Time sequence prediction enhancement method based on frequency spectrum segmentation and migration
By using spectrum segmentation and transfer methods to transform high-frequency components into low-frequency representations, the problem of high-frequency signal capture in time series prediction by deep learning models is solved, achieving high-precision time series prediction that is applicable to various prediction architectures.
Patent Information
- Application Number
- CN202511471698.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-15
- Publication Date
- 2026-02-17
AI Technical Summary
Existing deep learning models struggle to effectively capture high-frequency signals in time series forecasting, resulting in limited predictive performance for key high-frequency patterns such as abrupt changes and spikes.
By using spectrum segmentation and transfer methods, high-frequency components are transformed into low-frequency equivalent representations. An analytic signal is constructed using a differentiable bandpass filter and Hilbert transform, and then losslessly shifted down in the frequency domain. A prediction model with a self-attention mechanism is then used for joint training and prediction. Finally, the full-band prediction results are reconstructed in the time domain.
It significantly improves the prediction accuracy of high-frequency patterns, reduces the difficulty of optimizing high-frequency signals for model training, increases the training convergence speed, and provides a new perspective on representation learning for deep learning models, applicable to a variety of existing prediction architectures.
Smart Images
Figure CN121542713A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to time series analysis and prediction technology, belonging to the field of deep learning algorithms, specifically a time series prediction enhancement method based on spectrum segmentation and transfer learning. Background Technology
[0002] In recent years, time series data has been widely used in finance, healthcare, environmental monitoring, and other fields. In these scenarios, the high-frequency components of time series data often correspond to instantaneous and critical signals, such as sudden fluctuations in financial markets, rapid changes in vital signs, or sudden environmental disturbances detected by sensors. Accurate modeling of these high-frequency patterns is crucial for timely and precise prediction and response.
[0003] However, existing deep learning models still face significant challenges in capturing such high-frequency signals. Deep neural networks exhibit spectral bias during training, meaning they tend to preferentially fit low-frequency components while lacking the ability to learn high-frequency signals. This characteristic significantly limits the effectiveness of existing methods in capturing key high-frequency patterns such as abrupt changes and spikes.
[0004] Therefore, there is an urgent need for a time series representation and modeling method that can effectively alleviate the difficulties of high-frequency learning in deep neural networks and improve the prediction accuracy of high-frequency patterns, so as to break through the limitations of existing methods and meet the demand for high-precision prediction in complex application scenarios. Summary of the Invention
[0005] To address the inherent limitation of existing deep learning models in effectively capturing high-frequency signals during time series prediction, this invention proposes a frequency domain enhancement framework based on spectrum segmentation and transfer. By designing a differentiable frequency band segmentation module and a lossless spectrum downshifting mechanism, the high-frequency components in the original signal are transformed into a low-spectral equivalent representation, thereby overcoming the learning bottleneck of model spectrum bias. This framework is characterized by model independence, lightweight structure, and ease of integration, and can significantly improve prediction accuracy.
[0006] This invention is based on the following technical solution:
[0007] A time series prediction enhancement method based on spectrum segmentation and migration is characterized by the following steps:
[0008] S1. Perform a discrete Fourier transform on the input time series to obtain its frequency domain representation;
[0009] S2. Adaptive frequency band segmentation is performed on the frequency domain representation using a set of differentiable bandpass filters to obtain multiple non-overlapping continuous sub-frequency bands, wherein each sub-frequency band covers a specific frequency range;
[0010] S3. For each sub-band, an analytical signal is constructed through Hilbert transform, and complex exponential modulation is performed based on the lower cutoff frequency of the sub-band to losslessly shift the spectrum of the sub-band to the low-frequency region, forming a low-frequency representation that is easy for the model to learn;
[0011] S4. Combine all the sub-band signals with downshifted spectrum obtained in step S3, input them into the prediction model for joint training and prediction, and obtain the future multi-step prediction results for each frequency band;
[0012] S5. Band-limited filtering is performed on the prediction results of each sub-band output by the prediction model using the same differentiable bandpass filter as in step S2 to suppress high-frequency noise generated during the prediction process;
[0013] S6. Apply an inverse complex exponential modulation (IEP) to each sub-band prediction signal after filtering, with the frequency opposite to that in step S3, and shift its spectrum up to the frequency position corresponding to the original sub-band.
[0014] S7. Superimpose all the sub-band prediction signals after spectrum recovery in the time domain to reconstruct the final full-band time series prediction result.
[0015] Furthermore, the differentiable bandpass filter is as follows:
[0016]
[0017] in, To preserve the gradient flow of the sigmoid function, To control the hyperparameters of the transition zone steepness, and The respective The lower and upper cutoff frequencies of the sub-band, where k is the frequency index, representing the corresponding discrete frequency point number in the frequency domain.
