Non-stationary signal decomposition method based on deep learning

Abstract

The invention provides a non-stationary signal decomposition method based on deep learning, and the method specifically comprises the following steps: generating a synthetic sample signal containing a non-stationary main signal and stationary noise at the same time through setting a physically interpretable multi-scale signal model; performing data set division and feature normalization processing on the samples to form a training set, a verification set and a test set; constructing a lightweight deep learning signal decomposition model, and realizing end-to-end mapping from time sequence input to component output; a composite loss function and a self-adaptive optimization strategy are adopted for training, and stable model parameters with generalization ability are obtained; and verifying the decomposition performance by using a test set or real observation data, and outputting a non-stationary signal and a stationary noise component. According to the technical scheme, the problems that in the prior art, a stable and reliable decomposition result is difficult to obtain, and efficient distinguishing of different components such as trend, period and noise is difficult to achieve are solved.

Description

Technical Field

[0001] This invention relates to the field of signal decomposition, and more specifically to a non-stationary signal decomposition method based on deep learning. Background Technology

[0002] Signal decomposition techniques are a crucial foundation for time-series data analysis and modeling, widely applied in fields such as climate change, ocean dynamics, earthquake monitoring, and economic fluctuation analysis. By decomposing complex signals into components with different time-scale characteristics, it is possible to effectively identify trend changes, periodic oscillations, and random disturbances, thereby revealing the dominant dynamic characteristics and underlying mechanisms of the system. Existing signal decomposition methods mainly include wavelet transform, empirical mode decomposition, ensemble empirical mode decomposition, complete ensemble empirical mode decomposition, and variational mode decomposition. These methods can extract signal components at different scales to a certain extent, but they generally suffer from high parameter sensitivity, severe mode aliasing, susceptibility to noise interference, and low computational efficiency. Especially when dealing with complex non-stationary signals with wide-spectrum characteristics, their decomposition results often fail to accurately reflect the true physical composition.

[0003] In the field of Earth system science, observational and simulated time-series signals typically contain multiple components, including long-term trends (such as global warming), low- to mid-frequency oscillations (such as interannual or decadal variations), and high-frequency random disturbances (such as weather noise). These signals exhibit significant non-stationarity and multi-scale characteristics, making traditional decomposition methods prone to component mixing or over-filtering when trends, periods, and noise coexist. This hinders the accurate identification and separation of physical components from different sources, thus affecting the quantitative analysis of natural variability and forced trends.

[0004] With the rapid development of deep learning technology, neural network-based signal analysis methods have been gradually introduced into the field of non-stationary signal processing. Models such as convolutional neural networks, Fourier neural operators, and iterative residual convolutional neural networks have demonstrated powerful nonlinear modeling and adaptive learning capabilities in tasks such as time series prediction, signal denoising, and feature extraction. Unlike traditional methods, these models can directly learn complex time series patterns from data within an end-to-end framework, without the need for manually setting filter parameters or predefined modal structures, thus improving the flexibility and generalization of decomposition to a certain extent. However, most existing deep learning models primarily aim to improve prediction accuracy or denoising performance, lacking explicit decomposition mechanisms for non-stationary signals. They often only obtain overall reconstruction results and cannot adaptively distinguish different signal components such as trends, rates of change, and noise in the model structure or loss design, making it difficult for the decomposition results to directly reflect the multi-scale characteristics of the signal.

[0005] In summary, current signal decomposition techniques still have significant limitations when dealing with complex non-stationary signals: traditional methods are limited by parameter sensitivity, mode mixing, and noise interference, making it difficult to obtain stable and reliable decomposition results; while deep learning methods have strong fitting capabilities and end-to-end modeling advantages, they lack structural design and mechanism support for signal component separation, making it difficult to efficiently distinguish different components such as trends, periods, and noise.

[0006] Therefore, there is a need for a method that can combine adaptive features from deep learning to achieve adaptive separation of multi-scale components of non-stationary signals in an end-to-end framework, so as to improve the accuracy, robustness and automation of signal decomposition. Summary of the Invention

[0007] The main objective of this invention is to provide a non-stationary signal decomposition method based on deep learning, so as to solve the problems in the prior art of obtaining stable and reliable decomposition results and efficiently distinguishing different components such as trends, periods and noise.

