An ozone concentration prediction method combining two-stage decomposition and dimension selection

Abstract

The application relates to the field of environment prediction, and discloses an ozone concentration prediction method combining two-stage decomposition and dimension selection, which comprises the following steps: obtaining historical ozone concentration detection data composed of time and ozone concentration values; preprocessing the historical ozone concentration detection data to generate an original concentration time sequence X; performing secondary decomposition on the original concentration time sequence X to generate concentration sub-sequences; performing dimension reduction on the concentration sub-sequences to generate a best input dimension sub-sequence, wherein t represents a time sequence, and p represents a dimension; loading a TCN prediction model, inputting the best input dimension sub-sequence into the TCN prediction model, and realizing ozone concentration prediction of future time. According to the above technical scheme, the regular characteristics in the ozone sequence with violent fluctuation can be accurately captured, operation redundancy caused by decomposition can be effectively solved, and the prediction accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of environmental prediction, and more specifically, to a method for predicting ozone concentration that combines two-stage decomposition and dimension selection. Background Technology

[0002] With the continuous development of society, air pollution has attracted widespread attention. Ozone is a significant air pollutant, and excessive amounts of air pollutants are a major contributing factor to respiratory diseases in humans. Regional ozone concentration prediction can directly reflect changes in the spatial distribution of ozone, providing important early warning information for patients with respiratory diseases, helping individuals make prudent travel choices, and limiting the harm caused by air pollutants.

[0003] Currently, regional ozone concentration prediction typically employs three types of methods: First, deterministic models such as CMAQ and WRF-Chem predict ozone concentration by simulating atmospheric physicochemical processes, which can characterize the formation and diffusion mechanisms of pollutants; second, statistical prediction methods that rely on mining the correlations between variables from historical data, which do not require an understanding of the pollutant formation mechanism; and third, intelligent computing methods represented by machine learning, including artificial neural networks (ANN), support vector machines (SVM), long short-term memory networks (LSTM), and their hybrid models (such as CNN-LSTM), which have been widely used in ozone prediction in recent years, often achieving higher accuracy than traditional regression.

[0004] However, while deterministic models have clear physical meaning, their prediction accuracy is often lower than that of statistical prediction methods. Statistical prediction methods, on the other hand, lack an understanding of the pollutant formation mechanisms and rely solely on data correlation, thus lacking robustness. Machine learning methods, while highly accurate, face challenges due to highly complex data and noise interference. Furthermore, single models are insufficient for practical needs, requiring the introduction of optimization algorithms to construct hybrid models, which increases the computational burden. While signal decomposition techniques (such as EEMD) can reduce noise, the first mode after decomposition still has high complexity, and predicting multiple subsequences significantly increases runtime. Simultaneously, increased feature dimensionality leads to redundant features, resulting in prolonged training time and reduced classification accuracy, thus limiting the model's practicality.

[0005] Therefore, a technical solution is needed that can perform targeted analysis and feature extraction on the data characteristics of ozone concentration to achieve ozone data prediction. Summary of the Invention

[0006] To achieve the above objectives, this application provides a method for predicting ozone concentration that combines two-stage decomposition and dimension selection, comprising the following steps: Historical ozone concentration detection data is obtained, which consists of time and ozone concentration values; the historical ozone concentration detection data is preprocessed to generate the original concentration time series X; The original concentration time series X is decomposed twice to generate concentration subsequences. ; For concentration subsequence Perform dimensionality reduction to generate the optimal input dimension subsequence. Where t represents time series and p represents dimension; Load the TCN prediction model and input the optimal input dimension subsequence into the TCN prediction model. This enables the prediction of ozone concentrations in the future.

[0007] Preprocessing includes handling missing data and handling outliers; Missing data handling is achieved through KNN; outlier handling is achieved by determining outlier criteria using the 3σ criterion, which includes: determining outlier criteria as a sample distance exceeding the mean by 3σ. When the mean distance of sample data is significantly greater than 3σ, the sample data is considered an outlier and is removed from the sample.

