Embodied agent time series data modeling method based on frequency domain learning

Abstract

The application discloses a kind of embodied intelligent agent time series data modeling methods based on frequency domain learning, including adaptive block to original time series data sequence, feature is extracted by multi-scale convolution and generates position coding;Fourier transform is executed to feature block to extract frequency domain information, and carries out nonlinear transformation and residual compensation;Attention relationship between features is calculated and feature fusion is carried out;Construct time series dependency graph, extract time series aggregation features and dynamic system features;Construct probability prediction model, calculate the uncertainty of prediction result.The application improves the modeling accuracy by adaptive block and frequency domain feature extraction, enhances the feature expression capability by attention mechanism and graph structure modeling, improves the prediction reliability by uncertainty quantification, and is suitable for time series data modeling of embodied intelligent agent in complex environment.

Description

Technical Field

[0001] The present invention belongs to the field of data modeling, and in particular to a method for modeling time series data of an embodied intelligent body based on frequency domain learning. Background Art

[0002] The autonomous decision-making and behavioral control of embodied agents in complex environments require precise modeling and prediction of time series data. With the increasing intelligence and automation of industrial production, the time series data that embodied agents must process exhibits characteristics such as high dimensionality, strong coupling, multi-scale, and non-stationary nature. Accurately capturing the dynamic features, periodic patterns, and long-term dependencies in this complex time series data is crucial for improving the embodied agents' environmental perception capabilities, optimizing decision-making efficiency, and ensuring system stability. In particular, in fields such as industrial manufacturing, intelligent robotics, and automatic control, time series modeling methods based on frequency domain learning can effectively extract frequency features and periodic patterns from data, providing a reliable basis for the behavioral decisions of embodied agents.

[0003] Currently, time series data modeling primarily utilizes deep learning-based methods, such as recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and gated recurrent units (GRUs). These methods capture the dependencies of time series data by constructing complex network structures, but suffer from vanishing gradients and low computational efficiency when processing long sequences of data. Traditional frequency-domain analysis methods, such as Fourier transforms and wavelet transforms, while capable of extracting frequency features of signals, struggle with processing non-stationary signals and capturing complex time series dependencies. While the attention-based Transformer model addresses the long-range dependency issue to some extent, the computational complexity of its self-attention mechanism increases quadratically with the sequence length, limiting its application in processing long sequences of data.

[0004] However, existing time series modeling methods still suffer from the following technical issues: First, during the data preprocessing stage, fixed block partitioning strategies cannot adaptively adjust the window size based on the local characteristics of the data, which may cause important time series features to be segmented or confused. Second, existing frequency domain feature extraction methods often ignore the importance weights of frequency components, and using a unified frequency selection criterion may lose critical frequency information. Third, during feature fusion, simple feature concatenation or weighted averaging fails to fully consider the correlation and complementarity between different features, reducing the efficiency of feature expression. Fourth, traditional graph structure modeling methods often use fixed similarity metrics when constructing time series dependency graphs, which is difficult to adapt to the characteristics of different types of time series data. Finally, when evaluating the reliability of prediction results, existing methods lack a systematic quantification of prediction uncertainty, making it difficult to provide a credibility assessment for the decisions of embodied intelligent agents. These technical issues seriously restrict the performance and adaptability of embodied intelligent agents in complex environments. Summary of the Invention

[0005] The purpose of the invention is to provide a method for modeling time series data of embodied intelligent bodies based on frequency domain learning, in order to solve at least one technical problem existing in the prior art.

[0006] The technical solution is a method for modeling time series data of embodied intelligent agents based on frequency domain learning, which includes the following steps:

[0007] S1. Obtain the original time series data sequence and determine the adaptive block size sequence based on the temporal relationship of adjacent data points; based on the adaptive block size sequence, block the original time series data sequence to obtain data blocks; use the multi-scale convolution method to extract features from the data blocks and generate corresponding position coding information to obtain a multi-scale feature block set and a position coding matrix;

[0008] S2. Perform Fourier transform on each feature block in the multi-scale feature block set to extract frequency domain information; analyze the signal amplitude in the frequency domain information to determine the frequency selection parameter; based on the frequency selection parameter, perform nonlinear transformation and residual compensation on the frequency domain information to obtain a frequency domain feature matrix and a residual feature matrix;

[0009] S3. Based on the frequency domain feature matrix, the residual feature matrix and the position encoding matrix, the attention relationship between the features is calculated; based on the attention relationship, the features are fused to obtain a fused feature matrix;

[0010] S4. Based on the fusion feature matrix, a time series dependency graph is constructed. Based on the graph structure of the time series dependency graph, time series aggregation features are extracted, and system dynamic feature parameters are calculated to obtain dynamic system features.

[0011] S5. Based on the time series aggregation features and dynamic system characteristics, a probabilistic prediction model is constructed, the uncertainty of the prediction results is calculated, and the prediction distribution and confidence index are obtained.

[0012] Beneficial effects: The present invention realizes efficient feature extraction of time series data, ensuring the integrity and accuracy of feature expression; realizes intelligent integration of different types of features, and deeply characterizes complex time series dependencies; realizes reliability evaluation of prediction results, improves the accuracy and efficiency of time series data modeling, and enhances the reliability of prediction results, providing strong support for state prediction and decision optimization of complex systems; through multi-level feature extraction and fusion, it realizes effective transformation from data to knowledge, providing reliable technical support for intelligent decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Flowchart of the present invention.

[0014] Figure 2This is a flow chart of step S1 of the present invention.

[0015] Figure 3 This is a flow chart of step S2 of the present invention.

[0016] Figure 4 This is a flow chart of step S3 of the present invention.

[0017] Figure 5 This is a flow chart of step S4 of the present invention.

[0018] Figure 6 This is a flow chart of step S5 of the present invention. DETAILED DESCRIPTION

[0019] like Figure 1 As shown, the present invention proposes a method for modeling time series data of an embodied intelligent agent based on frequency domain learning, which includes the following steps:

[0020] S1. Obtain the original time series data sequence and determine the adaptive block size sequence based on the temporal relationship of adjacent data points; based on the adaptive block size sequence, block the original time series data sequence to obtain data blocks; use the multi-scale convolution method to extract features from the data blocks and generate corresponding position coding information to obtain a multi-scale feature block set and a position coding matrix;

[0021] S2. Perform Fourier transform on each feature block in the multi-scale feature block set to extract frequency domain information; analyze the signal amplitude in the frequency domain information to determine the frequency selection parameter; based on the frequency selection parameter, perform nonlinear transformation and residual compensation on the frequency domain information to obtain a frequency domain feature matrix and a residual feature matrix;

[0022] S3. Based on the frequency domain feature matrix, the residual feature matrix and the position encoding matrix, the attention relationship between the features is calculated; based on the attention relationship, the features are fused to obtain a fused feature matrix;

[0023] S4. Based on the fusion feature matrix, a time series dependency graph is constructed. Based on the graph structure of the time series dependency graph, time series aggregation features are extracted, and system dynamic feature parameters are calculated to obtain dynamic system features.

[0024] S5. Based on the time series aggregation features and dynamic system characteristics, a probabilistic prediction model is constructed, the uncertainty of the prediction results is calculated, and the prediction distribution and confidence index are obtained.

[0025] like Figure 2 As shown, according to one aspect of the present application, step S1 is further:

[0026] S11. Read the original time series data sequence from the database, perform an inner product operation on the data of adjacent time points to obtain an inner product result; add 1 to the inner product result and then perform a power operation to obtain an operation result; based on the operation result, construct similarity data of adjacent time points; determine the size of the data block based on the similarity data to obtain an adaptive block size sequence;

[0027] S12. Construct convolution kernel parameters of different sizes based on the adaptive block size sequence and the original time series data sequence; perform a convolution operation on each data block based on the convolution kernel parameters to obtain a convolution result; combine the convolution results in the channel dimension to obtain a multi-scale feature block set;

[0028] S13. Obtain the time index information of the data block in the multi-scale feature block set, calculate the sine function value as the initial position code; construct the position query data, calculate the correlation score between the position query data and the initial position code; normalize the correlation score to generate a position code matrix.

[0029] In one embodiment of the present application, the original time series data sequence X∈R is obtained. N×D (N is the sequence length, D is the feature dimension), based on the polynomial kernel function K(x, y) = (1 + x T y) d Calculate the similarity matrix S∈R of adjacent time points N×N , output adaptive block size sequence L = [l1, l2, ..., l k ], where l i Represents the size of the i-th block. Based on the original time series data sequence X and the adaptive block size sequence L, a multi-scale convolution kernel W = {W1, W2, ..., W m}, where W i ∈R ki×D×C , k i is the size of the i-th convolution kernel, C is the number of output channels; perform multi-scale convolution on each block: F i = Conv(X[l i :l i+1 ], W), output multi-scale feature block set B = {F1, F2, ..., F k Generate relative position code for each block: i =sin(ωt + φ), where t is the time index, ω and φ are learnable parameters; calculate the global position attention: A = softmax(QK T / sqrt(d))V, Q, K, V are position query matrices; output position encoding matrix P.

[0030] This embodiment achieves efficient feature extraction of time series data through a combination of multi-scale convolution and adaptive blocking. First, the block size is adaptively determined based on the similarity relationship between adjacent time points, avoiding the information loss or redundancy problems that may be caused by a fixed window size; by using inner product operations and power transformations to calculate the degree of similarity, the nonlinear relationship pattern of the data can be effectively captured. Secondly, a multi-scale convolution processing method is adopted to simultaneously extract feature information of multiple scales through convolution kernels of different sizes, which not only retains local fine features but also captures global time series dependencies. Finally, through the introduction of the position encoding matrix, the problem of position information loss in traditional time series modeling is solved, enabling the model to perceive the relative position relationship between different time points. This embodiment improves the model's ability to recognize patterns of different time scales while reducing computational complexity.

