Cellular traffic prediction method based on multi-level signal decomposition and dual-branch deep network fusion

Abstract

The invention provides a cellular traffic prediction method based on multi-level signal decomposition and dual-branch deep network fusion. Aiming at the defects of non-stationarity, high volatility and noise aliasing existing in a cellular traffic sequence, the method comprises the following steps: firstly, standardizing acquired data through missing value interpolation, anomaly elimination and z-score standardization; then, through the flow sequence subjected to multi-level signal decomposition standardization processing, four links of TVFEMD decomposition, component screening, EWT decomposition and multi-channel splicing are sequentially carried out, and multi-channel feature tensors spliced along the time dimension are output; a double-branch deep network composed of an internal time sequence branch BiTCN-MHA and an external environment branch ResNet-18 is constructed on a model level; a branch A captures multi-scale bidirectional dependence of a multi-channel feature tensor through forward and reverse expansion causal convolution, gating dynamic fusion and a multi-head attention mechanism; the branch B is used for deeply extracting nonlinear features of the standardized environment feature matrix by using a residual structure; and after the features of the two branches are spliced, a standardized domain prediction value is output through a full connection layer, and a physical quantity outline is recovered through anti-standardization to obtain a final cellular traffic prediction result.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent management of mobile communication networks, and particularly relates to a cellular traffic prediction method based on multi-level signal decomposition and double-branch deep network fusion, which is suitable for traffic scheduling, resource optimization and congestion control in 5G and 6G networks. BACKGROUND

[0002] As the core infrastructure of modern information society, cellular networks carry the key load of global digitalization process. In recent years, influenced by the rapid development of mobile Internet, Internet of Things, Internet of Vehicles, and virtual reality and augmented reality applications, traffic demand shows explosive growth. Accurate prediction of cellular traffic is of great significance for realizing network resource dynamic configuration, load balancing, energy saving control and user experience guarantee. For example, base station sleep strategy relies on accurate prediction of low traffic period, and dynamic allocation of slice resources also needs to be planned in advance according to business demand. If the prediction is inaccurate, it may lead to network congestion, low energy efficiency and even service interruption, causing economic losses of operators and decline of user experience. Therefore, how to realize high-precision and stable cellular traffic prediction has become a core problem of network intelligent management.

[0003] Traditional traffic prediction methods are mainly based on time series statistical models, such as autoregressive moving average and exponential smoothing model, which predict future traffic by fitting the linear relationship and trend of the sequence. The calculation is simple and easy to explain. However, actual cellular traffic often presents nonlinear relationship, long-range dependence and sudden fluctuations, and is jointly influenced by user behavior and environmental factors, with complex rules, which leads to limited prediction accuracy of this kind of method.

[0004] In order to improve the modeling ability of complex time series, deep learning methods have been widely applied in recent years. Recurrent neural network and its improved structure (RNN), such as long short-term memory network (LSTM) and gated recurrent unit, capture short-term and long-term dependence through hidden state update. However, when dealing with long sequences, this kind of model is prone to gradient vanishing or explosion, which affects the modeling of long-range dependence, and the model capacity and training stability are limited in multi-channel input and multi-scale mode.

[0005] On the other hand, for time series with non-stationary characteristics such as cellular network traffic, some researchers have introduced time-frequency decomposition methods. For example, empirical mode decomposition, ensemble empirical mode decomposition, and complete ensemble empirical mode decomposition (CEEMDAN) are combined with RNN, LSTM and other models. Literature shows that CEEMDAN-LSTM is superior to empirical mode decomposition and ensemble empirical mode decomposition in terms of decomposition quality and prediction accuracy, but still has problems such as noise residue, end effect and mode aliasing, which affect the overall prediction effect. Therefore, a multi-level signal preprocessing strategy with noise reduction and feature enhancement is needed, as well as an important feature extraction network that can model time series dependence and dynamically integrate, to achieve high-precision and robust prediction of complex cellular traffic sequences. SUMMARY

[0006] To solve the above technical problems, the present application provides a cellular traffic prediction method based on multi-level signal decomposition and double-branch deep network fusion. The method extracts multi-scale features of traffic through a multi-level signal decomposition model, and combines a BiTCN-MHA network and an 18-layer residual network (ResNet-18) branch to form a double-branch deep network fusion for dynamic feature fusion, achieving high-accuracy prediction of cellular traffic. The technical scheme adopted by the present application is as follows:

[0007] The cellular traffic prediction method based on multi-level signal decomposition and double-branch deep network fusion comprises the following steps:

[0008] Step 1: Collect historical traffic sequences of cellular base stations and synchronously collect environmental features with the same timestamp as the traffic. Perform missing value interpolation, outlier removal and standardization on the historical traffic sequences to obtain standardized traffic sequences. Standardize the environmental feature data to obtain a standardized environmental feature matrix;

[0009] Step 2: Perform multi-level signal decomposition on the standardized traffic sequences obtained in Step 1, and retain the low-frequency trend components and noise reduction detail components obtained after decomposition, and concatenate them into a multi-channel feature tensor in the time dimension;

[0010] Step 3: Input the multi-channel feature tensor constructed in Step 2 and the standardized environmental feature matrix obtained in Step 1 into the double-branch deep network fusion model; obtain the final cellular traffic prediction result;

[0011] The standardized traffic sequences and standardized environmental feature matrices in Step 1 refer to the input data of uniform dimension provided for subsequent models after missing value interpolation, outlier removal and standardization of the original data.

