Traffic flow prediction method based on time-frequency domain joint modeling

Abstract

The invention discloses a traffic flow prediction method based on time-frequency domain joint modeling, relates to the technical field of traffic flow prediction and depth time sequence analysis, and sets a model fusion strategy, fuses results of a time domain LSTM prediction model and a frequency domain DBFBlock prediction model, and generates a traffic flow prediction result. According to the method, time domain and frequency domain information is fully combined, the feature representation capability of the model is improved through comparative learning, and the accuracy and robustness of traffic flow prediction are effectively improved under the condition that the parameter quantity of the model is not remarkably increased.

Description

Technical Field

[0001] This invention relates to the field of traffic flow prediction and deep time series analysis technology, specifically to a traffic flow prediction method based on joint time-frequency domain modeling, which is particularly suitable for minute-level traffic flow prediction scenarios with significant periodic fluctuations in urban road networks. Background Technology

[0002] With the acceleration of urbanization and the rapid growth of private car ownership, urban traffic congestion has become a global challenge. Accurate and real-time traffic flow prediction is a core component of intelligent transportation systems, and it is of great significance for alleviating traffic congestion, optimizing traffic management, and improving road utilization.

[0003] Existing traffic flow prediction technologies are mainly divided into three categories: statistical methods, machine learning methods, and deep learning methods. Statistical methods such as ARIMA (Autoregressive Ensemble Moving Average) and exponential smoothing are simple and easy to use, but they struggle to capture nonlinear patterns and long-term dependencies. Traditional machine learning methods such as Support Vector Regression (SVR) and Random Forest improve nonlinear modeling capabilities, but they are highly dependent on feature engineering. Deep learning methods such as LSTM (Long Memory Network), GRU (Gated Recurrent Unit), and Transformer have achieved good results in recent years, automatically extracting features and modeling complex temporal dependencies.

[0004] However, existing traffic flow prediction technologies have the following main drawbacks: Insufficient multi-scale feature extraction: Traditional methods use fixed time windows (e.g., 5 minutes) for sequence modeling, lacking collaborative analysis of macro trends (hourly-level changes) and micro fluctuations (minute-level abrupt changes). Common downsampling operations (e.g., simple averaging) lose local details, leading to a delay in the prediction results' response to sudden events; Insufficient utilization of frequency domain information: Existing frequency domain analysis methods often directly apply Fourier transform to extract spectral features without considering the stationary characteristics of traffic data, resulting in mixed noise in the spectral components. Furthermore, the correlation between the real and imaginary parts of the complex spectrum is not effectively exploited, limiting the accuracy of periodic component extraction. The model fusion strategy is too simplistic: Hybrid models usually use parallel branch results splicing or voting fusion, which fails to dynamically adjust the contribution weight of each sub-model according to spatiotemporal characteristics, thus limiting the upper limit of prediction performance. Insufficient generalization performance of existing models: When faced with unseen traffic patterns or changes in conditions, the generalization performance of existing models usually drops significantly, especially when there are abnormal fluctuations in traffic flow, the prediction accuracy drops sharply. Summary of the Invention

[0005] The purpose of this invention is to address the problems in current traffic flow prediction technologies, such as insufficient utilization of single-domain information, difficulty in modeling time-varying characteristics, insufficient balance between long-term and short-term dependencies, limited feature representation capabilities, and insufficient model generalization performance. This invention provides a traffic flow prediction method based on joint time-frequency domain modeling. Through a dual-path parallel deep learning architecture, combined with an innovative contrastive learning mechanism and dynamic fusion strategy, it achieves comprehensive and accurate modeling of traffic flow data, significantly improving prediction accuracy and robustness.

[0006] The technical solution of the present invention is as follows: A traffic flow prediction method based on joint time-frequency domain modeling includes the following steps: Acquire and preprocess traffic flow data. Organize and divide the acquired raw data according to the set time interval (e.g., 5 minutes) to form a dataset format for subsequent processing. A temporal LSTM prediction model is constructed. The model captures both short-term fluctuations and long-term trends in traffic flow through a multi-scale LSTM structure and a Transformer encoder. A frequency domain DBF_Block prediction model is constructed. Traffic flow data is transformed into the frequency domain space through Fast Fourier Transform (FFT), and a complex neural network is used for modeling, with a contrastive learning method added. The frequency domain DBF_Block prediction model zero-padding the input sequence, transforms it to the frequency domain using fast Fourier transform, and performs spectral normalization. It encodes the frequency domain features using a neural network based on complex number operations, generates contrastive learning features using a projection head, and incorporates the contrastive loss function into the overall loss function to optimize model training and enhance the model's ability to represent key frequency features. Train the time-domain LSTM prediction model and the frequency-domain DBF_Block prediction model respectively, optimize the parameters of each model, and verify the performance of each model on the validation set. Set a model fusion strategy to fuse the results of the time-domain LSTM prediction model and the frequency-domain DBF_Block prediction model with certain weights to generate traffic flow prediction results; The performance of the fusion model was evaluated on the test set and compared with the prediction results of the single model.

[0007] By using the above methods, a dual-path deep learning model in the time and frequency domains is integrated, and a contrastive learning mechanism and adaptive high-frequency enhancement technology are introduced to significantly improve the accuracy, stability and generalization ability of single-step prediction of total road traffic at a 5-minute granularity.

