Multivariate time sequence prediction method based on dynamic complex spectrum filtering

Abstract

The invention discloses a multivariate time sequence prediction method based on dynamic complex spectrum filtering, which comprises the following steps: acquiring multivariate time sequence data of a target scene, determining a predicted target variable and a window length, and constructing a training set, a verification set and a test set based on the data; constructing a DCSFNet prediction model, wherein the model sequentially comprises a reversible instance normalization module, a frequency domain conversion module, a dynamic complex spectrum filtering module, a time domain projection module and an inverse reversible instance normalization module; and realizing multivariate time sequence prediction by using the trained DCSFNet model. According to the method, the frequency domain features are adaptively processed through the dynamic complex spectrum filtering module, and reversible normalization and time domain mapping are combined, so that the problems that an existing method is poor in adaptability to diversified time sequence data, frequency domain information is insufficient in utilization, and prediction precision and calculation efficiency are difficult to consider at the same time are effectively solved; and multivariate time sequence prediction with high precision, high efficiency and cross-scene adaptability is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multivariate time series prediction, and particularly relates to a multivariate time series prediction method based on dynamic complex spectrum filtering. BACKGROUND

[0002] Multivariate time series forecasting (MTSF) aims to use historical observation data containing multiple related variables to infer the trend of variable changes in the future period of time, and is a key basic capability in modern intelligent systems. In typical scenarios such as energy management, industrial manufacturing, weather analysis, and power dispatch, multivariate time series forecasting plays an important role in safety guarantee and decision support. For example, in the energy management scenario, accurate prediction of the temperature of the power transformer can help identify potential overload risks and ensure the reliable operation of the power grid equipment; in the industrial manufacturing scenario, device state prediction based on time series data collected by multiple sensors can help identify potential faults in advance and reduce production losses; in weather analysis, prediction of multiple factors such as temperature, precipitation, and wind speed can help prevent extreme weather in the early stage; in the power dispatch field, regional load forecasting is an important basis for maintaining the balance between supply and demand of the power grid and improving the efficiency of dispatching. As can be seen, the performance of multivariate time series forecasting directly affects the safety, stability, and economy of multiple key industries.

[0003] With the development of deep learning technology, time series prediction methods gradually evolve from traditional statistical models such as ARIMA and exponential smoothing to data-driven deep learning models. However, existing deep learning methods still have significant limitations and are difficult to fully adapt to the structural characteristics and dynamic patterns of complex and diverse time series data. Mainstream methods (such as multi-layer perception models and Transformer models based on self-attention mechanisms) usually directly process sequence data in the time domain. For example, in the prior art, CN112884230A discloses a power load prediction method based on multivariate time series, which includes obtaining time series raw data in the power load prediction process and preprocessing to obtain time series sample data; constructing a graph structure between variables of the time series sample data, obtaining a spatial vector representation of each variable according to the graph structure, and constructing a first feature matrix according to the spatial vector representation of each variable; performing feature fusion on the first feature matrix and the time series sample data to obtain a second feature matrix; extracting new features from the second feature matrix and performing normalization and full connection operations to construct a time series prediction model, and outputting a prediction value using the time series prediction model. This method has certain advantages in capturing nonlinear correlations, but its processing process often cannot effectively distinguish the multiple frequency components coexisting in time series data, including long-term trends, periodic fluctuations, and high-frequency noise caused by sensor acquisition. Due to the lack of explicit decomposition and independent modeling of these frequency characteristics, time-domain methods are susceptible to noise interference and have limited ability to describe periodic patterns, which further affects the accuracy and stability of the prediction results.

[0004] In addition, models represented by Transformer face the problem of high computational complexity when processing long sequences. The computational complexity of the self-attention mechanism grows quadratically with the sequence length, resulting in a significant increase in training and inference costs in practical applications, and limiting the model's ability to capture potential global patterns in long sequences. In application scenarios with high efficiency requirements (such as real-time power scheduling or industrial equipment online monitoring), such models are difficult to balance high accuracy and real-time performance.

[0005] To alleviate the limitations of time-domain methods, researchers have begun to introduce frequency domain analysis into time series prediction tasks in recent years. For example, Fourier transform-based prediction models (such as FEDformer, FITS, FreTS, etc.) convert time-domain signals to the frequency domain to capture the periodic structure of the sequence using frequency spectrum characteristics. However, such frequency-domain prediction methods still face the following prominent problems: (1) Static frequency spectrum processing: existing methods usually perform frequency domain feature extraction based on fixed frequency band division or pre-set filtering strategies, which cannot adaptively adjust to dynamic changes such as cycle intensity and noise structure in different scene data, resulting in insufficient generalization ability for diverse sequences.