[0012] The step 1 comprises the following steps:

[0013] S1.1, Collecting historical traffic sequences of cellular base stations through operator network management system or data warehouse interface Synchronously acquiring environment features with traffic time-stamp The environment features can include holiday markers, air temperature, humidity, rainfall, average load, etc. N is the number of time points included in the traffic sequence; x t represents the value of the original cellular traffic at time point t; e t represents the value of the environment feature at time point t.

[0014] S1.2, Extreme outliers will be amplified as pseudo-high-frequency noise in the decomposition stage and mislead the decomposition model, so they need to be removed. The processing process of extreme outliers is as follows: first, 3σ principle is used to coarsely screen extreme outliers, that is, preliminary abnormality judgment. Then, the quartile IQR is used for fine screening, and the calculation process of fine screening is as follows:

[0015] x t <Q1-1.5IQR or x t >Q3+1.5IQR

[0016] IQR=Q3-Q1

[0017] In the formula, x is the sample mean; σ is the standard deviation; Q1 and Q3 are the first and third quartiles respectively; IQR represents the quartile range. The data points meeting the above conditions can be directly removed.

[0018] S1.3, Time series breakpoints will be misidentified as high-frequency noise in the subsequent multi-level signal decomposition process, leading to modal aliasing, so missing values need to be filled. If there is sporadic missing (continuous missing point number ≤4) at time point t, linear interpolation is used for completion. The data gaps after removing abnormal points in S1.2 are also filled in this way. The calculation formula is as follows:

[0019]

[0020] In the formula, t a and t b are adjacent known time points before and after the missing point; x ta and x tb correspond to the effective traffic values at time points t a and t b ; t is the time index; x t is the original cellular traffic value observed at time step t.

[0021] If the continuous length of the missing section is >4, cubic spline interpolation is used to ensure the smoothness of the interpolation curve. The calculation formula is as follows:

[0022] S i (t)=a i +bi (t-x i )+c i (t-x i ) 2 +d i (t-x i ) 3 ,x i ≤t≤x i+1

[0023] where x i , x i+1 are adjacent known nodes, a i , b i , c i , d i are coefficients uniquely determined by end-point conditions and first and second derivative continuity; i is an index; S i (t) is the value of the interpolation function in the interval [x i , x i+1 ] in cubic spline interpolation. The above calculation ensures that the interpolated curve and its derivatives are smooth and continuous, avoiding the misjudgment of breakpoints as high-frequency points in subsequent multi-level signal decomposition.

[0024] S1.4, z-score standardization is performed on the data processed in S1.3 and the corresponding environmental features, so that the mean of each feature approaches 0 and the variance approaches 1, eliminating dimensional differences and preventing gradient descent from being biased towards large value features, thereby improving the convergence speed and stability of the subsequent step three model training. The calculation formula is as follows:

[0025]

[0026] where x t * is the normalized value; represents the global mean of the original sequence; and σ is the overall standard deviation of the original sequence.

[0027] S1.5, both decomposition and deep network require that the input matrix be completely aligned in the time axis and have uniform format, so it needs to be finally packaged for subsequent use. The normalized traffic vector is denoted as the normalized environmental feature matrix is denoted as According to the concatenation by timestamp (k is the environmental feature dimension, and R represents the real number field), and is written into the cache in the form of a data frame that is time-continuous, anomaly-free, and dimensionally uniform, providing reliable input for subsequent step two. Cellular traffic has strong non-stationary and frequency aliasing characteristics, and direct modeling is prone to overfitting. The time-continuous and dimensionally uniform data obtained in step one need to be subjected to multi-level signal decomposition.

[0028] The multi-level signal decomposition in the step two refers to a hierarchical connection decomposition process from coarse decomposition to extract main trend to fine decomposition to remove noise and retain details, including time-varying filter empirical mode decomposition (TVFEMD), component screening, empirical wavelet transform (EWT) decomposition, and multi-channel splicing four links. First, the TVFEMD is used to coarsely decompose the standardized flow sequence obtained in step one; then the component screening is performed, the signal is decomposed into multiple intrinsic mode functions (IMFs) from low to high frequency, among which the two components with the lowest frequency are reserved as the long-term trend of the flow, and the remaining high-frequency complex components are summarized to form a new component and remove the residual component; further, the EWT is used to finely decompose the summarized new component, and the high-frequency components (complex components) are divided into several narrow-band sub-components in the frequency domain to obtain the high-frequency detail components after denoising; finally, the low-frequency trend component and the high-frequency detail component after denoising are spliced in the time dimension to form a multi-channel feature tensor, realizing the hierarchical connection from coarse decomposition to extract main trend to fine decomposition to remove noise and retain details, and providing full-frequency information input containing long-term trend, short-term details and low-noise interference for subsequent deep prediction model.