[0008] Furthermore, the construction of the time-domain LSTM prediction model includes the following steps: Set up the input layer: receive input data of shape [batch size, sequence length, feature dimension], where the sequence length is the number of historical time steps, and the feature dimension is usually 1, representing the traffic flow value; Set up a multi-scale LSTM layer: including two parallel LSTM structures to process information at different time scales. The first LSTM structure processes the original time features, while the second LSTM structure processes sequences sampled at larger time intervals (e.g., once every 12 steps, equivalent to one data point per hour) to capture longer-term time dependencies. Set up a feature fusion layer: concatenate the output features of the two LSTMs and map them to the same dimensional space through a fully connected layer. , in, This represents the final hidden state of the short-run LSTM, with dimension 1. ; This represents the final hidden state of a long-term LSTM, with dimension 1. ; This indicates concatenation along the feature dimension, with the result dimension being... ; This represents the linear transformation weight matrix, with dimension 1. like ; Represents the bias term of the linear transformation; Set up a Transformer encoder layer: Use the self-attention mechanism to further process the fused features and capture the dependencies between different time steps; Set up the output layer: Map the output to the prediction dimension using a fully connected layer to generate traffic flow predictions. , in, This represents the output of the last time step of the Transformer (dimension D=128). This represents the first-layer weight matrix. This represents the second-layer weight matrix. , This indicates the bias term.

[0009] Furthermore, the LSTM structure includes three gating mechanisms and a cell state update process: Input Gate: , in, For time step The input (such as the first) (5 minutes of data usage) This is the hidden state from the previous time step. , Let represent the input gate weight matrix, corresponding to the linear transformations of the input and hidden states, respectively. , Indicates the input gate bias term. This represents the Sigmoid activation function, with an output range of [0,1], controlling the proportion of information retained. Forgotten Gate: , in, , This represents the forget gate weight matrix. , Indicates the forget gate bias term. Controlling cell state The proportion that needs to be forgotten; Cell status update: , , in, Indicates the state of candidate cells (new information is generated through tanh activation). This indicates the current cell state, updated jointly by the forget gate and the input gate. This represents element-wise multiplication (Hadamard product). , The cell state update weight matrix represents the cell state update weight matrix. , This represents the cell state update bias term; Output gate: , , in, This represents the output gate, controlling the current hidden state. The output ratio, This represents the current hidden state, which is passed to the next time step or used for prediction; , This represents the output gate weight matrix. , This indicates the output gate bias term.

[0010] Furthermore, the Transformer encoder layer includes: Self-attention: , , in, , , These represent the query, key, and value in the attention mechanism, respectively, and are vector representations obtained by multiplying the input sequence by a learnable weight matrix. Represents the input sequence and the number of time steps. Batch size Feature Dimension ; , , Represents a learnable weight matrix, generating Query, Key, and Value; The dimension of the key (usually D / nhead). This represents the scaling factor, preventing the gradient from vanishing due to excessively large dot product values. Multi-head attention: Implementation logic: Divide Q, K, V into Each head (e.g., 4 heads) independently computes attention, concatenates the outputs of all heads, and fuses them through a linear layer; Feedforward networks: , in, , Represents the weight matrix. , This indicates the bias term.

[0011] Furthermore, the structure for constructing the frequency domain DBF_Block prediction model includes: Time-domain padding: Zero-padding is applied to the input sequence to extend the sequence length to fit the prediction length. , in, Indicates the input time-domain sequence, Batch size Enter time step , characteristic number =1, Represents a zero-filling tensor. To predict the step size, This represents the padded time-domain sequence, whose purpose is to provide a complete time window for subsequent FFTs by padding the zero-expanded time dimension. Time-domain to frequency-domain conversion: The padded time-domain sequence is converted into a frequency-domain representation using the Fast Fourier Transform (FFT), resulting in a complex tensor. , in, This represents the Fast Fourier Transform, which outputs a complex tensor. , This represents the total number of time steps after padding. Its function is to convert the time-domain signal into a frequency-domain complex representation to capture periodic features. Frequency domain normalization: Normalizing frequency domain data based on the statistical properties of the spectrum. , , , in, Represents the frequency domain amplitude (complex modulus). This represents the frequency domain mean (calculated along the time dimension). Indicates the standard deviation in the frequency domain (calculated based on amplitude only); =1e-5 is the numerical stabilization term, which eliminates the dimensional differences in the frequency domain amplitude and improves the convergence stability of the model. Frequency domain feature encoding: Frequency domain features are encoded using a complex neural network, including a complex linear layer, a complex normalization layer, and a complex attention mechanism. The formula is as follows: Complex linear layer: , in, , This represents the weight matrix for the real and imaginary parts. , Represents the real and imaginary parts of a complex tensor. This indicates the output complex number characteristics, where j represents the imaginary unit; Complex normalization layer: , in, , Represents the mean and standard deviation along the feature dimension. = This represents the complex scaling parameter. = Indicates the complex bias parameter; Complex attention: , , in, Represents the complex numbers Query, Key, and Value, i.e., the query, key, and value in the attention mechanism; H represents the number of attention heads. = This represents the feature dimension of each head. The attention weight (based on the magnitude of the complex dot product) is used to extract frequency domain features through complex neural networks, thereby enhancing the model's ability to model key frequency components. Inverse Fourier Transform Prediction: The processed frequency domain features are transformed back to the time domain using the Inverse Fourier Transform (IFFT), and the corresponding predicted portion is extracted as the final output. , in, = This represents the frequency domain signal after denormalization. ( ) represents the inverse fast Fourier transform. This represents the time-domain signal after the inverse transform, which ultimately affects the prediction part. After truncation, the enhanced frequency domain features are converted back to the time domain, and the final predicted value is output.

[0012] Furthermore, the neural network for complex number operations includes: Complex linear layer: Performs a linear transformation on the complex input, processing the real part separately. The formula is as follows: , Represented in matrix form as follows: , in, This represents an input complex vector. For the real part, The virtual part, , Let be the weight matrix for the real and imaginary parts. , This is the offset term between the real and imaginary parts. This indicates that the output is a complex vector with dimension 1. ; Complex number normalization layer: Normalizes complex tensors while preserving their complex structure. The formula is as follows: standardization: , Affine transformation: , in, This represents the mean along the feature dimension. This represents the standard deviation along the feature dimension. It is a small constant. For complex scaling parameters, , It is worth learning. For complex bias parameters, It is worth learning. This represents element-wise complex multiplication; Complex attention mechanism: Attention is calculated based on complex tensors to handle complex queries, keys, and values. The formula is as follows: Attention Score: , Attention weights: , Output: , in, The query, key, and value are in complex form, where B is the batch size, H is the number of heads, L is the sequence length, and d is the head dimension. Represents the magnitude of a complex number. The dimension of the key is used for scaling.