[0008] To achieve the above objectives, this invention provides a non-stationary signal decomposition method based on deep learning, specifically including the following steps: S1 generates a synthetic sample signal that simultaneously contains non-stationary main signals and stationary noise by setting a physically interpretable multi-scale signal model.

[0009] S2 performs dataset partitioning and feature normalization on the samples to form training, validation, and test sets.

[0010] S3 constructs a lightweight deep learning signal decomposition model to achieve end-to-end mapping from time series input to component output.

[0011] S4 employs a composite loss function and an adaptive optimization strategy for training to obtain stable signal decomposition model parameters with generalization capabilities.

[0012] S5 verifies the decomposition performance of the signal decomposition model using test sets or real observation data, and outputs non-stationary signal and stationary noise components.

[0013] Furthermore, step S1 specifically includes the following steps: S1.1 simulates non-stationary signals at different time scales using preset mathematical functions, including: long-term trend signals, interdecadal signals, interannual signals, intra-seasonal signals, and synoptic-scale signals. Represented as: ; in, Indicates different times Components at scale For weight parameters, This represents the number of components superimposed in the current sample.

[0014] S1.2, introduce random noise to simulate uncertainties and interference factors in the actual observation environment. The noise includes: Gaussian white noise and non-Gaussian noise. Represented as: ,in, For noise variance, The distribution follows a zero-mean normal distribution; non-Gaussian noise is defined as a nonlinear random function. The noise term is obtained by weighting Gaussian noise and non-Gaussian noise. : ; in, This is the weighting factor.

[0015] S1.3, non-stationary signals are incorporated with random disturbances to obtain synthesized sample signals. : .

[0016] Furthermore, step S2 specifically includes the following steps: S2.1, the sample signal generated by simulation As input samples, Corresponding non-stationary signal and noise terms As supervisory labels, they constitute a complete sample. .

[0017] S2.2 employs a random sampling strategy to ensure that each sample has differences in signal type, amplitude range, noise intensity, and spectral structure. Subsequently, all samples are divided into training set, validation set, and test set according to the proportions.

[0018] S2.3, for each time series sample signal Standardization process: ; in, For the first One sample signal, The mean, Standard deviation The standardized sample signal.

[0019] Furthermore, the signal decomposition model in step S3 includes: a feature extraction module, an encoder, a decoder, a bottleneck residual unit at the bottom of the network, and an output prediction module. The original time input is processed by the feature extraction module, which performs stepwise compression of the temporal resolution and multi-scale feature extraction through the encoder. Then, the time resolution is restored through the decoder, and finally, the estimated result is output through the output prediction module.

[0020] Furthermore, the feature extraction module includes: interconnected one-dimensional convolutional layers, grouped normalization and GeLU activation layers, and lightweight multi-scale dilated convolutional residual units; the output prediction module includes: interconnected one-dimensional convolutional layers, grouped normalization and GeLU activation layers, channel fusion one-dimensional convolutional layers, and one-dimensional convolutional layers.

[0021] Furthermore, the encoder includes: interconnected downsampling one-dimensional convolutional layers, grouped normalization and GeLU activation layers, and lightweight multi-scale dilated convolutional residual units; the decoder includes: interconnected linear interpolation upsampling layers, one-dimensional convolutional layers, channel fusion one-dimensional convolutional layers, and lightweight multi-scale dilated convolutional residual units; the bottleneck residual unit at the bottom of the network includes multiple lightweight multi-scale dilated convolutional residual units.

[0022] Furthermore, the total loss function in step S4 Represented as: ; in, This represents the reconstruction error between the signal predicted by the signal decomposition model and the actual non-stationary signal. This indicates the deviation between the predicted noise and the reference noise; Used to constrain the consistency of the distribution of predicted noise and actual noise at the probability density function level. Used to constrain the overall statistical consistency between the two at the level of cumulative distribution function; , , , These are the weighting coefficients.

[0023] The present invention has the following beneficial effects: 1. A multi-scale non-stationary signal and noise dataset with realistic decomposition labels was established, providing high-quality training samples for the model and realizing signal decomposition modeling under supervised learning conditions.

[0024] 2. A multi-scale dilated convolution module based on depthwise separable convolution was designed, which can capture features at different time scales with low computational cost and achieve efficient representation of non-stationary signals.

[0025] 3. By introducing probability distribution consistency constraints on the basis of traditional reconstruction error, the model can maintain both temporal accuracy and statistical rationality during the optimization process, thereby improving the stability of the decomposition results.