[0008] The secondary decomposition includes the following steps: The original concentration time series X was decomposed into subsequences using ICEEMDAN. ,in, The subsequence number; the subsequence In, the first subsequence The sequence to be decomposed is denoted as , and the remaining subsequences are denoted as . to This constitutes the sequence to be reconstructed; The sequence to be decomposed is subjected to modal decomposition to form a first subsequence; the sequence to be reconstructed is then reconstructed to generate a second subsequence; the first and second subsequences constitute a concentration subsequence. .

[0009] Furthermore, the original concentration time series X was decomposed into subsequences using ICEEMDAN. Includes the following steps: Add to the original concentration time series X Group white noise constructs signal , is represented as: ,in, For white noise sequence number, It is white noise and , For white noise amplitude coefficient, This is a white noise preprocessing function; Determine the first modal component for: ,in, For the first modal component, Let be the first set of residuals, and: ,in, For the local mean of the signal, For mathematical expectation operations; Continue adding white noise and iterate to obtain the first... The order residual and j modal components are expressed as: , ,in, The modal component index and >1, For white noise amplitude coefficient, For the first Group residuals; and Constructing subsequences .

[0010] The variable mode decomposition of the sequence to be decomposed is achieved through VMD decomposition, including the following steps: Assume subsequence Depend on A finite bandwidth modal component Composition, the center frequency of each component is Satisfying signal reconstruction constraints ,in, The original signal; right Perform a Hilbert transform to obtain the one-sided spectrum, and then modulate it onto the corresponding baseband; where the one-sided spectrum is represented as: ,in, The modal component number is t, and the time series is t. For the Dirac delta function, The vector description of the center frequency in the complex plane; With finite bandwidth modal components Demodulation gradient With minimizing the square norm as the objective, we construct constraints, expressed as follows: , ,in, For the number of modal components with finite bandwidth, for A finite bandwidth modal component, for The frequency of each modal component For the Dirac delta function, The modal component number; Introducing a secondary penalty factor With Lagrange multipliers This yields the extended Lagrange function, expressed as: , in, For secondary penalty factor, For Lagrange multipliers, The inner product operator is used to characterize the correlation between two functions; the constraint is that the sum of all IMF components equals the original signal. The frequency domain component update formula is as follows, using the alternating direction multiplier method for iterative updating: ,in, The index is the IMF component index, n is the iteration number, and the superscript is... Indicates the first The result of the next iteration For center frequency, , , for , , Fourier transform; Update the center frequency, and iterate after the update. This forms the first subsequence.

[0011] Furthermore, reconstructing the sequence to be reconstructed includes the following steps: Each subsequence of the sequence to be reconstructed is represented as a sequence of length . time series ; Phase space reconstruction of a time series is represented as: Where i is the window number, For window vectors, Embedding dimension for phase space reconstruction For vectors The mean; Define a fuzzy membership function, expressed as: ,in, Let d be the similarity tolerance and d be the absolute distance. ; Calculate the mean similarity for each window. , is represented as: ,in, The embedding dimension for phase space reconstruction, where N is the time series length. For fuzzy membership function calculation structure, For time series numbering, For similarity tolerance; The fuzzy entropy of the time series is determined as follows: ,in, ; Calculate the fuzzy entropy value of each time series of the sequence to be reconstructed, and recombine the subsequences with similar fuzzy entropy values ​​into a new sequence. The new sequence constitutes the second subsequence.

[0012] Furthermore, regarding the concentration subsequence Dimensionality reduction includes the following steps: Input time series Then, the optimal dimension p is determined by calculating its partial autocorrelation function; After determining the optimal dimension p, a lag feature matrix is ​​constructed, a random forest regression model is trained, samples are mapped to forest leaf node indices, and high-dimensional binary leaf-encoded features are generated. The optimal input dimension subsequence is then determined. Where t represents time series and p represents dimension.

[0013] Furthermore, the TCN prediction model is constructed by introducing causal convolution, extended convolution, and residual modules on top of the convolutional network.

[0014] A convolutional network consists of an input layer, hidden layers, and an output layer. Extended convolution is represented as: ;in, to For input values, to This is a predicted value; Causal convolution serves as a constraint for hidden layer computation. For each element in the sequence, the element with index n in the input sequence determines the nth element in the output sequence. Residual networks can be used to shorten training time.