[0013] The above method uses a complex neural network to process frequency domain information, preserving the amplitude and phase information of complex signals. Compared with using only a real neural network, it can more comprehensively express frequency domain features. Traditional methods often only use amplitude information and ignore phase information when processing frequency domain information, resulting in information loss. This application constructs a complete complex neural network system through components such as complex linear layers, complex normalization layers, and complex attention mechanisms, which can simultaneously process and learn the amplitude and phase features of frequency domain signals, thereby extracting richer frequency domain representations.

[0014] Furthermore, the contrastive learning method optimizes feature representation by constructing positive and negative sample pairs, maximizing consistency between different views of the same data while minimizing similarity between different data sets. The loss function used by the contrastive learning method is as follows: , in, This represents the average contrast loss for the entire batch. This indicates the batch size, i.e., the number of samples. For the first The normalized embedding vector (after L2 normalization) of each sample in the first perspective (e.g., the data augmented version). For the first Normalized embedding vectors (after L2 normalization) of each sample in the second perspective (another data augmentation version). This is a temperature coefficient used to adjust the distribution of similarity; smaller ones... It will amplify similarity differences, making the model pay more attention to difficult samples. Representing vectors and The dot product (i.e., cosine similarity, since the vectors have been normalized). ( () represents an exponential function, used to amplify differences in similarity. ( () represents the natural logarithm, and is used to calculate the probability of a negative logarithm. This represents the similarity between positive sample pairs (the two perspectives of the i-th sample). This represents the sum of similarities between positive sample pairs and all negative sample pairs (j≠i). The goal is to minimize the loss, with the model maximizing the similarity of positive sample pairs while minimizing the similarity with negative sample pairs.

[0015] By introducing a contrastive learning method based on adaptive high-frequency enhancement, the sensitivity of the model to key features in traffic flow data is effectively improved. Changes in traffic flow data are reflected not only in overall trends (low-frequency information) but also in rapid changes caused by sudden events or abnormal situations (high-frequency information). By enhancing high-frequency information, the model can more accurately capture these change patterns, especially significantly improving its response to sudden events or abnormal situations. At the same time, the adaptive mechanism allows high-frequency enhancement to be dynamically adjusted according to the characteristics of the current data, avoiding the limitations of fixed parameters.

[0016] Furthermore, the model fusion strategy employs a weighted average method to fuse the prediction results of the time-domain LSTM model and the frequency-domain DBF_Block model. The model fusion formula is: , in, This represents the single-step prediction result of the TrafficLSTM model. This represents the single-step prediction result of the TrafficDBF_Blcok model. This indicates the final prediction result after fusion; The formula for the mean squared error (MSE) of a single-step prediction in the TrafficLSTM model is: , in, This indicates that the TrafficLSTM model is for the first... The predicted value for each sample, Indicates the first The true value of each sample The number of samples in the validation set; The formula for the mean squared error (MSE) of a single-step prediction in the TrafficDBF_Blcok model is: , in, This indicates that the TrafficDBF_Blcok model is for the first... The predicted value for each sample, Indicates the test set number The true value of each sample The number of validation set samples (batch size); The mean squared error (MSE) of the fusion model is given by the following formula: , in, Indicates the fusion model for the first The predicted value for each sample, Indicates the test set number The true value of each sample The number of validation set samples (batch size).

[0017] By employing the above method, a model fusion strategy is used to complement the advantages of different models, thereby further improving prediction performance. Experimental results show that the prediction results after model fusion are better than those of a single model, with a significant reduction in MSE loss. In particular, when facing complex and ever-changing traffic scenarios, the fused model exhibits stronger stability and accuracy.

[0018] Furthermore, the acquisition and preprocessing of traffic flow data includes the following specific steps: Raw data reading: Read monitoring data from an Excel file containing a "5 Minutes" time column and a "Flow (Veh / 5 Minutes)" traffic flow column, which records the number of vehicles passing through the monitoring point every 5 minutes. Time index standardization: Convert the date and time information in the raw data into a standard date and time format and set it as the index of the data frame; at the same time, strictly sort the data according to time order to ensure the accuracy and consistency of subsequent time series analysis; Data integrity check: By constructing an ideal complete time range sequence (from the earliest time to the latest time, at 5-minute intervals), it is compared with the actual dataset to identify possible missing time points; if missing data is found, time series linear interpolation is used to fill these missing values ​​to ensure the continuity and integrity of the data and avoid model training bias due to missing data. Data standardization: The StandardScaler standardization method is applied to process the traffic flow data, converting the raw flow values ​​into a standard normal distribution with a mean of 0 and a standard deviation of 1. This step helps eliminate the influence of large differences in flow rates across different time periods, accelerates model convergence, and improves the stability and prediction accuracy of model training. The standardization formula is as follows: , in This is the raw traffic data. It is the mean of the training data. It is the standard deviation. The data is standardized. Sliding window sequence generation: Based on a predefined sequence length (24 time steps, i.e., 2 hours) and prediction step size (1 time step, i.e., 5 minutes), a sliding window technique is used to construct input-output sample pairs. In each sample pair, the input is standardized traffic flow data for 24 consecutive time steps, and the output is the standardized traffic flow value for the immediately following time step. The sliding window sampling formula is as follows: Based on time series Generate the following samples: Input sequence : , Tag sequence : , in Indicates the length of the input sequence (e.g., 24 time points). Indicates the number of steps to predict the future (e.g., predicting the value of one step). Strict temporal partitioning: The generated sample pairs are divided into a training set (80%) and a test set (20%) according to a strict time order. Unlike the random partitioning in traditional machine learning, the partitioning of time series data must maintain the original time order. This ensures that model training is carried out on historical data and testing and evaluation are performed on future data, thereby maintaining the causality and effectiveness of time series prediction and preventing overfitting caused by information leakage.