[0031] According to one aspect of the present application, step S11 is further as follows:

[0032] S111. Obtain the original time series data sequence from the database, segment the original time series data sequence using the sliding window method, remove outliers in each segment of data, and obtain segmented data; perform Z-score standardization on the segmented data to obtain standardized time series data; apply wavelet transform to the standardized time series data to remove high-frequency noise, and obtain denoised standardized data and time series window data.

[0033] S112. Based on the denoised normalized data and the time series window data, calculate the inner product of the adjacent time window data to obtain inner product data; add 1 to the inner product data to obtain offset inner product data; perform a power operation on the offset inner product data to obtain power feature data; calculate the Pearson correlation coefficient of the power feature data; use a kernel function method to map the Pearson correlation coefficient to a high-dimensional feature space, and reduce the feature dimension through a local sensitive hashing method to obtain time series related features;

[0034] S113. Based on the time series related features and the power feature data, an adaptive neighborhood method is used to determine the feature cluster center; the Mahalanobis distance between each time point and the feature cluster center is calculated; based on the Mahalanobis distance and the power feature data, a sparse adjacency matrix is ​​constructed, and the spectral clustering method is applied to optimize the adjacency relationship to obtain a similarity matrix;

[0035] S114. Based on the similarity matrix, a dynamic programming method is used to calculate the changing trend of the similarity; based on the changing trend and power feature data, an adaptive threshold is constructed; the standardized time series data is divided into initial data blocks using the adaptive threshold, and the hierarchical clustering method is applied to the initial data blocks to optimize the block size, and finally an adaptive block size sequence is obtained.

[0036] In one embodiment of the present application, the Z-score normalization algorithm is: Z(x)=(x-μ) / σ+α·sign(x-μ)·log(1+|x-μ| / β); wherein Z(x) is the normalized data; x is the original data; μ is the sequence mean; σ is the sequence standard deviation; α is the nonlinear adjustment coefficient; β is the smoothing parameter; sign is the sign function; log is the natural logarithm; |·| represents the absolute value operation.

[0037] Wavelet transform denoising: W(a, b) = Σ(t)[x(t)·ψ((tb) / a)] + λ·soft(|W(a, b)|, τ(a)); where W(a, b) is the wavelet coefficient; x(t) is the input signal; ψ is the wavelet basis function; a is the scale parameter; b is the translation parameter; λ is the regularization coefficient; soft is the soft threshold function; τ(a) is the scale-adaptive threshold; and t is the time index.

[0038] Kernel function feature mapping method: K(x_i, x_j)=exp(-||φ(x_i)-φ(x_j)|| 2 / 2σ 2 )+α·cos(ω·<x_i,x_j>); where K(x_i,x_j) is the kernel function mapping result, which represents the similarity of two feature vectors in high-dimensional space; φ(x) is the feature mapping function, which maps the input features to high-dimensional space; x_i, x_j are the feature vectors of adjacent time windows; σ is the kernel function bandwidth parameter, which is obtained by cross-validation optimization; α is the weight coefficient of the cosine kernel term, which is used to enhance the extraction of periodic features; ω is the frequency parameter of the cosine kernel, which is adaptively adjusted according to the periodic characteristics of the data; ||·|| represents the Euclidean distance norm; <·,·> represents the vector inner product operation.

[0039] Locality sensitive hashing algorithm: H(x)=sign(W·x+b)·exp(-||W·x+b|| 2 / γ); where H(x) is the hash code; W is the random projection matrix; x is the input feature; b is the bias vector; γ is the Gaussian kernel parameter; sign is the sign function; ||·|| represents the Euclidean norm; · represents the matrix multiplication operation.

[0040] Hierarchical clustering algorithm: D(C_i, C_j)=θ·min_dist(C_i, C_j)+(1-θ)·avg_dist(C_i, C_j); where D(C_i, C_j) is the inter-cluster distance; C_i, C_j are data clusters; min_dist is the minimum distance function; avg_dist is the average distance function; θ is the weight coefficient; cluster merging criterion: merge(C_i, C_j)=argmin{D(C_i, C_j)+ρ·|size(C_i)-size(C_j)|}; where ρ is the balance coefficient.

[0041] Adaptive block algorithm: S(t,τ)=β·exp(-||f(t)-f(t+τ)|| 2 / λ 2 )+γ·|R(t,τ)|; where S(t,τ) is the similarity score between time points t and t+τ; f(t) is the eigenvector at time point t; τ is the time offset; R(t,τ) is the autocorrelation function of the time series; β is the distance term weight coefficient; γ is the autocorrelation term weight coefficient; λ is the distance scale parameter; ||·|| represents the Euclidean distance norm; |·| represents the absolute value operation.

[0042] This embodiment achieves high-quality feature extraction of original time series data through adaptive data preprocessing and similarity calculation. First, a combination of sliding window and Z-score normalization is adopted to effectively eliminate the scale differences and outlier effects of the data. Noise reduction processing is performed through wavelet transform, which not only retains the main features of the data but also suppresses the interference of random noise. Secondly, when calculating the similarity of adjacent time windows, the ability to capture nonlinear correlations is enhanced through the combination of inner product operation and power transformation. The relevant features are projected into high-dimensional space through kernel function mapping, which improves the expressive power of the features. Finally, the local sensitive hashing method is used for feature dimensionality reduction, which reduces the computational complexity while maintaining data similarity. This embodiment not only improves the accuracy of subsequent analysis, but also optimizes computational efficiency through dimensionality reduction and feature enhancement, laying a solid foundation for the modeling of time series data.

[0043] According to one aspect of the present application, step S12 is further as follows:

[0044] S121. Obtain the adaptive block size sequence and the original time series data sequence in the database, apply a stationarity test to each time series data block, generate statistical features of the data block, adaptively adjust the receptive field size of each convolution kernel according to the statistical features, use the Glorot initialization method to generate convolution kernel weights of different scales, perform sparsity constraints on the convolution kernel based on the data distribution characteristics, and obtain multi-scale convolution kernel parameters.

[0045] S122. Obtain multi-scale convolution kernel parameters, adaptive block size sequence and original time series data sequence, perform one-dimensional convolution operation on each data block to obtain a basic feature map, use exponential linear unit for nonlinear transformation to obtain an activation feature map, use maximum pooling operation to extract significant features to obtain a pooled feature map, and obtain a normalized feature map through batch normalization processing.

[0046] S123. Obtain a normalized feature map, use the channel attention mechanism to calculate the feature weights to obtain channel-weighted features, use the spatial pyramid pooling method to extract multi-scale spatial information to obtain pyramid features, perform adaptive weighted combination of features of all scales in the channel dimension, apply residual connection to retain the original information, and obtain a multi-scale feature block set.

[0047] In one embodiment of the present application, the convolution kernel parameters are adaptively adjusted: W(l, k) = η·tanh(V(l, k)) + ρ·sigmoid(U(l, k))·M(l); wherein W(l, k) is the parameter matrix of the kth convolution kernel of the lth layer; V(l, k) is the basic parameter matrix; U(l, k) is the modulation parameter matrix; M(l) is the hierarchical mask matrix; η is the basic weight coefficient; ρ is the modulation intensity coefficient; tanh is the hyperbolic tangent function; and sigmoid is the S-type activation function.

[0048] Spatial pyramid pooling algorithm: P(x, l) = Σ(i = 1 → 4 l )[pool(x, R_i(l))·exp(-d(R_i(l), c) / η)]; where P(x, l) is the pooling result of the lth layer; x is the input feature; pool is the pooling function; R_i(l) is the i-th region of the lth layer; d(R, c) is the distance from region R to center c; η is the distance attenuation parameter; 4 l is the number of regions in layer l.

[0049] This embodiment achieves a comprehensive characterization of time series data through multi-scale convolution feature extraction. First, the receptive field size of the convolution kernel is adaptively adjusted based on the stationarity test results of the data block, avoiding the information loss that may be caused by a fixed scale. Through the combination of Glorot initialization and sparsity constraints, the optimal configuration of the convolution kernel parameters is achieved, which improves the efficiency and robustness of feature extraction. Secondly, the exponential linear unit is used for nonlinear transformation to enhance the model's ability to express complex patterns. Significant features are extracted through the maximum pooling operation, reducing data redundancy. Finally, through the combination of channel attention mechanism and spatial pyramid pooling, the adaptive fusion of multi-scale features is achieved, which not only retains local detail information but also captures global temporal dependencies. This embodiment improves the model's ability to recognize patterns of different scales, and at the same time improves the efficiency of feature expression through feature fusion and attention mechanism.

