. By reasonably integrating the prediction results of these models, the accuracy and reliability of the prediction can be further improved. Then, the real-time data is predicted using each of the time series prediction models to obtain the prediction result corresponding to each model. All prediction results are then aggregated and fused using a time series ensemble prediction model to obtain the final prediction result of the monitoring data for a future preset time period. By using the time series ensemble prediction model, dynamic weight fusion of multi-model results is achieved, further enhancing the stability and reliability of the prediction results. This invention improves the accuracy of time series prediction while enhancing the stability and reliability of the prediction results, thus improving the prediction performance for time series prediction of monitoring data. Attached Figure Description

[0017] Figure 1 This is one of the flowcharts illustrating the time series set prediction method according to an embodiment of the present invention; Figure 2 This is a second flowchart illustrating the time series set prediction method according to an embodiment of the present invention; Figure 3This is the third flowchart illustrating the time series set prediction model according to an embodiment of the present invention; Figure 4 This is the fourth flowchart illustrating the time series set prediction model according to an embodiment of the present invention. Figure 5 This is one of the schematic diagrams of the multi-scale time-varying feature decomposition results in an embodiment of the present invention; Figure 6 This is the second schematic diagram of the multi-scale time-varying feature decomposition results in an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0019] In existing technologies, with the development of the Internet of Things, environmental monitoring, and industrial automation, monitoring data is widely used in numerous fields such as meteorological and hydrological monitoring, and ecological environment monitoring. Examples include time series of single-point temperature monitoring data acquired by meteorological sensors, time series of single-point water level monitoring data acquired by hydrological sensors, time series of product sales data, and time series of water quality parameter monitoring data acquired by ecological environment monitoring sensors. To grasp future development trends and better formulate relevant policies, decisions, and guidelines, time series forecasting of monitoring data is a necessary means with broad application needs. For example, single-point forecasting of temperature monitoring data time series helps to quickly understand local temperature changes, providing information support for agricultural production.

[0020] In related technologies, traditional time series forecasting methods for monitoring data, such as the Autoregressive Integrated Moving Average (ARIMA) model and the Autoregressive Conditional Heteroskedasticity (GARCH) model, can provide relatively accurate prediction results for monitoring data time series in steady-state scenarios. However, their prediction performance is limited when facing complex dynamic processes such as nonlinearity, non-stationarity, and a mixture of long-term and short-term variations. Artificial intelligence models (such as Long Short-Term Memory (LSTM) networks and the Transformer attention mechanism model) have improved modeling capabilities to some extent, but they rely solely on a single decomposition technique or model and lack a dynamic fusion mechanism for the prediction results of multiple models. This makes it difficult to fully utilize the complementary advantages of different methods, and they only focus on point prediction without fully incorporating the time-varying characteristic distribution patterns to optimize the decomposition process. This results in limited prediction accuracy and fails to meet the strong demand for prediction interval and uncertainty modeling in practical applications.

[0021] To address the problems existing in the aforementioned related technologies, this embodiment provides a time series set prediction method, system, and storage medium.

[0022] Combination Figure 1 As shown in the figure, an embodiment of the present invention provides a time series set prediction method, which is applied to a monitoring system. The method includes: Obtain historical time series and real-time data of the monitoring data from the monitoring system.

[0023] Specifically, by constructing a time-series database of monitoring data, the predictive model can be trained based on actual monitoring data, providing a comprehensive and accurate data foundation for the subsequent construction of the predictive model. This ensures the accuracy and timeliness of model training, thereby better capturing the temporal variation characteristics in the data. In a preferred embodiment of the invention, the monitoring data can be environmental data, such as temperature monitoring data and water level monitoring data. Environmental data exhibits typical temporal variation characteristics, such as daily and seasonal variations in temperature, and flood and dry season variations in water levels. By integrating historical and real-time data, the temporal evolution patterns of the monitoring data can be more comprehensively reflected, providing sufficient information support for the training and optimization of the predictive model. When the monitoring data is temperature data, the monitoring system includes a temperature sensor; when the monitoring data is water level data, the monitoring system includes a water level sensor; when the monitoring data is water quality data, the monitoring system includes a water quality sensor; when the monitoring data is product sales data (e.g., movie box office revenue), the monitoring system includes a terminal data acquisition device.

[0024] Based on the historical time series, multiple time series prediction models for the monitoring data are constructed.

[0025] Specifically, by constructing multiple prediction models, the rich information contained in historical time series data is fully explored and utilized, including trends, periodicity, and random fluctuations within different time periods, thereby providing a more solid foundation for subsequent predictions. In a preferred embodiment of the invention, the constructed multiple prediction models can capture the changing characteristics of basis functions with different characteristic periods at different time periods, thereby more accurately decomposing the data and improving the stability and predictability of the decomposed data. A multi-scale time-varying feature data decomposition method is combined, and spectral analysis is used to extract typical multi-scale time-varying features of the monitoring data. By constructing basis functions dependent on characteristic periods and decomposing the time series to obtain multi-scale time-varying component sequences, the complex dynamic characteristics in the monitoring data can be captured more effectively, improving the accuracy and reliability of the prediction model.

[0026] Based on the real-time data, predictions are made on the real-time data using each of the time series prediction models to obtain the prediction results corresponding to each of the time series prediction models.

[0027] Specifically, each prediction model processes and analyzes real-time data based on its internal eigenvalue decomposition and parameter estimation to generate corresponding predicted values, fully leveraging the advantages of different models and ensuring the diversity of prediction results. The existence of multiple prediction models provides the possibility and flexibility for subsequent prediction result fusion. By rationally integrating the prediction results of these models, the accuracy and reliability of predictions can be further improved. In addition, this step further enhances the model's adaptability and predictive performance to complex dynamic monitoring data by constructing a prediction model based on multi-scale time-varying eigenvalue decomposition, providing stronger support for the decision-making and operation of the monitoring system.

[0028] All the prediction results are summarized and fused using a time series ensemble prediction model to obtain the final prediction result of the monitoring data in the future preset time period.

[0029] Specifically, the time series ensemble forecasting model integrates the results of multiple forecasting models, comprehensively considering the advantages and characteristics of different models to generate more accurate and reliable forecasts. Because the time series ensemble forecasting model combines multi-channel convolutional neural networks, stacked bidirectional gated recurrent unit networks, and attention mechanisms, it achieves dynamic weight fusion of multiple model results, fully utilizing the advantages of different models to achieve more stable and reasonable forecasts. In this way, the final forecast results can more comprehensively reflect the future trends of monitoring data, providing strong support for decision-making in practical applications. Furthermore, this method also supports confidence interval forecasting. By designing a forecast interval generation module, it provides both point and interval forecasts, enhancing the ability to control uncertainty in practical applications.

[0030] It should be noted that data such as temperature, water level, water quality, and product sales volume (online game sales, movie box office, etc.) are all trend data that change over time and remain relatively stable in a short period of time. Even if there are changes, they are gradual over time and will not abruptly change. For example, the temperature gradually rises from 20℃ to 30℃, but will not jump from 20℃ to 30℃; the water level gradually decreases from 10m to 5m, but will not jump from 10m to 5m. Therefore, past time series data can be used to predict monitoring data for a preset future time period. It is necessary to ensure that the monitoring data remains stable or changes continuously within the preset future time period. Therefore, the preset future time period can be as short as possible, and can be set according to the actual situation. For example, when the monitoring data is temperature and water level, the preset future time period can be 1 hour or 2 hours; when the monitoring data is water quality, the preset future time period can be 1 day or 2 days; when the monitoring data is product sales data, the preset future time period can be 2 hours or 3 hours.