[0019] Timestamp Extraction and Alignment: Extract and save the corresponding timestamp information for each sample, especially the timestamps of the test set samples. This time information will be used for subsequent result visualization and model evaluation analysis, enabling the prediction results to accurately correspond to the actual time points, facilitating intuitive evaluation of model performance and interpretation of results.

[0020] Furthermore, the preprocessing includes cleaning, normalizing, and standardizing the data to ensure data quality and consistency.

[0021] Compared with existing technologies, the advantages of this invention are: 1. A traffic flow prediction method based on joint time-frequency domain modeling. By simultaneously utilizing time-domain and frequency-domain information, this method fully explores the multi-dimensional features in traffic flow data. The time-domain LSTM model can effectively capture the temporal dependence of traffic flow, especially by simultaneously modeling short-term fluctuations and long-term trends through a multi-scale structure. The frequency-domain DBF_Block model analyzes traffic data from a frequency perspective, which can better identify periodic patterns and frequency characteristics. This dual modeling method overcomes the limitations of a single model and significantly improves prediction accuracy. 2. A traffic flow prediction method based on joint time-frequency domain modeling significantly improves the model's feature representation ability and generalization performance by introducing a contrastive learning framework. Contrastive learning optimizes the distribution of samples in the feature space by constructing positive and negative sample pairs, making similar traffic patterns closer in the feature space and different traffic patterns more distinct. This feature optimization not only improves the model's ability to identify normal traffic patterns but also enhances its robustness to abnormal situations. Most importantly, contrastive learning can significantly improve model performance through data augmentation and feature optimization even with limited data. Attached Figure Description Figure 1 This is a flowchart of the method described in this application.

[0022] Figure 2 This is a diagram of the network structure of the temporal LSTM model in the method of this application.

[0023] Figure 3 This is a network structure diagram of the frequency domain DBF_Block model in the method of this application.

[0024] Figure 4 This is a schematic diagram of the model fusion strategy in the method of this application.

[0025] Figure 5 This is a graph showing the trend of traffic flow in each lane over time in the experiment of this application.

[0026] Figure 6 This is a graph showing the trend of traffic flow over time for all lanes in the experiment of this application.

[0027] Figure 7 The image shows the prediction results of the experiment using only contrastive learning.

[0028] Figure 8 The image shows the prediction results for the experiment using only the F_Block module.

[0029] Figure 9 The image shows the prediction results of the experiment using only the LSTM and Transformer modules.

[0030] Figure 10 The figure shows the prediction results of the experiment using the method of this application. Detailed Implementation

[0031] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0032] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0033] Traffic flow prediction is a key task in intelligent transportation systems, directly impacting traffic signal optimization, congestion warning, and road network management. Existing prediction methods mainly include: Temporal LSTM / GRU models can effectively capture short-term trends and medium-term dependencies, but they are difficult to model global correlations spanning multiple hours or even days. For traffic flow with complex periodic fluctuations, their single temporal model often fails to identify hidden periodic signals.

[0034] Transformer temporal model: It can directly model arbitrary distance dependencies through self-attention, which can supplement long-distance associations, but it is not good at capturing local short-term dynamics and continuous details; in multi-scale information fusion, it is difficult to balance the weights of features of different granularities without design.

[0035] Frequency domain analysis methods, such as Fourier transform, can reveal the periodicity of sequences, but methods based solely on the frequency domain have low integration with deep networks and are difficult to optimize end-to-end.

[0036] Contrastive learning has significantly improved feature discrimination in fields such as images and text, but it has not been integrated with multi-scale time-frequency domain features in traffic flow prediction, resulting in limited representation capabilities.

[0037] Please see Figure 1-10 A traffic flow prediction method based on joint time-frequency domain modeling, such as Figure 1 As shown, it includes the following steps: Traffic flow data for one month on a four-lane main road in Changsha was obtained from traffic monitoring equipment. The data was recorded at 5-minute intervals. The raw data was then read from an Excel file, and the time information was standardized (e.g., the "5 Minutes" time column was converted to a standard date and time format and set as an index). The data was also sorted in strict chronological order. By constructing a complete 5-minute interval sequence, checking data integrity, and using time series linear interpolation to fill in missing values, the continuity and consistency of the data for subsequent processing were ensured. Finally, StandardScaler was used to standardize the raw traffic flow values ​​into a standard normal distribution with a mean of 0 and a standard deviation of 1. , in, For raw traffic data, For the mean of training data, To determine the standard deviation, a sliding window technique is used to construct input-output sample pairs. Each sample's input consists of standardized flow rates over 24 consecutive time steps (i.e., 2 hours of historical data), and the output is the standardized flow rate value for the immediately following 5-minute time step. The samples are strictly divided into an 80% training set and a 20% test set according to chronological order, while retaining timestamp information for subsequent alignment with actual times. This ensures that the prediction results are accurately mapped to actual time points in the visualization analysis.

[0038] Given time series Generate the following samples: Input sequence : , Tag sequence : , in Indicates the length of the input sequence (e.g., 24 time points). This indicates the number of steps to predict the future (e.g., predicting the value of one step).

[0039] To fully capture the short-term dynamic changes and long-term trends in traffic flow data, this application constructs two prediction models in parallel: a time-domain LSTM model and a frequency-domain DBF_Block model.