[0015] The ozone concentration prediction method provided by this invention can accurately capture the regular features in drastically fluctuating ozone sequences, effectively solve the operational redundancy caused by decomposition, and improve prediction accuracy. In the implementation process, it can accurately identify sequence features, select the optimal features to reduce the model input dimension, and avoid overfitting problems. When making concentration predictions, it can accurately capture data features, deeply analyze the feature information of historical data, and effectively and efficiently utilize these features to improve prediction accuracy. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the ozone concentration prediction method combining two-stage decomposition and dimension selection according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of the TCN prediction model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the residual network structure of the TCN prediction model provided in an embodiment of the present invention; Figure 4This is a schematic diagram of a historical ozone concentration detection data sequence provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the subsequence generated by decomposing the original concentration time series X using ICEEMDAN, according to an embodiment of the present invention. Figure 6 This is a schematic diagram of VMD decomposition provided according to an embodiment of the present invention; Figure 7 This diagram illustrates a comparison of ozone concentration prediction results from different models based on case data. Detailed Implementation

[0017] This invention provides an ozone concentration prediction method combining two-stage decomposition and dimension selection. First, an improved fully adaptive noise ensemble empirical mode (iceemdan) is used to decompose the original sequence of historical concentration data to reduce data volatility and complexity. Second, variable mode decomposition (VMD) is employed to further decompose the complex sequence from the first decomposition, and fuzzy entropy (FE) is used to reconstruct the remaining subsequences, forming a two-stage sequence. Then, a dual-scale method using partial autocorrelation function (PACF) and random forest (RF) is used to filter subsequences from the two-stage sequence and determine the optimal input dimension, thereby reducing irrelevant features in the sequence and forming an optimal input dimension subsequence. Finally, a temporal convolutional network (TCN) is used to predict ozone concentrations for future times based on the optimal input dimension subsequence.

[0018] The specific implementation of the present invention will now be described in detail with reference to the accompanying drawings.

[0019] Figure 1 The implementation steps of the ozone concentration prediction method combining two-stage decomposition and dimension selection are provided, as shown in the figure, including: Step S100: Obtain historical ozone concentration detection data, preprocess the historical ozone concentration detection data, and generate the original concentration time series X; Historical ozone concentration monitoring data can be the daily ozone observation values ​​of a certain observation station over a period of time (such as five years), consisting of time and ozone concentration values.

[0020] Because historical ozone concentration detection data contains missing and outlier values, the historical ozone concentration detection data is preprocessed to generate the original concentration time series. The preprocessing includes missing data processing and outlier processing.

[0021] Missing data processing is implemented using KNN (K-Nearest Neighbors): the k nearest neighbors to the missing data sample are found using Euclidean or Mahalanobis distance, and the missing data of the sample is estimated by weighted averaging of the values ​​of these k samples.

[0022] Outlier handling is achieved by determining the outlier criteria using the 3σ criterion: Specifically, according to the definition of the standard distribution, the probability of exceeding the mean by 3σ is P(|x-δ|>3σ)=0.003, which is an extremely low probability event. Therefore, the outlier criterion is that the distance between the sample and the mean exceeds 3σ. When the mean distance of the sample data is significantly greater than 3σ, the sample is considered an outlier and is removed from the sample. The original concentration time series X is formed by supplementing missing data and removing outliers, and the data content includes time and ozone concentration values.

[0023] This invention provides a specific example, selecting ozone concentration data from a city in China as historical ozone concentration monitoring data. The data covers daily ozone observations from January 1, 2015 to November 21, 2021, with an average concentration of 95.52, a standard value of 59.50, a minimum value of 0, and a maximum value of 311. The preprocessed raw concentration time series X is shown below. Figure 4 As shown.