[0006] (2) Phase information is underutilized: Most frequency-domain methods focus on amplitude spectrum processing, amplifying or suppressing the amplitude to extract periodic components or filter noise. However, phase information is crucial for maintaining the accurate alignment of spectral components in the time domain and is the key to ensuring the time consistency of prediction results. Ignoring phase modulation often leads to time position offset, affecting the prediction accuracy.

[0007] At the same time, existing deep learning models generally have the problem of difficulty in balancing accuracy and efficiency in multivariate time series prediction. On the one hand, complex models rely on a large number of parameters and computing resources, making it difficult to adapt to edge computing or online prediction scenarios; on the other hand, overly lightweight models have limited representation ability and are difficult to capture complex sequence patterns, resulting in insufficient prediction accuracy and failing to meet the demand for high reliability prediction in energy, industry and other industries.

[0008] In summary, existing multivariate time series prediction techniques still have obvious deficiencies in the adaptability of spectral feature extraction, effective use of phase information, and balance between model accuracy and efficiency. There is an urgent need for a new prediction method that can simultaneously process dynamic frequency domain characteristics, fully modulate amplitude and phase information, and has high accuracy and efficiency, to break through the limitations of existing technology and meet the demand for multivariate time series prediction in complex real-world scenarios. SUMMARY

[0009] The purpose of the present application is to overcome the deficiencies of the prior art and provide a multivariate time series prediction method based on dynamic complex spectrum filtering.

[0010] The purpose of the present application can be achieved by the following technical solutions: The present application provides a multivariate time series prediction method based on dynamic complex spectrum filtering, comprising the following steps: Step S1: Obtain multivariate time series data of a target scene; Step S2 prediction: Determine the target variable and window length for prediction, and construct a training set, a validation set and a test set based on the multivariate time series data; Step S3: Construct a DCSFNet prediction model, which comprises a reversible instance normalization module, a frequency domain conversion module, a dynamic complex spectrum filtering module, a time domain projection module and an inverse reversible instance normalization module connected in sequence; Step S4: Train the DCSFNet prediction model based on the constructed training set, validation set and test set, and obtain the trained DCSFNet prediction model; Step S5: Based on the trained DCSFNet prediction model, according to the determined target variable and window length for prediction, realize multivariate time series prediction.

[0011] Furthermore, the target scenarios include energy management scenarios, industrial manufacturing scenarios, meteorological analysis scenarios, and power dispatching scenarios; The multivariate time series data includes time-stamped multivariate observation data acquired by multiple monitoring devices or data acquisition terminals in the target scenario. The multivariate observation data includes historical observation values ​​of the target variable to be predicted and historical observation values ​​of several auxiliary variables used to characterize equipment status, environmental conditions, or load changes.

[0012] Furthermore, the reversible instance normalization module is used to normalize the input multivariate time series data according to the variable channels. The normalization process includes: calculating statistical features along the time dimension for the time series segment of each variable channel and performing numerical standardization on the time series segment based on the statistical features.

[0013] Furthermore, the normalization process is described by the following formula: in, Indicates the first Each variable channel at time step The original observations; Represents the first calculated along the time dimension The mean of each variable channel is given by the following formula: Represents the first calculated along the time dimension The standard deviation of each variable channel is given by the formula: in, The length of the current time segment; To prevent division by zero, a numerical stability constant is required; Represents the normalized i-th Each variable channel at time step The value.

[0014] Furthermore, the frequency domain conversion module is used to convert the reversible instance normalized multivariate time series data from the time domain to the frequency domain, including amplitude and phase information, specifically including the following steps: For normalized time series segments Perform a real-number fast Fourier transform to obtain the complex-valued spectrum data in the frequency domain. The formula is: in, This represents multivariate time series data after reversible instance normalization. Represents the Fast Fourier Transform of real numbers; represents frequency domain complex-valued spectrum data, containing amplitude information and phase information; the frequency domain complex-valued spectrum data The real part corresponds to the amplitude information of the frequency component, and the imaginary part corresponds to the phase information of the frequency component.