[0031] The time series ensemble prediction method of this invention first acquires historical time series and real-time data of the monitoring system, providing a comprehensive and accurate data foundation for subsequent prediction model construction, ensuring the accuracy and timeliness of model training. Next, based on the historical time series, multiple time series prediction models for the monitoring data are constructed. By utilizing historical time series data to build multiple prediction models, the rich information contained in the data can be fully explored and utilized, including trends, periodicity, and random fluctuations within different time periods, thus providing a more solid foundation for subsequent predictions. Secondly, constructing multiple prediction models can capture the changing characteristics of basis functions with different characteristic periods at different times, thereby more accurately decomposing the data and improving the stability and predictability of the decomposed data. This effectively avoids the limitations and biases that may exist in a single model, and the mutual complementarity of multiple models helps to more comprehensively reflect the complex dynamic characteristics of the monitoring data. Furthermore, the existence of multiple prediction models provides the possibility and flexibility for subsequent prediction result fusion. By reasonably integrating the prediction results of these models, the accuracy and reliability of the prediction can be further improved. Then, the real-time data is predicted using each of the time series prediction models to obtain the prediction result corresponding to each model. All prediction results are then aggregated and fused using a time series ensemble prediction model to obtain the final prediction result of the monitoring data for a future preset time period. By using the time series ensemble prediction model, dynamic weight fusion of multi-model results is achieved, further enhancing the stability and reliability of the prediction results. This invention improves the accuracy of time series prediction while enhancing the stability and reliability of the prediction results, thus improving the prediction performance for time series prediction of monitoring data.

[0032] Optionally, combined Figure 2 As shown, the step of constructing multiple time series prediction models for the monitoring data based on the historical time series includes: A monitoring data time series is constructed based on the historical time series; spectral analysis is performed on the monitoring data time series to obtain the typical time-varying features of the monitoring data at multiple scales; basis functions are constructed for each typical time-varying feature at multiple scales; the monitoring data time series is decomposed using all the basis functions to obtain multi-scale time-varying component sequences; the multi-scale time-varying component sequences are filtered based on their variance contribution rates; a time series prediction model is constructed for each filtered multi-scale time-varying component sequence based on a deep learning model; and a time series prediction model for the monitoring data is constructed based on the time series prediction models for each multi-scale time-varying component sequence.

[0033] Specifically, the monitoring data time series is first constructed from historical time series data. For example, preprocessing is used to organize and transform the raw historical monitoring data into a form suitable for further analysis. Next, spectral analysis is performed on the constructed monitoring data time series, using mathematical tools such as Fourier transform to convert it from the time domain to the frequency domain. In the spectral analysis, key information such as Fourier coefficients and power spectral density is calculated, thereby identifying the main energy-concentrated frequency bands in the monitoring data. The periods corresponding to these frequency bands are typical time-varying features, reflecting significant periodic patterns in the data and potentially representing key factors such as seasonal variations and equipment operating cycles. Based on the extracted multi-scale typical time-varying features, basis functions are constructed for each multi-scale time-varying feature. The basis functions adopt the form of cosine functions, where the characteristic period is fixed and determined by the spectral analysis results, while the variation characteristics and decomposition coefficients change over time. The monitoring data time series is represented as a combination of these basis functions, forming a mathematical expression that includes component sequences without a periodic variation and multiple basis function terms dependent on the characteristic period. Each basis function term has corresponding time-varying coefficients and phase parameters. These coefficients and parameters change over time to characterize the variation and distribution patterns of the basis functions at different time points. By selecting several feature points over the entire time period and using interpolation methods, the relationship between the time-varying coefficients and phase parameters corresponding to these feature points and the time-varying coefficients and phase parameters at all time points can be obtained. Interpolation coefficients can be obtained using various methods such as linear interpolation, Cressman interpolation, or spline interpolation. Based on the least squares method, for the time series, the phase parameters and time-varying coefficients of the component sequences without a periodicity and the basis functions are solved simultaneously to obtain the multi-scale time-varying component sequences. Finally, the variance contribution rate of each multi-scale time-varying component sequence is calculated, and important multi-scale time-varying component sequences are selected. The output results of the prediction models corresponding to each selected multi-scale time-varying component sequence are fused to construct the final monitoring data time series prediction model. According to the selected fusion strategy, the output results of the prediction models for each component sequence are fused to obtain the final monitoring data time series prediction model. This model can integrate the prediction results of each component sequence to achieve high-precision prediction of the original monitoring data time series. Through the above steps, the present invention can make full use of the multi-scale time-varying characteristics of monitoring data and combine the powerful modeling capabilities of deep learning models to achieve high-precision prediction of monitoring data time series.

[0034] In a preferred embodiment of the present invention, Fourier transform is used to perform frequency domain analysis on the original monitoring data time series to identify the frequency bands where the main energy is concentrated and to extract typical variation cycles.

[0035] The monitoring data time series X(t) can be represented as: ; Where t is time; i is the imaginary unit; ω is the angular frequency, representing the angular frequency of the k-th frequency component; These are the Fourier coefficients, representing the frequency response of the time series. The complex amplitude at that point contains the amplitude and phase information of the signal.

[0036] The average power is: ; in, T represents the total duration of the signal. a k and b k These are the real and imaginary coefficients of the Fourier series, used to represent the sine and cosine components of the signal.

[0037] because and Therefore, discrete power spectra are typically plotted only on the positive half-axis. Therefore, it is ordered that: ; in, This represents the power spectral density of the positive half-axis.

[0038] The average power can then be written as: ; First, analyze the time series of the monitoring data. Perform a Fourier transform to obtain the Fourier coefficients. , , (Take only integers), then calculate By utilizing the relationship between wave number and period, the period of each component wave can be calculated. T k That is, The horizontal axis is... Plot the power spectrum on the vertical axis. The power spectrum value represents the peak value. T k The corresponding period is the typical change period, which is the corresponding typical time-varying characteristic (manifested as period or frequency).

[0039] In this optional embodiment, typical time-varying features of the monitoring data are accurately extracted through spectral analysis, providing a solid foundation for subsequent modeling. Complex time series are finely decomposed into multiple relatively simple component sequences, facilitating a precise understanding of the changing patterns at different scales within the data. Component sequences are selected, and a prediction model is built based on a deep learning model, highlighting key features while leveraging the powerful fitting capabilities of deep learning to achieve accurate predictions. This effectively improves prediction accuracy, enhances the model's adaptability to complex dynamic monitoring data, makes prediction results more reliable, and provides strong support for decision support in the monitoring system.

[0040] Optionally, the step of decomposing the monitoring data time series using all the basis functions to obtain a multi-scale time-varying component series includes: determining an expression for the monitoring data time series based on the basis functions; substituting the monitoring data time series into the expression; and decomposing the monitoring data time series using the expression to obtain multiple multi-scale time-varying component series, wherein the multiple multi-scale time-varying component series include at least one component series with a period of change and one component series without a period of change. The expression for the time series of the monitoring data is: ; in, t For time variables, X ( t ) represents the time series of the monitoring data. x 0( t () refers to the component sequence that does not have a period of change. For the basis functions, ω k For the first k The characteristic frequencies of the basis functions φ k ( t ) is the first k The phase parameters of the basis functions. A k ( t ) is the first k The time-varying coefficients of the aforementioned basis functions change over time. K The number of basis functions. For the first k The expression for the multi-scale time-varying component sequence.

[0041] Specifically, the monitoring data time series is decomposed using all basis functions to obtain multi-scale time-varying component sequences. First, the expression for the monitoring data time series is determined based on the basis functions. This expression represents the time series as the sum of a component sequence without a periodicity and multiple basis functions dependent on a characteristic period. The basis functions are in cosine form, each with a fixed characteristic frequency corresponding to the reciprocal of the characteristic period. The phase parameter and time-varying coefficients change over time to characterize the variation and distribution of the basis functions across different time periods. Next, the monitoring data time series is substituted into the determined expression. Decomposing the monitoring data time series using this expression aims to break it down into multiple multi-scale time-varying component sequences. These component sequences include at least one component sequence with a periodicity and one component sequence without a periodicity. Each component sequence corresponds to a different characteristic period, thus capturing the time-varying features at different scales within the time series.

