An adaptive quadratic decomposition feature extraction method and system for an ozone concentration time series
By selecting high-frequency components using normalized mutual information and combining it with the center frequency observation method to adaptively select VMD modes, the adaptive selection problem of ozone concentration time series decomposition in existing technologies is solved, achieving efficient ozone concentration prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ANHUI UNIV OF SCI & TECH
- Filing Date
- 2026-05-27
- Publication Date
- 2026-07-21
AI Technical Summary
In the current technology for ozone concentration time series prediction, the CEEMDAN and VMD decomposition methods have insufficient adaptive selection mechanisms, resulting in insufficient or excessive decomposition of high-frequency components, ambiguity in the determination of mode number, and affecting the prediction effect.
Normalized mutual information is used to adaptively select high-frequency components, and the number of VMD modes is adaptively determined by combining the center frequency observation method. The high-frequency components are refined through an adaptive quadratic decomposition process to avoid the generation of redundant modes.
It achieves differentiated and refined decomposition of high-frequency components, improves the decomposition effect and prediction performance of ozone concentration prediction, and enhances data adaptability and generalization ability.
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Figure CN122432641A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of atmospheric pollution prediction technology, specifically relating to an adaptive secondary decomposition feature extraction method and system for ozone concentration time series. Background Technology
[0002] Ozone concentration time series exhibits strong non-stationarity and multi-scale fluctuations, making it susceptible to interference from high-frequency noise and complex dynamic changes when directly used in prediction models. Existing methods often employ signal decomposition techniques, such as Empirical Mode Decomposition (EMD), Fully Adaptive Noise Ensemble Empirical Mode Decomposition (CEEMDAN), and Variational Mode Decomposition (VMD), to preprocess the series to reduce non-stationarity. However, the following key shortcomings still exist:
[0003] (1) Regarding the CEEMDAN decomposition results, existing studies generally suffer from technical bias: either they fixate on selecting the first intrinsic mode function ( Alternatively, all intrinsic mode functions (IMFs) can be selected for subsequent processing, but an adaptive selection mechanism is lacking. Fixed selection... Secondary decomposition cannot distinguish components of different levels of complexity in high-frequency components, leading to over-decomposition of high-frequency components with simple structures and the introduction of redundant features; while the decomposition of high-frequency components with complex structures is insufficient.
[0004] (2) The problem of pre-setting the number of modes for VMD decomposition has not been properly solved. Existing methods require pre-setting the number of modes. Existing methods mostly use a fixed number of modes. The value can be determined through trial and error (such as grid search). However, such methods have the following limitations: computational cost increases with... The value range grows exponentially; different data sources require manual reset of the search range, and cannot be adaptively adjusted; grid search determines... Values often lack physical meaning and are not directly related to the frequency band structure of the signal itself.
[0005] Therefore, there is an urgent need for a preprocessing method that can adaptively select the high-frequency components that need to be decomposed in the secondary decomposition based on the characteristics of the data itself, and automatically determine the optimal number of VMD modes, so as to systematically solve the one-size-fits-all problem of existing methods in two dimensions (the selection dimension of high-frequency components in the secondary decomposition and the determination dimension of the number of VMD decomposition modes). Summary of the Invention
[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0007] An adaptive quadratic decomposition feature extraction method for ozone concentration time series includes:
[0008] Step 1: Obtain historical ozone concentration time series from monitoring stations within the study area. ,in, For sequence length, Historical ozone concentration time series The specific values of ozone concentration at the corresponding discrete time points;
[0009] Step 2: Use CEEMDAN to analyze the historical ozone concentration time series obtained in Step 1. Decompose to obtain eigenmode functions and a residual term ;
[0010] Step 3: Calculate the relationship between each IMF component and the historical ozone concentration time series. The normalized mutual information; if there is a normalized mutual information value lower than the first preset threshold. The IMF components, from the normalized mutual information being lower than a first preset threshold Among the IMF components, only the IMF component with the smallest normalized mutual information value is selected as the high-frequency component to be decomposed in the second step; otherwise, skip to step 5.