[0015] Further, the dynamic complex spectrum filtering module is used for adaptively processing the frequency domain complex-valued spectrum data obtained by the frequency domain conversion module, simultaneously modulating the amplitude and the phase, extracting the global spectrum features of the multivariate time sequence and suppressing high-frequency noise. The dynamic complex spectrum filtering module comprises: A global feature extraction unit is configured to process the input time domain data through a one-dimensional convolution layer and a global adaptive pooling layer to extract global features. A dynamic weight generation unit is configured to input the global features into a multilayer perceptron (MLP) to generate dynamic weights, wherein the MLP comprises two linear transformations and is processed through a StarReLU activation function. A dynamic complex filter synthesis unit is configured to generate a dynamic complex filter based on the dynamic weights and a plurality of preset learnable complex filter bases, wherein the dynamic complex filter bases are initialized in a normal distribution. A frequency domain filtering unit is configured to multiply the frequency domain complex-valued spectrum data output by the frequency domain conversion module by the dynamic complex filter element by element, and sum along the intermediate channel dimension to obtain a filtered frequency domain signal.

[0016] Further, the processing process of the dynamic complex spectrum filtering module comprises: The frequency domain complex-valued spectrum data is converted back to the time domain through an inverse real fast Fourier transform to obtain time domain data , and global features are extracted through a one-dimensional convolution layer and a global average pooling , and the formula is: wherein, is the time domain data; represents a one-dimensional convolution operation, and the kernel size is 3 and padding=1; represents that the global average pooling is performed on the time dimension of the convolution output; is the global feature; The global feature is input into a multilayer perceptron MLP to generate dynamic weights , and the formula is: wherein, is the dynamic weight; represents the multilayer perceptron; is an activation function; based on the dynamic weights with K a set of learnable complex filter bases The dynamic complex filter is generated by the formula: wherein, represents the generated dynamic complex filter; represents a complex filter representation along the frequency domain dimension; represents the i-th learnable complex filter base; a set of learnable complex filter bases The frequency domain complex-valued spectral data is element-wise multiplied with the dynamic complex filter and summed along the intermediate channel dimension to obtain the filtered frequency domain signal , which is generated by the formula: wherein, is the number of intermediate channels; represents an element-wise complex multiplication.

[0017] Further, the time domain projection module is configured to convert the filtered frequency domain signal output by the dynamic complex spectrum filtering module to the time domain, and perform feature mapping on the converted time domain data to generate time domain output meeting the prediction length requirement; the time domain projection module comprises: a frequency domain inverse transform unit configured to perform inverse Fourier transform on the filtered frequency domain data to obtain corresponding filtered time domain data; a time domain mapping unit configured to input the filtered time domain data into a feedforward neural network for feature mapping, wherein the feedforward neural network comprises two layers of linear transformation structures, and is configured to map the time domain data from an intermediate representation space to a target output space corresponding to the prediction length.

[0018] Further, the processing process of the time domain projection module comprises: performing inverse real fast Fourier transform on the filtered frequency domain signal output by the dynamic complex spectrum filtering module to obtain corresponding time domain reconstruction data , which is generated by the formula: wherein, represents the filtered frequency domain signal; represents the time domain reconstruction data; represents the inverse real fast Fourier transform; inputting the time domain reconstruction data into a feedforward neural network comprising two layers of linear transformation structures for feature mapping to obtain output features corresponding to the prediction length, and the calculation expression of the feedforward neural network is: ​ in, , These represent the learnable weight matrices for the first and second linear transformations, respectively. , These represent the bias vectors for the first and second linear transformations, respectively. It is a linear rectified activation function with leakage parameters; This is a random deactivation operation.

[0019] Furthermore, the loss function of the DCSFNet prediction model is: in, To predict the number of samples; Indicates the first The actual observed values ​​of each sample; Indicates the first Predicted values ​​for each sample; Represents the regularization coefficient; This represents the learnable parameters in the DCSFNet prediction model; This represents the square of the L2 norm.

[0020] Compared with the prior art, the present invention has the following advantages: (1) In existing technologies, multivariate time series forecasting methods typically process the original sequence directly in the time domain, failing to effectively distinguish between long-term trends, periodic patterns, and high-frequency noise mixed within the sequence. This results in decreased prediction accuracy in data scenarios containing periodic interference or noise fluctuations. This invention performs a real-number fast Fourier transform on the input sequence using a frequency domain transformation module, converting the original time-domain data into a frequency-domain complex-valued spectrum representation containing amplitude and phase information. This allows the model to explicitly analyze different frequency components in the frequency domain, enhancing periodic features and distinguishing noise components. Through this technical feature, this invention enables the prediction model to more accurately identify the periodic structure and trend components of the sequence, significantly improving accuracy and stability in scenarios with significant periodicity, such as load forecasting and temperature forecasting.