[0029] The step two includes the following steps:

[0030] S2.1, TVFEMD decomposition is performed, and TVFEMD can significantly reduce the complexity of the signal and suppress the end effect by adaptively extracting IMFs through time-varying filtering. TVFEMD uses extreme point positioning filter support points and instantaneous frequency to guide narrow-band extraction, so first, the extreme value search is performed on the standardized flow sequence x(t) to obtain the extreme value point set {u i}, wherein u i represents the i-th local maximum or minimum value. Then, the Hilbert transform H[·] is used to construct an analytical signal, and the instantaneous amplitude A(t), the instantaneous phase φ(t) and the instantaneous frequency f(t) are calculated.

[0031]

[0032] S2.2, in order to avoid mixing different frequency bands into the same IMF component, the two-point instantaneous frequency between adjacent extreme values is calculated The calculation formula is as follows:

[0033]

[0034] In the formula, ρ is a frequency variable threshold, which is empirically taken as 0.1. The extreme value u i greater than ρ is marked as an intermittent point e j . Then, e j is classified as a rising edge or a falling edge according to the increase or decrease direction of , so as to adaptively adjust the local cutoff frequency in the next step.

[0035] S2.3, in each interval of intermittence, according to the instantaneous frequency upper and lower bounds f1(t), f2(t), calculate the local cutoff frequency f cutoff (t), and construct a time-varying filter with B-order spline:

[0036]

[0037] y(t) = BSpline B [x(t), f cutoff (t)]

[0038] In the formula, y(t) is the local mean value of the signal after B-order spline (BSpline) time-varying filtering, which is the IMF extraction baseline; BSpline B represents the B-order B-spline time-varying filtering operator; f cutoff (t) is the calculated local cutoff frequency, which is used to construct a time-varying filter. Further, the Loughlin instantaneous bandwidth B L (t) and the weighted average instantaneous frequency Calculate the bandwidth ratio τ(t):

[0039]

[0040] In the formula, the bandwidth ratio τ(t) is used to judge whether the component is a narrowband IMF.

[0041] S2.4, if τ(t) < ζ, it is determined that the current component is an IMF c v (t); otherwise, y(t) is deducted from the original signal and circulates. At the end of the entire recursion, we get:

[0042]

[0043] In the formula, ζ is the IMF determination threshold, which defines the narrowband criterion; K is the number of IMFs; c res (t) is the final residual term, IMF c v (t) represents the vth eigenmode function, and v represents the index.

[0044] S2.5, keep c1(t) and c2(t) of the two low-frequency IMFs, and merge the remaining IMFs into a component, denoted as complex component C(t).

[0045] S2.6, for the complex component C(t), use EWT for frequency spectrum adaptive segmentation. First, divide its Fourier spectrum in the frequency domain into subbands, and the calculation formula is as follows:

[0046] Λ n = [ω n-1 , ω n ], 0 < ω n ​<π

[0047] where, denotes the Fourier spectrum of the complex component C(t); Λ n denotes the nth sub-band frequency interval; n is an index; ω n-1 and ω n denotes the sub-band division frequency boundary, which ensures that each sub-band only covers a narrow frequency energy, and the transition bandwidth is τ n = γω n where γ is a proportionality coefficient, and τ n is the transition bandwidth.

[0048] S2.7, filter coefficient and information entropy denoising. For each sub-band, construct the wavelet to obtain the time-domain coefficients Then calculate the information entropy:

[0049]

[0050] where W(n, t) is the time-domain representation of the wavelet coefficients of the nth sub-band; F -1 denotes the inverse Fourier transform; denotes the wavelet function of the nth sub-band (frequency domain representation); denotes the complex conjugate of the wavelet function; H n denotes the information entropy of the nth sub-band; p n (u) is the coefficient probability density; H th denotes the entropy threshold. If H n ≤ H th (H th = 0.7) is retained; otherwise, it is considered as noise. The reconstruction result that meets the condition is taken as the denoised detail component, which is expressed as follows:

[0051]

[0052] S2.8, multi-channel feature splicing. Finally, the two main trends c1(t), c2(t) of TVFEMD and the EWT denoised details D(t) are spliced into a tensor along the time axis:

[0053] T = [c1, c2, D] ∈ R N×L

[0054] where T represents the final input tensor; N represents the length of the time series (the same as N in step one). L is the number of tensor channels. This tensor retains the long-term trend and the denoised local details, forming an L-channel tensor input bidirectional time convolution-multi-head attention (BiTCN-MHA) network, providing full-frequency information of "trend + detail".

[0055] Considering that cellular traffic data is affected by both its own historical patterns and external environmental conditions, in order to simultaneously mine the time sequence structure of the data itself and the deep connection with the external environment, and improve the prediction accuracy, step three adopts a double-branch fusion prediction module. Branch-A focuses on the time sequence characteristics of the traffic itself, taking the L-channel tensor T ∈ R N×L generated in step two as input, and extracts multi-scale internal features using the BiTCN-MHA structure; Branch-B takes the standardized environmental feature matrix E generated in step one as input, and extracts external nonlinear representations through an 18-layer residual network (ResNet-18). The two branches are spliced at the end, and the single-step traffic prediction is output through a fully connected layer. Finally, the physical dimension is restored through inverse standardization.