[0042] In a preferred embodiment of the present invention, based on the multi-scale time-varying characteristics, a basis function dependent on the feature period is constructed, and a multi-scale time-varying feature data decomposition method with optimal decomposition as the objective and key parameters of the basis function changing over time is constructed. The monitoring data time series is decomposed into multi-scale time-varying features to obtain multi-scale time-varying component sequences. Based on the multi-scale characteristics and typical change periods of the monitoring data time series obtained in the above steps, a variable coefficient multi-scale feature data decomposition method with scale characteristics as the basis and optimal decomposition as the objective is proposed.

[0043] This method treats the time series of monitoring data as a combination of a series of basis functions with characteristic periods. Each basis function is in the form of a cosine function with a fixed characteristic period, obtained from spectral analysis. The variation characteristics and decomposition coefficients change with time, specifically expressed as follows: ; in, X ( t (This refers to the time series of monitoring data.) x 0( t () is a component sequence that does not have a period of change. For basis functions that depend on characteristic periods, ω k For the first k The characteristic frequencies of the basis functions φ k ( t ) is the first k The phase parameters of each basis function vary with time. A k ( t ) is the first k The time-varying coefficients of each basis function change with time. K The number of basis functions.A k and φ k The changes over time can characterize the variation and distribution patterns of basis functions that depend on different characteristic periods at different times.

[0044] In this optional embodiment, the time series is decomposed into multiple component sequences with different characteristic periods. This facilitates in-depth analysis of the characteristics and variation patterns of each component, thus providing a solid foundation for subsequent prediction model construction. This effectively improves the stability and reliability of the prediction results, enhances adaptability and predictive performance to complex dynamic monitoring data, ensures that the prediction results more accurately reflect the future trends of the monitoring data, and provides strong support for decision-making in practical applications.

[0045] Optionally, the step of substituting the monitoring data time series into the expression and decomposing the monitoring data time series through the expression to obtain multiple multi-scale time-varying component sequences, wherein the multiple multi-scale time-varying component sequences include at least one component sequence with a periodicity and one component sequence without a periodicity, includes: determining the characteristic period of the monitoring data time series based on the typical time-varying characteristics, and determining the characteristic frequency based on the characteristic period; selecting multiple feature points from the monitoring data time series, and obtaining the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series; and determining the characteristic frequency based on the characteristic frequency and the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points in the monitoring data time series. By considering the relationship between the number and time-varying coefficients and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series, the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points are obtained using the least squares method. Based on the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points in the monitoring data time series and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series, and the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points, the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series are obtained. Based on the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series, at least one component sequence with a periodicity and one component sequence without a periodicity are obtained.

[0046] Specifically, by performing spectral analysis on the time series of monitoring data, the main energy concentration frequency bands are identified. The periods corresponding to these frequency bands are the typical time-varying characteristics of the monitoring data. The corresponding periods, i.e., characteristic periods, are extracted from these typical time-varying characteristics. The characteristic frequency is the reciprocal of the characteristic period, representing the frequency with which each periodic feature repeats in the time series. Several characteristic points are selected over the entire time period. These characteristic points can be evenly distributed or non-uniformly selected based on the changing characteristics of the time series to better capture key changes in the time series. For each selected characteristic point, the relationship between the phase parameters and time-varying coefficients of the basis functions at that point and the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series is determined. This relationship can be established using interpolation methods, such as linear interpolation, Cressman interpolation, or spline interpolation, to ensure the continuity and smoothness of the parameters in the time series. Based on the time series of monitoring data and the determined relationships between basis function parameters, a system of equations is constructed. This system represents the monitoring data time series as a combination of a component sequence without a periodicity and multiple basis functions with periodsicity. The characteristic frequencies of the basis functions are known, while the phase parameters and time-varying coefficients at the characteristic points are to be determined. The system of equations is solved using the least squares method to obtain the phase parameters and time-varying coefficients of the basis functions at the characteristic points. The least squares method estimates the unknown parameters by minimizing the difference between the actual and predicted values, thus obtaining the optimal parameter solution. Based on the previously determined correspondence between the phase parameters and time-varying coefficients of the basis functions at the characteristic points and all time points, the obtained parameter values ​​at the characteristic points are substituted into this relationship. Through interpolation or other mathematical methods, the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series are calculated. This step ensures that the parameters of the basis functions are known throughout the entire time series, allowing for a complete reconstruction of the shape of each basis function. Using the phase parameters and time-varying coefficients of the basis functions at all time points, the variation of each basis function throughout the entire time series is reconstructed. Substituting the reconstructed basis functions into the original decomposition expression yields multiple multi-scale time-varying component sequences. These sequences include at least one component sequence with a periodicity (composed of basis functions with characteristic periods) and one component sequence without a periodicity. Each component sequence with a periodicity reflects the variation characteristics of the monitored data over a specific period, while the component sequence without a periodicity captures trends or other non-periodic changes in the data.

[0047] In a preferred embodiment of the present invention, to facilitate the solution, several feature points are selected over the entire time period, assuming that the first... j At the feature point k The time-varying coefficients and phase parameters of the basis functions are respectively , Then the time-varying coefficients at all time pointsA k and phase parameters φ k can be and Interpolation yields: ; in, and For the corresponding interpolation coefficients, linear interpolation, Cressman interpolation, spline interpolation, etc. can be used.

[0048] Based on the least squares method, for monitoring data time series X ( t ), can be solved simultaneously x 0( t ), and Based on the interpolation coefficients, it can be obtained A k ( t )and φ k ( t Therefore, the multi-scale time-varying component sequence can be obtained as follows: .

[0049] In this optional embodiment, determining the characteristic period of the monitoring data time series through spectral analysis can accurately identify typical time-varying features at different scales within the time series, providing crucial information for subsequent decomposition. This ensures that the decomposed component sequences accurately reflect the inherent periodicity of the monitoring data, such as daily and seasonal variations in temperature data, and flood and dry season variations in water level monitoring data, thus laying the foundation for high-precision prediction. Selecting multiple feature points from the monitoring data time series and establishing the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to these feature points and the parameters corresponding to all time points effectively reduces computational load while maintaining decomposition accuracy. In this way, the changing characteristics of the monitoring data time series at key feature points can be quickly captured, and the parameter change trends of the entire time series can be inferred using the information from these feature points, improving decomposition efficiency and enabling the model to respond to data changes more promptly.

[0050] By using the least squares method to solve for the phase parameters and time-varying coefficients of the basis functions corresponding to feature points, the parameter values ​​of the basis functions at feature points can be accurately determined based on established parameter relationships and characteristic frequencies. This method minimizes the sum of squared errors between predicted and actual values, ensuring that the solved parameters best fit the true changes in the monitoring data time series. This guarantees high accuracy of the decomposed multi-scale time-varying component sequences, providing a reliable data foundation for subsequent prediction model construction. Through the phase parameters and time-varying coefficients at feature points and the established parameter relationships, the phase parameters and time-varying coefficients of the basis functions at all time points in the monitoring data time series can be accurately derived. This achieves the restoration of the complete characteristics of the monitoring data time series. Based on this complete parameter information, at least one component sequence with a periodicity and one component sequence without a periodicity can be accurately generated. This decomposition method in this embodiment can fully explore the different characteristic components in the monitoring data time series. The component series with a change period can be used to capture the periodic change trend of the monitoring data, while the component series without a change period can reflect the non-periodic fluctuation or long-term trend of the data. This provides accurate and representative data support for the subsequent construction of prediction models for different component series, which helps to improve the prediction model's ability to grasp the complex change patterns of the monitoring data, and ultimately achieve more accurate time series prediction of monitoring data.