[0050] According to one aspect of the present application, step S13 is further as follows:

[0051] S131. Based on the multi-scale feature block set, extract the time index information of the data block, calculate the continuous time function using polynomial interpolation to obtain a continuous time series; decompose the continuous time series using wavelet basis functions to obtain time feature components; construct a multi-scale time representation based on the time feature components to obtain a hierarchical time feature and an initial time code;

[0052] S132. Based on the hierarchical time features and the initial time code, a periodic sine function value is calculated to obtain an initial position code; based on the initial position code, adaptive frequency modulation is applied to obtain a modulated position code; based on the modulated position code and the initial position code, a dot product between the codes is calculated to obtain an initial correlation score; based on the initial correlation score and pre-stored time scale information, a multi-scale position code is obtained;

[0053] S133. Based on the multi-scale position encoding and the initial correlation score, construct a position attention query matrix to obtain a position query feature; calculate the correlation between the position query feature and the position encoding to obtain a position correlation score; normalize the position correlation score to obtain a normalized correlation score; apply a kernel function transformation based on the normalized correlation score to obtain a kernelized position feature;

[0054] S134. Based on the kernelized position features and the normalized correlation scores, perform spectral decomposition to obtain a characteristic spectrum matrix; based on the characteristic spectrum matrix, calculate the importance of the eigenvalues ​​and perform dimensionality reduction processing to obtain reduced-dimensionality position features; combine the reduced-dimensionality position features and the normalized correlation scores to perform weighted processing to obtain weighted position features; based on the weighted position features, perform orthogonal processing to obtain a position coding matrix.

[0055] In one embodiment of the present application, a multi-scale time representation is provided: T(t, s) = μ·sin(2πt / s)+ν·cos(2πt / s)+θ·wavelet(t, s); wherein T(t, s) is a representation vector of time point t at scale s; wavelet(t, s) is a wavelet transform result; μ is a sine term weight; ν is a cosine term weight; θ is a wavelet term weight; t is a time index; s is a time scale parameter; and π is pi.

[0056] Adaptive frequency modulation algorithm: F(t, ω)=α·sin(ω·t+φ(t))+β·cos(ω·t+φ(t))·exp(-|dφ(t) / dt| / μ); where F(t, ω) is the modulated signal; ω is the fundamental frequency; φ(t) is the phase function; α and β are modulation coefficients; μ is the phase change rate attenuation parameter; dφ(t) / dt is the phase change rate; and t is the time variable.

[0057] This embodiment achieves accurate modeling of temporal position information through advanced position coding and adaptive correlation calculation. First, a combination of polynomial interpolation and wavelet decomposition is used to construct a continuous time function representation, which solves the information loss problem caused by discrete sampling. Through multi-scale time representation, the characterization of position relationships on different time scales is achieved. Secondly, the use of periodic sine functions with adaptive frequency modulation enhances the expressive power of position coding, enabling the model to better perceive long-distance dependencies. Through spectral decomposition and eigenvalue importance analysis, dimensionality reduction optimization of position features is achieved, which not only retains key position information but also reduces computational complexity. Finally, the kernel function transformation and orthogonalization processing are used to improve the distinguishing ability of position coding. This embodiment not only improves the model's ability to understand temporal dependencies, but also improves computational efficiency through dimensionality optimization and feature enhancement.

[0058] like Figure 3 As shown, according to one aspect of the present application, step S2 is further:

[0059] S21. Obtain a multi-scale feature block set, perform Fourier transform on the feature block data to obtain a Fourier transform result; based on the Fourier transform result, calculate the amplitude of the transformed signal to obtain amplitude data; based on the amplitude data, generate a frequency selection parameter through a multi-layer perceptron operation and a sigmoid function; multiply the frequency selection parameter by the Fourier transform result to obtain a frequency domain feature matrix;

[0060] S22. Based on the multi-scale feature block set and the frequency domain feature matrix, a polynomial expansion operation is performed on the feature block data using the polynomial coefficients to obtain a polynomial expansion result; a difference operation is performed between the polynomial expansion result and the frequency domain feature matrix to obtain a residual feature matrix.

[0061] In one embodiment of the present application, based on the multi-scale feature block set B, the block-level Fourier transform is calculated: i (ω) = ∫ b i (t)e -jωt dt,b i ∈B, where b i (t) is the i-th feature block in the multi-scale feature block set, representing the time domain signal; e -jωtis a complex exponential function, representing the frequency component in the Fourier transform, j is the imaginary unit, ω is the angular frequency, and t is time; dt is the integral variable, representing the time differential; an adaptive frequency selection mechanism is introduced: α(ω) = sigmoid(MLP(|F(ω)|)), where sigmoid is the activation function, MLP( ) is the nonlinear transformation function, F(ω) is the frequency domain feature, and the frequency domain feature matrix F is output, where each element F[i, j] represents the feature of the i-th block at frequency j. Nonlinear feature extraction is performed using Chebyshev polynomial expansion: g(x) = Σ i c i T i (x), where g(x) is a nonlinear feature extraction function, c i are the coefficients in the Chebyshev polynomial expansion, T i (x) is a Chebyshev polynomial, representing the basis function in nonlinear feature extraction; calculate the high-frequency compensation term: H = g(B) – F; output the residual feature matrix R.

[0062] This embodiment achieves a comprehensive characterization of time series data through the dual mechanisms of frequency domain transformation and residual compensation. In the frequency domain feature extraction process, the time domain signal is first converted to the frequency domain space through Fourier transform, and then the frequency selection parameters are adaptively determined based on the signal amplitude, which can effectively extract the periodic patterns and frequency features in the data. Through the combination of multi-layer perceptron and sigmoid function, adaptive optimization of frequency selection parameters is achieved, so that the model can dynamically adjust the importance weights of frequency components according to the characteristics of the data. At the same time, through polynomial expansion and residual compensation mechanism, the nonlinear features and detail information that may be lost in the frequency domain transformation are captured, forming a complete characterization of the original data. This embodiment not only ensures the accurate capture of periodic patterns, but also does not lose important non-periodic features, thereby improving the generalization ability of the model.

[0063] According to one aspect of the present application, step S21 is further as follows:

[0064] S211, obtaining a set of multi-scale feature blocks, applying a Hanning window function to each feature block for windowing processing to obtain windowed feature data; calculating an autocorrelation function of the windowed feature data to obtain a correlation sequence; estimating a periodic feature of the signal based on the correlation sequence to obtain periodic feature data;

[0065] S212, performing a fast Fourier transform based on the windowed characteristic data and the periodic characteristic data to obtain an initial spectrum; estimating a power spectrum density using the Welch method based on the initial spectrum to obtain power spectrum data; and adaptively smoothing the initial spectrum based on the power spectrum data and the periodic characteristic data to obtain a smoothed spectrum;

[0066] S213. Based on the smoothed spectrum and power spectrum data, the frequency importance score is calculated using a multilayer perceptron to obtain the frequency weight; based on the frequency weight, the sigmoid function is applied to perform normalization to obtain the normalized weight; the Bootstrap method is used to evaluate the uncertainty of the normalized weight to obtain the weight reset confidence interval; based on the weight reset confidence interval, the weight is corrected to obtain the frequency selection parameter;

[0067] S214. Based on the smoothed spectrum and the frequency selection parameters, perform frequency domain filtering to obtain a filtered spectrum; based on the filtered spectrum, apply an inverse Fourier transform to obtain a reconstructed time domain signal; based on the reconstructed time domain signal, calculate the reconstruction error and update the frequency selection parameters to finally obtain a frequency domain feature matrix.

[0068] In one embodiment of the present application, the Welch method: P(f)=1 / K·Σ(k=1→K)[|FFT(x_k·w)| 2 ]·exp(-λ·var(|FFT(x_k·w)| 2 )); where P(f) is the power spectral density estimate; x_k is the kth data segment; w is the window function; K is the number of data segments; FFT is the fast Fourier transform; var is the variance function; λ is the smoothing parameter; |·| represents the modular operation.

[0069] Frequency importance score: I(f, t) = δ·softmax(MLP(P(f, t))) + ε·exp(-|dP(f, t) / dt| / ζ); where I(f, t) is the importance score of frequency f at time t; P(f, t) is the time-frequency spectrum density; MLP is the multilayer perceptron function; dP(f, t) / dt is the time derivative of the spectrum density; δ is the static importance weight; ε is the dynamic importance weight; ζ is the time-varying rate scaling parameter; softmax is the normalized exponential function; |·| represents the absolute value operation.

[0070] Bootstrap method: U(θ)=sqrt(1 / B·Σ(b=1→B)[θ_b-θ_mean] 2 )·(1+γ·skew(θ_b)); where U(θ) is the uncertainty estimate of parameter θ; θ_b is the b-th Bootstrap sample estimate; θ_mean is the mean; B is the number of Bootstrap samples; skew is the skewness function; and γ is the skewness adjustment coefficient.

[0071] This embodiment achieves effective capture of the periodic pattern of time series data through frequency domain feature extraction and adaptive frequency selection. First, the Hanning window function is used for windowing processing to reduce the influence of the spectrum leakage effect. The periodic characteristics of the signal are evaluated by calculating the autocorrelation function, which provides a reliable reference basis for frequency selection. Secondly, the Welch method is used to estimate the power spectral density, which improves the stability and reliability of the spectrum estimation. Through the combination of multi-layer perceptron and sigmoid function, the adaptive evaluation of frequency importance is achieved, so that the model can dynamically adjust the weight of the frequency component according to the characteristics of the data. Finally, the uncertainty of the weight is evaluated by the Bootstrap method, which improves the robustness of the frequency selection. This embodiment not only accurately captures the periodic pattern of the data, but also improves the expression efficiency of the feature through the optimization of frequency selection, and provides high-quality frequency domain features for subsequent time series modeling.

[0072] According to one aspect of the present application, step S22 is further as follows:

[0073] S221. Obtain a set of multi-scale feature blocks, calculate the Chebyshev polynomial coefficients of the feature blocks to obtain a polynomial coefficient matrix, construct an orthogonal basis function based on the coefficients to obtain a feature basis function, and use the basis function to perform feature expansion to obtain a polynomial expansion result.