[0056] The step three includes the following steps:

[0057] S3.1, construct the tensor T into a forward sequence T fwd in the original time order rev = reverse(T), where reverse represents the time reversal operation. The double sequence is input into the subsequent convolution stack in parallel to ensure that the model not only utilizes historical information but also captures the reverse dependency relationship of “future→now”

[0058] S3.2, in the forward branch, the calculation formula of the causal convolution output of the lth layer is as follows:

[0059]

[0060] wherein, is the output of the lth layer of the forward branch at time step s; w l,i is the convolution kernel weight; is the forward output of the previous layer; d l = 2 l-1 is the dilation coefficient; k is the length of the convolution kernel; i is the index. It can be seen that the dilated convolution introduces interval sampling to make the receptive field exponentially grow when stacking layers. For example, when d l = 2, the convolution calculation will sample the input value every other time step, so that the network can capture longer time sequence dependencies with fewer layers.

[0061] However, with the increase of network depth, gradient propagation is prone to decay or even vanish, leading to difficulty in effective training of the model. Therefore, a residual connection is introduced after each convolutional layer, i.e., the input and output of the layer are added and then processed by a ReLU activation function, thereby forming a cross-layer information channel to alleviate the gradient vanishing problem of deep networks. The combination of the two constitutes a basic structural unit of "convolution-residual-activation": the convolutional layer extracts local and dilated features, the residual connection establishes a direct channel between different levels of the network, and the ReLU activation introduces a nonlinear transformation for the convolutional output. The three work together to make the multi-layer convolutional stack not only have sufficient nonlinear modeling ability, but also maintain the characteristics of stable gradient and easy training. S3.3, using the same set of convolutional weights on the reverse sequence to obtain the following calculation formula:

[0062]

[0063] wherein, is the output of the lth layer of the reverse branch at time step s; x - -1 is the reverse output of the previous layer.

[0064] S3.4, the continuous output of is denoted as o + (s), the continuous output of - (s). In order to effectively splice the forward and reverse information, a gating mechanism is introduced for adaptive weighting, and the calculation formula is as follows:

[0065]

[0066]

[0067] wherein, α s is the fusion weight at time step s, output by the Sigmoid activation function σ(·), α s ∈(0, 1); W f is the gating layer weight matrix; b f is the bias vector; [o + (s); o - (s)] represents the splicing of forward and reverse features; ⊙ represents element-wise multiplication; the dynamic gating fusion makes the model adaptively adjust the importance of forward and reverse features according to the context, enhances the expressiveness and generalization, and the fusion output G s forms a sequence G, which is input into the subsequent multi-head attention module.

[0068] S3.5, to capture the multi-scale dependency relationship within the sequence, the multi-head attention transformation is performed on G, and the calculation formula is as follows:

[0069]

[0070] where Q h , K h , V h are query, key, value matrices respectively; is the output of the h-th head; d h is the single-head dimension used for scaling; the outputs of all H heads are concatenated along the feature dimension as and averaged-pooled along the time dimension to obtain the internal temporal feature vector h s A , which is used to represent the internal global dynamic feature.

[0071] S3.6, Standardized environment matrix As input, multi-layer nonlinear abstract features are extracted by ResNet-18. ResNet-18 is composed of 18 layers of convolution and residual block. Through the skip connection mechanism of the residual structure, the gradient vanishing problem of the deep network is effectively alleviated, and the environment variable representation ability is enhanced. Finally, through global average pooling, the external environment representation vector h B ∈R 512 is obtained.

[0072] S3.7, Fusion of internal cellular traffic data temporal feature state and external environment condition, at each time step s, the internal vector h s A is concatenated with the external vector h B to obtain z s , where [;] represents the vector concatenation operation.

[0073] S3.8, The fusion vector z s is output through the fully connected layer to predict the standardized domain:

[0074]

[0075] and the physical dimension is restored through the inverse standardization:

[0076]

[0077] where represents the prediction result (standardized domain) at time step s, which is a scalar; z s represents the fusion input vector at time step s, which is concatenated by the internal cellular traffic data temporal feature and the external environment feature, and d is the fusion vector dimension; Wo represents the weight matrix of the output layer, which is used to map the fusion vector to the prediction value; bo is the bias, which is used for the translation of linear mapping; σ respectively are the mean and standard deviation recorded in step one, and finally the cellular traffic prediction value with the unit of Gb·s -1 is obtained

[0078] Through the technical scheme, the low-frequency trend and high-frequency noise detail of the cellular traffic are extracted by using the multi-level signal decomposition model, the bidirectional time sequence convolution-multi-head attention network and the ResNet-18 environment branch are combined, the decomposition preprocessing of 'coarse first and then fine' and the dynamic fusion prediction framework of 'internal time sequence + external environment' double branch are constructed, the joint modeling of the cellular traffic sequence is realized, the expression ability of the complex traffic mode is enhanced, and the accuracy and stability of the future cellular traffic prediction are improved. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 The overall block diagram of the method of the application is shown.