[0051] Optionally, the step of filtering the multi-scale time-varying component sequences based on the variance contribution rate of the multi-scale time-varying component sequences includes: calculating the variance contribution rate of all the multi-scale time-varying component sequences obtained from the decomposition; sequentially superimposing the multi-scale time-varying component sequences in order from low frequency to high frequency, and summing the variance contribution rates to obtain the cumulative variance contribution rate; determining whether the cumulative variance contribution rate exceeds a preset given threshold; if the cumulative variance contribution rate exceeds the preset given threshold, then using the currently sequentially superimposed multi-scale time-varying component sequences as the filtered multi-scale time-varying component sequences.

[0052] Specifically, the first step is to calculate the variance contribution rate of all multi-scale time-varying component sequences obtained from the decomposition. The variance contribution rate reflects the variability and importance of each component sequence within the overall time series. Calculation requires quantifying the variance of each component sequence and determining its proportion within the total time series variance. For example, for each component sequence, the variance contribution rate can be obtained by calculating its variance and then dividing it by the total variance of the original time series. The multi-scale time-varying component sequences are then stacked sequentially from low frequency to high frequency. Based on this frequency-to-high arrangement, an approximate representation of the original time series is gradually constructed. Low-frequency components typically capture long-term trends and slow changes in the time series, while high-frequency components reflect short-term fluctuations and rapid changes. During the stacking process, the values ​​of each component sequence are added at corresponding positions on the time axis to form a synthetic sequence that progressively approximates the original sequence. Simultaneously, by accumulating the variance contribution rate of each component sequence, the extent to which the stacked component sequences explain the variability of the original time series is tracked. For example, initially stacking a low-frequency component sequence might explain 50% of the variability in a time series. As subsequent component sequences are added, the cumulative variance contribution gradually increases. Finally, it is determined whether the cumulative variance contribution exceeds a preset threshold. This threshold is typically set according to the specific needs of the prediction task, such as 85% or 90%. If the cumulative variance contribution reaches or exceeds this threshold, the stacked component sequences are considered to adequately explain the main variability features of the original time series. At this point, the multiple multi-scale time-varying component sequences that have been stacked sequentially are identified as the filtered multi-scale time-varying component sequences for subsequent prediction model construction. This step ensures that the selected component sequences capture the key features of the time series while avoiding high-frequency components containing excessive noise or secondary information, thus improving the efficiency and accuracy of the prediction model.

[0053] In an optional embodiment, the calculation and accumulation of variance contribution rates enable effective screening of multi-scale time-varying component sequences, ensuring that the selected component sequences can explain the main variability features of the original time series to the greatest extent. This not only improves the accuracy of the prediction model but also enhances its stability and reliability. By setting appropriate thresholds, key information can be retained while reducing model complexity and improving computational efficiency, laying a solid foundation for building efficient and accurate time series prediction models.

[0054] Optionally, combined Figure 3As shown, the step of constructing multiple time series prediction models for the monitoring data based on the historical time series includes: constructing a monitoring data time series based on the historical time series; performing endpoint extremum extension preprocessing on the monitoring data time series, and then performing layer-by-layer decomposition on the extended preprocessed monitoring data time series using the empirical mode decomposition method to obtain multiple intrinsic mode functions and trend terms; after the intrinsic mode functions and trend terms are decomposed, deleting the pseudo data in the extension part of the intrinsic mode functions and trend terms; based on the intrinsic mode functions and trend terms after deleting the pseudo data in the extension part, constructing a time series prediction model corresponding to each intrinsic mode function and trend term based on a deep learning model; and constructing a time series prediction model for the monitoring data based on the time series prediction model corresponding to each intrinsic mode function and trend term.

[0055] Specifically, historical time series of monitoring data are collected. This data may cover various environmental data monitored by industrial sensors, such as temperature, water level, and economic indicators. The collected data is arranged and integrated in chronological order to form a complete and orderly time series. Data cleaning is then performed to remove outliers and handle missing values, ensuring data quality and reliability. Subsequently, the data is normalized or standardized to unify data of different dimensions on the same scale, providing a data foundation for subsequent analysis and modeling. Endpoint extreme value extension preprocessing is performed on the monitoring data time series to eliminate boundary effects and ensure the stability and accuracy of the subsequent decomposition process. Specifically, extreme value extension processing is performed on the left and right endpoints of the original monitoring data time series X(t): extending M maxima and M minima to the left endpoint to construct an extended envelope; extending M maxima and M minima to the right endpoint to maintain the continuity of the data boundary fluctuation pattern; the extension uses interpolation based on symmetrical mirroring of historical extreme points to ensure that the extended data is consistent with the original sequence in amplitude and phase, maintaining the continuity of the decomposition.

[0056] Next, the extended preprocessed monitoring data time series is decomposed layer by layer using the Empirical Mode Decomposition (EMD) method to obtain multiple intrinsic mode functions (IMFs) and a trend term. The EMD method transforms the non-stationary time series into a set of IMFs and a trend term through adaptive decomposition.

[0057] Specifically, this includes: using the empirical mode decomposition method to decompose the extended monitoring data time series layer by layer to obtain multiple intrinsic mode functions and trend terms.

[0058] Empirical Mode Decomposition (EMD) adaptively decomposes non-stationary monitoring data time series. X ( t Transform it into a set of intrinsic modulo functions and trend terms: ; in, X ( t () represents the original signal. C j For the first j Each intrinsic modulus function n The number of intrinsic moduli. r This represents the trend.

[0059] Find the time series of monitoring data X ( t Find all the maxima and fit them to the upper envelope of the original data sequence using a cubic spline function; find all the minima and fit them to the lower envelope of the original data sequence using a cubic spline function; the mean of the upper and lower envelopes is the average envelope of the original data sequence. m 1; Subtracting the average envelope from the original data sequence yields a new data sequence with low frequencies removed. h 1: ; Generally speaking, h 1 is not necessarily a stationary data sequence, therefore the above processing procedure needs to be repeated for it. If... h The average envelope of sequence 1 is m 11 The data sequence after removing the low-frequency components represented by this envelope is h 11 Then there is ; Repeat the above process. k This process is repeated until the average envelope approaches zero, at which point the first eigenmode function is obtained. C 1: ; ; in, For the kth The sequence obtained in one iteration. m 1k The average envelope is calculated in the k-th iteration. h 1k This is the new residual sequence.

[0060] The first intrinsic modulus function represents the most frequent component in the original data sequence.

[0061] Time series of raw monitoring data X ( t Subtract the first intrinsic modulus function C1. This can yield a new data sequence with high frequencies removed. r 1. For r The second intrinsic modulus function can be obtained by performing the above stabilization process. C 2. Repeat this process until the last difference sequence is reached. r Until it can no longer be decomposed.

[0062] Obtain the decomposed intrinsic modulus functions C j and trend items r .

[0063] After decomposition, pseudo-data in the extended portions of the intrinsic modulus function and trend term needs to be removed. Since endpoint extremum extensions were performed on the sequence at the beginning, the data in these extended portions are artificially added and do not belong to the original monitoring data time series. Therefore, after the intrinsic modulus function and trend term decomposition, it is crucial to clearly distinguish which data belongs to the pseudo-data generated by the extended portion and which is the valid data corresponding to the original monitoring data time series. Pseudo-data in the extended portions of the intrinsic modulus function and trend term are then removed, retaining only the valid portions corresponding to the original time periods. This ensures that subsequent analysis and modeling are based on real monitoring data, avoiding interference from the extended data on the prediction model. Based on the characteristics of the intrinsic modulus function and trend term after removing the pseudo-data in the extended portion, time series prediction models corresponding to each intrinsic modulus function and trend term are constructed using deep learning models (such as LSTM, CNN, Transformer, etc.). For example, for high-frequency fluctuating intrinsic modulus functions, an LSTM model can be selected to capture their short-term dependencies; for low-frequency trend terms, a Transformer model can be used to grasp their long-term trends. Historical data is used to train each prediction model, and an optimization algorithm (such as the Adam optimizer) is employed to minimize the error between the predicted and actual values. During training, the training and validation errors are monitored to prevent overfitting and ensure good generalization ability. A time series prediction model for the monitoring data is constructed based on the time series prediction models corresponding to each intrinsic modulus function and trend term. Simple linear superposition, weighted averaging, or more complex nonlinear fusion methods can be used. The outputs of each intrinsic modulus function and trend term prediction model are integrated according to the selected fusion strategy to obtain the final time series prediction model for the monitoring data. This model can integrate the prediction results of various intrinsic modulus functions and trend terms, achieving high-precision prediction of the original monitoring data time series, fully exploring different feature components in the monitoring data, and improving the accuracy and reliability of the prediction.