[0040] like Figure 2 As shown, the time-domain model first feeds the input data into two parallel LSTM branches. The first branch directly processes the original 5-minute sampled data to capture short-term dynamic features; the second branch processes the downsampled sequence (e.g., sampling once every 12 steps, equivalent to one data point per hour) to extract long-term trend information. Its core LSTM calculation process is based on the following formula: Forget gate calculation: The forget gate is used to determine which information from the cell's previous state needs to be forgotten. Its formula is: , in, , This represents the forget gate weight matrix. , Indicates the forget gate bias term. Controlling cell state The proportion that needs to be forgotten; Input gate calculation: The input gate controls the contribution of the current input information to the cell state update, and its formula is as follows: , in, For time step Input, This is the hidden state from the previous time step. , Let represent the input gate weight matrix, corresponding to the linear transformations of the input and hidden states, respectively. , Indicates the input gate bias term. This represents the Sigmoid activation function, with an output range of [0,1], controlling the proportion of information retained. Candidate cell state update establishes candidate cell state The new information currently being input is obtained using the hyperbolic tangent function: , , in, Indicates the state of candidate cells. This indicates the current cell state, updated jointly by the forget gate and the input gate. This represents element-wise multiplication; , The cell state update weight matrix represents the cell state update weight matrix. , This represents the cell state update bias term; Output gate and hidden state update: The output gate determines which information from the current cell state will be passed to the hidden state. The formula is: , The final hidden state is calculated as follows: , in, This represents the output gate, controlling the current hidden state. The output ratio, This represents the current hidden state, which is passed to the next time step or used for prediction; , This represents the output gate weight matrix. , This indicates the output gate bias term.

[0041] These formulas work together to enable LSTM to capture the dependencies between time series data and flexibly control the flow of information through gating mechanisms, thereby achieving effective modeling of short-term fluctuations and long-term trends in traffic flow.

[0042] The hidden states output by the two LSTM branches are concatenated through a feature fusion layer and then mapped to a unified feature space through a fully connected layer. The expression is as follows: , The fused feature sequence is input into the Transformer encoder, which uses a self-attention mechanism to capture global dependencies between different time steps. Its core formula is:

[0043] .

[0044] The features are deeply modeled using mechanisms such as multi-head parallel attention, feedforward networks, and residual connections. The final output is a temporal prediction result generated by mapping through a fully connected layer. .

[0045] like Figure 3 As shown, simultaneously, to fully exploit the periodic features and frequency domain information contained in the data, the frequency domain DBF_Block model first zero-padding the input time domain sequence to expand the time steps, resulting in: , in, To predict the step size, this invention employs a frequency domain analysis method to compensate for the shortcomings of traditional time domain methods in extracting periodic information. Traditional traffic flow prediction models are typically based on time series modeling, but they struggle to accurately capture the periodic components in traffic flow data. Therefore, this application uses the Fast Fourier Transform (FFT) to transform traffic flow data into the frequency domain to analyze the periodic characteristics within the data. The mathematical expression for FFT is as follows: , in, This represents the total number of time steps after expansion; subsequently, the mean is calculated based on the spectral amplitude. and standard deviation The frequency domain data is standardized. This application employs mean and variance normalization methods to ensure consistency in amplitude values ​​across different time steps. The normalized spectrum data is represented as follows: , Subsequently, to further explore frequency domain information, this invention employs a complex neural network to encode the features of the frequency domain data. Compared to traditional real neural networks, complex networks can simultaneously process amplitude and phase information (this network includes a complex linear layer, a complex normalization layer, and a complex attention mechanism) to preserve the complete features of the spectral signal. The goal of the complex linear layer is to perform a linear transformation on the normalized frequency domain data while preserving complex characteristics. The complex linear layer operation in this application is as follows: , in, , This represents the weight matrix for the real and imaginary parts. , Represents the real and imaginary parts of a complex tensor. Indicates the output complex number characteristics, Represents the imaginary unit; This transformation structure can fuse real and imaginary information from the input while preserving phase information. The complex normalization layer is used to normalize the complex features, calculated as follows: , in, and These are the mean and standard deviation of the complex feature, respectively. and These are the learnable complex scaling parameter and bias parameter, respectively. The encoded frequency domain features are denormalized, then transformed back to the time domain using an inverse fast Fourier transform (IFFT), and the predicted portion is extracted as the frequency domain prediction result. The expression is: , Final prediction part After truncation, the enhanced frequency domain features are converted back to the time domain, and the final predicted value is output. Based on the separate training and parameter optimization of the two models, this application also introduces a contrastive learning method to further optimize feature representation and improve the model's generalization ability. This involves constructing positive sample pairs generated under different data augmentation conditions with negative sample pairs compared to other samples, and using the following contrastive loss function for feature optimization: , in, This represents the average contrast loss for the entire batch. This indicates the batch size, i.e., the number of samples. For the first The normalized embedding vector of each sample in the first perspective For the first The normalized embedding vector of each sample in the second perspective. This is a temperature coefficient used to adjust the distribution of similarity; smaller ones... It will amplify similarity differences, making the model pay more attention to difficult samples. Representing vectors and dot product, ( () represents an exponential function, used to amplify differences in similarity. ( () represents the natural logarithm, and is used to calculate the probability of a negative logarithm. Indicates the similarity between positive sample pairs. This represents the sum of similarities between positive sample pairs and all negative sample pairs. The goal is to minimize the loss; the model will maximize the similarity of positive sample pairs while minimizing the similarity with negative sample pairs.

[0046] Finally, a weighted fusion strategy is used to synthesize the prediction results of the time-domain model and the frequency-domain model, such as... Figure 4 As shown, the final predicted value is generated by a weighted fusion of the time-domain LSTM model and the frequency-domain DBF_Block model. The fusion formula is as follows: , in, This represents the single-step prediction result of the TrafficLSTM model. This represents the single-step prediction result of the TrafficDBF_Blcok model. This indicates the final prediction result after fusion; Contrastive learning optimizes feature distribution, making similar samples closer in the feature space while further widening the differences between different samples, thereby enhancing the model's ability to distinguish complex traffic patterns. The mean squared error (MSE) is used to evaluate each sub-model and the fusion model. MSE is used to assess the error of the prediction model, specifically the average of the squared differences between the predicted and actual values. MSE is a common metric for measuring model prediction error; the smaller the MSE value, the closer the model's prediction is to the actual value.