[0080] Figure 2 The flowchart of the data preprocessing stage is shown.

[0081] Figure 3 The method schematic diagram of the multi-level signal decomposition stage is shown, the trend component is extracted by coarse decomposition, and the high-frequency complex component is finely decomposed and denoised.

[0082] Figure 4 The structural schematic diagram of the double-branch deep network fusion model is shown, including forward and reverse time sequence convolution, multi-head attention module and ResNet-18 branch for environment feature extraction.

[0083] Figure 5 The missing value interpolation effect schematic diagram is shown.

[0084] Figure 6 The TVF-EMD(time-varying filter empirical mode decomposition) decomposition result schematic diagram is shown, and the components are arranged from high to low according to frequency.

[0085] Figure 7 The schematic diagram of the detail component obtained after performing EWT(empirical wavelet transform) decomposition on the high-frequency complex component is shown.

[0086] Figure 8 The result schematic diagram of the method of the application on the cellular traffic prediction task is shown, and the predicted value and the true value (randomly selected a continuous 300 sample points) are compared. DETAILED DESCRIPTION

[0087] To solve the above technical problems, the application provides a multi-level signal decomposition and double-branch deep network fusion cellular traffic prediction method. The method extracts traffic multi-scale features by TVF-EMD-EWT double decomposition, and dynamically fuses the features by combining BiTCN-MHA network and ResNet-18 environment branch, realizes high-accuracy prediction of cellular traffic.

[0088] The technical scheme adopted by the present application is:

[0089] The cellular traffic prediction method based on multi-level signal decomposition and double-branch deep network fusion comprises the following steps:

[0090] Step one: collect the historical traffic sequence of the cellular base station, and synchronously collect the environmental characteristics with the same time stamp as the traffic; perform missing value interpolation, outlier rejection and standardization processing on the historical traffic sequence to obtain a standardized traffic sequence; and perform standardization processing on the environmental characteristic data to obtain a standardized environmental characteristic matrix;

[0091] Step two: perform multi-level signal decomposition on the standardized traffic sequence obtained in step one, retain the low-frequency trend component and the noise reduction detail component obtained after decomposition, and splice them into a multi-channel feature tensor according to the time dimension;

[0092] Step three: input the multi-channel feature tensor constructed in step two and the standardized environmental characteristic matrix obtained in step one into a double-branch deep network fusion model; and obtain the final cellular traffic prediction result.

[0093] The standardized traffic sequence and the standardized environmental characteristic matrix in step one refer to the input data of uniform dimension provided for the subsequent model after the original data is subjected to missing value interpolation, outlier rejection and standardization processing.

[0094] Step one comprises the following steps:

[0095] S1.1, collect the historical traffic sequence of the cellular base station through the operator network management system or the data warehouse interface Synchronize to obtain the environmental characteristics with the same time stamp as the traffic The environmental characteristics can include holiday markers, air temperature, humidity, rainfall, average load, etc. N is the number of time points included in the traffic sequence; x t represents the value of the original cellular traffic at time t; e t represents the value of the environmental characteristics at time t.

[0096] S1.2, extreme outliers will be amplified as pseudo-high-frequency noise in the decomposition stage and mislead the decomposition model, so they need to be removed. The processing process of extreme outliers is as follows: first, 3σ principle is used to coarsely screen extreme outliers, that is, preliminary judgment of abnormality. Then, fine screening is performed by using quartile IQR, and the calculation process of fine screening is as follows:

[0097] x t <Q1-1.5IQR or x t >Q3+1.5IQR

[0098] IQR=Q3-Q1

[0099] In the formula, For sample mean; σ is the standard deviation; Q1, Q3 are the first and third quartiles, respectively; IQR represents the interquartile range. Data points meeting the above conditions can be directly removed.

[0100] S1.3, the timing breakpoint will be misidentified as high-frequency noise in the subsequent multi-level signal decomposition process, leading to modal aliasing, so the missing values need to be filled. If the flow has sporadic missing at time t (continuous missing point number ≤4), linear interpolation is used to complete the filling. The data gaps after S1.2 removes the outliers are also filled in this way. The calculation formula is as follows:

[0101]

[0102] In the formula, t a and t b are the adjacent known time points before and after the missing point; x ta and x tb correspond to the effective flow values at time t a and t b ; t is the time index; x t is the original cell flow value observed at time step t.

[0103] If the continuous length of the missing section is >4, use cubic spline interpolation to ensure the smoothness of the interpolated curve. The calculation formula is as follows:

[0104] S i (t)=a i +b i (t-x i )+c i (t-x i ) 2 +d i (t-x i ) 3 ,x i ≤t≤x i+1

[0105] In the formula, x i and x i+1 are adjacent known nodes, a i , b i , c i , and d i are coefficients uniquely obtained by endpoint conditions and first and second derivative continuity; i is the index; S i (t) is the interpolation function value in the interval [x i , x i+1 ] in the cubic spline interpolation. Through the above calculation, the interpolated curve and its derivative are smooth and continuous, avoiding the misjudgment of breakpoints as high-frequency points in the subsequent multi-level signal decomposition.