[0021] (2) The existing frequency domain method usually uses a static filtering method (such as fixed low-pass filtering, pre-set frequency decomposition rules), which lacks adaptive ability for different scenarios and different variable characteristics, making it difficult to handle different intensity periodic fluctuations or correlation changes in device monitoring, energy fluctuation, multi-factor environmental prediction and other scenarios. The present application comprises a dynamic complex spectrum filtering module, which is composed of global feature extraction-dynamic weight generation-complex filter base fusion to form an input adaptive complex filtering mechanism. It can dynamically generate a dedicated complex filter for different input sequences and realize the joint modulation of amplitude and phase. This technical feature enables the model to automatically adjust the filtering strategy according to the dynamic rules of the input sequence, breaking through the limitations of the poor adaptability of existing static frequency domain methods, and significantly improving the adaptability of the model in energy management, industrial manufacturing, meteorological analysis and other multi-scenario, multi-variable structures. It avoids the problem of needing to design a separate filtering structure for different scenarios in traditional solutions.

[0022] (3) Most existing frequency domain processing methods ignore phase modulation and only filter the amplitude, resulting in a failure to maintain accurate alignment on the time axis during frequency spectrum reconstruction, causing position drift of periodic characteristics and seriously affecting the time-dependent structure of the prediction sequence. The present application uses a complex form of a learnable filter to simultaneously control amplitude and phase information, ensuring that the time structure is correct when the frequency domain filtered signal is transformed back to the time domain. This technical feature effectively avoids time alignment drift, making the prediction results more consistent at key time points such as periodic positions and peak valley times, and is particularly suitable for scenarios that require high accuracy in time positioning, such as early detection of device failure fluctuations, peak valley regulation of power load, etc.

[0023] (4) Existing deep learning time series models are prone to overfitting on high-dimensional multi-variable data, and lack a unified scale processing method. The numerical differences between input variables can cause gradient oscillation and unstable training, and it is difficult to restore the true scale during the prediction phase. The present application uses a reversible instance normalization module to calculate the mean and standard deviation for each variable along the time dimension, and performs inverse normalization after prediction. This not only unifies the numerical scale of the input sequence, improving the stability of model training, but also ensures that the output results can be restored to the true physical scale, making it more suitable for engineering deployment needs. This technical feature significantly improves the training difficulty caused by variable scale differences, enhances the model's transferability on datasets with different variable quantities and different time granularities, and provides better versatility for cross-domain applications. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The method flowchart in the embodiment of the present application; Figure 2 The overall architecture of the DCSFNet prediction model in the embodiment of the present application; Figure 3This is a schematic diagram of the internal structure and workflow of the dynamic complex spectrum filtering module in an embodiment of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0026] Example 1: like Figure 1 As shown in the figure, this embodiment provides a multivariate time series prediction method based on dynamic complex spectrum filtering. The specific implementation process of this method is as follows: Figure 3 As shown, the details are as follows: Step S1: Obtain multivariate time series data for the target scene; The target scenarios include energy management, industrial manufacturing, meteorological analysis, and power dispatching. Multivariate time series data includes time-stamped multivariate observation data acquired by multiple monitoring devices or data acquisition terminals in the target scenario. The multivariate observation data includes historical observations of the target variable to be predicted and historical observations of several auxiliary variables used to characterize equipment status, environmental conditions or load changes.

[0027] In this embodiment, the target scenario is load forecasting. The multivariate time series data includes historical load observations of various substations or electricity consumption nodes within the region, power equipment operating status data (such as transformer temperature, current, and voltage), environmental condition data (such as temperature, humidity, and wind speed), and other auxiliary variables related to load changes (such as holiday identifiers and electricity consumption category information). All of the above data are recorded in timestamp order to form a multivariate time series, which is used to describe the load change trend and the influence of multiple factors, providing complete input features for subsequent multivariate time series forecasting.

[0028] Step S2 Prediction: Determine the target variable and window length for prediction, and construct training, validation, and test sets based on multivariate time series data; The multivariate time series historical data is preprocessed, and the missing values ​​in the data are filled in by forward imputation (i.e., the valid data before the missing value is taken as the imputation value) to avoid the interference of incomplete data on model training. For custom datasets (such as industrial equipment data collected by users), the dataset is randomly divided in a 7:2:1 ratio, where the training set is used for learning model parameters, the validation set is used for tuning model hyperparameters, and the test set is used for evaluating the final performance of the model.