[0064] In this optional embodiment, the performance of the prediction model can be effectively improved by introducing endpoint extremum extension preprocessing and empirical mode decomposition. Endpoint extremum extension preprocessing eliminates boundary effects, ensuring the stability and accuracy of the decomposition process; empirical mode decomposition decomposes the time series into multiple intrinsic mode functions and trend terms, making the characteristics and variation patterns of each component sequence clearer, facilitating subsequent modeling and prediction; constructing prediction models separately can fully utilize the powerful fitting ability of deep learning, accurately capture the features of each component sequence, and improve the accuracy and reliability of the prediction results.

[0065] Optionally, constructing multiple time series prediction models for the monitoring data based on the historical time series includes: constructing a monitoring data time series based on the historical time series; decomposing the monitoring data time series using a variational mode decomposition method to obtain multiple variational mode functions; constructing a time series prediction model corresponding to each variational mode function based on a deep learning model for each variational mode function; and constructing a time series prediction model for the monitoring data based on the time series prediction model corresponding to each variational mode function.

[0066] Specifically, historical time series of monitoring data are collected. This data may cover various environmental data monitored by industrial sensors, such as temperature, water level, and economic indicators. The collected data is arranged and integrated in chronological order to form a complete and orderly time series. The collected data undergoes cleaning, removing outliers and handling missing values ​​to ensure data quality and reliability. Subsequently, the data is normalized or standardized to unify data of different dimensions on the same scale, providing a data foundation for subsequent analysis and modeling. Variational Mode Decomposition (VMD) is a signal decomposition technique that decomposes a signal into multiple intrinsic mode functions (VMFs). Each VMF has a unique center frequency and bandwidth. Compared with traditional methods such as EMD, VMD is more stable and adaptable during the decomposition process and can effectively avoid mode aliasing problems. The monitoring data time series is input into the VMD model, and the time series is decomposed into multiple variational mode functions through optimization algorithms. The goal of VMD is to minimize the sum of the bandwidths of each mode function while ensuring that the sum of the mode functions equals the original signal. Based on the characteristics of each variational mode function, time series prediction models corresponding to each variational mode function are constructed using deep learning models (such as LSTM, CNN, Transformer, etc.). For example, for high-frequency fluctuating variational mode functions, LSTM models can be selected to capture their short-term dependencies; for low-frequency trend terms, Transformer models can be used to grasp their long-term trends.

[0067] Historical data is used to train each prediction model, and an optimization algorithm (such as the Adam optimizer) is employed to minimize the error between the predicted and actual values. During training, the training and validation errors are monitored to prevent overfitting and ensure good generalization ability. A time series prediction model for the monitoring data is constructed based on the time series prediction model corresponding to each variational mode function. The outputs of each variational mode function prediction model are integrated according to a selected fusion strategy to obtain the final time series prediction model for the monitoring data. This model can synthesize the prediction results of various variational mode functions, achieving high-precision prediction of the original monitoring data time series, fully exploring the different feature components in the monitoring data, and improving the accuracy and reliability of the prediction.

[0068] In a preferred embodiment of the present invention, the specific steps of using variational mode decomposition can be as follows: decompose the monitoring data time series using the variational mode decomposition method to obtain several variational mode functions; The solution process of the variational mode decomposition method mainly includes two constraints: (1) the sum of the bandwidths of the center frequencies of each mode component must be minimized; (2) the sum of all mode components must be equal to the original signal, i.e.: ; in, X ( t (This refers to the time series of monitoring data.) x k For the first k One eigenmode function r k For the first k The bandwidth of the center frequency of each intrinsic mode function.

[0069] The eigenmode functions of the variational mode decomposition method are defined as the component mode functions of amplitude modulation and frequency modulation, as follows: ; in, A k ( t )and φ k ( t ) are respectively the first k Individual eigenmode functions x k ( t The envelope amplitude and instantaneous phase of ).

[0070] To ensure that the intrinsic mode functions are modal components with a finite bandwidth and a center frequency, and that the sum of the estimated bandwidths of all intrinsic mode functions is minimized, the constraint condition is that the sum of all modes is equal to the original signal. The constrained variational model of the variational mode decomposition method is as follows: ; in, For the first k The center frequencies of the eigenmode functions t Indicates time t The partial derivative, δ ( t ) represents the Dirac function, j For imaginary units, ∥ ∥2 is the L2 norm.

[0071] By introducing Lagrange multipliers and penalty parameters α By transforming the constrained variational problem into an unconstrained problem, we obtain the augmented Lagrangian function. L , monitoring data time series X ( t Input the variational mode decomposition model, and let the Lagrangian function... L About all x k and The derivative is 0. Find the corresponding gradient expression, and then use the gradient descent algorithm iteratively to find the optimal value. x k and Each intrinsic mode function was determined, and variational mode decomposition of the original monitoring data time series was achieved.

[0072] In this optional embodiment, variational mode decomposition stably decomposes the time series monitoring data into multiple variational mode functions (VMFs). Each VMF has a definite center frequency and bandwidth, effectively avoiding the mode aliasing problem common in traditional decomposition methods such as empirical mode decomposition (EMD). This allows for more accurate extraction of features at different scales in the time series, providing cleaner and more representative feature components for subsequent prediction model construction. A suitable deep learning model is selected for each variational mode function for separate modeling, fully leveraging the advantages of different deep learning models. For example, LSTM excels at capturing short-term dependencies in sequence data and is suitable for high-frequency fluctuating VMF components; Transformer can grasp long-term trends and is suitable for low-frequency trend terms. This targeted modeling approach in this embodiment can more accurately capture the unique variation patterns of each VMF component, thereby improving prediction accuracy.

[0073] By fusing the prediction results of multiple variational mode functions (VMFs) to construct the final time series prediction model for monitoring data, the advantages of each VMF component prediction model can be fully utilized, achieving complementary strengths. The fused prediction model is more adaptable to the data and can more effectively cope with the complex changes and uncertainties in the monitoring data time series, enhancing the model's robustness and generalization ability. The VMD decomposition process can adaptively determine the number and characteristics of VMF components without manual pre-setting, making it applicable to different types of monitoring data time series. Simultaneously, the deep learning model can automatically learn complex patterns and regularities in the data during training, exhibiting strong adaptability and versatility, and meeting the prediction needs of different types of monitoring data. VMD decomposition simplifies the complex original time series into multiple relatively simple VMF components, reducing the prediction difficulty and computational complexity of each component. During training and prediction, the deep learning model for each VMF component can be trained and predicted in parallel, further improving the overall training and prediction efficiency of the prediction model.

[0074] In summary, this embodiment, through the organic combination of variational mode decomposition and deep learning models, fully explores the multi-scale features in the monitoring data time series, achieving high-precision, high-robustness, and high-efficiency monitoring data time series prediction.

[0075] Optionally, the step of summarizing all the prediction results and fusing them through a time series ensemble prediction model to obtain the final prediction result of the monitoring data in a future preset time period includes: summarizing all the prediction results and normalizing them to obtain a standardized prediction matrix; inputting the standardized prediction matrix as input data into the time series ensemble prediction model to predict the future value and prediction interval of the monitoring data; wherein, the time series ensemble prediction model includes a multi-channel convolutional neural network, a stacked bidirectional gated recurrent unit network and an attention fusion module; using multiple parallel one-dimensional convolutional sub-modules of the multi-channel convolutional neural network to extract features from the standardized prediction matrix to obtain local temporal feature representations at different scales; using at least two layers of forward gated recurrent unit networks and two layers of backward gated recurrent unit networks of the stacked bidirectional gated recurrent unit network to capture the long-term dependencies of the time series of the standardized prediction matrix to obtain a temporal feature representation; using the attention fusion module to fuse the local temporal feature representation and the temporal feature representation using dynamic weighting to obtain a fused feature representation; and outputting the final prediction result through a fully connected layer based on the fused feature representation.