[0026] 4. The model can automatically identify and separate stationary and non-stationary components from the input time series without the need for manual setting of thresholds or filtering parameters, and has strong adaptability and versatility.

[0027] 5. The model has a simple structure and high computational efficiency, making it suitable for widespread application in various time series scenarios, such as climate, ocean, earthquake, and financial signal analysis. Attached Figure Description

[0028] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 A structural diagram of the signal decomposition model of the present invention is shown.

[0029] Figure 2 The non-stationary signal obtained by decomposition using the method provided in this invention is shown.

[0030] Figure 3 The stationary signal obtained by decomposition using the method provided in this invention is shown.

[0031] Figure 4 The non-stationary signal prediction error of the method provided by the present invention is illustrated.

[0032] Figure 5 The method provided by this invention illustrates the stationary signal prediction error. Detailed Implementation

[0033] The technical solution of the present invention will now be clearly and completely described 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 are within the scope of protection of the present invention.

[0034] A deep learning-based method for decomposing nonstationary signals includes the following steps: S1 generates a synthetic sample signal that simultaneously contains non-stationary main signals and stationary noise by setting a physically interpretable multi-scale signal model.

[0035] S2 performs dataset partitioning and feature normalization on the samples to form training, validation, and test sets.

[0036] S3 constructs a lightweight deep learning signal decomposition model to achieve end-to-end mapping from time series input to component output.

[0037] S4 employs a composite loss function and an adaptive optimization strategy for training to obtain stable signal decomposition model parameters with generalization capabilities.

[0038] S5 verifies the decomposition performance of the signal decomposition model using test sets or real observation data, and outputs non-stationary signal and stationary noise components.

[0039] Specifically, step S1 includes the following steps: S1.1 uses preset mathematical functions to simulate non-stationary signals at different time scales, including: long-term trend signals, interdecadal signals, interannual signals, intra-seasonal signals, and synoptic-scale signals. For example, long-term trend signals can be represented as polynomial functions. ,in, It is a non-zero constant; seasonal signals can be represented by a sine function. ,in, For amplitude, The length of the seasonal variation cycle, For phase shift, interannual or interdecadal signals can be achieved using low-frequency modulation functions. Non-stationary signals. Represented as: ; in, Indicates different times Components at scale For weight parameters, This refers to the number of deterministic non-stationary timescale components participating in the synthesis, i.e., the number of components superimposed in the current sample.

[0040] S1.2, introduce random noise to simulate uncertainties and interference factors in the actual observation environment. The noise includes: Gaussian white noise and non-Gaussian noise. Represented as: ,in, For noise variance, The noise follows a zero-mean normal (Gaussian) distribution; non-Gaussian noise is defined as a nonlinear random function. The noise term is obtained by weighting Gaussian noise and non-Gaussian noise. : ; in, This is the weighting factor.

[0041] S1.3, non-stationary signals are incorporated with random disturbances to obtain synthesized sample signals. : .

[0042] This signal contains both non-stationary components and random disturbances in the time dimension, which can effectively simulate real non-stationary signal environments.

[0043] This invention first proposes a method for generating simulated data for multi-source signals, used to construct simulated sequences containing multi-scale components. To train and evaluate the proposed signal decomposition deep learning model, a synthetic dataset is constructed that can systematically generate multi-component non-stationary time series with known real decompositions. Each sample is generated by randomly selecting a set of non-stationary components and linearly combining them, followed by superimposing a random noise process. The generated sample signal can be represented as: ; in, This represents a subset randomly selected from the set of non-stationary components: ; Corresponding to trends (Trend, Decadal, Interannual Seasonal Intraseasonal ), Weather-scale ) and tides (Tidal) (and other components at different time scales). Each component Indicates the first The weight of a deterministic component (such as a trend, interdecadal or interannual component, etc.) The amplitude coefficient is randomly selected within a preset range.

[0044] also, This represents the superimposed stationary noise term, which is taken from the set , These correspond to white noise, log-normal noise, Weibull noise, and Gambel noise, respectively. The synthetic signal constructed in this way can simultaneously reflect non-stationary characteristics at multiple time scales and different types of random perturbations, thus providing the model with a diverse and controllable training sample environment.