[0029] Step S3: Constructing the DCSFNet prediction model, as shown in Figure 2 The DCSFNet prediction model includes, in sequence, a reversible instance normalization module, a frequency domain conversion module, a dynamic complex spectrum filtering module, a time domain projection module, and an inverse reversible instance normalization module. The reversible instance normalization module is used to eliminate the distribution deviation of non-stationary time series data (such as the fluctuation of data mean and variance in different time periods). The core logic is as follows: for each time series segment of each variable channel, the mean and standard deviation are calculated along the time dimension; normalization is performed in the manner of “(original data-mean) / (standard deviation+small constant ε)”, where ε=10 -6 , to avoid calculation errors caused by a standard deviation of 0; to restore the original data distribution, the module stores the mean and standard deviation of each time series segment, and in the prediction stage, the inverse operation of “normalized result×standard deviation+mean” is used to restore the predicted value to the numerical range of the original data.

[0030] The normalization process is as follows: Wherein, represents the original observation value of the i-th variable channel at time step t; represents the mean of the i-th variable channel calculated along the time dimension, and the formula is: represents the standard deviation of the i-th variable channel calculated along the time dimension, and the formula is: Wherein, is the length of the current time series segment; is a numerical stability constant to prevent division by zero; represents the value of the i-th normalized variable channel at time step t. The frequency domain conversion module is used to convert time domain data into frequency domain data containing amplitude and phase information, providing a basis for dynamic complex spectrum filtering; the normalized time series segment is converted using real fast Fourier transform (RFFT) to obtain complex spectrum data. Each element of the complex spectrum data contains a real part and an imaginary part, corresponding to the amplitude and phase information of the frequency domain signal, respectively. The subsequent dynamic complex spectrum filtering module will perform full spectrum modulation based on this information.

[0031] The frequency domain conversion module is used to convert time domain data into frequency domain data containing amplitude and phase information, providing a basis for dynamic complex spectrum filtering; the normalized time series segment is converted using real fast Fourier transform (RFFT) to obtain complex spectrum data. Each element of the complex spectrum data contains a real part and an imaginary part, corresponding to the amplitude and phase information of the frequency domain signal, respectively. The subsequent dynamic complex spectrum filtering module will perform full spectrum modulation based on this information.

[0032] ​​​​​The frequency domain conversion module is used for converting the normalized multi-element time series data of the reversible instance from the time domain to the frequency domain, including amplitude and phase information, and specifically including the following steps: normalizing the time series segment performing real fast Fourier transform to obtain frequency domain complex spectrum data , the formula is: wherein, represents the normalized multi-element time series data of the reversible instance; represents the real fast Fourier transform; represents the frequency domain complex spectrum data, including amplitude information and phase information; the real part of the frequency domain complex spectrum data corresponds to the amplitude information of the frequency component, and the imaginary part corresponds to the phase information of the frequency component.

[0033] The dynamic complex spectrum filtering module is the core of the DCSFNet prediction model, and is used for adaptively processing the frequency domain data while modulating the amplitude and the phase. The construction process of the dynamic complex spectrum filtering module includes four subunits: a global feature extraction unit adopts a 1D convolution layer + a global adaptive pooling layer to extract the global features of the time domain data; a dynamic weight generation unit: the extracted global features are input into a multi-layer perceptron (MLP), and the MLP includes two linear transformations and a StarReLU activation function for enhancing the nonlinear expression capability; a dynamic filter synthesis unit: a plurality of preset learnable complex filter bases are adopted, and the parameters are initialized in a normal distribution to ensure that the frequency responses of the filter bases are different in the initial state; based on the dynamic weight and the filter base, a dynamic complex filter is obtained through Einstein summation fusion, and the filter can adapt to the feature difference of the current input time series data; a frequency domain filtering unit: the complex spectrum data output by the frequency domain conversion module is multiplied by the dynamic complex filter through a broadcast mechanism element by element, the amplitude and the phase are modulated at the same time, and then the sum of the filtered frequency domain data along the dimension of the intermediate channel number is obtained.

[0034] The dynamic complex spectrum filtering module includes: a global feature extraction unit, configured to process input time domain data through a one-dimensional convolution layer and a global adaptive pooling layer to extract global features; a dynamic weight generation unit, configured to input the global features into a multi-layer perceptron (MLP) to generate dynamic weights, and the MLP includes two linear transformations and is processed through a StarReLU activation function; a dynamic complex filter synthesis unit, configured to generate a dynamic complex filter based on the dynamic weight and a plurality of preset learnable complex filter bases, and the dynamic complex filter base is initialized in a normal distribution; A frequency domain filtering unit is configured to multiply the frequency domain complex-valued spectrum data output by the frequency domain conversion module with the dynamic complex filter element by element, and sum along the intermediate channel dimension to obtain a filtered frequency domain signal.