[0018] Furthermore, the lower cutoff frequency and upper cutoff frequency The calculation is dynamically based on the number of subbands n and the sequence length N, specifically as follows:
[0019]
[0020] in, .
[0021] Furthermore, the frequency domain representation of the i-th sub-band is as follows:
[0022]
[0023] Performing an inverse Fourier transform on it yields the subband time-domain signal. .
[0024] Furthermore, the construction of the analytical signal in step S3 is described as follows:
[0025]
[0026] in, Represents the Hilbert transform. It represents the imaginary unit.
[0027] Furthermore, in step S3, the frequency of the complex exponential modulation is the lower cutoff frequency of the sub-band.
[0028]
[0029] The signal after the downshift signal is:
[0030]
[0031] in, This indicates taking the real part of a complex number.
[0032] Furthermore, in step S4, the prediction model is a Transformer model or variant based on a self-attention mechanism, a recurrent neural network, or a convolutional neural network. The prediction model processes all downshifted sub-band signals simultaneously and outputs a prediction sequence with the same number of sub-bands.
[0033] Compared with the prior art, the beneficial effects of the present invention are:
[0034] (1) The spectrum segmentation and downshifting strategy alleviates the spectrum bias problem in high-frequency component modeling of deep neural networks, enabling the model to learn high-frequency patterns more fully, thereby improving prediction accuracy. It reduces the optimization difficulty of the model when training high-frequency signals and improves the training convergence speed.
[0035] (2) The spectrum segmentation and downshifting strategy adopts non-orthogonal decomposition, which supplements the orthogonal characteristics of the self-attention mechanism in the feature space, thus providing a new perspective and capability for deep learning models to learn representations in time series.
[0036] (3) This framework is a model-independent design that can be plugged and played into various existing prediction architectures without changing the core network structure, making it easy to deploy in practice. Attached Figure Description
[0037] Figure 1 This is a flowchart of the time series prediction enhancement method based on spectrum segmentation and migration according to the present invention. Detailed Implementation
[0038] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the scope of protection of the present invention.
[0039] Please see Figure 1 , Figure 1 This is a flowchart of the time series prediction enhancement method based on spectrum segmentation and migration according to the present invention. As shown in the figure, a time series prediction enhancement method based on spectrum segmentation and migration includes the following steps:
[0040] (1) Perform Discrete Fourier Transform (DFT) on the target time series to obtain the frequency domain representation, which is used to analyze its energy distribution in different frequency ranges.
[0041] (2) Based on a pre-defined bandpass filter bank, the spectrum of the input signal is divided into multiple sub-bands. Each bandpass filter is implemented using a differentiable sigmoid function to preserve gradient information and improve training stability, ensuring that each sub-band covers a specific frequency range that does not overlap.
[0042] (3) For each sub-band signal, an analytical signal is constructed using Hilbert transform, and the sub-band is shifted to a low-frequency region by frequency modulation, thereby reducing the learning difficulty of high-frequency components and enabling subsequent prediction models to model time-dependent features more efficiently.
[0043] (4) Input all the downshifted sub-band signals into the prediction model (which can be Transformer and its variants, recurrent neural networks or other time series prediction backbone networks) to predict the signal change trend of each sub-band within the future time window and output a prediction sequence that matches the number of sub-bands.
[0044] (5) The prediction results are filtered and the high-frequency noise introduced during the prediction process is removed by using a bandwidth-limited filter to ensure the smoothness and stability of the reconstructed signal.
[0045] (6) Perform a frequency upshift operation on the shaped low-frequency prediction result to restore it to the original spectrum position, and obtain a predicted sub-band signal that is consistent with the spectrum structure of the input signal.
[0046] (7) All predicted sub-band signals restored to their original frequency positions are superimposed in the time domain to obtain a complete prediction result, thereby realizing full-band prediction output of the input time series.
[0047] Example:
[0048] 1. Adaptive spectrum segmentation
[0049] First, the input timing signal 101 (e.g., sequence length N=1024) Perform Discrete Fourier Transform (DFT) to obtain the corresponding frequency domain information 102.
[0050] Differentiable filter banks are used to divide the frequency band. ( =0,1,... The bandpass filter response of the subband is:
[0051] in, To preserve the gradient flow of the sigmoid function, To control the steepness of the transition band, the upper and lower cutoff frequencies of each sub-band are set from... and Sure, = This process corresponds to Figure 1 Module ① converts the original signal into a frequency domain multi-subband representation 103.
[0052] No. The frequency domain signal of each sub-band is expressed as: ;right Performing the inverse Fourier transform (iDFT) yields the subband time-domain signal. 104.
[0053] 2. High-frequency components shift downwards:
[0054] For each sub-band signal 104, its analytic signal is constructed using the Hilbert transform. The formula is as follows:
[0055]
[0056] in, This represents the Hilbert transform.