[0076] Specifically, the structure of the time series ensemble prediction model is as follows: Input layer: Receives the standardized prediction matrix This serves as the input for subsequent feature extraction networks; The multi-channel convolutional neural network (CNN) feature extraction branch contains multiple parallel one-dimensional convolutional sub-modules with kernel sizes of 3, 5, and 7, used to extract local temporal features at different scales. Each sub-branch includes a one-dimensional convolutional layer, a batch normalization layer, a modified linear unit activation layer, and a max-pooling layer. The output features of multiple convolutional branches are concatenated to form the CNN feature matrix. .

[0077] Stacked Bidirectional Gated Recurrent Unit Network (BiGRU) Feature Extraction Branch: Contains at least two layers of forward-gated recurrent unit networks (GRUs) and two layers of backward-gated recurrent unit networks (GRUs), used to capture long-term dependencies in the time series of monitoring data and output a long-term dependency feature matrix. .

[0078] Attention Fusion Module: Used to fuse high-order feature representations from the outputs of CNN and BiGRU branches, dynamically weighting the importance of different time steps; it integrates the CNN feature matrix... With long-term dependency feature matrix The features are concatenated to obtain the fused feature matrix. F fused : ; Introducing an attention mechanism for dynamic weighted fusion: ; in, For attention weights, q Let `score(.)` be the query vector, and `score(.)` be a learnable scoring function. F attm This is the feature matrix after dynamic weighted fusion.

[0079] Output structure: Includes one or more fully connected layers, outputting the final predicted point values.

[0080] Fusion features Input two parallel output branches: Point prediction branch: ; in, For point prediction results; Variance estimation branch: ; in, For variance, and A training neural network mapping function with parameters.

[0081] Prediction interval generation unit: Based on the variance estimation results and combined with the normal distribution assumption, it generates the upper and lower bounds of the prediction interval at a specified confidence level.

[0082] By integrating the prediction results of multiple feature decomposition-based monitoring data time series prediction models, a monitoring data time series ensemble prediction model is constructed to predict future values ​​and intervals of the monitoring data time series. Specifically, the prediction results of the multiple feature decomposition-based monitoring data time series prediction models are summarized and normalized to form a standardized prediction matrix. ; in, This represents the prediction result of the i-th monitoring data time series prediction model based on eigenvalue decomposition at time point t.

[0083] Assuming the predicted residuals follow a normal distribution, given a confidence level... The prediction interval is calculated as follows: ; in This is the critical value under a normal distribution. Standard deviation For point prediction results, This is the lower bound of the interval prediction value. This is the upper bound of the interval prediction value.

[0084] The dataset is divided into a training set, a validation set, and a test set; The original dataset is divided into training, validation, and test sets, with a ratio of, for example, 70%-15%-15%. The training set is used for model training, the validation set is used to monitor generalization ability, and the test set is used for final performance evaluation.

[0085] The neural network model is trained on both the training and validation sets using the Adam optimizer. The learning rate and regularization parameters are determined empirically or through cross-validation. The loss function L, which comprehensively considers both point prediction error and uncertainty estimation accuracy, is defined as: ; in, Here, y is the weighting coefficient, T is the total number of data points, and yt is the t-th data observation. Let t be the predicted value of the data point. Let t be the variance of the t-th data point. Let be the variance of the historical estimate or the variance of the target residual for the t-th data point.

[0086] The model hyperparameters are adjusted and optimized based on the prediction performance of the validation set. Combining the prediction error and interval reliability of the validation set, grid search or Bayesian optimization is performed on the network structure hyperparameters (such as CNN kernel size, number of BiGRU layers, attention dimension, Dropout ratio, etc.) to improve the final performance.

[0087] The test set data is input into the trained model, and the prediction output is inversely normalized to obtain the final point prediction value and confidence interval prediction result of the monitoring data time series. The final point prediction value and confidence interval prediction result of the monitoring data time series are used as the final prediction result.

[0088] In this optional embodiment, a multi-channel CNN of the time series ensemble prediction model extracts local features at different scales, a stacked bidirectional GRU captures long-term dependencies, and an attention mechanism is used to dynamically fuse features, accurately capturing complex patterns in time series. Normalization ensures consistency in prediction results, the advantages of multiple models are combined to improve prediction accuracy and reliability, and the uncertainty of prediction intervals is quantified, enhancing decision support capabilities in practical applications.

[0089] In summary, acquiring historical and real-time data from the monitoring system to construct a monitoring data time-series database provides a comprehensive and accurate data foundation for subsequent prediction model construction. Next, based on the historical time series, a monitoring data time series is constructed. Multi-scale typical time-varying characteristics are obtained through spectral analysis, and basis functions are constructed based on these characteristics. These basis functions are then used to decompose the time series into multi-scale time-varying component sequences. Subsequently, the data is filtered based on variance contribution rates, and prediction models are constructed for each filtered multi-scale time-varying component sequence using a deep learning model. Simultaneously, improved EMD and VMD methods are used to decompose the monitoring data time series to obtain IMF and VMF components, and corresponding prediction models are constructed for each. Then, each constructed time-series prediction model is used to predict real-time data, yielding prediction results for each model. Finally, all prediction results are aggregated and normalized to form a standardized prediction matrix, which is then input into the time-series ensemble prediction model. This model integrates multi-channel CNN, stacked bidirectional GRU, and an attention mechanism. The multi-channel CNN extracts local temporal features at different scales, the stacked bidirectional GRU captures long-term dependencies in the time series, and the attention mechanism dynamically fuses these features. Finally, the model outputs the final prediction result and prediction range via a fully connected layer. The model is then trained on both training and validation sets, with hyperparameters adjusted using the validation set's prediction performance. Finally, the model is evaluated on a test set, ultimately outputting the final prediction result and prediction range for the monitored data within a predetermined future time period.

[0090] In a preferred embodiment of the invention, the invention is applied to the prediction of water level monitoring data. Specifically, hourly sea level height data from Xiamen Station throughout 1986 are used as the research object. The experimental data used in this study is the water level data from Xiamen Station throughout 1986, with the first 70% of the data used as the training set and the remaining 30% as the prediction set. First, a time series prediction model based on multi-scale time-varying feature decomposition of monitoring data is constructed and applied to water level prediction. Combined with... Figure 5 As shown, by inputting 30 days of hourly water level monitoring data into the model and performing fine multi-scale time-varying feature decomposition, the water level change characteristics at different time scales can be clearly displayed.

[0091] For example, high-frequency components reflecting daily tidal changes and low-frequency components reflecting seasonal sea-level fluctuations can be decomposed. These decomposed components are used as input to a Long Short-Term Memory (LSTM) artificial neural network to predict the water level for the next hour. As shown in Table 1, the comparison between the model prediction results and actual monitoring data shows that this method can accurately capture the trend and fluctuation of water level changes. The mean square error (MSE) is 0.093796, the root mean square error (RMSE) is 0.30626, the mean absolute error (MAE) is 0.24061, the mean absolute percentage error (MAPE) is 5.697%, and the coefficient of determination (R²) is as high as 0.9552. This indicates that the model has excellent interpretability of water level changes and high prediction accuracy, providing an efficient and reliable solution for water level prediction at Xiamen Station. This helps to provide early warning of potential abnormal water level fluctuations and provides strong support for flood control, disaster reduction, and water resource management in coastal areas.