[0106] S1.4, perform z-score standardization on the data processed in S1.3 and the corresponding environmental features, so that the mean of each feature approaches 0 and the variance approaches 1, eliminating the dimensional difference and preventing the gradient descent from being biased towards large value features, thereby improving the convergence speed and stability of the subsequent step three model training. The calculation formula is as follows:

[0107]

[0108] In the formula, x t * is the standardized value; x represents the global mean of the original sequence; and σ is the overall standard deviation of the original sequence.

[0109] S1.5, the decomposition and deep network both require that the input matrix be completely aligned in the time axis and have a uniform format, so the last encapsulation is required for subsequent use. The standardized traffic vector is denoted as The standardized environmental feature matrix is denoted as According to the splicing according to the timestamp (k is the environmental feature dimension, and R represents the real number domain), and is written into the cache, so as to provide reliable input for the subsequent step two in the form of time-continuous, anomaly-free and dimensionally uniform data frames. The cellular traffic has strong non-stationary and frequency aliasing characteristics, and direct modeling is prone to overfitting. Therefore, the time-continuous and dimensionally uniform data obtained in step one need to be subjected to multi-level signal decomposition.

[0110] The multi-level signal decomposition in the step two refers to a hierarchical connection decomposition process from coarse decomposition to extract the main trend to fine decomposition to remove noise and retain details, including time-varying filter empirical mode decomposition (TVFEMD), component screening, empirical wavelet transform (EWT) decomposition, and multi-channel splicing. First, the TVFEMD is used to coarsely decompose the standardized traffic sequence obtained in step one; then, the component screening is performed, the signal is decomposed into multiple intrinsic mode functions (IMFs) according to the frequency from low to high, among which the two components with the lowest frequency are taken as the long-term trend of the traffic, and the remaining high-frequency complex components are combined to form a new component and remove the residual component; further, the EWT is used to finely decompose the combined new component, and the high-frequency components (complex components) are divided into several narrow-band sub-components in the frequency domain, thereby obtaining the high-frequency detail components after denoising; finally, the low-frequency trend component and the high-frequency detail component after denoising are spliced in the time dimension to form a multi-channel feature tensor, thereby realizing the hierarchical connection from coarse decomposition to extract the main trend to fine decomposition to remove noise and retain details, and providing the deep prediction model with full-frequency information input containing long-term trend, short-term details and low-noise interference.

[0111] The step two includes the following steps:

[0112] S2.1, TVFEMD is used to reduce the complexity of the signal and suppress the end effect. TVFEMD uses the extreme value point to locate the support point of the filter and uses the instantaneous frequency to guide the narrowband extraction. Therefore, the extreme value search is first performed on the normalized flow sequence x(t) to obtain the extreme value point set {u i} where u i represents the ith local maximum or minimum value. Then the Hilbert transform H[•] is used to construct the analytic signal to calculate the instantaneous amplitude A(t), the instantaneous phase φ(t) and the instantaneous frequency f(t).

[0113]

[0114] S2.2, in order to avoid mixing different frequency bands into the same IMF component, the two-point instantaneous frequency between adjacent extreme values is calculated The calculation formula is as follows:

[0115]

[0116] In the formula, p is a frequency variable threshold, which is empirically taken as 0.1. The extreme value u i greater than p is marked as an intermittent point e j . Then e j is classified as a rising edge or a falling edge according to the increasing or decreasing direction of f , so as to adaptively adjust the local cutoff frequency in the next step.

[0117] S2.3, in each intermittent interval, the local cutoff frequency f cutoff (t) is calculated according to the upper and lower bounds of the instantaneous frequency f1(t), f2(t), and a time-varying filter is constructed by a B-order spline:

[0118]

[0119] y(t) = BSpline B [x(t), f cutoff (t)]

[0120] In the formula, y(t) is the local mean value of the signal after B-order spline (BSpline) time-varying filtering, which is used as the IMF extraction baseline; BSpline B represents the B-order B-spline time-varying filtering operator; f cutoff (t) is the calculated local cutoff frequency, which is used to construct the time-varying filter. Further, the Loughlin instantaneous bandwidth B L (t) and the weighted average instantaneous frequency are used to calculate the bandwidth ratio τ(t):

[0121]

[0122] In the formula, the bandwidth ratio τ(t) is used to determine whether the component is a narrowband IMF.

[0123] S2.4 If τ(t) < ζ, then the current component is considered to be IMFc. v (t); otherwise, subtract y(t) from the original signal and loop. At the end of the recursion, we get:

[0124]

[0125] In the formula, ζ is the IMF decision threshold, defining the narrowband criterion; K is the number of IMF entries; c res (t) represents the final residual term, IMFc v (t) represents the v-th intrinsic mode function, where v represents the index.

[0126] S2.5. Retain c1(t) and c2(t) of the two low-frequency IMFs, and merge the remaining IMFs into one component, denoted as complex component C(t).