[0035] The dynamic complex spectrum filtering module has a processing procedure including: The frequency domain complex-valued spectrum data is converted back to time domain data by an inverse real fast Fourier transform , and global features are extracted by a one-dimensional convolution layer and a global average pooling , and the formula is: wherein, is the time domain data; represents a one-dimensional convolution operation, and the kernel size is 3 and padding=1; represents that the global average pooling is performed on the time dimension of the convolution output; is the global feature; The global feature is input into a multi-layer perception (MLP) to generate a dynamic weight , and the formula is: wherein, is the dynamic weight; represents the multi-layer perception; is an activation function; Based on the dynamic weight , a dynamic complex filter is generated with K learnable complex filter bases , and the formula is: wherein, represents the generated dynamic complex filter; represents a complex filter representation along the frequency domain dimension; represents the learnable complex filter base; The frequency domain complex-valued spectrum data is multiplied with the dynamic complex filter element by element, and summed along the intermediate channel dimension to obtain a filtered frequency domain signal , and the formula is: wherein, is the number of intermediate channels; represents element-wise complex multiplication.

[0036] In summary, the DCSFNet prediction model based on dynamic complex spectrum filtering constructed by the application is established on the basis of deep neural network research on frequency domain adaptive feature extraction and time domain projection fusion. The dynamic complex spectrum filtering module solves the problems of weak frequency spectrum decomposition ability of traditional time domain methods and poor adaptability of static frequency domain methods. The reversible instance normalization is used to eliminate data distribution deviation. The lightweight network structure is combined to achieve "high precision-high efficiency" balance. The loss function and evaluation index used are the common standards in the field of time series prediction. In view of the shortcomings of the existing prediction methods, the application fully utilizes the frequency spectrum characteristics of multivariate time series, and proposes a hybrid prediction framework of "frequency domain dynamic filtering-time domain accurate projection". The framework considers the multi-spectrum components (trend, period, noise) of time series data in feature extraction. Through the fusion of complex filter base and dynamic weight, full-spectrum amplitude-phase collaborative modulation is realized, and the space-time dependence of oil temperature change is fully tapped. The network architecture can effectively extract deep spectrum features of multivariate time series data and process abnormal fluctuation scenarios that are difficult to predict by traditional models. The application has the advantages of capturing multi-spectrum characteristics of multivariate time series data, adapting to different prediction length requirements, and balancing precision and efficiency. It can be popularized to industrial equipment state prediction, meteorological element prediction and other multivariate time series scenarios, and has practical application value and prospect.

[0037] The time domain projection module is used for converting the filtered frequency domain data back to the time domain and mapping to the prediction length. First, the filtered frequency domain data output by the dynamic complex spectrum filtering module is converted back to the time domain through inverse Fourier transform to obtain filtered time domain data, which has completed high-frequency noise suppression and key spectrum component reservation. Then, a two-layer feedforward neural network is used to map the filtered time domain data to the prediction length and perform inverse reversible instance normalization module on the predicted data to restore the numerical distribution range of the original data, completing the initialization of the DCSFNet prediction model.

[0038] The time domain projection module includes the following processing process: The filtered frequency domain signal output by the dynamic complex spectrum filtering module Inverse real fast Fourier transform is performed to obtain corresponding time domain reconstruction data The formula is: Among them, The filtered frequency domain signal is represented by f (t) ; The time domain reconstruction data is represented by x (t) ; The inverse real fast Fourier transform is represented by IFFT; The time domain reconstruction data is input into a feedforward neural network including two linear transformation structures for feature mapping to obtain output features corresponding to the prediction length. The calculation expression of the feedforward neural network is: Among them, , respectively represent the learnable weight matrices of the first layer linear transformation and the second layer linear transformation; , respectively represent the bias vectors of the first layer linear transformation and the second layer linear transformation; is a linear rectifier activation function with a leaky parameter; is a random dropout operation.

[0039] The inverse reversible instance normalization module, the processing process comprises: First, the mean and standard deviation of each variable channel along the time dimension stored by the reversible instance normalization module and a constant for numerical stability are obtained, then the normalized multivariate time series data is inversely transformed by variable channel, the data is restored to the original numerical scale by multiplying the normalized numerical value by the standard deviation of the corresponding channel and adding the mean, finally the restored multivariate time series is output, which is used to generate the final prediction result or subsequent analysis.