[0092] Table 1 Performance Indicators of Water Level Prediction Model

[0093] Secondly, the monitoring data time series prediction model based on improved empirical mode decomposition has also played an important role in water level prediction. This model also uses 30 days of hourly water level data, and after improved EMD decomposition, extracts multiple intrinsic mode functions (IMFs) and trend terms. Each IMF component represents the fluctuation characteristics of water level data at a specific time scale, covering everything from high-frequency short-term fluctuations to low-frequency long-term trends.

[0094] These IMF components and trend terms were input into the LSTM model for prediction. As shown in Table 2, the results demonstrate that the model can accurately reproduce the actual water level changes, with a mean squared error (MSE) of 0.11366, a root mean square error (RMSE) of 0.33713, a mean absolute error (MAE) of 0.26914, a mean absolute percentage error (MAPE) of 6.4681%, and a coefficient of determination (R²) of 0.9459. This indicates that the improved EMD method effectively decomposes the water level signal, extracts valuable feature information, and provides high-quality input for the LSTM model, enabling it to achieve satisfactory results in water level prediction tasks. This further enriches the toolbox of water level prediction models and provides a robust prediction method for dealing with complex water level changes.

[0095] Table 2 Performance Indicators of the LSTM Water Level Prediction Model Based on EMD Decomposition

[0096] Furthermore, the time series prediction model based on variational mode decomposition (VMD) of monitoring data also performed well in water level prediction. The VMD method was used to decompose 30 days of hourly water level data, yielding multiple variational mode functions (VMFs). Each VMF has a distinct center frequency and bandwidth, highlighting the different modal characteristics of water level changes. These VMF components were input into an LSTM model for prediction. As shown in Table 3, the model performed well on the test set, with a mean squared error (MSE) of 0.11888, a root mean square error (RMSE) of 0.34478, a mean absolute error (MAE) of 0.27615, a mean absolute percentage error (MAPE) of 6.4629%, and a coefficient of determination (R²) of 0.9432.

[0097] This demonstrates the advantages of the VMD method in processing water level time series data. It can reasonably decompose the signal and extract feature components that help improve prediction accuracy, providing a new perspective and method for water level prediction. It complements the multi-scale time-varying feature decomposition and the improved EMD method, together forming a comprehensive water level prediction model system.

[0098] Table 3 Performance Indicators of the LSTM Water Level Prediction Model Based on VMD Decomposition

[0099] Finally, the application of the time series ensemble prediction model for monitoring data has elevated the accuracy of water level prediction to a new level. This model innovatively integrates the prediction results of three prediction models: multi-scale time-varying feature decomposition, improved EMD, and VMD, and inputs them as multivariate variables into an ensemble prediction model based on CNN-BiGRU-Attention. This integration method fully leverages the advantages of each individual model, achieving optimized prediction results. As shown in Table 4, the prediction results on the test set demonstrate that the ensemble prediction model significantly reduces its mean square error (MSE) to 0.0047209, root mean square error (RMSE) to 0.068709, mean absolute error (MAE) to 0.054208, mean absolute percentage error (MAPE) to only 1.2076%, and its coefficient of determination (R²) to a high 0.9977.

[0100] Table 4 Performance Indicators of Ensemble Prediction Model for Water Level Prediction

[0101] These indicators all outperform the predictions of single models, fully demonstrating the significant advantages of ensemble prediction models in improving the accuracy of water level forecasts. This model can more accurately capture subtle characteristics of water level changes, providing more reliable water level forecast information. It has important practical application value for tidal management, flood warning, and port operations in coastal cities, setting a new benchmark in the field of water level forecasting.

[0102] In a preferred embodiment of the invention, the invention is applied to the prediction of financial data. In the field of financial forecasting, the method of this invention uses the CSI 300 Index as the research object, fully demonstrating its powerful capability in predicting complex financial time series. This embodiment uses daily closing price data from January 5, 2010 to January 11, 2022, a long time span covering multiple economic cycles and market fluctuation stages, providing rich and diverse data scenarios for model training and validation. Similarly, the data is divided according to the ratio of the first 70% as the training set and the last 30% as the prediction set, ensuring that the model can effectively predict future market trends based on a thorough learning of historical data characteristics. The application of the monitoring data time series prediction model based on multi-scale time-varying feature decomposition in financial forecasting has achieved significant results. Figure 6 As shown, the model performs multi-scale time-varying feature decomposition on the daily stock index closing price data over 30 days, successfully separating the high-frequency components reflecting short-term market fluctuations and the low-frequency components reflecting long-term market trends.

[0103] As shown in Table 5, these decomposed components were input into a Long Short-Term Memory (LSTM) artificial neural network for prediction. The results show that the model can track the dynamic changes of the stock index well, with a mean squared error (MSE) of 16531.8633, a root mean square error (RMSE) of 128.5763, a mean absolute error (MAE) of 96.5948, a mean absolute percentage error (MAPE) of 2.2578%, and a coefficient of determination (R²) of 0.9652. Although the complexity and uncertainty of financial markets pose significant challenges to prediction, this model, with its accurate decomposition and effective modeling of multi-scale features, performs excellently in capturing the patterns of stock index fluctuations, providing investors with some forward-looking market information and helping to optimize investment decisions and risk management strategies.

[0104] Table 5 Performance metrics of the LSTM CSI 300 prediction model based on multi-scale time-varying eigenvalue decomposition

[0105] The time series forecasting model based on improved empirical mode decomposition (EMD) of monitoring data is also competitive in financial forecasting. By decomposing 30 days of daily stock index closing price data using the improved EMD method, multiple intrinsic mode functions (IMFs) and trend terms are obtained. Each IMF component corresponds to the fluctuation pattern of the stock index at different time scales. As shown in Table 6, these components are input into an LSTM model for prediction. The model performs excellently on the test set, with a mean squared error (MSE) of 16228.4453, a root mean square error (RMSE) of 127.3909, a mean absolute error (MAE) of 99.357, a mean absolute percentage error (MAPE) of 2.3941%, and a coefficient of determination (R²) of 0.9661. The improved EMD method performs well in handling non-stationary financial time series, effectively improving the signal decomposition quality. This allows the LSTM model to learn and predict based on purer and more representative features, further enhancing the model's fitting and predictive capabilities for stock index trends.

[0106] Table 6 Performance metrics of the LSTM daily stock index forecasting model based on improved EMD

[0107] The performance of time series forecasting models based on variational mode decomposition (VMD) in financial forecasting is also noteworthy. Using the VMD method, 30 days of daily stock index closing price data were decomposed to obtain multiple variational mode functions (VMFs), each representing the volatility characteristics of the stock index under a specific mode. As shown in Table 7, these VMF components were input into an LSTM model for forecasting. The model prediction results show a mean squared error (MSE) of 18326.7832, a root mean square error (RMSE) of 135.3764, a mean absolute error (MAE) of 97.5632, a mean absolute percentage error (MAPE) of 2.3374%, and a coefficient of determination (R²) of 0.9616. The VMD method effectively avoids mode aliasing when decomposing financial time series, extracting more valuable feature information, providing strong support for LSTM model forecasting, further enriching the methodological system of financial time series forecasting models, and providing new technical means for financial market analysis and forecasting.

[0108] Table 7 Performance metrics of the VMD-based LSTM daily stock index prediction model

[0109] The ensemble prediction model for time series monitoring data has achieved remarkable results in financial forecasting. This innovative model integrates the prediction results of three prediction models—based on multi-scale time-varying feature decomposition, improved EMD, and VMD—as multivariate inputs into a CNN-BiGRU-Attention-based ensemble prediction model. This integration strategy fully leverages the advantages of each individual model, significantly improving prediction accuracy through mutual complementarity and synergy. As shown in Table 8, the prediction results on the test set demonstrate that the ensemble prediction model significantly reduces its mean squared error (MSE) to 2295.7141, root mean square error (RMSE) to 47.9136, mean absolute error (MAE) to 30.1446, mean absolute percentage error (MAPE) to only 0.71029%, and its coefficient of determination (R²) to a high 0.9951. Compared to individual models, the ensemble prediction model exhibits significant advantages in all error metrics, resulting in more accurate and reliable predictions. This model can more keenly capture subtle changes and potential trends in the financial market, providing investors with more accurate market forecast information, which helps to improve investment returns and risk management. It has broad application prospects and promotional value in the field of financial forecasting.