[0045] After completing the simulation generation of multi-component non-stationary signals, to ensure that the deep learning model can accurately learn the distinguishing features between non-stationary signals and stationary noise during training, this invention further proposes a systematic dataset construction and feature normalization method. This step aims to organize the multi-source synthetic signals into a supervised learning sample set with a unified format, enabling the model to simultaneously identify and separate the two types of time series components within an end-to-end training framework.

[0046] Specifically, step S2 includes the following steps: S2.1, the sample signal generated by simulation As input samples, Corresponding non-stationary signal and noise terms As supervisory labels, they constitute a complete sample. .

[0047] in, It is composed of the superposition of deterministic non-stationary signals at multiple time scales, with the addition of stationary noise; while the label contains Characterizing the trend and rate structure of change over time. This represents a random perturbation term whose statistical properties remain unchanged over time. Through this method of constructing sample pairs, the model can simultaneously learn the statistical characteristics and temporal differences of two types of signals during training, thus possessing adaptive decomposition capabilities.

[0048] S2.2 employs a random sampling strategy to ensure that each sample has differences in signal type, amplitude range, noise intensity, and spectral structure. Subsequently, all samples are divided into training set, validation set, and test set according to the proportions.

[0049] To ensure data coverage of diverse physical characteristics and noise environments, this invention employs a random sampling strategy during the generation phase, ensuring that each sample exhibits differences in signal type, amplitude range, noise intensity, and spectral structure. Subsequently, all samples are proportionally divided into training, validation, and test sets. The training set is used for model parameter optimization, the validation set for monitoring the training process and adjusting the learning rate, and the test set for independent performance evaluation. A fixed random seed is used during sample partitioning to ensure repeatability and comparability between training experiments of different models.

[0050] S2.3, for each time series sample signal Standardization process: ; in, For the first One sample signal, The mean, Standard deviation The standardized sample signal.

[0051] Regarding data standardization, to eliminate dimensional differences between different samples and stabilize the model training process, this invention performs feature normalization on all input signals and output components. This operation concentrates the numerical distribution of the data within the range of zero mean and unit variance, thereby preventing large-value signals from dominating the training gradient and improving the convergence stability of the model. Normalization parameters and It is recorded during training and used for inverse normalization during the inference phase to ensure that the non-stationary signal output by the model maintains the true physical amplitude ratio to the noise.

[0052] Specifically, such as Figure 1 As shown, the signal decomposition model in step S3 includes: a feature extraction module, an encoder, a decoder, a bottleneck residual unit at the bottom of the network, and an output prediction module. The original time input is processed by the feature extraction module, which performs stepwise compression of the temporal resolution and multi-scale feature extraction through the encoder. Then, the time resolution is restored through the decoder, and finally, the estimated result is output through the output prediction module.

[0053] Specifically, the feature extraction module includes: interconnected one-dimensional convolutional layers, grouped normalization and GeLU activation layers, and lightweight multi-scale dilated convolutional residual units; the output prediction module includes: interconnected one-dimensional convolutional layers, grouped normalization and GeLU activation layers, channel fusion one-dimensional convolutional layers, and one-dimensional convolutional layers.

[0054] Specifically, the encoder includes interconnected downsampling one-dimensional convolutional layers, grouped normalization and GeLU activation layers, and lightweight multi-scale dilated convolutional residual units; the decoder includes interconnected linear interpolation upsampling layers, one-dimensional convolutional layers, channel fusion one-dimensional convolutional layers, and lightweight multi-scale dilated convolutional residual units; the bottleneck residual unit at the bottom of the network includes multiple lightweight multi-scale dilated convolutional residual units. The one-dimensional convolutional layers are used for temporal feature reconstruction, and the channel fusion one-dimensional convolutional layers are used for linear fusion and compression of features from different channels.

[0055] The model recovers a single-channel target component from the input time series (which can be configured as a non-stationary master signal or stationary noise according to the training configuration). The overall model adopts an encoder-decoder structure and a cross-layer skip connection mechanism to meet the requirements of accurate reconstruction under multi-scale time features with low memory and low parameter count, while maintaining numerical stability and engineering deployability.