[0011] Step 4: For the high-frequency components to be decomposed in Step 3, perform adaptive VMD decomposition based on the center frequency observation method.
[0012] Step 5: If step 4 was executed, then combine all the outputs obtained in step 4 with the output obtained in step 2. All other IMFs that were not selected as high-frequency components for secondary decomposition in step 3, as well as the residual terms. Following the same time point index, the features are directly concatenated along the feature dimension to form a multi-scale time feature matrix; if step 4 is skipped, then all the features obtained in step 2 are directly used. IMF and residuals The matrix is spliced into a multi-scale time feature matrix, which serves as the input for subsequent ozone concentration prediction models.
[0013] An adaptive quadratic decomposition feature extraction system for ozone concentration time series includes:
[0014] The data acquisition module obtains the historical ozone concentration time series of monitoring stations within the study area. ,in, For sequence length, Historical ozone concentration time series The specific values of ozone concentration at the corresponding discrete time points;
[0015] The CEEMDAN decomposition module uses CEEMDAN to analyze the historical ozone concentration time series obtained by the data acquisition module. Decompose to obtain eigenmode functions and a residual term ;
[0016] The high-frequency component selection module calculates the relationship between each IMF component and historical ozone concentration time series. The normalized mutual information; if there is a normalized mutual information value lower than the first preset threshold. The IMF components, from the normalized mutual information being lower than a first preset threshold Among the IMF components, only the IMF component with the smallest normalized mutual information value is selected as the high-frequency component to be decomposed in the second step; otherwise, the process jumps to the operation of the feature merging module.
[0017] The VMD secondary decomposition module performs adaptive VMD decomposition based on the center frequency observation method for the high-frequency components to be decomposed in the high-frequency component selection module.
[0018] If the feature merging module has executed the VMD secondary decomposition module's operations, then it will merge all the outputs obtained from the VMD secondary decomposition module with the outputs obtained from the CEEMDAN decomposition module. All other IMFs in the IMFs that were not selected by the high-frequency component selection module as high-frequency components to be decomposed in the secondary decomposition, as well as the residual terms. Following the same time point index, the features are directly concatenated along the feature dimension to form a multi-scale time feature matrix; if the VMD secondary decomposition module is skipped, all the features obtained from the CEEMDAN decomposition module are directly used. IMF and residuals The matrix is spliced into a multi-scale time feature matrix, which serves as the input for subsequent ozone concentration prediction models.
[0019] The present invention has the following beneficial effects:
[0020] (1) This invention adopts normalized mutual information (NMI) to adaptively select high-frequency IMFs that need secondary decomposition, and specifically selects the IMF with the smallest NMI from all IMFs with NMI below a preset threshold for decomposition and abandons the processing of the remaining low NMI components. This achieves differentiated and refined selection of the secondary decomposition objects, overcomes the technical bias of fixed selection of the first IMF or uniform processing of all IMFs in the prior art, and solves the problem of not being able to adaptively select decomposition objects according to the complexity of the data itself.
[0021] (2) This invention adopts the center frequency observation method and innovatively introduces a back-off one-order mechanism to adaptively determine the number of VMD modes K. At the same time, it associates the judgment threshold with the data sampling frequency, realizes the automatic determination of the number of VMD modes, overcomes the defects of offline trial and error or fixed K value in the prior art, solves the ambiguity problem of when to stop increasing the number of modes, and ensures that the optimal decomposition is obtained without introducing redundant modes.
[0022] (3) This invention combines the IMF with the smallest NMI with the VMD decomposition based on the center frequency observation method, which is backed up one order and the threshold is linked to the sampling frequency, to form a complete adaptive secondary decomposition process. This allows high-frequency complex components to be decomposed in a refined manner while simple components are not over-decomposed. This results in a better decomposition effect and prediction performance improvement than each individual feature processing method, achieving unexpected technical results.