[0040] Step S4: based on the constructed training set, validation set and test set, the DCSFNet prediction model is trained to obtain the trained DCSFNet prediction model; The DCSFNet prediction model, the loss function is: wherein, is the number of prediction samples; represents the real observed value of the i-th sample; represents the predicted value of the i-th sample; represents the regularization coefficient; represents the learnable parameters in the DCSFNet prediction model; represents the square of the L2 norm. Step S5: based on the trained DCSFNet prediction model, according to the determined predicted target variable and window length, the multivariate time series prediction is realized.

[0041] Embodiment 2:

[0042] Embodiment 2: ​The embodiments also provide a dynamic complex spectrum filtering based multi-variate time series prediction device, comprising a memory, a processor, and a program stored in the memory, characterized in that the processor implements the foregoing method when executing the program. The device processor includes a central processing unit (CPU) that can perform various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for device operation (such as preprocessed data sets, model parameter files) can also be stored. The CPU, ROM, and RAM are connected to each other through a bus. An input / output (I / O) interface is also connected to the bus. Various components in the device are connected to the I / O interface, including: an input unit, such as a keyboard and a mouse (for setting model hyperparameters and selecting prediction lengths); an output unit, such as a liquid crystal display and a printer (for displaying prediction curves and outputting evaluation reports); a storage unit, such as a solid state disk and a mechanical hard disk (for persistently storing data sets and models); and a communication unit, such as an Ethernet card and a wireless communication module (for obtaining transformer data from a power grid monitoring system in real time or pushing prediction results to a dispatch center). The communication unit allows the device to exchange information / data with other devices through a computer network (such as a power grid intranet). The processing unit performs various methods and processes described above, such as steps S1 to S23 in the foregoing embodiments. For example, in some embodiments, the steps in the foregoing embodiments can be implemented as a computer software program tangibly embodied in a machine-readable medium (such as the storage unit). In some embodiments, part or all of the computer program can be loaded and / or installed on the device via the ROM and / or the communication unit. When the computer program is loaded into the RAM and executed by the CPU, one or more steps of the methods described above can be performed. Alternatively, in other embodiments, the CPU can be configured to perform the foregoing methods by any other appropriate means (for example, with the help of firmware). The functions described above can be at least partially performed by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that can be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), system on a chips (SOCs), complex programmable logic devices (CPLDs), and the like.

[0043] If the above functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or the parts of the present application that essentially contribute to the prior art or the parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0044] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A multivariate time series prediction method based on dynamic complex spectrum filtering, characterized in that, Includes the following steps: Step S1: Obtain multivariate time series data for the target scene; Step S2 Prediction: Determine the target variable and window length for prediction, and construct training, validation and test sets based on the multivariate time series data; Step S3: Construct a DCSFNet prediction model, which includes a reversible instance normalization module, a frequency domain transformation module, a dynamic complex spectrum filtering module, a time domain projection module, and an inverse reversible instance normalization module connected in sequence. Step S4: Based on the constructed training set, validation set and test set, train the DCSFNet prediction model to obtain the trained DCSFNet prediction model; Step S5: Based on the trained DCSFNet prediction model, multivariate time series prediction is achieved according to the determined target variable and window length.

2. The multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 1, characterized in that, The target scenarios include energy management scenarios, industrial manufacturing scenarios, meteorological analysis scenarios, and power dispatching scenarios; The multivariate time series data includes time-stamped multivariate observation data acquired by multiple monitoring devices or data acquisition terminals in the target scenario. The multivariate observation data includes historical observation values ​​of the target variable to be predicted and historical observation values ​​of several auxiliary variables used to characterize equipment status, environmental conditions, or load changes.

3. The multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 1, characterized in that, The reversible instance normalization module is used to normalize the input multivariate time series data according to the variable channels. The normalization process includes: calculating statistical features along the time dimension for the time series segment of each variable channel and performing numerical standardization on the time series segment based on the statistical features.

4. The multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 3, characterized in that, The normalization process is formulated as follows: in, Indicates the first Each variable channel at time step The original observations; Represents the first calculated along the time dimension The mean of each variable channel is given by the following formula: Represents the first calculated along the time dimension The standard deviation of each variable channel is given by the formula: in, The length of the current time segment; To prevent the numerical stability constant from being divided by zero; Represents the normalized i-th Each variable channel at time step The value.