[0056] At the underlying operator level, the model introduces one-dimensional depthwise separable convolutions to replace standard convolution kernels, thereby significantly reducing multiply-accumulate operations and memory overhead without reducing the receptive field; reflection padding is used to avoid boundary artifacts. All convolutional layers are post-grouped normalized and subjected to non-linear activation functions (such as GeLU) to improve training stability under different batch sizes and alleviate the gradient vanishing / exploding problem. To enhance the perception of multi-timescale patterns, parallel multi-scale dilated convolutional residual units are designed: several branches (such as 1, 2, and 4) run in parallel on the same channel width, and the branch outputs are summed and fused rather than concatenated by channels, which maintains multi-scale response and avoids the parameter and memory costs caused by channel dimensionality dilation; residual connections are used at the end of the unit to ensure smooth flow of high and low frequency information in both forward and backward propagation.

[0057] The encoder consists of several stacked downsampling blocks to achieve progressive compression of temporal resolution and multi-scale feature extraction. Each stage first reduces temporal resolution and expands channel dimensions through convolutional units with downsampling capabilities, followed by a multi-scale dilated convolutional residual structure to refine temporal features. The encoding results of each stage are cached sequentially during downlinking for cross-layer skip connections in the decoding stage to maintain the continuous transmission of detailed information. A lightweight bottleneck residual unit is placed at the bottom of the network to further fuse long-short-term dependencies without significantly increasing computation, enhancing the model's ability to represent and compress broadband non-stationary features.

[0058] The decoder uses stepwise linear interpolation upsampling and convolution to restore temporal resolution, replacing deconvolution operations, reducing checkerboard artifacts and lowering memory usage. After each upsampling, the corresponding encoded-level features after alignment and cropping are concatenated and fused, then convolved back to the predetermined number of channels, and the reconstructed result is refined through multi-scale dilated convolutional residual units. This "upsampling-skip-connection-lightweight fusion" paradigm effectively preserves the structural priors captured in the encoding stage, enabling the model to simultaneously achieve global background consistency and local detail fidelity in separating non-stationary main signals and stationary noise.

[0059] At the output, a prediction head consisting of local convolutional units, a normalization layer, a nonlinear activation function, and an output convolutional unit is configured to directly generate a single-channel sequence of the same length as the input, which is used as the estimation result for the target component (configured as a non-stationary main signal or stationary noise according to the training settings). To meet the smoothing requirements of extremely low-frequency components in certain application scenarios, the model provides an optional non-trainable smoothing layer: a one-dimensional average convolutional kernel with fixed coefficients (odd length) is used to achieve mild temporal smoothing. This smoothing layer is turned off in the default training configuration to avoid over-smoothing that would impair the amplitude recovery of true spikes or sudden events; it can be enabled as needed in inference or specific denoising scenarios.

[0060] To accommodate different hardware conditions and task scales, the network offers multiple optional configuration modes (such as lightweight and standard). Through unified channel alignment and structure-sharing design, it maintains a linear scalability in parameter scale and computational cost across different configurations. The entire model uses only basic primitives such as one-dimensional convolution, linear interpolation, and normalization, facilitating efficient deployment in CPU / GPU environments and inference engines. Practice shows that the above structure, while maintaining extremely low parameter count and memory usage, can fully capture the multi-scale dynamics of non-stationary time series. Furthermore, in conjunction with the loss function and optimization strategy proposed in this invention, it achieves high-precision and robust reconstruction of the binary decomposition target of "non-stationary main signal - stationary noise".

[0061] Specifically, in the model training process, to simultaneously consider the temporal reconstruction accuracy and statistical distribution consistency of non-stationary signal decomposition, this invention designs a multi-constraint composite loss function, combined with an adaptive optimization algorithm and a dynamic learning rate strategy, to achieve rapid convergence of the training process and high robustness of the results. In the signal decomposition problem, the model not only needs to accurately reconstruct the main trends and variability components of the original signal, but also needs to maintain the consistency between the noise distribution and the real situation in a statistical sense. Therefore, the loss function is constructed as a weighted combination of multiple constraints to balance the contributions of each optimization objective. The total loss function in step S4... Represented as: ; in, This represents the reconstruction error between the signal predicted by the signal decomposition model and the actual non-stationary signal. This indicates the deviation between the predicted noise and the reference noise; Used to constrain the consistency of the distribution of predicted noise and true noise at the probability density function level, and This is used to constrain the overall statistical consistency between the two at the level of cumulative distribution function, thereby ensuring that the model accurately reproduces its statistical characteristics while maintaining consistent noise energy. , , , These are the weighting coefficients.