[0023] (4) Through the above-mentioned adaptive selection and adaptive decomposition parameter determination collaborative mechanism, the present invention enables the entire preprocessing process to eliminate the need for manual setting of key parameters (such as secondary decomposition objects and VMD modality number), achieving good data adaptability and generalization ability, and solving the problems of existing methods relying on manual experience and poor applicability across datasets. Attached Figure Description
[0024] Figure 1 This is a flowchart of the adaptive quadratic decomposition feature extraction method for ozone concentration time series according to the present invention;
[0025] Figure 2 This is a schematic diagram illustrating how normalized mutual information varies with the order of the IMF. Detailed Implementation
[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0027] like Figure 1 As shown, this invention provides an adaptive quadratic decomposition feature extraction method for ozone concentration time series, comprising the following steps:
[0028] Step 1: Obtain historical ozone concentration time series data for monitoring stations within the study area. ,in, The sequence length is expressed in terms of the number of discrete sampling points, and the value is a positive integer. Historical ozone concentration time series The specific value of ozone concentration at the corresponding discrete time point, in micrograms per cubic meter (μg / m³).
[0029] Step 2: Use Fully Adaptive Noise Ensemble Empirical Mode Decomposition (CEEMDAN) to process the historical ozone concentration time series obtained in Step 1. Decompose to obtain One intrinsic mode function (IMF) and a residual term CEEMDAN effectively suppresses mode aliasing by adaptively adding white noise and ensemble averaging; the termination condition is: when the residual term The decomposition stops when the function is monotonic or has fewer than 2 extreme points, yielding an adaptive quantity. One IMF component.
[0030] Step 3: Calculate the relationship between each IMF component and the historical ozone concentration time series. Normalized mutual information (NMI). The NMI value reflects the relationship between the IMF component and the historical ozone concentration time series. The degree of uncertainty in the relationship between them.
[0031] Typically, the first eigenmode function It contains the highest frequency random noise and rapid fluctuations, exhibiting the strongest non-stationarity, and is consistent with historical ozone concentration time series. The deterministic association is the weakest, therefore the NMI value is also the smallest. Figure 2 The variation trend of the normalized mutual information between each IMF component and the original sequence in this embodiment is shown. It can be seen that as the IMF order increases, the NMI value generally shows an upward trend. Among them, the NMI value of the first intrinsic mode function is significantly lower than that of the subsequent components, which verifies the rationality of the present invention in selecting the low-order IMF with the smallest NMI as the object to be decomposed in the second stage. , While the components of the second and third intrinsic mode functions may also have low NMIs, they reflect historical ozone concentration time series more accurately. It contains predictable non-stationary components with a certain periodicity. For these sub-high frequency IMFs (… , Performing secondary decomposition of VMD can easily lead to over-segmentation of already relatively clear frequency bands, generating redundant modes with similar center frequencies. This not only fails to extract effective features but also increases the dimensionality of the model input and the risk of overfitting. Therefore, if the normalized mutual information value is lower than the first preset threshold... The IMF components, then, are derived from these normalized mutual information values that are below a first preset threshold. Among the IMF components, only the IMF component with the smallest normalized mutual information value is selected as the high-frequency component to be decomposed in the second decomposition (if there are multiple IMF components with the smallest normalized mutual information value, the IMF component with the smallest order is selected), and the normalized mutual information values of the remaining components are not selected if they are lower than the first preset threshold. The IMF components are then subjected to a secondary decomposition. If no normalized mutual information exists below the first preset threshold... If the IMF component is found, it indicates that the overall complexity of the original sequence is low, and no secondary decomposition is required. We can proceed directly to step 5.
[0032] The NMI component The calculation formula is:
[0033] ;
[0034] in, For mutual information, For information entropy, For the first One eigenmode function This is a time series of historical ozone concentrations.