[0127] S2.6. For the complex component C(t), adaptive spectrum segmentation is performed using EWT. First, its Fourier spectrum is processed in the frequency domain. The area is divided into sub-bands, and the calculation formula is as follows:

[0128] Λ n =[ω n-1 ,ω n ],0<ω n <π

[0129] In the formula, Represents the Fourier spectrum of the complex component C(t); Λ n This represents the nth sub-band frequency range; n is the index; ω n-1 and ω n This represents the sub-band division frequency boundary, which ensures that each sub-band covers only a narrow frequency range of energy, with a transition bandwidth of τ. n =γω n Where γ is the proportionality constant, τ n This is for transition bandwidth.

[0130] S2.7, Perform denoising using filter coefficients and information entropy. Construct wavelets for each sub-band. Obtain time-domain coefficients Then calculate the information entropy:

[0131]

[0132] In the formula, W(n,t) represents the time-domain representation of the wavelet coefficients of the nth subband; F -1 [.] indicates the inverse Fourier transform; Wavelet function representing the nth sub-band (frequency domain representation); Complex conjugate of the wavelet function; n Information entropy of the nth sub-band; n (u) is the coefficient probability density; th Indicates the entropy threshold. If H n ≤ H th (H th = 0.7) the sub-band is retained; otherwise it is considered noise. The reconstruction result that meets the condition is taken as the denoising detail component, which is expressed as follows:

[0133]

[0134] S2.8, multi-channel feature splicing. Finally, the two main trends c1(t), c2(t) of TVFEMD and the EWT denoising details D(t) are spliced into a tensor along the time axis:

[0135] T = [c1, c2, D] ∈ R N×L

[0136] In the formula, T represents the final input tensor; N represents the length of the time series (the same as N in step one). L is the number of tensor channels. The tensor retains the long-term trend and the local details after denoising, forms an L-channel tensor input bidirectional time convolution-multi-head attention (BiTCN-MHA) network, and provides full-frequency information of “trend + detail”.

[0137] Considering that the cellular traffic data is not only affected by its own historical patterns, but also driven by external environmental conditions. In order to simultaneously mine the time sequence structure of the data itself and the deep correlation with the external environment, and improve the prediction accuracy, step three adopts a double-branch fusion prediction module. Branch-A focuses on the time sequence characteristics of the traffic itself, and takes the L-channel tensor T ∈ R N×L as input, and extracts multi-scale internal features using the BiTCN-MHA structure; Branch-B takes the standardized environmental feature matrix E generated in step one as input, and refines external nonlinear representation through an 18-layer residual network (ResNet-18). The two branches are spliced at the end, and the single-step traffic prediction is output through the full connection layer. Finally, it is restored to the physical dimension through the inverse standardization.

[0138] The step three includes the following steps:

[0139] S3.1, the tensor T is constructed as a forward sequence T fwd , and the reverse sequence T rev = reverse(T) is obtained along the time axis, where reverse represents the time reversal operation. The double sequences are input into the subsequent convolution stack in parallel to ensure that the model not only utilizes historical information, but also captures the reverse dependency relationship of “future → now”

[0140] S3.2、In the forward branch, the calculation formula of the l-th layer causal convolution output is as follows:

[0141]

[0142] wherein, is the output of the l-th layer in the forward branch at time step s; w l,i is the convolution kernel weight; is the output of the previous layer in the forward branch;

[0143] is the output of the previous layer in the forward branch; d l = 2 l-1 is the dilation coefficient; k is the length of the convolution kernel; i is the index. It can be seen that the dilated convolution introduces interval sampling to make the receptive field exponentially grow when stacking layers. For example, when d l = 2, the convolution calculation samples the input value every other time step, so that the network can capture longer distance temporal dependencies with fewer layers.

[0144] However, with the increase of network depth, the gradient propagation is prone to attenuation or even disappearance, which makes it difficult for the model to be effectively trained. Therefore, a residual connection is introduced after each convolution layer, that is, the input and output of the layer are added and then processed by a ReLU activation function, so as to form a cross-layer information channel and alleviate the gradient disappearance problem of deep network. The combination of the two constitutes a basic structure unit of “convolution-residual-activation”: the convolution layer extracts local and dilated features, the residual connection establishes a direct channel between different levels of the network, and the ReLU activation introduces a nonlinear transformation for the convolution output. The three work together to make the multi-layer convolution stack not only have sufficient nonlinear modeling ability, but also maintain the characteristics of stable gradient and easy training.

[0145]

[0146] wherein, is the output of the l-th layer in the reverse branch at time step s; is the output of the previous layer in the reverse branch.

[0147] S3.4、The continuous output of is denoted as o + (s), The continuous output of - (s). In order to effectively splice the forward and reverse information, a gating mechanism is introduced for adaptive weighting, and the calculation formula is as follows:

[0148]

[0149]

[0150] where α s is the fusion weight at time step s, output by the Sigmoid activation function σ(·), α s ∈(0, 1); W f is the gating layer weight matrix; b f is the bias vector; [o + (s); o - (s)] represents the forward and backward feature concatenation; ⊙ represents element-wise multiplication; the gating dynamic fusion makes the model adaptively adjust the importance of the forward and backward features according to the context, enhances the expressiveness and generalization, and outputs the fusion G s to constitute a sequence G, which is input into the subsequent multi-head attention module.