[0024] Step S110: Perform a secondary decomposition on the original concentration time series X to generate concentration subsequences. The secondary decomposition includes the following steps: Step S111: Decompose the original concentration time series X into subsequences using ICEEMDAN. ; In this step, the adaptive noise complete set empirical mode decomposition algorithm (CEEMDAN) is improved to form ICEEMDAN; The CEEMDAN algorithm is a decomposition method that adds a fixed proportion of white noise in each decomposition stage k. The noise intensity has a simple linear relationship with the residual standard deviation, but it is prone to generating high-frequency pseudo-components in the first decomposition stage. This invention improves the CEEMDAN algorithm by adding a local adaptive factor, which dynamically adjusts the noise amplitude of the white noise according to the signal characteristics of the current stage. Therefore, the CEEMDAN algorithm can solve the residual noise and pseudo-mode problems existing in CEEMDAN.

[0025] In this step, the original concentration time series X is decomposed into subsequences using ICEEMDAN. Specifically, it includes the following steps: 1) Add to the original concentration time series X Group white noise constructs signal , is represented as: ,in, This is the white noise sequence number. It is white noise and ; Determine the first modal component for: ,in, For the first modal component, Let be the first set of residuals, and: ,in, For the local mean of the signal, For mathematical expectation operations; 2) Continue adding white noise and iterate to obtain the th... The order residual and j modal components are expressed as: , ,in, The modal component index and >1, This represents the amplitude coefficient of white noise.

[0026] In the ICEEMDAN model, the white noise amplitude coefficient is used as a local adaptive factor to control the intensity of the added Gaussian white noise, which can be adaptively adjusted according to the signal-to-noise ratio of the signal to be decomposed. The number of Gaussian white noise groups added is used to control the decomposition stability. The larger the value, the more stable the decomposition result, but the computational load increases accordingly; the mathematical expectation operation is used to average the decomposition results of multiple white noise sets, thereby reducing the interference of noise on the decomposition results.

[0027] and Constructing subsequences ,in, This is the subsequence index. Since the first subsequence... The sequence with the highest complexity is used as the sequence to be decomposed; the remaining subsequences... to This constitutes the sequence to be reconstructed.

[0028] According to a specific example provided by the present invention, the original concentration time series X is decomposed into 11 subsequences, such as Figure 5 shown to , Figure 5 The horizontal axis represents the observation record ID, and the vertical axis represents the decomposed sequence value; compared with the original sequence, the subsequence has more obvious regularity characteristics.

[0029] Step S112: Perform variable mode decomposition on the sequence to be decomposed to form the first subsequence; Variational mode decomposition is an adaptive signal decomposition method that determines the center frequency and bandwidth of each component by iteratively searching for the optimal solution of the variational model, thereby achieving signal frequency domain partitioning and effective separation. In this step, VMD decomposition is used to achieve variable mode decomposition; first, assume the subsequence Depend on A finite bandwidth modal component The structure (where t represents the timing) has the following center frequencies: Satisfying signal reconstruction constraints ,in, The original signal (i.e., the subsequence) ); Further, the following steps should be taken: 1) To Perform a Hilbert transform to obtain the one-sided spectrum, and then modulate it onto the corresponding baseband. The one-sided spectrum is represented as follows: ,in, The modal component number is t, and the time series is t. The Dirac delta function (unit impulse function) is the core kernel function of the Hilbert transform, used to characterize the instantaneous properties of a signal; The vector description of the center frequency in the complex plane; 2) Using finite bandwidth modal components component demodulation gradient With minimizing the square norm as the objective, we construct constraints, expressed as follows: , , in, For the number of modal components with finite bandwidth, for A finite bandwidth modal component, for The frequency of each modal component For the Dirac delta function, The modal component number; Introducing a secondary penalty factor With Lagrange multipliers This yields the extended Lagrange function: , in, This is a quadratic penalty factor used to balance the fitting accuracy and regularization of the variational problem, controlling the bandwidth of the IMF components. The larger the value, the narrower the component bandwidth; The Lagrange multiplier is used to enforce the satisfaction of constraints. The inner product operator is used to characterize the correlation between two functions; the constraint is that the sum of all IMF components equals the original signal.