[0047] The MSE formula of the fusion model combines the prediction results of the time-domain LSTM and frequency-domain DBF_Block models, and uses weights... Dynamic adjustments are made to optimize prediction performance. The MSE calculation formulas for the time-domain LSTM model, the frequency-domain DBF_Block model, and the fusion model are given below: , in, This indicates that the TrafficLSTM model is for the first... The predicted value for each sample, Indicates the first The true value of each sample The number of samples in the validation set; , in, This indicates that the TrafficDBF_Blcok model is for the first... The predicted value for each sample, Indicates the test set number The true value of each sample The number of samples in the validation set; , in, Indicates the fusion model for the first The predicted value for each sample, Indicates the test set number The true value of each sample The number of samples in the validation set.

[0048] Experimental results show that, compared with a single model, the fusion model can more effectively adapt to different traffic patterns, improve prediction accuracy, and exhibit better robustness in complex traffic scenarios. The fusion model not only compensates for the shortcomings of the time-domain model in terms of periodic features, but also makes up for the deficiencies of the frequency-domain model in short-term dynamic prediction, ultimately forming a traffic flow prediction scheme that combines short-term prediction capabilities, long-term trend learning capabilities, and strong robustness.

[0049] In the frequency domain model, adaptive high-frequency enhancement technology is used to perform energy statistics, normalized median calculation, and normalized distance calculation on the spectrum data after FFT transformation, which effectively enhances the capture of sudden anomalies or subtle changes. Contrastive learning further optimizes the model feature representation, making similar traffic patterns closer in high-dimensional space, while different patterns are separated, thereby improving the generalization performance of the prediction model in complex traffic scenarios.

[0050] In summary, this application combines time-domain and frequency-domain information, capturing short-term and long-term temporal dependencies through the gating mechanism of the LSTM model, integrating global features using a Transformer encoder, extracting frequency-domain amplitude and phase information through a complex neural network, and further enhancing the model's ability to distinguish complex traffic patterns through contrastive learning. Finally, a weighted fusion strategy is employed to combine the advantages of both models. This ensures the rigor and efficiency of the model training and prediction process, significantly improving the accuracy and robustness of traffic flow prediction, and providing efficient and reliable decision support for intelligent traffic management.

[0051] The test platform and experimental environment are as follows: The experimental environment uses a Windows operating system, an A40 graphics card with 48GB of video memory, an Intel(R) Xeon(R) Platinum 8358P CPU @ 2.60GHz, CUDA version 11.1.0, PyTorch version 1.9.0, and Python language environment 3.8.10.

[0052] The dataset used is one month of continuous traffic flow monitoring data from a four-lane main road in Changsha City. Visualization is as follows: Figure 5 and Figure 6 As shown: Evaluation indicators: In this experiment, Mean Squared Error (MSE) was used to quantitatively evaluate the predictive performance of three models—time-domain LSTM, frequency-domain DBF_Block, and the fusion model proposed in this application. MSE measures the squared average of the differences between predicted and actual values. This provides a more comprehensive and accurate understanding of traffic flow patterns, offering strong support for subsequent improvements to scheduling strategies and optimization of traffic management.

[0053] The system displays the traffic flow trends of each lane over time, with traffic flow data collected every five minutes. The horizontal axis represents the specific date and time, helping to observe and compare traffic flow fluctuations, anomalies, and peak / off-peak conditions for each lane in different time periods. It also displays the traffic flow trends of all roads over time, recording overall traffic flow in a time series to comprehensively reflect the traffic dynamics and overall congestion of the entire road network. All calculations are aligned with time-series data in 5-minute units to ensure that the evaluation results accurately reflect short-term traffic flow fluctuation patterns.

[0054] In another specific implementation case, to verify the effectiveness of the algorithm, an ablation experiment was conducted on the same dataset using the model adopted in this application. The prediction results are as follows: Figure 7-10 As shown: Comparison of performance indicators in ablation experiments: The performance of each model on the traffic flow trend curve over time is analyzed: Using only contrastive learning: This method can capture the global trend in traffic flow data to some extent, but the curve deviates significantly from the true value, especially at local peaks and troughs, indicating that simple contrastive learning is not ideal in dealing with fine-grained temporal fluctuations.

[0055] Using only the F_Block module: This model mainly focuses on extracting local features and can reflect fluctuations in a short period of time relatively well. However, due to the lack of a comprehensive judgment on the overall time series structure, its prediction curve deviates from the overall trend. Although local details are clear, they are difficult to accurately connect with the dynamic changes of the entire time period.

[0056] Using the LSTM+Transformer module: This model combines the long short-term memory model's ability to capture long-term dependencies with the Transformer's ability to model complex temporal patterns, resulting in a smoother overall curve that follows the true trend well. However, there are still issues with inaccurate local predictions, and some errors are still visible at local extrema.

[0057] LSTM+Transformer+F_Block+Contrastive Learning (Ours): By integrating the advantages of time-domain and frequency-domain feature extraction and global contrastive learning, the final predicted curve more closely matches the actual traffic flow changes. Whether considering global trends or local fluctuations, the model demonstrates high prediction accuracy and robustness, with smooth curves and ample detail. This proves the effectiveness of collaborative work between modules, comprehensively handling temporal dependencies and local feature variations, and significantly reducing prediction errors.

[0058] A comparative analysis of the performance of each model on the evaluation metric—mean squared error (MSE)—is conducted. As shown in Table 1, the performance of each model exhibits significant differences in terms of mean squared error (MSE). When using the LSTM model alone, the MSE is 0.0414, approximately 2.73% higher than the fusion model in this application (0.0403 lower). This indicates that while relying solely on time-domain information capture can reflect temporal dependencies to some extent, it introduces certain errors in fine-grained prediction. When using the DBF module alone, the MSE reaches 0.0458, an increase of approximately 13.65% compared to the fusion model, demonstrating that relying solely on frequency-domain feature extraction cannot fully compensate for the limitations of temporal relationships. Ultimately, the fusion model (Ours), which integrates LSTM and DBF modules, achieves the lowest MSE (0.0403) by combining time-domain and frequency-domain information, significantly improving prediction accuracy and robustness. Therefore, the shortcomings of each independent module are complemented by fusion, proving the superior performance of the fusion model in traffic flow prediction.