[0151] S3.5, to capture the multi-scale dependency relationship within the sequence, the multi-head attention transformation is performed on G, and the calculation formula is as follows:

[0152]

[0153] where Q h , K h , and V h are the query, key, and value matrices, respectively; is the output of the hth head; d h is the single-head dimension used for scaling; the outputs of all H heads are concatenated along the feature dimension to obtain which is then averaged-pooled along the time dimension to obtain the internal time series feature vector used to represent the internal global dynamic feature.

[0154] S3.6, the standardized environment matrix is input, and multi-layer nonlinear abstract features are extracted by ResNet-18. ResNet-18 is composed of 18 layers of convolution and residual blocks. Through the skip connection mechanism of the residual structure, the gradient vanishing problem of the deep network is effectively alleviated, and the environment variable representation ability is enhanced. Finally, the external environment representation vector h B ∈ R 512 is obtained through global average pooling.

[0155] S3.7, the time series feature state of the internal cellular traffic data is fused with the external environmental conditions. At each time step s, the internal vector h s A is concatenated with the external vector h B to obtain z s , where [; ] represents the vector concatenation operation.

[0156] S3.8, the fusion vector z sThe output of the full connection layer is the prediction in the normalized domain:

[0157]

[0158] And the physical dimension is recovered by inverse normalization:

[0159]

[0160] wherein, represents the prediction result (normalized domain) at time step s, which is a scalar; z s represents the fusion input vector at time step s, which is spliced from the time series features of internal cellular traffic data and external environmental features, d is the dimension of the fusion vector; Wo represents the weight matrix of the output layer for mapping the fusion vector to the prediction value; bo is the bias for the translation of linear mapping; σ respectively represents the mean and standard deviation recorded in step one, and finally the cellular traffic prediction value is obtained in the unit of Gb·s -1 ​

Claims

1. A method for cellular traffic prediction based on multi-level signal decomposition and dual-branch deep network fusion, characterized in that, The method comprises the following steps: Step 1: Collecting historical traffic sequences of cellular base stations and synchronously collecting environmental characteristics with the same time stamp as the traffic; Performing missing value interpolation, outlier rejection and standardization processing on the historical traffic sequences to obtain a standardized traffic sequence. Perform standardization processing on the environmental characteristic data to obtain a standardized environmental characteristic matrix; Step 2: Performing multi-level signal decomposition on the standardized traffic sequence obtained in step 1, retaining the low-frequency trend component and the noise reduction detail component obtained after decomposition, and splicing into a multi-channel feature tensor in the time dimension; Step 3: Inputting the multi-channel feature tensor constructed in step 2 and the standardized environmental characteristic matrix obtained in step 1 into a double-branch deep network fusion model; obtaining the final cellular traffic prediction result.

2. The method of claim 1, wherein, The missing value interpolation process is: when the number of continuous missing points is not more than 4, linear interpolation is adopted; when the number of continuous missing points is more than 4, cubic spline interpolation is adopted, so as to ensure the smoothness and continuity of the interpolation curve and its derivative. This processing method prevents misjudgment as high-frequency noise in subsequent decomposition. 3.The cellular traffic prediction method based on multi-level signal decomposition and dual-branch deep network fusion of claim 1, wherein, The outlier rejection first performs preliminary screening by using the three standard deviation principle, and then performs fine screening by using the interquartile range method. This processing method prevents a small amount of outliers from affecting decomposition and training.

4. The method of claim 1, wherein, The multi-level signal decomposition comprises four links of time-varying filter empirical mode decomposition (TVFEMD) decomposition, component screening, empirical wavelet transform (EWT) decomposition and multi-channel splicing, so as to improve the accuracy and robustness of the prediction model by reducing the complexity of the sequence.

5. The multi-level signal decomposition of claim 4, wherein, The component screening is to retain the two lowest frequency intrinsic mode functions (IMF) after TVFEMD decomposition as low-frequency trend components, and the remaining IMFs are combined and marked as complex components. This processing method uses the lowest frequency component to represent the trend component, and the remaining IMFs are summarized into complex components to facilitate unified EWT denoising.

6. The method of claim 1, wherein, The double-branch deep network fusion model is composed of branch A and branch B. After splicing the outputs of branch A and branch B, a fully connected layer is connected to output the final prediction value.

7. The method of claim 6, wherein, The branch A is composed of forward and reverse dilated causal convolution stacks sharing convolution kernel weights. After each layer of convolution, residual connection and linear rectifier unit (ReLU) are set, and then the forward and reverse features are dynamically fused through a gating mechanism, and then a multi-head attention mechanism layer is connected.

8. The method of claim 6, wherein, The branch B is composed of an environmental feature vector output by an 18-layer residual network (ResNet-18) after global average pooling.

9. The method of claim 1, wherein, The double-branch deep network fusion model is composed of the model of branch A and the environmental feature model of branch B. The outputs of the two branches are spliced in the feature dimension, and then a fully connected layer is connected to regress the prediction value, so as to construct an efficient, accurate and robust cellular traffic prediction system, which is suitable for traffic scheduling, resource optimization and congestion control of 5G and 6G networks.

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