[0035] Specifically, mutual information Information entropy , for Marginal probability mass function (i.e. The value falls on the (the probability of each bin) for Marginal probability mass function (i.e. The value falls on the The probability of each bin). for The binned values are indexed in the range of 1, 2, ... ; for The binned values are indexed in the range of 1, 2, ... , The total number of bins (a positive integer, adaptively determined based on the sequence length); for The value falls on the Each box and The value falls on the The joint probability mass function of each bin.
[0036] The equal-width binning method was used in the calculation. and The range of values is evenly divided into The compartments are divided into sections, with the left-closed and right-open sections used during containerization. The compartments are divided, with the last compartment using a closed section. , These are the left and right endpoints of the interval used for the last bin. Values strictly equal to the right endpoint of a bin (except for the last bin) are assigned to the next bin; values exceeding the original range due to floating-point calculations are forcibly assigned to the nearest bin interval (if exceeding the upper limit, assigned to the last bin; if exceeding the lower limit, assigned to the first bin). Mutual information is calculated after calculating the joint and marginal probabilities. and information entropy .
[0037] Total number of boxes Based on sequence length Adaptive determination: when hour, ;when hour, ;when hour, ;in, When the value is 10000 or 30000, they are respectively assigned to [the appropriate category]. and The range. First preset threshold. The value range is from 0.1 to 0.3.
[0038] Step 4: For the high-frequency components selected in Step 3 to be decomposed in the second step, perform adaptive VMD decomposition based on the center frequency observation method, specifically as follows:
[0039] Step 41, Initialize parameters: Initialize the number of candidate modes Preset the maximum number of VMD modes , The value range is 8 to 12; the sampling frequency of the high-frequency component to be decomposed is For sampling at equal time intervals, ,in, The sampling time interval is in seconds.
[0040] The parameters for VMD decomposition are set as follows: Penalty factor Used to control the bandwidth of each component, with a value range of 500 to 3000, and noise margin. Convergence Criterion In VMD decomposition, the initial center frequencies of each mode are initialized uniformly, specifically by setting the frequency range of the signal to be decomposed to a uniform initialization method. Divided into equal parts (here) It is equal to both the number of candidate modes and the total number of variational mode functions (VMFs) expected to be obtained. There are 3 intervals, and the frequency value of the midpoint of each interval is used as the initial center frequency of the corresponding mode.
[0041] Step 42, Perform VMD and extract the center frequency: Perform VMD decomposition on the high-frequency components to be decomposed in the secondary decomposition to obtain... Each VMF is decomposed. The center frequency of each VMF is extracted after VMD decomposition. (Unit: Hz). The center frequency of each VMF is determined as follows: Perform a Fast Fourier Transform on the time-domain signal of each VMF to obtain its amplitude-frequency response, search for the global maximum value of the amplitude-frequency response, and the frequency value corresponding to the maximum value is the center frequency of the VMF;
[0042] Step 43: Calculate the maximum difference between adjacent center frequencies. :
[0043] ;
[0044] in, This is the index of the VMF, with values ranging from 2, 3, ... , For the total number of VMFs, For the first The center frequency of each VMF, For the first The center frequency of each VMF, It is the absolute value symbol.
[0045] Step 44, Judgment and Decision: [The sentence is incomplete and requires more context to be translated accurately.] A second preset threshold associated with the sampling frequency In comparison, among which, , This is a preset coefficient, with a value range of 0.015 to 0.025.
[0046] like :
[0047] First scenario: If If the frequency band of the high-frequency component to be decomposed is too narrow, VMD decomposition is not required, and the high-frequency component to be decomposed is directly used as the processing result of step 4, thus terminating step 4.
[0048] Second scenario: If Then determine the number of candidate modes. Given redundant modes with overlapping center frequencies, determine the optimal number of modes. (Back off by one order mechanism), and then use the VMD decomposition obtained in the previous iteration (i.e., when the number of candidate modes is K) to perform the decomposition. The VMF is output, and step 4 is terminated.