[0074] S222. Obtain the polynomial expansion result and the frequency domain feature matrix, calculate the difference between the two to obtain a difference feature matrix, apply sparse coding to extract significant differences to obtain sparse difference features, and obtain key difference features through adaptive threshold screening.

[0075] S223. Obtain key difference features and difference feature matrices, construct a nonlinear mapping network to obtain transformation features, apply a dynamic weighting method to obtain weighted features, and combine the original features to obtain combined features.

[0076] S224 , obtaining the combined features and the difference feature matrix, performing feature selection to obtain the optimal features, applying residual correction to obtain the corrected features, and integrating all the features to obtain the residual feature matrix.

[0077] In one embodiment of the present application, the Chebyshev polynomial expansion is: C(x,n)=Σ(k=0→n)[ψ_k·T_k(x)]·exp(-k 2 / κ); where C(x, n) is the result of the n-th order polynomial expansion; T_k(x) is the k-th order Chebyshev polynomial; ψ_k is the k-th order expansion coefficient; x is the input feature; n is the expansion order; κ is the attenuation parameter; Σ represents the summation operation; and k is the polynomial order index.

[0078] This embodiment achieves accurate characterization of nonlinear time series patterns through polynomial expansion and residual feature extraction. First, a combined method of Chebyshev polynomial coefficient calculation and orthogonal basis function construction is adopted to provide a complete basis function set for feature expansion, ensuring the integrity and orthogonality of feature expression. Sparse coding technology is used to extract significant difference features, effectively reducing data redundancy and highlighting key pattern information. Secondly, a nonlinear mapping network is used to process transformation features, which enhances the model's ability to express complex nonlinear relationships. The features are adaptively combined through a dynamic weighting method to achieve intelligent adjustment of the contribution of different features. Finally, the dual mechanism of feature selection and residual correction is adopted to ensure the representativeness of the features and supplement the detailed information that may be lost. This embodiment not only improves the ability to capture nonlinear patterns, but also improves the accuracy and completeness of feature expression through feature selection and residual compensation.

[0079] like Figure 4 As shown, according to one aspect of the present application, step S3 is further:

[0080] S31. Based on the frequency domain feature matrix and the residual feature matrix, linearly transform the feature data to obtain a query vector, a key vector, and a value vector; calculate the similarity score between the query vector and the key vector, normalize the similarity score to obtain a normalized score; multiply the normalized score by the value vector to obtain an attention feature matrix;

[0081] S32. Based on the attention feature matrix, the frequency domain feature matrix, the residual feature matrix and the position encoding matrix are connected in the feature dimension, and the gating parameters are calculated through linear transformation and sigmoid function; based on the gating parameters, the frequency domain feature matrix and the residual feature matrix are weightedly combined to obtain the fusion feature matrix.

[0082] In one embodiment of the present application, based on the frequency domain feature matrix F and the residual feature matrix R, the multi-head attention is calculated: Ahead_i = softmax((FW i q )(RW k ) T / sqrt(d))(RW v ), where W i q is the transformation matrix of the query vector, W k is the transformation matrix of the key vector, W vis the transformation matrix of the value vector, d is the scaling factor of the feature dimension; output is the attention feature matrix A. Use the gating mechanism: g = sigmoid(W[F; R; P]), where P is the position code, g is the gating parameter, and W[ ] is the weight matrix; calculate the fused feature: H = gΘF + (1-g) ΘR, Θ is the element-level multiplication operation, and output is the fused feature matrix H.

[0083] This embodiment realizes the intelligent integration of different types of features through the attention mechanism and feature fusion strategy. First, by designing the query vector, key vector and value vector, a correlation metric between features is established, and important feature patterns can be automatically identified and highlighted through attention calculation. Secondly, a gating mechanism is used to adaptively weight frequency domain features and residual features, avoiding the information redundancy problem that may be caused by simple feature splicing. The gating parameters are calculated by the sigmoid function to realize the dynamic evaluation and selection of feature importance. Finally, by incorporating position encoding, the model can fully consider the temporal dependency of features. This embodiment not only improves the model's perception of key features, but also enhances the modeling capability of long-term dependencies, while reducing the negative impact of feature redundancy on model performance.

[0084] According to one aspect of the present application, step S31 is further as follows:

[0085] S311. Obtain the frequency domain feature matrix and the residual feature matrix, generate a query matrix through linear mapping, apply the projection algorithm to generate a key matrix, use a nonlinear activation function to obtain a value matrix, and perform batch normalization on the three matrices to obtain a standardized query matrix, a standardized key matrix, and a standardized value matrix.

[0086] S312. Obtain the standardized query matrix, the standardized key matrix, and the standardized value matrix, calculate the dot product of the query and the key to obtain the attention score, divide the attention score by the scaling factor to obtain the scaling score, perform a softmax operation on the scaling score to obtain the normalized attention score, and multiply the normalized attention score by the standardized value matrix to obtain the multi-head attention feature.

[0087] S313. Obtain multi-head attention features, use a feature aggregation network to merge the outputs of multiple attention heads to obtain aggregated features, use a feedforward neural network to process the aggregated features to obtain transformed features, and apply a layer normalization method to obtain an attention feature matrix.

[0088] In one embodiment of the present application, the attention matrix is ​​generated as follows: A(Q, K) = softmax(Q·K T / sqrt(d)+M)·V; where A(Q,K) is the attention matrix; Q is the query matrix; K is the key matrix; V is the value matrix; d is the feature dimension; M is the position bias matrix; softmax is the normalized exponential function; T represents matrix transpose operation; represents matrix multiplication; sqrt represents square root operation.

[0089] This embodiment realizes the intelligent integration of different types of features through a multi-head attention mechanism and a feature fusion strategy. First, a method of generating query, key, and value matrices using linear mapping is adopted to construct a correlation metric between features. Batch normalization is used to improve the numerical stability and convergence speed of attention calculations. Secondly, the scaled dot product attention mechanism is used to calculate the correlation between features, avoiding the gradient vanishing problem. Through the softmax operation, the sparsity of the attention weights and the generalization ability of the model are enhanced. Finally, the dual processing of the feature aggregation network and the feedforward neural network is adopted to realize the effective fusion of the multi-head attention output. This embodiment not only improves the model's ability to recognize key features, but also enhances the robustness and reliability of feature extraction through a multi-head mechanism and regularization strategy.

[0090] According to one aspect of the present application, step S32 is further as follows:

[0091] S321. Based on the attention feature matrix, concatenate the frequency domain feature matrix, the residual feature matrix, and the position encoding matrix in the feature dimension to obtain a concatenated feature matrix; perform feature dimensionality reduction on the concatenated feature matrix to obtain reduced dimensionality features; based on the reduced dimensionality features, perform nonlinear transformation processing to obtain transformed features; based on the transformed features, apply the attention mechanism to calculate feature weights to obtain weighted features;

[0092] S322, obtaining weighted features, and obtaining initial gating parameters through linear transformation and sigmoid function calculation; based on the initial gating parameters, estimating parameter importance through feature entropy to obtain parameter importance; based on the parameter importance, updating the initial gating parameters to obtain optimized gating parameters; based on the optimized gating parameters, applying dynamic threshold adjustment to obtain adaptive gating parameters;

[0093] S323. Use adaptive gating parameters to weight the frequency domain feature matrix and the residual feature matrix to obtain weighted frequency domain features and weighted residual features; based on the weighted frequency domain features and weighted residual features, adopt an adaptive fusion strategy to obtain initial fusion features; based on the initial fusion features, apply residual connection to obtain a fusion feature matrix.

[0094] In one embodiment of the present application, the dynamic gating parameter is: G(h, t) = χ·sigmoid(L(h)) + ω·tanh(H(t))·exp(-E(h) / τ); wherein G(h, t) is the gating parameter of feature h at time t; L(h) is the linear transformation function; H(t) is the time encoding function; E(h) is the feature entropy; χ is the static gating weight; ω is the dynamic gating weight; τ is the entropy scaling parameter; sigmoid is the S-type activation function; and tanh is the hyperbolic tangent function.

[0095] This embodiment achieves efficient fusion of multi-source features through an adaptive gating mechanism and a feature combination strategy. First, through the combination of feature dimensionality reduction and nonlinear transformation, feature redundancy is reduced and feature expression capabilities are enhanced. The attention mechanism is used to calculate feature weights, which enables automatic identification and highlighting of important features. Secondly, the importance of parameters is estimated based on feature entropy, providing a reliable reference for gating parameter optimization. Through the dynamic threshold adjustment mechanism, the adaptive update of gating parameters is achieved, enabling the model to dynamically adjust the importance weights of features according to data characteristics. Finally, a combination strategy of residual connection and adaptive fusion is adopted to retain the original feature information and achieve effective integration of features. This embodiment not only improves the flexibility and adaptability of feature integration, but also enhances the expression ability and stability of the model through residual connection and adaptive fusion.

[0096] like Figure 5 As shown, according to one aspect of the present application, step S4 is further:

[0097] S41. Based on the fusion feature matrix, a graph structure is constructed to reflect the dependency relationship between time points; message transmission and update operations are performed on the node features in the graph structure to obtain updated node features; the updated node features are aggregated to obtain time series aggregation features;

[0098] S42. Based on the time series aggregation features and the fusion feature matrix, calculate the rate of change of features over time and generate the system stability index; based on the time series aggregation features and the fusion feature matrix, extract the change pattern of features in different time periods through time scale analysis and time window division, and generate the feature time scale; based on the time series aggregation features and the fusion feature matrix, evaluate the diversity and nonlinearity of features through complexity analysis, entropy calculation and nonlinear measurement, and obtain the complexity index; combine the system stability index, feature time scale and complexity index to generate dynamic system characteristics.