[0059] Table 1 Comparison of Mean Square Error of MSE in Ablation Experiments

[0060] The embodiments described above merely illustrate specific implementation methods of this application, and while the descriptions are detailed and specific, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the technical solution of this application, and these modifications and improvements all fall within the scope of protection of this application.

Claims

1.A traffic flow prediction method based on joint modeling in time-frequency domain, characterized in that, The method comprises the following steps: Obtaining and preprocessing traffic flow data, arranging and dividing the obtained raw data according to the set time interval to form a data set format for subsequent processing; Building a time domain LSTM prediction model, which simultaneously captures short-term fluctuations and long-term trends of traffic flow through a multi-scale LSTM structure and a Transformer encoder; Building a frequency domain DBF_Block prediction model, which converts traffic flow data into a frequency domain space through a fast Fourier transform, uses a complex neural network for modeling, and adds a contrast learning method; The frequency domain DBF_Block prediction model extends the input sequence by zero padding, converts it to the frequency domain through a fast Fourier transform and performs frequency spectrum standardization; the frequency domain features are encoded through a complex neural network, and contrast learning features are generated through a projection head; a contrast loss function is added to the overall loss function to optimize the model training; Respectively training the time domain LSTM prediction model and the frequency domain DBF_Block prediction model, optimizing the parameters of each model, and verifying the performance of each model on the validation set; Setting a model fusion strategy to fuse the results of the time domain LSTM prediction model and the frequency domain DBF_Block prediction model to generate traffic flow prediction results; Evaluating the performance of the fusion model on the test set and comparing it with the prediction results of the single model. 2.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1, characterized in that, The method for building the time domain LSTM prediction model comprises the following steps: Setting an input layer: receiving input data with a shape of [batch size, sequence length, feature dimension], where the sequence length is the number of historical time steps, and the feature dimension is usually 1, representing the traffic flow value; Setting a multi-scale LSTM layer: including two parallel LSTM structures to process information of different time scales, where the first LSTM structure processes the original time features, and the second LSTM structure processes sequences sampled at a larger time interval; Setting a feature fusion layer: concatenating the output features of the two LSTM and mapping them to the same dimension space through a fully connected layer: ， wherein, represents the final hidden state of the short-term LSTM, with dimension ; represents the final hidden state of the long-term LSTM, with dimension ; represents concatenation along the feature dimension, with the resulting dimension ; represents the linear transformation weight matrix, with dimension ; represents the linear transformation bias term; Setting a Transformer encoder layer: using a self-attention mechanism to further process the fused features and capture the dependency between different time steps; Setting an output layer: mapping to the prediction dimension through a fully connected layer to generate traffic flow prediction values: ， wherein, denotes the output of the Transformer at the last time step, denotes the first layer weight matrix, denotes the second layer weight matrix, , denotes the bias term. 3.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 2, characterized in that, The LSTM structure includes three gating mechanisms and a cell state update process: Input gate: , wherein, is the input at time step , is the hidden state at the previous time step, , denotes the input gate weight matrix, corresponding to the linear transformation of the input and hidden state respectively, , denotes the input gate bias term, denotes the Sigmoid activation function, the output range [0, 1], controlling the information retention ratio; Forget gate: , wherein, , denotes a forget gate weight matrix, , denotes a forget gate bias term, controls the proportion of the cell state that needs to be forgotten; Cell state update: ， ， wherein, represents a candidate cell state, represents a current cell state, updated by the forget gate and the input gate together, represents an element-wise multiplication; , represents a cell state update weight matrix, , represents a cell state update bias term; Output gate: ， ， wherein, denotes an output gate, controlling the output proportion of the current hidden state , denotes the current hidden state, passed to the next time step or used for prediction; , denotes an output gate weight matrix, , denotes an output gate bias term. 4.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 2 or 3, characterized in that, The Transformer encoder layer includes: Self-attention: ， ， wherein, , , respectively represent Query, Key and Value in the attention mechanism, which are vector representations obtained by multiplying the input sequence with a learnable weight matrix, represent the input sequence, the number of time steps , the batch size , the feature dimension ; , , represent a learnable weight matrix, generating Query, Key, Value; represent the dimension of Key, represent a scaling factor to prevent gradient vanishing caused by excessively large dot product values; Multi-head attention: Implementation logic: split Q, K, V into heads, each head computes attention independently, concatenate the outputs of all heads and fuse through a linear layer. Feedforward network: , wherein, , denotes a weight matrix, , denotes a bias term. 5.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1, characterized in that, The structure of the frequency domain DBF_Block prediction model comprises: Time domain padding: zero padding the input sequence to expand the sequence length to adapt to the prediction length: , where, denotes the input time-domain sequence, Batch size , input time step , number of features = 1, denotes a zero padding tensor, is the prediction step, denotes the padded time-domain sequence, which serves to expand the time dimension by padding zeros to provide a complete time window for the subsequent FFT; Time domain to frequency domain: converting the padded time domain sequence to a frequency domain representation through a fast Fourier transform to obtain a complex tensor: ， wherein, denotes a fast Fourier transform, outputting a complex tensor , denotes the total number of padded time steps, which serves to convert the time domain signal into a frequency domain complex representation, capturing periodic characteristics; Frequency domain normalization: standardizing the frequency domain data based on the statistical characteristics of the frequency spectrum: ， ， ， wherein, represents the frequency domain amplitude, represents the frequency domain mean, represents the frequency domain standard deviation; = 1e-5 is a numerical stability term, which functions to eliminate the dimensional difference of the frequency domain amplitude and improve the stability of model convergence. Frequency domain feature encoding: encoding the frequency domain features through a complex neural network, including a complex linear layer, a complex normalization layer, and a complex attention mechanism, with the formula being: Complex linear layer: ， wherein , denotes the real and imaginary weight matrix, , denotes the real and imaginary components of the complex tensor, denotes the output complex feature, j denotes the imaginary unit; Complex normalization layer: ， wherein, , denotes the mean and the standard deviation along the feature dimension, = denotes a complex scaling parameter, = denotes a complex bias parameter;​​ Complex attention: ， ， wherein, represents complex Query, Key, Value, i.e. query, key and value in attention mechanism; H is the number of attention heads, = represents the feature dimension of each head, is an attention weight, which functions to extract frequency domain features through a complex neural network and enhance the modeling capability of the model on key frequency components; Inverse transform prediction: the processed frequency domain features are converted back to the time domain through inverse Fourier transform, and the corresponding prediction part is intercepted as the final output: ， wherein, = denotes the inverse fast Fourier transform, denotes the inverse fast Fourier transform, denotes the inverse fast Fourier transform, denotes the inverse fast Fourier transform,​​ 6.