[0049] like Then proceed to step 45;
[0050] Step 45, Iterate or terminate: The maximum number of modes is preset;
[0051] if Then let (i.e., update) The value of . Let This indicates the number of candidate modes. Increment by 1), and return to step 42;
[0052] if If the loop stops, then the optimal number of modes is determined. Then directly use it in the candidate mode number equal The result of performing VMD decomposition at that time One VMF is used as the output.
[0053] Step 5: If the high-frequency components to be decomposed in step 3 were selected and step 4 was executed, then all the outputs obtained from step 4 are compared with the CEEMDAN decomposition results obtained in step 2. All other IMFs that were not selected as high-frequency components for secondary decomposition in step 3, as well as the residual terms. Following the same time point index, the features are directly concatenated (i.e., horizontally concatenated) along the feature dimension to form a multi-scale time feature matrix; if step 3 determines that there is no normalized mutual information lower than the first preset threshold... The IMF components thus skipped step 4, and directly decomposed all the components obtained from CEEMDAN. IMF and residuals The matrix is concatenated into a multi-scale time feature matrix; the final multi-scale time feature matrix is then used as the input for the subsequent ozone concentration prediction model.
[0054] When the historical ozone concentration time series When the concentration sequence is hourly, the first preset threshold in step 3 The value is 0.2; the preset coefficient mentioned in step 4 The value is 0.02; the preset maximum number of modes mentioned in step 4 The value is 10; the penalty factor in step 41 The value is 2000.
[0055] This invention further provides a time series preprocessing system for ozone concentration prediction based on adaptive quadratic decomposition, comprising:
[0056] The data acquisition module obtains the historical ozone concentration time series of monitoring stations within the study area. ,in, For sequence length, Historical ozone concentration time series The specific values of ozone concentration at the corresponding discrete time points;
[0057] The CEEMDAN decomposition module uses CEEMDAN to analyze the historical ozone concentration time series obtained by the data acquisition module. Decompose to obtain eigenmode functions and a residual term ;
[0058] The high-frequency component selection module calculates the relationship between each IMF component and historical ozone concentration time series. The normalized mutual information; if there is a normalized mutual information value lower than the first preset threshold. The IMF components, from the normalized mutual information being lower than a first preset threshold Among the IMF components, only the IMF component with the smallest normalized mutual information value is selected as the high-frequency component to be decomposed in the second step; otherwise, the process jumps to the operation of the feature merging module.
[0059] The VMD secondary decomposition module performs adaptive VMD decomposition based on the center frequency observation method for the high-frequency components to be decomposed in the high-frequency component selection module.
[0060] If the feature merging module has executed the VMD secondary decomposition module's operations, then it will merge all the outputs obtained from the VMD secondary decomposition module with the outputs obtained from the CEEMDAN decomposition module. All other IMFs in the IMFs that were not selected by the high-frequency component selection module as high-frequency components to be decomposed in the secondary decomposition, as well as the residual terms. Following the same time point index, the features are directly concatenated along the feature dimension to form a multi-scale time feature matrix; if the VMD secondary decomposition module is skipped, all the features obtained from the CEEMDAN decomposition module are directly used. IMF and residuals The matrix is spliced into a multi-scale time feature matrix, which serves as the input for subsequent ozone concentration prediction models.
[0061] The basis for determining the parameters involved in this invention is explained below:
[0062] Normalized mutual information threshold Explanation of the determination of the value range: The value range was set to 0.1 to 0.3, which was determined statistically optimal after conducting 500 Monte Carlo cross-validations for each of the hourly ozone concentration data from 68 monitoring stations in three typical cities from 2021 to 2024. Endpoint value comparison experiments showed that: The overly high sensitivity of time identification leads to approximately 23% of normal sequences (IMF components with NMI between 0.1 and 0.15 actually contain valid fluctuation information) being misjudged as requiring secondary decomposition, resulting in unnecessary computational overhead; The omission rate for identifying sequences of moderate complexity (IMF components with NMI between 0.25 and 0.3) is about 15%, resulting in some high-frequency components that should have been finely decomposed not being screened. It achieves the best balance between recognition accuracy and computational efficiency.