5. The multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 1, characterized in that, The frequency domain conversion module is used to convert the reversible instance normalized multivariate time series data from the time domain to the frequency domain, including amplitude and phase information, specifically including the following steps: For normalized time series segments Perform a real-number fast Fourier transform to obtain the complex-valued spectrum data in the frequency domain. The formula is: in, This represents multivariate time series data after reversible instance normalization. Represents the Fast Fourier Transform of real numbers; This represents complex-valued spectrum data in the frequency domain, including amplitude and phase information; complex-valued spectrum data in the frequency domain The real part corresponds to the amplitude information of the frequency component, and the imaginary part corresponds to the phase information of the frequency component.

6. The multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 1, characterized in that, The dynamic complex spectrum filtering module is used to adaptively process the frequency domain complex value spectrum data obtained by the frequency domain transformation module, while modulating the amplitude and phase, extracting the global spectral features of the multivariate time series and suppressing high-frequency noise. The dynamic complex spectrum filtering module includes: The global feature extraction unit is used to process the input temporal data through a one-dimensional convolutional layer and a global adaptive pooling layer to extract global features; The dynamic weight generation unit is used to input global features into a multilayer perceptron (MLP) to generate dynamic weights. The MLP includes two linear transformations and is processed by the StarReLU activation function. A dynamic complex filter synthesis unit is used to generate a dynamic complex filter based on dynamic weights and multiple preset learnable complex filter bases, wherein the dynamic complex filter bases are initialized using a normal distribution. The frequency domain filtering unit is used to multiply the frequency domain complex-valued spectrum data output by the frequency domain conversion module with the dynamic complex filter element by element, and sum along the intermediate channel dimension to obtain the filtered frequency domain signal.

7. A multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 6, characterized in that, The dynamic complex spectrum filtering module includes the following processing steps: frequency domain complex value spectrum data The data is obtained by converting the inverse real fast Fourier transform back to the time domain. Global features are extracted through one-dimensional convolutional layers and global average pooling. The formula is: in, For time-domain data; This represents a one-dimensional convolution operation with a kernel size of 3 and padding=1. This indicates that global average pooling is performed on the convolution output over time. For global features; global features Input to a multilayer perceptron (MLP) to generate dynamic weights The formula is: in, Dynamic weights; Represents a multilayer perceptron; For activation functions; Based on dynamic weights and K A learnable complex filter basis The formula for generating a dynamic complex filter is: in, This represents the generated dynamic complex filter; Represents a complex filter along the frequency domain dimension; Indicates the first A learnable complex filter basis; frequency domain complex value spectrum data With dynamic complex filters Element-wise multiplication and summation along the middle channel dimension yields the filtered frequency domain signal. The formula is: in, This refers to the number of intermediate channels; This represents element-wise complex multiplication.

8. The multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 1, characterized in that, The time-domain projection module is used to convert the filtered frequency domain signal output by the dynamic complex spectrum filtering module to the time domain, and perform feature mapping on the converted time-domain data to generate a time-domain output that meets the prediction length requirements. The time-domain projection module includes: The frequency domain inverse transform unit is used to perform an inverse Fourier transform on the filtered frequency domain data to obtain the corresponding filtered time domain data; The temporal mapping unit is used to input the filtered temporal data into the feedforward neural network for feature mapping. The feedforward neural network includes a two-layer linear transformation structure, which is used to map the temporal data from the intermediate representation space to the target output space corresponding to the prediction length.

9. A multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 8, characterized in that, The time-domain projection module's processing includes: The filtered frequency domain signal output by the dynamic complex spectrum filtering module Perform an inverse real-number fast Fourier transform to obtain the corresponding time-domain reconstructed data. The formula is: in, This represents the filtered frequency domain signal; Represents time-domain reconstructed data; This represents the inverse real fast Fourier transform; The temporal reconstructed data is input into a feedforward neural network containing a two-layer linear transformation structure for feature mapping to obtain the output features corresponding to the predicted length. The calculation expression of the feedforward neural network is as follows: in, , These represent the learnable weight matrices for the first and second linear transformations, respectively. , These represent the bias vectors for the first and second linear transformations, respectively. It is a linear rectified activation function with leakage parameters; This is a random deactivation operation.

10. A multivariate time series prediction method based on dynamic complex spectrum filtering according to claim 1, characterized in that, The loss function of the DCSFNet prediction model is: in, To predict the number of samples; Indicates the first The actual observed values ​​of each sample; Indicates the first Predicted values ​​for each sample; Represents the regularization coefficient; This represents the learnable parameters in the DCSFNet prediction model; This represents the square of the L2 norm.

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