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1, characterized in that, The complex number operation neural network comprises: Complex linear layer: perform linear transformation on complex input, process real part respectively, and the formula is: ， Expressed by matrix as: ， wherein, represents an input complex vector, is a real part, is an imaginary part, , is a weight matrix for the real and imaginary parts, , is a bias term for the real and imaginary parts, represents an output complex vector of dimension ; Complex normalization layer: normalize the complex tensor, keep the complex structure, and the formula is: Standardization: ， Affine transformation: ， wherein, denotes the mean along the feature dimension, denotes the standard deviation along the feature dimension, is a small constant, is a complex scaling parameter, , is learnable, is a complex bias parameter, is learnable, denotes element-wise complex multiplication; Complex attention mechanism: calculate attention based on complex tensor, process complex query, key and value, and the formula is: Attention score: ， Attention weight: ， Output: ， wherein, query, key, value, B is batch size, H is head number, L is sequence length, d is head dimension, denotes the magnitude of a complex number, is the dimension of the key, used for scaling. 7.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1, characterized in that, The contrast learning method optimizes the feature representation by constructing positive sample pairs and negative sample pairs, maximizes the consistency between different views of the same data, and minimizes the similarity between different data, and the loss function formula used by the contrast learning method is as follows: ， where, represents the average contrastive loss of the whole batch, represents the batch size, i.e., the number of samples, is the normalized embedding vector of the th sample at the first view, is the normalized embedding vector of the th sample at the second view, is the temperature coefficient, used to adjust the distribution of similarity; a smaller will amplify the difference in similarity, making the model pay more attention to difficult samples, represents the dot product of vectors and , ( ) represents the exponential function, which is used to amplify the difference in similarity, ( ) represents the natural logarithm, which calculates the negative log probability; represents the similarity of a positive sample pair, represents the sum of similarities of a positive sample pair and all negative sample pairs, the goal is that by minimizing the loss, the model will maximize the similarity of the positive sample pair while minimizing the similarity with the negative sample pairs. 8.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1, characterized in that, The model fusion strategy adopts a weighted average manner to fuse the prediction results of the time domain LSTM model and the frequency domain DBF_Block model. The model fusion formula is: ， wherein, represents the single-step prediction result of the TrafficLSTM model, represents the single-step prediction result of the TrafficDBF_Blcok model, represents the final prediction result after fusion; The mean square error MSE of single-step prediction of the TrafficLSTM model is: ， wherein, represents the predicted value of the TrafficLSTM model for the i-th sample, represents the true value of the i-th sample, is the number of validation set samples;​​ The mean square error MSE of single-step prediction of the TrafficDBF_Blcok model is: ， wherein, represents the predicted value of the TrafficDBF_Blcok model for the i-th sample of the test set, represents the predicted value of the TrafficDBF_Blcok model for the i-th sample of the test set, represents the true value of the i-th sample of the test set, represents the true value of the i-th sample of the test set, is the number of samples of the validation set; The mean square error MSE of the fusion model is: ， wherein, represents the predicted value of the fusion model for the i-th sample of the test set, represents the predicted value of the fusion model for the i-th sample of the test set, represents the true value of the i-th sample of the test set, represents the true value of the i-th sample of the test set, is the number of samples of the validation set. 9.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1, characterized in that, The acquisition and preprocessing of traffic flow data comprises the following specific steps: Raw data reading: read the monitoring data from the Excel format file, which contains the "5 Minutes" time column and the "Flow (Veh / 5 Minutes)" traffic flow column, and records the number of vehicles passing through the monitoring point every 5 minutes; Time index standardization: convert the date and time information in the original data into a standard date and time format, and set it as the index of the data frame; at the same time, strictly sort the data according to time sequence to ensure the accuracy and consistency of subsequent time series analysis; Data integrity check: compare the actual data set with the ideal complete time range sequence from the earliest time to the latest time at 5-minute intervals to identify possible missing time points; If missing data is found, linear interpolation method is used to fill in the missing values to ensure the continuity and integrity of the data and avoid model training bias caused by missing data; Data standardization processing: apply StandardScaler standardization method to process the traffic flow data, and convert the original flow value to standard normal distribution with mean of 0 and standard deviation of 1; the standardization processing formula is as follows: ， wherein is the original flow data, is the mean of the training data, is the standard deviation, is the normalized data; Sliding window sequence generation: based on the pre-defined sequence length and prediction step, use sliding window technology to build input-output sample pairs; in each sample pair, the input is the standardized traffic flow data of the next 24 time steps, and the output is the standardized traffic flow value of the first time step; the sliding window sampling formula is as follows: According to the time series , the following samples are generated: Input sequence : ， Tag sequence : ， wherein denotes the length of the input sequence, denotes the number of steps into the future to predict. Strict time sequence division: divide the generated sample pairs into training set and test set according to strict time sequence; Timestamp extraction and alignment: extract and save the corresponding timestamp information for each sample. 10.The traffic flow prediction method based on time-frequency domain joint modeling according to claim 1 or 9, characterized in that, The preprocessing includes cleaning, normalizing and standardizing the data, ensuring the quality and consistency of the data.

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