[0110] Table 8 Performance Indicators of Ensemble Forecasting Models in Financial Forecasting

[0111] The present invention also provides a time series ensemble prediction system, comprising: a processor and a memory, wherein the memory is used to store a computer program; when the computer program is loaded by the processor, the processor causes the processor to execute the time series ensemble prediction method as described in any of the preceding claims.

[0112] The time series ensemble prediction system of the present invention has the same advantages over the prior art as the aforementioned time series ensemble prediction method over the prior art, and will not be repeated here.

[0113] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the time series set prediction method described above.

[0114] The computer-readable storage medium of the present invention has the same advantages over the prior art as the aforementioned time series set prediction method over the prior art, and will not be repeated here.

[0115] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for predicting time series sets, characterized in that, The method is applied to a water level monitoring system, and the method includes: Obtain historical time series and real-time data of water level monitoring data from the water level monitoring system; Based on the historical time series, multiple time series prediction models for the water level monitoring data are constructed; wherein the water level monitoring data is obtained through water level sensors. Specifically, the process includes: constructing a water level monitoring data time series based on the historical time series; performing spectral analysis on the water level monitoring data time series to obtain multi-scale typical time-varying features of the water level monitoring data; the multi-scale typical time-varying features are used to characterize the periodic variation patterns of the water level monitoring data at different time scales, including daily tidal variations and seasonal variations; constructing basis functions corresponding to each of the multi-scale typical time-varying features; decomposing the water level monitoring data time series using all the basis functions to obtain multi-scale time-varying component sequences; filtering the multi-scale time-varying component sequences based on their variance contribution rates; constructing a time series prediction model for each of the filtered multi-scale time-varying component sequences based on a deep learning model; and constructing a time series prediction model for the water level monitoring data based on the time series prediction models corresponding to each of the multi-scale time-varying component sequences. A water level monitoring data time series is constructed based on the historical time series. The water level monitoring data time series undergoes endpoint extremum extension preprocessing, and then the extended preprocessed water level monitoring data time series is decomposed layer by layer using the empirical mode decomposition method to obtain multiple intrinsic mode functions and trend terms. Each intrinsic mode function represents the fluctuation characteristics of the water level monitoring data at a corresponding time scale. After the intrinsic mode functions and trend terms are decomposed, pseudo-data in the extended portion of the intrinsic mode functions and trend terms is deleted. Based on the intrinsic mode functions and trend terms after deleting the pseudo-data in the extended portion, a time series prediction model corresponding to each intrinsic mode function and trend term is constructed using a deep learning model. Based on the time series prediction model corresponding to each intrinsic mode function and trend term, a time series prediction model for the water level monitoring data is constructed. A water level monitoring data time series is constructed based on the historical time series; the water level monitoring data time series is decomposed using the variational mode decomposition method to obtain multiple variational mode functions; each variational mode function has a center frequency and bandwidth, used to characterize the modal features of the water level monitoring data in different frequency bands; for each variational mode function, a time series prediction model corresponding to each variational mode function is constructed based on a deep learning model; a time series prediction model for the water level monitoring data is constructed based on the time series prediction model corresponding to each variational mode function. Based on the real-time data, the real-time data is predicted using each of the time series prediction models to obtain the prediction result corresponding to each of the time series prediction models; All the prediction results are summarized and fused using a time series ensemble prediction model to obtain the final prediction result of the water level monitoring data for a future preset time period; specifically including: All prediction results are aggregated and normalized to obtain a standardized prediction matrix. This standardized prediction matrix is ​​then used as input data to the time series ensemble prediction model for prediction, yielding the final water level prediction result for the water level monitoring data within the preset future time period. The time series ensemble prediction model includes a multi-channel convolutional neural network, a stacked bidirectional gated recurrent unit network, and an attention fusion module. Multiple parallel one-dimensional convolutional sub-modules of the multi-channel convolutional neural network extract features from the standardized prediction matrix to obtain local temporal feature representations at different scales. At least two layers of forward-gated recurrent unit networks and two layers of backward-gated recurrent unit networks of the stacked bidirectional gated recurrent unit network capture the long-term dependencies of the time series of the standardized prediction matrix, obtaining a temporal feature representation. The attention fusion module uses dynamic weighting to fuse the local temporal feature representation and the temporal feature representation to obtain a fused feature representation. A fully connected layer outputs the final water level prediction result based on the fused feature representation.

2. The time series ensemble prediction method according to claim 1, characterized in that, The process of decomposing the water level monitoring data time series using all the aforementioned basis functions to obtain a multi-scale time-varying component series includes: The expression for the time series of water level monitoring data is determined based on the basis functions; The water level monitoring data time series is substituted into the expression, and the water level monitoring data time series is decomposed by the expression to obtain multiple multi-scale time-varying component sequences. The multiple multi-scale time-varying component sequences include at least one component sequence with a change period and one component sequence without a change period. The expression for the time series of water level monitoring data is: ； in, t For time variables, X ( t ) represents the time series of the water level monitoring data. x 0( t () refers to the component sequence that does not have a period of change. For the basis functions, ω k For the first k The characteristic frequencies of the basis functions It is the first k The phase parameters of the basis functions. A k ( t ) is the first k The time-varying coefficients of the aforementioned basis functions change over time. K The number of basis functions. For the first k The expression for the multi-scale time-varying component sequence.

3. The time series ensemble prediction method according to claim 2, characterized in that, The process involves substituting the water level monitoring data time series into the expression, and then decomposing the water level monitoring data time series using the expression to obtain multiple multi-scale time-varying component sequences. These multiple multi-scale time-varying component sequences include at least one component sequence with a periodicity and one component sequence without a periodicity. Based on the typical time-varying characteristics, the characteristic period of the water level monitoring data time series is determined, and based on the characteristic period, the characteristic frequency is determined; Multiple feature points are selected from the water level monitoring data time series, and the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points and the phase parameters and time-varying coefficients of the basis functions at all time points in the water level monitoring data time series is obtained. Based on the characteristic frequency, the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the characteristic points in the water level monitoring data time series and the phase parameters and time-varying coefficients of the basis functions at all time points in the water level monitoring data time series, the phase parameters and time-varying coefficients of the basis functions corresponding to the characteristic points are obtained by the least squares method. Based on the relationship between the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points in the water level monitoring data time series and the phase parameters and time-varying coefficients of the basis functions at all time points in the water level monitoring data time series, and the phase parameters and time-varying coefficients of the basis functions corresponding to the feature points, the phase parameters and time-varying coefficients of the basis functions at all time points in the water level monitoring data time series are obtained. Based on the phase parameters and time-varying coefficients of the basis functions at all time points in the water level monitoring data time series, at least one component sequence with a periodicity and one component sequence without a periodicity are obtained.

4. The time series set prediction method according to claim 1, characterized in that, The step of filtering the multi-scale time-varying component sequences based on their variance contribution rates includes: Calculate the variance contribution rate of all the multi-scale time-varying component sequences obtained from the decomposition; The multi-scale time-varying component sequences are superimposed sequentially from low frequency to high frequency, and the variance contribution rates are summed to obtain the cumulative variance contribution rate. Determine whether the cumulative variance contribution rate exceeds a preset threshold; If the cumulative variance contribution rate exceeds the preset given threshold, then the multiple multi-scale time-varying component sequences that are currently superimposed in sequence will be used as the filtered multi-scale time-varying component sequences.

5. A time series ensemble prediction system, characterized in that, include: Processor and memory, the memory being used to store computer programs; When the computer program is loaded by the processor, it causes the processor to execute the time series set prediction method as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the time series set prediction method as described in claims 1-4.

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