[0062] To balance the relative importance of each constraint term, weighting parameters are used. , , , The weighting can be determined based on the task scenario and signal characteristics. For example, it can be dynamically set through cross-validation, adaptive weight adjustment, or sensitivity analysis based on the objective function to maintain stable decomposition performance under different noise intensities and signal complexities. This design can improve the overall reconstruction accuracy of the model while enhancing its robustness and generalization ability in complex noise environments.

[0063] In terms of optimization strategy, this invention employs an optimization algorithm based on adaptive gradient adjustment to iteratively update model parameters. To prevent training oscillations caused by an excessively large learning rate or slow convergence caused by an excessively small learning rate, the system introduces a dynamic learning rate scheduling mechanism, which automatically adjusts the learning rate based on changes in validation set loss. When the model does not show significant performance improvement within several consecutive training cycles, the learning rate will gradually decrease according to a preset ratio, thereby achieving smooth convergence in the training process. Simultaneously, to prevent model overfitting and improve training efficiency, the system sets an early stopping strategy; when the validation set performance does not show significant improvement within several consecutive cycles, the training process is automatically terminated. The entire training uses mini-batch stochastic gradient descent to achieve a balance between memory usage, gradient estimation accuracy, and training speed.

[0064] Through the above-mentioned composite loss function design and adaptive optimization mechanism, the deep learning model proposed in this invention can maintain stable convergence under various noise types and different signal-to-noise ratios, and achieve high-precision decomposition and reconstruction of complex signal components, providing a reliable training foundation for the model's application in multi-source data and cross-domain tasks. Figures 2-5 This paper demonstrates the decomposition results of the method of the present invention on synthetic samples, including a comparison of the prediction results for non-stationary signals and stationary signals (i.e., noise) and the error distribution. Figure 2 As can be seen, the predicted signal is highly consistent with the real signal, with a root mean square error (RMSE) of only 0.0472 and a correlation coefficient of 0.998, indicating that the model can accurately capture the main components of the non-stationary signal. Figure 3 A comparison of the actual noise and the predicted noise is presented. The two noises largely overlap in time series, and the RMSE remains at a low level. Figure 4 and Figure 5 Error sequences for non-stationary signals and noise are presented separately. The overall error amplitude is close to zero, indicating that the model has good stability. These results demonstrate that the method of this invention can achieve accurate separation of signal and noise components under complex noise interference, exhibiting high decomposition accuracy and robustness.

[0065] The proposed deep learning-based non-stationary signal decomposition method enables adaptive separation of non-stationary main signals and stationary noise signals in time series within an end-to-end framework. This method combines a lightweight neural network structure with a multi-constraint loss function design, significantly improving the accuracy, stability, and interpretability of signal decomposition while maintaining model simplicity, demonstrating strong potential for widespread application.

[0066] Regarding decomposition accuracy and stability, this invention introduces a multi-scale dilated convolution structure, enabling the model to simultaneously perceive dynamic features at different time scales, thereby more fully capturing the trend changes and local fluctuations of non-stationary signals. The residual connections and normalization mechanisms employed in the network effectively alleviate the gradient degradation problem of deep models, ensuring stable convergence during training. Verification using multiple combinations and experimental samples shows that the model can accurately recover the dominant change patterns of the signal and effectively suppress noise interference; the decomposition results exhibit good consistency in both the time domain and statistical characteristics.

[0067] Regarding loss constraints and optimization strategies, the composite loss function proposed in this invention not only considers signal reconstruction errors but also incorporates probability distribution-level constraints, enabling the model to simultaneously maintain temporal accuracy and statistical consistency during optimization. Through dynamic learning rate adjustment and early stopping mechanisms, the training process exhibits good adaptability and convergence, maintaining stable performance under various initial conditions and noise environments.

[0068] In terms of structural design and computational efficiency, the model uses depthwise separable convolution and linear upsampling to replace traditional high-parameter operators, effectively reducing computational complexity and memory usage while retaining strong feature representation capabilities. This design makes the model easier to deploy in different computing environments, exhibiting high engineering feasibility and operational efficiency.

[0069] In terms of physical interpretability and application, the two signal components output by the model of this invention have clear physical meanings: the non-stationary component represents the trend change or low-frequency variability of the system, while the stationary component corresponds to random disturbances or noise terms. The decomposition results can intuitively reflect the dominant change characteristics of the system and the sources of its uncertainty, providing valuable input for fields such as climate signal identification, ocean dynamic process analysis, seismic data filtering, and financial time series analysis.