[0099] In one embodiment of the present application, based on the fusion feature matrix H, a time sequence graph is constructed: G = (V, E), where V is a set of time points and E is a set of time sequence dependency edges; a graph attention network is applied: h' i = σ(Σ j ∈Ni α ij Wh j ), where h' i is the updated feature of node i, which represents the temporal aggregation feature calculated by the graph attention network; σ( ) is the activation function, Σ j ∈N i Indicates the sum of neighbor nodes j of node i, α ij is the attention weight between node i and node j, W is the weight matrix, h j is the feature vector of node j, and the output is the time series aggregation feature T. The system stability is calculated based on the Lyapunov exponent: λ = lim(t→∞) 1 / t ln|df / dx|, where λ is the Lyapunov exponent. The system dynamic characteristics are extracted: D = [λ, τ, μ], where τ is the characteristic time scale and μ is the system complexity index. The dynamic system characteristics D are output.

[0100] This embodiment achieves an in-depth characterization of complex time series relationships through graph structure modeling and dynamic feature extraction. First, a time series dependency graph is constructed based on fusion features, and the dependency relationship of time series data is converted into a connection relationship between nodes in the graph structure, which not only retains the time series order of the data, but also can capture the potential correlation between non-continuous time points. Secondly, through message passing and node feature updates on the graph structure, effective aggregation and propagation of time series information are achieved. Finally, by calculating the rate of change of features and system stability indicators, a comprehensive characterization of the dynamic characteristics of the system is obtained. This embodiment improves the model's ability to understand complex time series patterns, and at the same time, through the extraction of dynamic system features, it enhances the model's ability to predict changes in system states.

[0101] According to one aspect of the present application, step S41 is further as follows:

[0102] S411. Obtain a fusion feature matrix, calculate the Euclidean distance between feature vectors to obtain a distance matrix, calculate the time series alignment score based on the dynamic time warping algorithm to obtain an alignment score, and construct a time series dependency feature by combining the distance matrix and the alignment score.

[0103] S412. Obtain temporal dependency features, use the K-nearest neighbor algorithm to construct initial graph connections to obtain an initial graph structure, apply a graph sparsification algorithm to optimize connection relationships to obtain a sparse graph structure, and calculate edge weights to obtain a weighted graph structure.

[0104] S413. Obtain the weighted graph structure and fusion feature matrix, perform graph convolution operation to update node features to obtain updated node features, apply skip connection to retain original information to obtain residual node features, and selectively update through the gating mechanism to obtain selective node features.

[0105] S414. Obtain selective node features, use the attention pooling method to aggregate node information to obtain pooled features, use the sequence compression network to extract key information to obtain compressed features, and combine features of different scales to obtain temporal aggregation features.

[0106] In one embodiment of the present application, the dynamic time warping algorithm is as follows: DTW(X, Y)=min{Σ(i=1→n, j=1→m)[w_k·d(x_i, y_j)]}; where DTW(X, Y) is the alignment distance of time series X and Y; d(x_i, y_j) is the local distance between sequence points x_i and y_j; w_k is the path weight coefficient; n, m are the sequence lengths; the local distance is calculated using: d(x_i, y_j)=||x_i-y_j|| 2 +λ·|ij|; the path update adopts: D(i, j)=min{D(i-1, j-1), D(i-1, j), D(i, j-1)}+d(x_i, y_j); where D(i, j) is the cumulative distance matrix; λ is the time penalty coefficient.

[0107] Graph structure optimization: R(i, j) = φ·exp(-D(i, j) / σ) + ξ·cos(π·S(i, j)); where R(i, j) is the relationship strength between nodes i and j; D(i, j) is the node feature distance; S(i, j) is the temporal similarity; φ is the distance term weight; ξ is the similarity term weight; σ is the distance scaling parameter; π is the circumference of a circle; exp is the exponential function; and cos is the cosine function.

[0108] Graph sparsification algorithm: E(i, j) = w_ij · exp(-D_ij / σ) · I(R_ij > τ(d_i, d_j)); where E(i, j) is the edge weight; w_ij is the initial weight; D_ij is the node distance; R_ij is the relevance score; σ is the distance scale parameter; I is the indicator function; τ(d_i, d_j) is the adaptive threshold function; d_i, d_j are the node degrees.

[0109] This embodiment achieves an in-depth characterization of complex temporal relationships through graph structure modeling and node feature updates. First, a combination of Euclidean distance and dynamic time warping algorithms is used to accurately characterize the similarity relationship between time series data points. The initial graph connection is constructed through the K-nearest neighbor algorithm, which provides a good initial state for subsequent graph structure optimization. Secondly, the connection relationship is optimized using a graph sparsification algorithm, which reduces the complexity of the graph structure and highlights important dependencies. Node features are updated through graph convolution operations to achieve information propagation and aggregation on the graph structure. Finally, a combination of jump connections and gating mechanisms is used to retain the original node information and achieve selective updates of features. This embodiment not only improves the modeling capability of complex temporal dependencies, but also improves the expression efficiency and accuracy of the model through feature selection and information propagation mechanisms.

[0110] like Figure 6 As shown, according to one aspect of the present application, step S5 is further:

[0111] S51. Calculate the parameters of the mixed Gaussian distribution based on the time series aggregation features and the dynamic system features; generate a conditional probability distribution based on the parameters of the mixed Gaussian distribution to obtain a predicted distribution;

[0112] S52. Calculate the entropy value of the predicted distribution; calculate the stability score based on the dynamic system characteristics; combine the entropy value and the stability score to obtain a confidence index.

[0113] In one embodiment of the present application, based on the temporal aggregation feature T and the dynamic system feature D, a hybrid density network is constructed: p(y|x) = Σ i π i (x)N(μ i (x), σ i 2 (x)), where p(y|x) is the conditional probability distribution, which represents the probability distribution of output y given input x; π i (x) is the weight of the mixture component, which represents the weight of the i-th mixture component under input x; N(μ i (x), σ i 2 (x)) is the normal distribution of the i-th mixture component, indicating that the mean is μ i (x), with variance σ i 2 (x); output prediction distribution P(Y|X). Calculate the predicted entropy: H = -∫p(y|x)log p(y|x)dy; calculate the system stability index based on the dynamic characteristics: s = exp(-||D||2), and output the confidence index C = [H, s].

[0114] This embodiment implements a reliability assessment of prediction results. First, a mixed Gaussian distribution model is constructed based on time series aggregation features and dynamic system characteristics. Through parameter optimization, an accurate conditional probability distribution is obtained, enabling the model to make probabilistic predictions of future states. Second, by calculating the entropy of the predicted distribution and the system stability index, a quantitative assessment of the uncertainty of the prediction results is achieved. This embodiment not only provides point estimates but also confidence intervals for the predictions, providing more comprehensive reference information for decision-making.

[0115] According to one aspect of the present application, step S51 is further as follows:

[0116] S511. Obtain time series aggregation features and dynamic system features, use kernel density estimation to calculate feature distribution to obtain distribution parameter estimates, use maximum likelihood method to optimize parameters to obtain optimized distribution parameters, and evaluate parameter uncertainty to obtain parameter confidence intervals.

[0117] S512. Obtain optimized distribution parameters, calculate the mixing weights by variational inference to obtain initial mixing weights, optimize the mixing weights using the EM algorithm to obtain optimized mixing weights, and apply the Dirichlet process for non-parametric modeling to obtain adaptive mixing weights.

[0118] S513. Obtain optimized distribution parameters and adaptive mixing weights, construct a Gaussian mixture model to obtain a mixture probability model, calculate the conditional probability distribution to obtain a conditional probability matrix, and integrate all components to obtain a predicted distribution.

[0119] In one embodiment of the present application, variational inference optimization: Q(z|x)=N(μ(x),Σ(x))·exp(KL(P||Q) / η); wherein Q(z|x) is the variational posterior distribution; N(μ,Σ) is the Gaussian distribution; μ(x) is the mean function; Σ(x) is the covariance function; P is the prior distribution; KL is the KL divergence; η is the temperature parameter; exp is the exponential function; z is the latent variable; and x is the observed variable.

[0120] EM algorithm: Q(θ|θ_t)=E_z[log P(X, Z|θ)]+λ·R(θ); where Q(θ|θ_t) is the Q function; θ is the model parameter; θ_t is the parameter of the tth iteration; X is the observed data; Z is the latent variable; P(X, Z|θ) is the complete data likelihood function; E_z is the expectation about Z; λ is the regularization coefficient; R(θ) is the regularization term; the parameter update is: θ_(t+1)=argmax_θ{Q(θ|θ_t)·exp(-μ·||θ-θ_t|| 2 )}.

[0121] Dirichlet process: DP(G_0,η)=lim(K→∞)Σ(k=1→K)[π_k·δ(θ_k)]; where G_0 is the basis distribution; η is the concentration parameter; π_k is the mixing weight; θ_k is the component parameter; δ is the Dirac function; weight generation: π_k=v_k·Π(i=1→k-1)(1-v_i); where v_k~Beta(1,η).