[0030] 3) The alternating direction multiplier method (ADMM) is used for iterative updating. The frequency domain component update formula is as follows: ,in, The index is the IMF component index, n is the iteration number, and the superscript is... Indicates the first The result of the next iteration For center frequency, , , for , , The Fourier transform (i.e. the result after the transformation); 4) Based on the power spectrum centroid (e.g. Figure 6 The center frequency is updated based on the VMD spectral decomposition results shown, and the convergence criterion is set as follows: , , , in, The superscript indicates the number of iterations. They represent the first Next and first The result of the next iteration; This is the update step size for the Lagrange multipliers, used to control the convergence speed of the constraints; The convergence threshold is the criterion for stopping the algorithm's iteration; it is typically set to [value missing]. That is, the iteration terminates when the component change between two consecutive iterations is less than this value; for The square of the norm is used to calculate the energy of the signal (sum of squared amplitudes).

[0031] Through the above steps, the iterative update is complete. This forms the first subsequence.

[0032] Based on the specific case provided, the first subsequence of this city... The modal decomposition is performed into five new subsequences, such as... Figure 6 As shown, these are VMF1 to VMF5, respectively; and subsequences. In comparison, the results of VMD decomposition exhibit more pronounced fluctuation patterns, thereby reducing... The complexity.

[0033] Step S113: Reconstruct the sequence to be reconstructed to generate the second subsequence; The refactoring process includes the following steps: 1) Represent the sequence to be reconstructed as a given length of time series ; 2) Perform phase space reconstruction, represented as: , Where i is the window number; For window vectors; The embedding dimension for phase space reconstruction is , which is the core parameter of fuzzy entropy and is usually set to 1, 2, or 3 to characterize the local pattern dimension of the sequence. For vectors The mean of the vector is used to eliminate the DC component of the vector and avoid the influence of DC offset on the similarity calculation. 3) Define the fuzzy membership function, expressed as: , in, As a similarity tolerance, it is typically taken as 0.1 to 0.25 times the standard deviation of the time series, used to measure the similarity between two phase space vectors; d is the absolute distance, and In the formula, the maximum absolute value of the difference between the two elements is k=0,1,....,m-1; the absolute distance is the maximum element difference between two phase space vectors, which is used to quantify the similarity between vectors. 4) Calculate the mean similarity for each window. , is represented as: ,in, The embedding dimension for phase space reconstruction, where N is the time series length. For fuzzy membership function calculation structure, For time series numbering, For similarity tolerance; 5) The fuzzy entropy of the finite-time series is determined as: ;in, ; Fuzzy entropy can be used to measure the complexity of a time series; the larger the entropy value, the higher the sequence complexity. Therefore, in this step, the fuzzy entropy value of the sequence to be reconstructed is calculated, and subsequences with similar fuzzy entropy values ​​are recombined into a new sequence to achieve fuzzy entropy reconstruction. This new sequence constitutes the second subsequence.

[0034] first subsequence The second subsequence constitutes the concentration subsequence .

[0035] Since fuzzy entropy can be used to measure sequence complexity, for the case provided in this invention, the fuzzy entropy value is calculated for the subsequences of the original concentration time series X after ICEEMDAN decomposition. Meanwhile, the entropy values ​​after decomposing the original concentration time series X using other standard decomposition algorithms (EMD, EEMD, and CEEMDAN) are also provided, as shown in Table 1.

[0036] Table 1 Comparison of entropy values ​​of EMD, EEMD, CEEMDAN, and ICEEMDAN decomposed subsequences

[0037] As shown in Table 1, the fuzzy entropy of IMF1 is the highest among all subsequences, and although the fuzzy entropy of IMF1 obtained by different decomposition algorithms varies, the differences are not significant. Based on this, IMF1 is introduced into VMD for secondary decomposition. Figure 6 The results of the VMD quadratic decomposition of IMF1 are shown: IMF1 is decomposed into five new subsequences. Compared with the original IMF1, the subsequences obtained by VMD decomposition have more obvious fluctuation patterns, thus reducing the complexity of IMF1.