[0070] Overall, the method of this invention is compact in structure, clear in concept, and highly feasible. It can automatically learn signal characteristics at different time scales and achieve adaptive separation of non-stationary and stationary components without relying on manually set parameters or empirical filtering conditions. This method has good development prospects and research value in subsequent practical data analysis and application expansion.

[0071] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A non-stationary signal decomposition method based on deep learning, characterized in that, Specifically, the steps include the following: S1 generates a synthetic sample signal that simultaneously contains non-stationary main signals and stationary noise by setting a physically interpretable multi-scale signal model. S2, perform dataset partitioning and feature normalization on the samples to form training set, validation set and test set; S3, construct a lightweight deep learning signal decomposition model to achieve end-to-end mapping from time series input to component output; S4 uses a composite loss function and an adaptive optimization strategy for training to obtain stable signal decomposition model parameters with generalization ability; S5 verifies the decomposition performance of the signal decomposition model using test sets or real observation data, and outputs non-stationary signal and stationary noise components.

2. The non-stationary signal decomposition method based on deep learning according to claim 1, characterized in that, Step S1 specifically includes the following steps: S1.1 simulates non-stationary signals at different time scales using preset mathematical functions, including: long-term trend signals, interdecadal signals, interannual signals, intra-seasonal signals, and synoptic-scale signals. Represented as: ； in, Indicates different times Components at scale For weight parameters, This represents the number of superimposed components in the current sample. S1.2, introduce random noise to simulate uncertainties and interference factors in the actual observation environment. The noise includes: Gaussian white noise and non-Gaussian noise. Represented as: ,in, For noise variance, The distribution follows a zero-mean normal distribution; non-Gaussian noise is defined as a nonlinear random function. The noise term is obtained by weighting Gaussian noise and non-Gaussian noise. : ； in, As a weighting factor; S1.3, non-stationary signals are incorporated with random disturbances to obtain synthesized sample signals. : 。 3. The non-stationary signal decomposition method based on deep learning according to claim 1, characterized in that, Step S2 specifically includes the following steps: S2.1, the sample signal generated by simulation As input samples, Corresponding non-stationary signal and noise terms As supervisory labels, they constitute a complete sample. ; S2.2, a random sampling strategy is adopted to make the signal type, amplitude range, noise intensity and spectral structure of each sample different. Then, all samples are divided into training set, validation set and test set according to the proportion. S2.3, for each time series sample signal Standardization process: ； in, For the first One sample signal, The mean, Standard deviation The standardized sample signal.

4. The non-stationary signal decomposition method based on deep learning according to claim 1, characterized in that, The signal decomposition model in step S3 includes a feature extraction module, an encoder, a decoder, a bottleneck residual unit at the bottom of the network, and an output prediction module. The original time input is processed by the feature extraction module, then by the encoder for progressive compression of the temporal resolution and multi-scale feature extraction. Subsequently, the time resolution is restored by the decoder, and finally the estimated result is output by the output prediction module.

5. The non-stationary signal decomposition method based on deep learning according to claim 4, characterized in that, The feature extraction module includes: interconnected one-dimensional convolutional layers, grouped normalization and GeLU activation layers, and lightweight multi-scale dilated convolutional residual units; the output prediction module includes: interconnected one-dimensional convolutional layers, grouped normalization and GeLU activation layers, channel fusion one-dimensional convolutional layers, and one-dimensional convolutional layers.

6. The non-stationary signal decomposition method based on deep learning according to claim 4, characterized in that, The encoder includes: Interconnected downsampled one-dimensional convolutional layers, grouped normalization and GeLU activation layers, and lightweight multi-scale dilated convolutional residual units; The decoder includes: interconnected linear interpolation upsampling layers, one-dimensional convolutional layers, channel fusion one-dimensional convolutional layers, and lightweight multi-scale dilated convolutional residual units; The bottleneck residual unit at the bottom of the network consists of multiple lightweight multi-scale dilated convolution residual units.

7. The non-stationary signal decomposition method based on deep learning according to claim 1, characterized in that, Total loss function in step S4 Represented as: ； in, This represents the reconstruction error between the signal predicted by the signal decomposition model and the actual non-stationary signal. This indicates the deviation between the predicted noise and the reference noise; Used to constrain the consistency of the distribution of predicted noise and actual noise at the probability density function level. Used to constrain the overall statistical consistency between the two at the level of cumulative distribution function; , , , These are the weighting coefficients.

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