[0122] This embodiment achieves an accurate estimation of the predicted distribution through a mixed probability model and variational inference. First, a combination of kernel density estimation and maximum likelihood method is used to model the feature distribution, avoiding the model bias that may be caused by the parameter distribution assumption. By evaluating the uncertainty of the parameters, the reliability and stability of the distribution estimation are improved. Secondly, the variational inference method is used to optimize the mixed weights, thereby achieving efficient learning of the model parameters. The mixed weights are iteratively optimized by the expectation maximization (EM) algorithm to ensure the convergence and accuracy of the parameter estimation. Finally, the Dirichlet process is used for non-parametric modeling to enhance the model's ability to express complex distributions. This embodiment can not only accurately characterize the distribution characteristics of the data, but also improve the flexibility and computational efficiency of the model through non-parametric modeling and variational inference. By considering the uncertainty of the parameters, the model can provide more reliable prediction results and confidence intervals, providing an important reference for decision-making in practical applications.

[0123] According to one aspect of the present application, step S52 is further as follows:

[0124] S521. Obtain the predicted distribution, calculate the entropy of the distribution to obtain the initial entropy value, use the bootstrap method to estimate the entropy confidence interval to obtain the entropy confidence interval, generate the entropy uncertainty index based on the interval information, and combine the multi-scale analysis to obtain the multi-scale entropy value.

[0125] S522. Obtain dynamic system characteristics and multi-scale entropy values, calculate the norm of the characteristics to obtain the characteristic norm value, use exponential function transformation to obtain an initial stability score, apply adaptive smoothing to obtain a smoothed stability score, and combine the system dynamic characteristics to obtain a system stability index.

[0126] S523. Obtain the entropy uncertainty index and system stability index, build a combined evaluation model to obtain a combined evaluation score, apply a weighted average strategy to obtain a weighted confidence, combine historical evaluation information to obtain a time series confidence, and finally integrate to obtain a confidence index.

[0127] In one embodiment of the present application, the adaptive smoothing algorithm is: S(x, h) = Σ(i)[(x_i K((x-x_i) / h(x))] / Σ(i)[K((x-x_i) / h(x))]; where S(x, h) is the smoothing result; x_i is a data point; K is the kernel function; h(x) is the local bandwidth function; and bandwidth update: h(x) = h_0 (1+γ |dx / dt|) -α ; Where h_0 is the basic bandwidth; γ is the adjustment coefficient; α is the attenuation exponent.

[0128] Combined evaluation model: E(x)=w_1·f_1(x)+w_2·f_2(x)+...+w_n·f_n(x); where E(x) is the combined evaluation score; f_i is a single evaluation indicator; w_i is the adaptive weight; weight update: w_i(t+1)=w_i(t)·exp(η·R_i(t)) / (Σ_j[w_j(t)·exp(η·R_j(t))]); where R_i is the performance score of indicator i; η is the learning rate.

[0129] This embodiment achieves a comprehensive evaluation of the prediction results through entropy calculation and stability analysis. First, by calculating the entropy of the prediction distribution and estimating the confidence interval of the entropy using the bootstrap method, reliable quantification of the prediction uncertainty is achieved. Based on the multi-scale analysis method, the changing characteristics of the entropy value at different time scales are evaluated, providing a more comprehensive uncertainty measurement. Secondly, by calculating the characteristic norm and exponential function transformation, a quantitative evaluation index of the system stability is constructed. Adaptive smoothing is used to reduce the influence of noise in the stability assessment. Finally, by combining the evaluation model and the weighted average strategy, a comprehensive integration of entropy and stability indicators is achieved. This embodiment not only provides a quantification of the credibility of the prediction results, but also enhances the reliability of the evaluation results through multi-dimensional stability analysis. By considering the time series characteristics, the evaluation results can reflect the dynamic changes of the system state, providing more comprehensive decision support for the practical application of the model. At the same time, the adaptive weight update mechanism ensures that the evaluation index can be dynamically adjusted according to the changes in the system state, improving the timeliness and accuracy of the evaluation results.

[0130] In another embodiment of the present application, step S11 can also be: reading the original time series data sequence from the database, performing minimum-maximum normalization processing on the data to obtain normalized data, calculating the sliding average of the normalized data to obtain smoothed data, performing cosine similarity calculation on adjacent time points in the smoothed data to obtain a similarity sequence, based on the similarity sequence, using Gaussian kernel function transformation to obtain kernel transformed data, combining the kernel transformed data with the original sampling interval through a dynamic programming algorithm to calculate the optimal block to obtain an adaptive block size sequence.

[0131] Step S12 can also be: obtaining an adaptive block size sequence and an original time series data sequence, calculating the autocorrelation function of each data block to obtain a correlation coefficient sequence, estimating the optimal convolution kernel size based on the correlation coefficient sequence by the variational Bayesian method to obtain a kernel size parameter, inputting the kernel size parameter into the Gaussian-Xavier initialization algorithm to generate an initial convolution kernel, applying L1 regularization constraint to the initial convolution kernel to obtain a sparse convolution kernel, using the sparse convolution kernel to perform a one-dimensional convolution operation on the data block to obtain a convolution feature map, applying the LeakyReLU activation function to the convolution feature map to obtain an activation feature map, and processing the activation feature map through a spatial pyramid pooling network to obtain a multi-scale feature block set.

[0132] The Gaussian-Xavier initialization algorithm is specifically: W_l=ξ·N(0, sqrt(2 / (n_in+n_out)))·M_l; where W_l is the weight matrix of the lth layer; N(0, σ) is a Gaussian distribution with mean 0 and standard deviation σ; n_in is the input dimension; n_out is the output dimension; ξ is the scaling factor; M_l is the mask matrix.

[0133] In another embodiment of the present application, step S3 may also be:

[0134] S3a. Obtain the frequency domain feature matrix and the residual feature matrix, generate the query, key, and value matrices through linear projection to obtain the initial attention tensor, perform scaled dot-product attention calculation on the initial attention tensor to obtain the attention score, regularize the attention score by dropout to obtain the regularized score, calculate the weighted sum based on the regularized score and the value matrix to obtain the weighted feature, and apply layer normalization to the weighted feature to obtain the attention feature matrix.

[0135] S3b. Obtain the frequency domain feature matrix, residual feature matrix and position encoding matrix, map the three matrices to the same feature space through a nonlinear projection layer to obtain a unified feature, calculate the mutual information of the unified feature to obtain the feature correlation, generate the adaptive gating parameter based on the feature correlation through a soft-shrinkage algorithm to obtain the gating coefficient, multiply the gating coefficient with the original feature matrix to obtain the weighted feature, and perform residual connection on the weighted feature to obtain the fused feature matrix.

[0136] The soft-shrinkage algorithm is specifically as follows: S(x, λ)=sign(x)·max(|x|-λ·(1+α·|dx / dt|), 0); where S(x, λ) is the value after shrinkage; x is the input value; λ is the basic threshold parameter; α is the dynamic adjustment coefficient; dx / dt is the rate of change; sign is the sign function; max is the maximum value operation; |·| represents the absolute value.

[0137] In another embodiment of the present application, step S5 may also be:

[0138] S5a. Obtain time series aggregation features and dynamic system features, generate initial mixed Gaussian distribution parameters through random sampling to obtain initial distribution parameters, use variational expectation maximization algorithm to optimize the initial distribution parameters to obtain optimized distribution parameters, construct a conditional Gaussian mixture model based on the optimized distribution parameters to obtain a mixed probability model, and apply Monte Carlo sampling to the mixed probability model to obtain a predicted distribution.

[0139] The variational expectation maximization algorithm is specifically: L(q)=E_q[log P(X, Z)]-E_q[log q(Z)]+α·H(q); where L(q) is the variational lower bound; q(Z) is the variational posterior distribution; P(X, Z) is the joint distribution; E_q is the expectation with respect to q; H(q) is the entropy term; α is the entropy weight coefficient; variational distribution update: q*(Z_i)∝exp(E_{q(Z_¬i)}[log P(X, Z)])+β·KL(q_old||q_new), Z_i is the latent variable, E_{q(Z_¬i)} is the expectation with respect to q(Z_¬i), which represents the variational posterior distribution of other latent variables excluding the latent variable Z_i; q_old is the old variational distribution, q_new is the new variational distribution, and β is the weight coefficient of KL divergence.

[0140] S5b. Obtain the predicted distribution and dynamic system characteristics, calculate the differential entropy of the predicted distribution to obtain the entropy value sequence, use the block bootstrap method to estimate the confidence interval of the entropy value sequence to obtain the entropy confidence, calculate the Lyapunov exponent of the dynamic system characteristics to obtain the stability index, and combine the entropy confidence and stability index through the additive model to obtain the confidence index.

[0141] The block bootstrap algorithm is specifically as follows: B(x, l)=Σ(i=1→n / l)[x_(b_i:b_i+l)·w_i]; where B(x, l) is the block bootstrap sample; x is the original sequence; l is the block length; b_i is the block starting position; w_i is the block weight; n is the sequence length; the block length is adaptively selected: l*=argmin{MSE(B(x, l))+ρ·var(l)}; where MSE is the mean square error, l* is the optimal block length, ρ is the penalty coefficient, and var(l) is the variance of the block length.

[0142] According to one aspect of the present application, a method for modeling time series data of an embodied intelligent agent based on frequency domain learning includes the following steps:

[0143] Step 1: Input processing and feature extraction.

[0144] Step 1.1, multi-scale convolution module. The input data x is fed into the multi-scale convolution module, which captures the local features in the data through convolution operations of multiple scales. Specifically, for input x∈R B×Cin×D , B is the batch size, Cin is the number of input channels, D=(D1, D2, ..., Dn) is the size of the spatial dimension, this module uses multiple convolutional layers Conv(x) to process the input data to obtain multi-level features: x multi-scale =MultiScaleConv(x), where MultiScale is a multi-scale convolution module.