[0038] In this case, the first subsequence obtained by VMD decomposition and the reconstructed second subsequence are collectively referred to as FEn, where n represents the number of sequences. FE1-FE5 are new sequences obtained by VMD decomposition of IMF1, while FE6-FE10 are new reconstructed sequences. As shown in Table 2, IMF2 is reconstructed into FE6, IMF3 and IMF4 are reconstructed into FE7, FE8 is composed of the reconstructions of IMF5, IMF6 and IMF7, IMF8 and IMF9 are reconstructed into FE9, and FE10 is composed of the original IMF10 and IMF10.

[0039] Table 2. Fuzzy Entropy Reconstruction Sequence Mapping Table

[0040] Step S120: For concentration subsequences Dimensionality reduction is performed to generate a standard concentration sequence; the standard concentration sequence has the optimal input dimension.

[0041] In this step, the concentration subsequence is first determined using the partial autocorrelation function (PACF). The possible input dimensions are determined, and then a random forest is applied to filter and extract effective information from the input variables determined by PACF, thereby determining the optimal input dimensions for the prediction model; specifically, the following steps are included: Step S121: Input time series Then, the optimal dimension p is determined by calculating its partial autocorrelation function (PACF). PACF measures the effect of intermediate lags after calculation. and Net correlation coefficient Determine the threshold based on the net correlation coefficient. Determine the optimal dimension p; the optimal dimension p represents the effective memory length of the sequence, indicating... It relies solely on the first p historical values, thus mapping the original one-dimensional time series to a p-dimensional feature space, providing a simplified lag input structure for subsequent modeling.

[0042] Step S122: After determining the optimal dimension p, construct the lag feature matrix, train the random forest regression model, map the samples to the forest leaf node indices, generate high-dimensional binary leaf-encoded features, and finally output the optimal input dimension subsequence after importance filtering. Where t represents time series and p represents dimension.

[0043] In this invention, the PACF algorithm is used to calculate the potential input dimensions of each subsequence from lag 0 to 20 and provide a 95% confidence interval. Subsequently, random forest feature selection is performed on all possible input features of each subsequence to determine the optimal input dimensions and reduce the input of irrelevant features. Based on the random forest algorithm, the top six most important features of each subsequence are selected as the standard concentration sequence to form the subsequent model input.

[0044] Step S130: Load the TCN prediction model and input the standard concentration sequence into the TCN prediction model to achieve ozone concentration prediction for future times.

[0045] The TCN prediction model can infer new possible information from the input data. It is composed of causal convolution, extended convolution and residual modules introduced on the basis of convolutional network.

[0046] A convolutional network consists of an input layer, hidden layers, and an output layer. Extended convolution is represented as: ;in, to For input values, to These are predicted values.

[0047] Causal convolution serves as a constraint on hidden layer computation. For each element in the sequence, the element with index n in the input sequence determines the nth element of the output sequence, expressed as: ,in, For a convolution kernel / convolution filter with an inflation factor of d, The original input time series, The k-th weight coefficient in the convolution kernel. This represents the total size of the convolution kernel. d represents the nth weight position in the convolution kernel, and d is the dilation factor (hole coefficient) of the dilated convolution.

[0048] In long-term prediction, the visual range of the extended convolution is adjusted by changing the number of convolution kernels or increasing the dilation factor, as shown below: Where T is the total receptive field width, n is the number of layers below the new layer, For level number, is the dilation factor of the i-th layer, and k is the kernel size.

[0049] The residual network uses a skip connection structure, such as Figure 3 As shown, this can shorten training time and avoid the gradient vanishing problem in deep models.

[0050] Since the network depth, kernel size, and expansion number d jointly determine the receiving area of ​​a TCN, it is essential to ensure that the coefficients of n, k, and d are large enough to allow the TCN to achieve a sufficiently large receiving area. In this invention, the structure of the TCN prediction model is as follows: Figure 2 As shown, the core size is 4 and the number of expansions is 1, 2 and 4.

[0051] In this invention, the input information of the TCN prediction model is the optimal input dimension subsequence. It outputs the prediction results for each dimension, and obtains the final prediction result by accumulating the prediction results of each subsequence.