[0057] Then, a critical spectrum migration operation is performed. Figure 1 Module ②): Applying a frequency of to the analytic signal. Complex exponential modulation, taking the real part, generates a downshifted signal. 105. This step shifts the effective frequency domain range 103 of each sub-band towards the low-frequency region 106, solving the problem of difficult high-frequency component modeling.
[0058] 3. Multi-band joint prediction:
[0059] All down-shifted subband signals 105 are concatenated along the feature dimension to form an enhanced input feature matrix.
[0060] Input the feature matrix into the prediction model 107. This embodiment uses the Transformer model as the prediction backbone network, and its input dimension is... The output dimension is n×N, where H=96 is the prediction step size. The prediction model outputs the prediction results for each subband in the next H steps. 108, This lays the structural foundation for subsequent reconstruction.
[0061] 4. Spectrum Reconstruction Optimization
[0062] For the prediction results of each sub-band output by the prediction model, the same bandpass filter as in the segmentation stage is used. Bandwidth-constrained filtering is performed to suppress high-frequency noise generated during the prediction process. Figure 1 (Module ③) to obtain the subband signal 108 that is consistent with the spectrum range of the downshifted subband.
[0063] Perform inverse spectrum shift on the filtered signal 108 ( Figure 1 Module ④), applying inverse complex exponential modulation Taking the real part yields the signal recovered to the original frequency band: 109.
[0064] Finally, through time-domain superposition Reconstructed full-band prediction results 110 ( Figure 1 Module ⑤).
[0065] The spectral decomposition and frequency shifting method of this invention is not only applicable to univariate time series prediction, but can also be extended to multivariate scenarios. By independently performing the above steps for each dimension and performing multidimensional splicing in the model input and output stages, accurate prediction of high-dimensional, multi-frequency mixed time series can be achieved.
[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A time series prediction enhancement method based on spectrum segmentation and migration, characterized in that, The method comprises the following steps: S1. Discrete Fourier transform is performed on the input time series to obtain a frequency domain representation; S2. A set of differentiable band-pass filters is used to adaptively segment the frequency domain representation into a plurality of non-overlapping continuous sub-bands, each of which covers a specific frequency range; S3. For each sub-band, an analytic signal is constructed by Hilbert transform, and a complex exponential modulation is performed based on the lower cutoff frequency of the sub-band to downshift the frequency spectrum of the sub-band to a low frequency region without loss, forming a low frequency representation easy for model learning; S4. The sub-band signals after frequency spectrum downshift obtained in step S3 are combined and input into a prediction model for joint training and prediction to obtain future multi-step prediction results corresponding to each frequency band; S5. The sub-band prediction results output by the prediction model are band-limited filtered by the same differentiable band-pass filter as in step S2 to suppress high-frequency noise generated in the prediction process; S6. The filtered sub-band prediction signals are subjected to reverse complex exponential modulation opposite to the modulation frequency in step S3 to upshift their frequency spectrum to the frequency position corresponding to the original sub-band; S7. The sub-band prediction signals after frequency spectrum recovery are superimposed in the time domain to reconstruct the final full-band time series prediction result.
2. The time series prediction enhancement method based on spectrum segmentation and migration according to claim 1, characterized in that, The differentiable band-pass filter is as follows: ； in, To preserve the gradient flow of the sigmoid function, To control the hyperparameters of the transition zone steepness, and The respective The lower and upper cutoff frequencies of the sub-band, where k is the frequency index, representing the corresponding discrete frequency point number in the frequency domain.
3. The time series prediction enhancement method based on spectrum segmentation and migration according to claim 2, characterized in that, The lower cutoff frequency and the upper cutoff frequency According to the dynamic calculation of the sub-band number n and the sequence length N, specifically: ； wherein .
4. The time series prediction enhancement method based on spectrum segmentation and migration according to claim 1, characterized in that, The frequency domain expression of the i-th sub-band is ； Inverse Fourier transforming the same gives a subband time domain signal .
5. The method of claim 1, wherein, The analytic signal constructed in step S3 is expressed as: ； wherein denotes the Hilbert transform, represents the imaginary unit.
6. The time series prediction enhancement method based on spectrum segmentation and migration according to claim 1, characterized in that, The frequency of the complex exponential modulation in step S3 is the lower cutoff frequency of the sub-band ； The signal after downshifting is: ； wherein denotes taking the real part of a complex number.
7. The time series prediction enhancement method based on spectrum segmentation and migration according to claim 1, characterized in that, The prediction model in step S4 is a Transformer model based on a self-attention mechanism and variants, a recurrent neural network or a convolutional neural network, which simultaneously processes all downshifted sub-band signals and outputs the same number of prediction sequences as the number of sub-bands.