[0145] Step 1.2, Block Module and Position Encoding. To further enhance the representation of spatial information, a block module is used to segment the input data according to the specified block size (M1, M2, ..., Mn). Local features are extracted independently within each block, and the data after block segmentation is represented as: blocks =Block(x, (M1, M2, ..., Mn)), where Block is a block module; then, positional encoding is added to the features of each position to ensure that the model can effectively utilize the position information of the input data. The positional encoding is generated by a function f(q), where q represents the coordinates of each position in the input data: x encoded = x blocks +f(q).

[0146] Step 1.3, convolution residual Fourier layer. Based on the convolution operation, the convolution residual Fourier layer is used to model the frequency domain information. The output y of the convolution residual Fourier layer is out is the Fourier layer y fft The output of the convolutional layer and the high-frequency features y conv Fusion via residual connections: y out =y fft +y conv +b, b is the bias term.

[0147] Step 2: Feature fusion.

[0148] Step 2.1, self-attention. The processed multi-scale features and Fourier domain convolution features are fed into the multi-head self-attention module. This module establishes the dependency between different features through the multi-head attention mechanism and learns the interaction between features. Specifically, given the feature matrix X features ∈R B×N×D , the multi-head attention mechanism is calculated by the following formula: Y attn =MultiHeadAttention(X features ), where MultiHeadAttention is a multi-head self-attention mechanism.

[0149] Step 2.2, Cross Attention. On this basis, this embodiment also combines the cross attention mechanism, and the interaction with other latent variables further enhances the ability of feature representation. The cross attention mechanism calculates the cross attention output through the following formula: cross =CrossAttention(X features , Z latent ), where Z latent is the representation of latent variables, and CrossAttention is the cross attention mechanism.

[0150] Step 3: Time series aggregation and output generation. After feature extraction and attention mechanism processing, the time series information of the input data is aggregated by the time series aggregation module. This module aggregates the processed features according to the time dimension and extracts the temporal dependencies in the time series. Assume that the processed feature sequence is Y features =[y1, y2, ..., yT], the time series aggregation operation can be expressed as: aggregated =TimeAggregation(Y features ), where TimeAggregation is the time series aggregation module.

[0151] Traditional dynamic system modeling usually relies on discretization and numerical solution of partial differential equations. Although these methods can effectively describe the changes of the system to a certain extent, their computational cost is high and time efficiency is low when dealing with high-dimensional space. In this embodiment, by converting time series data into frequency domain space, frequency domain representation learning can effectively identify and utilize the periodicity and frequency characteristics in the data, improve the model's ability to handle spatiotemporal changes, and reduce the need for redundant calculations in high-dimensional space. When faced with actual application scenarios with high noise or lack of sufficient data, the frequency domain-based representation learning method has stronger adaptability and practicality than traditional reinforcement learning. Frequency domain representation captures the regularity in the data through frequency characteristics. Even when data is scarce or the noise is large, it can still effectively identify the key characteristics of the system and improve the robustness of the model.

[0152] In one embodiment of the present application, multi-scale convolution is introduced to expand the receptive field of the convolution kernel. In the process of data segmentation, features at different levels are extracted, so that the convolution kernel can cover a wider area in the input data and capture more context information while controlling the parameters at a lower level. In multi-scale convolution, the elements in the convolution kernel are separated. Assuming that the input data is x(t), the convolution kernel is w(k), and the scale is r: y(t)=(x*w)(t)=∑ k=0 K-1x(tr·k)·w(k); Unlike standard convolution, where the receptive field size is equal to the kernel size, in multi-scale convolution, assuming the input data size is N, the kernel size is K, the stride is S, and the scale is r, the receptive field R' can be expressed as: R' = (K-1)·r+1. To ensure that the output feature map after the convolution operation is the same size as the input data (or at least maintains a certain size), the input data needs to be padded, and the amount of padding needs to be adjusted according to the scale. For different convolution kernels K, the padding amount P of the dilated convolution can be calculated as follows: P = └(K-1)·r / 2┘, where └ ┘ is a floor symbol. To simultaneously extract features at multiple scales, assume there are N different scales r1, r2, …, rN, and create a separate convolutional layer for each scale. Finally, the outputs of all convolutional layers are concatenated along the channel dimension to combine features from different scales. For example, if four scales [r1, r2, r3, r4] are selected, the output of the convolution operation can be expressed as: y(t)=[(x*w r1 )(t),(x*w r2 )(t),(x*w r3 )(t),(x*w r4 )(t)]; By performing concatenation operations on the channel dimension, the outputs of each scale can be combined to form a richer feature representation.

[0153] In order to make full use of the features of different frequencies, this embodiment combines Fourier transform, convolution operation and residual connection, with the goal of optimizing the feature extraction process of Fourier neural operator. For a d-dimensional input signal x, after Fourier transform, we get: x'(l)= ∫ Rd x(q)e -i2πl·q dq; where x'(l) is the frequency domain representation of the signal, x(q) is the original signal, l is the vector in the frequency space, and q is the position in the time-space domain. After Fourier transform, only the low-frequency part in the frequency domain is retained, l trunc is the threshold of the cutoff frequency. The low-frequency cutoff operation is as follows: x'(l) = x'(l), if |l|≤l trunc ;x''(l)=0,if∣l∣>l trunc In the frequency domain, the convolution operation can be implemented by element-by-element multiplication. For the Fourier transform x' of the input signal and the Fourier transform w' of the convolution kernel, the frequency domain convolution operation is expressed as: y'(l) = x'(l) w'(l). Once the convolution operation is completed in the frequency domain, the result needs to be converted back to the time-space domain for subsequent processing: y(q) = F -1 (y'(l))= ∫ Rd y'(l) e i2πl·q dl, where y(q) is the signal in the time and space domain, F -1Indicates the inverse Fourier transform, and y'(l) is the signal in the frequency domain. In addition to processing the low-frequency part in the frequency domain, it is still necessary to process the high-frequency part through the convolution layer: y conv =Conv(x). In order to improve the expressiveness of the model and speed up the training process, residual connections are used. The output of the convolution is directly added to the input signal: y out =y fft +y conv +b. In summary, the loss function includes reconstruction loss and feature matching loss. In reconstruction loss, y' is the predicted output feature patch, y target is the target feature patches, B is the batch size, S=Π i=1 N G i represents the total spatial dimension, G i is the size of the spatial dimension, and the reconstruction loss L reconstruction =(1 / B·S)∑ b=1 B ∑ s=1 S ∣∣y' bs -y target，bs ∣∣ 2 2, where y' bs is the feature block predicted by the model, y target，bs is the target feature block; the feature matching loss matches the features of different scales to the target features: feature matching loss L Fourier =(1 / B·N f )∑ b=1 B ∑ f=1 Nf ∣∣F' f，b，f -F f，target，b，f ∣∣ 2 2; where F' f，b，f is the frequency domain spatial feature of the model output, Nf is the number of features, F f，target，b，f is the target frequency domain spatial feature. The complete loss can be expressed as follows: L=λL reconstruction +L Fourier , λ is the weight coefficient.

[0154] This invention achieves intelligent modeling and prediction of complex time series data through the fusion of frequency domain learning and embodied agents. First, a combined approach of adaptive blocking and multi-scale convolution achieves efficient feature extraction of time series data. Frequency domain transformation and residual compensation mechanisms ensure the integrity and accuracy of feature representation. Second, an attention mechanism and feature fusion strategy enable intelligent integration of different types of features. Graph structure modeling and dynamic feature extraction provide a deep understanding of complex time series dependencies. Finally, a hybrid probability model and uncertainty quantification method are employed to assess the reliability of prediction results. This invention not only improves the accuracy and efficiency of time series data modeling but also enhances the reliability of prediction results through uncertainty quantification. It has broad application value in industrial production, financial forecasting, intelligent manufacturing, and other fields, providing strong support for state prediction and decision optimization of complex systems. The introduction of embodied agents equips the model with environmental awareness and adaptability, further improving the system's robustness and generalization performance in practical applications. Through multi-level feature extraction and fusion, this invention achieves the effective transformation from data to knowledge, providing reliable technical support for intelligent decision-making.

[0155] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the scope of protection of the present invention.

Claims

1. A method for modeling time series data of embodied intelligent agents based on frequency domain learning, characterized by: The steps include: S1. Obtain the original time series data sequence and determine the adaptive block size sequence based on the temporal relationship between adjacent data points; based on the adaptive block size sequence, block the original time series data sequence to obtain data blocks; use the multi-scale convolution method to extract features from the data blocks and generate corresponding position coding information to obtain a multi-scale feature block set and a position coding matrix; this method is used in the field of industrial production, where the original time series data sequence includes position, dynamic features, frequency features, periodic patterns, and long-term dependencies in the spatiotemporal domain; S2. Perform Fourier transform on each feature block in the multi-scale feature block set to extract frequency domain information; analyze the signal amplitude in the frequency domain information to determine the frequency selection parameter; based on the frequency selection parameter, perform nonlinear transformation and residual compensation on the frequency domain information to obtain a frequency domain feature matrix and a residual feature matrix; S3. Calculate the attention relationship between features based on the frequency domain feature matrix, residual feature matrix and position encoding matrix; Based on the attention relationship, the features are fused to obtain the fused feature matrix; S4. Construct a temporal dependency graph based on the fused feature matrix; Based on the graph structure of the time series dependency graph, the time series aggregation features are extracted, the system dynamic feature parameters are calculated, and the dynamic system features are obtained; S5. Based on the time series aggregation features and dynamic system characteristics, a probabilistic prediction model is constructed, the uncertainty of the prediction results is calculated, and the prediction distribution and confidence index are obtained.

2. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 1, characterized in that: Step S1 is further as follows: S11. Read the original time series data sequence from the database, perform an inner product operation on the data at adjacent time points to obtain an inner product result; add 1 to the inner product result and then perform a power operation to obtain an operation result; Based on the calculation results, construct the similarity data of adjacent time points; According to the similarity data, the size of the data block is determined to obtain an adaptive block size sequence; S12. Construct convolution kernel parameters of different sizes based on the adaptive block size sequence and the original time series data sequence; perform a convolution operation on each data block based on the convolution kernel parameters to obtain a convolution result; combine the convolution results in the channel dimension to obtain a multi-scale feature block set; S13, obtaining time index information of the data block in the multi-scale feature block set, and calculating the sine function value as the initial position code; Constructing location query data and calculating the correlation score between the location query data and the initial location code; The relevance scores are normalized to generate a position encoding matrix.

3. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 2, characterized in that: Step S2 is further as follows: S21. Obtain a multi-scale feature block set, perform Fourier transform on the feature block data to obtain a Fourier transform result; based on the Fourier transform result, calculate the amplitude of the transformed signal to obtain amplitude data; based on the amplitude data, generate a frequency selection parameter through a multi-layer perceptron operation and a sigmoid function; multiply the frequency selection parameter by the Fourier transform result to obtain a frequency domain feature matrix; S22. Based on the multi-scale feature block set and the frequency domain feature matrix, a polynomial expansion operation is performed on the feature block data using the polynomial coefficients to obtain a polynomial expansion result; a difference operation is performed between the polynomial expansion result and the frequency domain feature matrix to obtain a residual feature matrix.

4. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 3 is characterized in that: Step S3 is further as follows: S31. Based on the frequency domain feature matrix and the residual feature matrix, linearly transform the feature data to obtain a query vector, a key vector, and a value vector; calculate the similarity score between the query vector and the key vector, normalize the similarity score to obtain a normalized score; multiply the normalized score by the value vector to obtain an attention feature matrix; S32. Based on the attention feature matrix, the frequency domain feature matrix, the residual feature matrix and the position encoding matrix are connected in the feature dimension, and the gating parameters are calculated through linear transformation and sigmoid function; based on the gating parameters, the frequency domain feature matrix and the residual feature matrix are weightedly combined to obtain the fusion feature matrix.

5. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 4 is characterized in that: Step S4 is further as follows: S41. Based on the fusion feature matrix, a graph structure is constructed to reflect the dependency relationship between time points; message transmission and update operations are performed on node features in the graph structure to obtain updated node features; Summarize the updated node features to obtain time series aggregate features; S42. Based on the time series aggregated features and the fused feature matrix, calculate the rate of change of the features over time and generate a system stability index; based on the time series aggregated features and the fused feature matrix, extract the change pattern of the features in different time periods through time scale analysis and time window division, and generate a feature time scale; Based on the time series aggregation features and fusion feature matrix, the diversity and nonlinearity of the features are evaluated through complexity analysis, entropy calculation and nonlinear measurement to obtain the complexity index; combined with the system stability index, characteristic time scale and complexity index, the dynamic system characteristics are generated.

6. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 5, characterized in that: Step S5 is further as follows: S51. Calculate the parameters of the mixed Gaussian distribution based on the time series aggregation features and the dynamic system features; generate a conditional probability distribution based on the parameters of the mixed Gaussian distribution to obtain a predicted distribution; S52. Calculate the entropy value of the predicted distribution; calculate the stability score based on the dynamic system characteristics; combine the entropy value and the stability score to obtain a confidence index.

7. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 6, characterized in that: Step S11 is further as follows: S111. Obtain an original time series data sequence from a database, segment the original time series data sequence using a sliding window method, remove outliers in each segment of data, and obtain segmented data; perform Z-score normalization on the segmented data to obtain standardized time series data; apply wavelet transform to the standardized time series data to remove high-frequency noise, and obtain denoised standardized data and time series window data; S112. Based on the denoised normalized data and the time series window data, calculate the inner product of the adjacent time window data to obtain inner product data; add 1 to the inner product data to obtain offset inner product data; perform a power operation on the offset inner product data to obtain power feature data; calculate the Pearson correlation coefficient of the power feature data; use a kernel function method to map the Pearson correlation coefficient to a high-dimensional feature space, and reduce the feature dimension through a local sensitive hashing method to obtain time series related features; S113, based on the time series correlation feature and the power feature data, using an adaptive neighborhood method to determine the feature cluster center; Calculate the Mahalanobis distance between each time point and the feature cluster center; construct a sparse adjacency matrix based on the Mahalanobis distance and power feature data, and apply the spectral clustering method to optimize the adjacency relationship to obtain the similarity matrix; S114. Based on the similarity matrix, a dynamic programming method is used to calculate the change trend of the similarity; Construct adaptive thresholds based on change trends and power feature data; Adaptive thresholds are used to divide the normalized time series data into initial data blocks, and the hierarchical clustering method is applied to the initial data blocks to optimize the block size, and finally an adaptive block size sequence is obtained.

8. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 6, characterized in that: Step S13 is further as follows: S131. Based on the multi-scale feature block set, extract the time index information of the data block, calculate the continuous time function using polynomial interpolation to obtain a continuous time series; decompose the continuous time series using wavelet basis functions to obtain time feature components; construct a multi-scale time representation based on the time feature components to obtain a hierarchical time feature and an initial time code; S132. Calculate a periodic sine function value based on the layered time feature and the initial time code to obtain an initial position code; apply adaptive frequency modulation based on the initial position code to obtain a modulated position code; Based on the modulated position code and the initial position code, the dot product between the codes is calculated to obtain the initial correlation score; Based on the initial correlation score and pre-stored time scale information, a multi-scale position encoding is obtained; S133. Based on the multi-scale position encoding and the initial relevance score, a position attention query matrix is ​​constructed to obtain the position query feature; Calculate the correlation between the location query feature and the location code to obtain the location correlation score; Normalizing the position correlation score to obtain a normalized correlation score; Based on the normalized correlation score, kernel function transformation is applied to obtain kernelized position features; S134. Based on the kernelized position features and the normalized correlation scores, perform spectral decomposition to obtain a characteristic spectrum matrix; based on the characteristic spectrum matrix, calculate the importance of eigenvalues ​​and perform dimensionality reduction processing to obtain reduced-dimensionality position features; combine the reduced-dimensionality position features and the normalized correlation scores, perform weighted processing, and obtain weighted position features; Based on the weighted position features, the position encoding matrix is ​​obtained through orthogonalization.

9. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 6, characterized in that: Step S21 is further as follows: S211, obtaining a set of multi-scale feature blocks, applying a Hanning window function to each feature block for windowing processing to obtain windowed feature data; calculating an autocorrelation function of the windowed feature data to obtain a correlation sequence; estimating a periodic feature of the signal based on the correlation sequence to obtain periodic feature data; S212, performing a fast Fourier transform based on the windowed characteristic data and the periodic characteristic data to obtain an initial spectrum; estimating a power spectrum density using the Welch method based on the initial spectrum to obtain power spectrum data; and adaptively smoothing the initial spectrum based on the power spectrum data and the periodic characteristic data to obtain a smoothed spectrum; S213, based on the smoothed spectrum and power spectrum data, calculating the frequency importance score by a multi-layer perceptron to obtain the frequency weight; Based on the frequency weight, the sigmoid function is applied for normalization to obtain the normalized weight; The Bootstrap method was used to evaluate the uncertainty of the normalized weights and obtain the confidence intervals of the weights; Based on the weight confidence interval, the weight is modified to obtain the frequency selection parameter; S214. Based on the smoothed spectrum and the frequency selection parameters, perform frequency domain filtering to obtain a filtered spectrum; based on the filtered spectrum, apply an inverse Fourier transform to obtain a reconstructed time domain signal; based on the reconstructed time domain signal, calculate the reconstruction error and update the frequency selection parameters to finally obtain a frequency domain feature matrix.

10. The method for embodied intelligent agent time series data modeling based on frequency domain learning according to claim 6, characterized in that: Step S32 is further as follows: S321. Based on the attention feature matrix, the frequency domain feature matrix, the residual feature matrix, and the position encoding matrix are connected in the feature dimension to obtain a connection feature matrix; feature dimensionality reduction is performed on the connection feature matrix to obtain reduced dimensionality features; based on the reduced dimensionality features, nonlinear transformation is performed to obtain transformed features; Based on the transformed features, the attention mechanism is applied to calculate the feature weights to obtain weighted features; S322, obtaining weighted features, and obtaining initial gating parameters through linear transformation and sigmoid function calculation; Based on the initial gating parameters, the parameter importance is estimated by feature entropy to obtain the parameter importance; Based on the parameter importance, the initial gating parameters are updated to obtain the optimized gating parameters; based on the optimized gating parameters, dynamic threshold adjustment is applied to obtain the adaptive gating parameters; S323, using adaptive gating parameters to weight the frequency domain feature matrix and the residual feature matrix to obtain weighted frequency domain features and weighted residual features; based on the weighted frequency domain features and weighted residual features, using an adaptive fusion strategy to obtain initial fusion features; Based on the initial fused features, residual connection is applied to obtain the fused feature matrix.

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