[0052] To determine the predictive effectiveness of the ozone concentration prediction method proposed in this invention, ELM, LSSVM, and LSTM models were introduced and compared with the TCN model used in this invention, and four sets of experiments were conducted. In the experiments, 80% of the data was used as the training set, and 20% as the test set, to highlight the interpretability of each model for ozone sequences. In the first set of experiments, the raw data was directly input into the model for prediction without decomposition, aiming to verify the effectiveness of each individual model and select the best prediction model. In the second set of experiments, the Iceemdan algorithm was used to decompose the raw sequence, and then TCN and other comparative models were established and used for prediction. In the third set of experiments, based on the second set, the VMD decomposition algorithm was added to further decompose the data. Perform two decompositions to verify the high decomposition complexity. Can the complexity be reduced while improving prediction accuracy? The fourth set of experiments introduces dual-scale feature selection using PACF and RF. RF further filters the potential input dimensions obtained from PACF to optimize the input dimensions of the prediction model and achieve dimensionality reduction. For the data provided in this invention, the prediction results of different models for ozone prediction values ​​are as follows: Figure 7 As shown in Table 3, the evaluation metrics for each model are as follows: Table 3 Evaluation indicators of ozone prediction values ​​for different models

[0053] Experimental results show that dual-scale feature selection can reduce the input of irrelevant features, prevent model overfitting, improve prediction accuracy, and shorten model running time to some extent. The proposed hybrid model iceemdan-VMD-FE-PACF-RF-TCN outperforms other models when predicting ozone sequences with significant fluctuations, with a mean absolute error (MAE) of 0.5351, a mean absolute deviation (RMSE) of 0.7346, and a mean relative deviation (SMAPE) of 0.8433%. Experimental results demonstrate that this hybrid model exhibits excellent generalization ability even in challenging ozone sequences.

[0054] In this invention, the raw ozone concentration data undergoes a two-stage decomposition and dual-scale feature selection, which is then combined with a TCN model for ozone concentration prediction. Experimental results show that the ozone concentration prediction method provided by this invention can accurately capture the regular features in drastically fluctuating ozone sequences. In the specific implementation process, the characteristics of O3 concentration data can be successfully extracted through the Iceemdan decomposition technique. The quantization and reconstruction of fuzzy entropy can effectively solve the operational redundancy caused by decomposition and improve prediction accuracy. In terms of feature selection, dual-scale feature selection can not only accurately identify sequence features but also select the optimal features to reduce the dimensionality of the model input and avoid overfitting. In terms of prediction model selection, the TCN model is set with a sufficiently wide field of view, enabling it to more accurately capture data features, deeply analyze the feature information of historical data, and effectively and efficiently utilize these features to improve prediction accuracy.

[0055] The above-disclosed embodiments are merely a few specific examples of the present invention. However, the present invention is not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A method for predicting ozone concentration combining two-stage decomposition and dimension selection, characterized in that, Includes the following steps: Historical ozone concentration detection data is obtained, which consists of time and ozone concentration value; the historical ozone concentration detection data is preprocessed to generate the original concentration time series X; The original concentration time series X is decomposed twice to generate concentration subsequences. ; For the concentration subsequence Perform dimensionality reduction to generate the optimal input dimension subsequence. Where t represents time series and p represents dimension; Load the TCN prediction model and input the optimal input dimension subsequence into the TCN prediction model. This enables the prediction of ozone concentrations in the future.

2. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 1, characterized in that, The preprocessing includes missing data processing and outlier processing; The missing data processing is implemented using KNN; The outlier handling is achieved by determining the outlier criteria using the 3σ criterion, which includes: determining the outlier criterion as a sample distance exceeding the average value by 3σ; when the average distance of the sample data is significantly greater than 3σ, the sample data is an outlier and is removed from the sample.

3. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 1, characterized in that, The secondary decomposition includes the following steps: The original concentration time series X was decomposed into subsequences using ICEEMDAN. ,in, The subsequence number; the subsequence In, the first subsequence The sequence to be decomposed is denoted as , and the remaining subsequences are denoted as . to This constitutes the sequence to be reconstructed; The sequence to be decomposed is subjected to modal decomposition to form a first subsequence; the sequence to be reconstructed is then reconstructed to generate a second subsequence; the first and second subsequences constitute a concentration subsequence. .

4. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 3, characterized in that, The original concentration time series X is decomposed into subsequences using ICEEMDAN. Includes the following steps: Add to the original concentration time series X Group white noise constructs signal , is represented as: ,in, This is the white noise sequence number. It is white noise and , For white noise amplitude coefficient, This is a white noise preprocessing function; Determine the first modal component for: ,in, For the first modal component, Let be the first set of residuals, and: ,in, For the local mean of the signal, For mathematical expectation operations; Continue adding white noise and iterate to obtain the first... The order residual and j modal components are expressed as: , ,in, The modal component index and >1, The amplitude coefficient of white noise; and Constructing subsequences .

5. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 3, characterized in that, The variable mode decomposition of the sequence to be decomposed is achieved through VMD decomposition, including the following steps: Assume subsequence Depend on A finite bandwidth modal component Composition, the center frequency of each component is Satisfying signal reconstruction constraints ,in, The original signal; right Perform a Hilbert transform to obtain the one-sided spectrum, and then modulate it onto the corresponding baseband; where the one-sided spectrum is represented as: ,in, The modal component index is represented by t, and the time series is represented by t. For the Dirac delta function, The vector description of the center frequency in the complex plane; With finite bandwidth modal components Demodulation gradient With minimizing the square norm as the objective, we construct constraints, expressed as follows: , ,in, For the number of modal components with finite bandwidth, for A finite bandwidth modal component, for The frequency of each modal component For the Dirac delta function, The modal component number; Introducing a secondary penalty factor With Lagrange multipliers This yields the extended Lagrange function, expressed as: ， in, For secondary penalty factor, For Lagrange multipliers, The inner product operator is used to characterize the correlation between two functions; the constraint is that the sum of all IMF components equals the original signal. The frequency domain component update formula is as follows, using the alternating direction multiplier method for iterative updating: ,in, The index is the IMF component index, n is the iteration number, and the superscript is... Indicates the first The result of the next iteration For center frequency, , , They are respectively , , Fourier transform; Update the center frequency, and iterate after the update. This forms the first subsequence.

6. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 3, characterized in that, Reconstructing the sequence to be reconstructed includes the following steps: Each subsequence of the sequence to be reconstructed is represented as a sequence of length... time series ; Phase space reconstruction of a time series is represented as: Where i is the window number, For window vectors, Embedding dimension for phase space reconstruction For vectors The mean; Define a fuzzy membership function, expressed as: ,in, Let d be the similarity tolerance and d be the absolute distance. ; Calculate the mean similarity for each window. , is represented as: ,in, The embedding dimension for phase space reconstruction, where N is the time series length. The result of fuzzy membership function calculation. For time series numbering, For similarity tolerance; The fuzzy entropy of the time series is determined as follows: ,in, ； Calculate the fuzzy entropy value of each time series of the sequence to be reconstructed, and recombine the subsequences with similar fuzzy entropy values ​​into a new sequence. The new sequence constitutes the second subsequence.

7. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 1, characterized in that, The concentration subsequence Dimensionality reduction includes the following steps: Input time series Then, the optimal dimension p is determined by calculating its partial autocorrelation function; After determining the optimal dimension p, a lag feature matrix is ​​constructed, a random forest regression model is trained, samples are mapped to forest leaf node indices, and high-dimensional binary leaf-encoded features are generated. The optimal input dimension subsequence is then determined. Where t represents time series and p represents dimension.

8. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 1, characterized in that, The TCN prediction model is constructed by introducing causal convolution, extended convolution, and residual modules on top of a convolutional network.

9. The ozone concentration prediction method combining two-stage decomposition and dimension selection according to claim 8, characterized in that, The convolutional network includes an input layer, hidden layers, and an output layer; The extended convolution is represented as: ;in, to For input values, to This is a predicted value; The causal convolution serves as a constraint for the computation of the hidden layer. For each element in the sequence, the element with index n in the input sequence determines the nth element of the output sequence. The residual network is used to shorten training time.

Images