[0063] Preset maximum number of VMD modes Explanation of the range of values: Based on the high-frequency component of ozone concentration (first intrinsic mode function) Determination of bandwidth statistical characteristics The value range was set to 8 to 12. Spectral analysis of 500 ozone IMF1 samples showed that the theoretical maximum number of resolvable modes corresponding to its effective bandwidth was concentrated between 9 and 11. Endpoint value comparison experiments showed that: At that time, the decomposition of signals with bandwidths exceeding this range (accounting for approximately 18% of the test samples) was insufficient, resulting in high residual energy. At that time, approximately 10% of the sequences exhibited redundant modes, and the computational cost was relatively high. Up 42%; It basically covers the effective bandwidth of more than 95% of the samples, and the occurrence rate of redundant modes is less than 3%.
[0064] Preset coefficients Instructions for determining the preset coefficient: Based on the sampling frequency exist to Ozone sequences within the Hz range were optimized using a grid search. A BiLSTM (Bidirectional Long Short-Term Memory) network was used as the downstream prediction model, and RMSE (Root Mean Square Error) was used as the primary evaluation metric. exist A grid search was performed within the range with a step size of 0.001. The results show that when... Within the range of 0.015 to 0.025, the average RMSE on the three-city dataset is at a low level and fluctuates little; When the mean RMSE reaches its minimum, it is considered the optimal value. Sensitivity analysis shows that... Exceeding this range may result in over-decomposition or under-decomposition. This application prefers a preset coefficient. The value range is from 0.015 to 0.025.
[0065] Punishment factor Explanation of the determination: The value range was set to 500 to 3000, and different values were applied to 500 groups of high-frequency ozone components. The values were obtained through decomposition stability and center frequency separation tests. Too small a value (<500) will result in excessively large modal bandwidth and severe frequency aliasing; An excessively large value (>3000) would over-constrain the bandwidth, resulting in the loss of effective frequency details. For the ozone hourly concentration data targeted by this invention, the frequency band structure of its high-frequency components is relatively stable. In specific implementations, a value of 2000 can be selected to achieve a balance between modal purity and frequency resolution.
[0066] Example 1: An adaptive quadratic decomposition feature extraction method for ozone concentration time series, comprising:
[0067] Step 1: Obtain the historical ozone concentration time series of monitoring stations within the study area. This example uses the hourly ozone concentration series from 2021 to 2024 from an air quality monitoring station in a certain city as an example. The series length is... Sampling time interval Seconds, therefore, the sampling frequency of the high-frequency components to be decomposed in the second step. Hz.
[0068] In this embodiment, other parameters of VMD decomposition are set using conventional methods: penalty factor. Noise tolerance The center frequency is initialized to a uniform distribution, and the convergence criterion is... .
[0069] Step 2, CEEMDAN decomposition parameters: Add white noise with a standard deviation of 0.2, ensemble mean of 100, and maximum number of iterations of 500. The decomposition yields... One IMF and one residual.
[0070] Step 3: Calculate the NMI of each IMF and the original sequence. The results are as follows: 0.12, 0.25, 0.45, 0.62, 0.78, 0.85, 0.91, 0.95, 0.97. Let the first preset threshold be... The NMI (0.12) of IMF1 is lower than the first preset threshold. And all values below the first preset threshold The IMF with the smallest value is selected. Therefore, IMF1 is chosen as the high-frequency component to be decomposed in the second step.
[0071] Step 4: Perform center frequency observation on IMF1. Let... Hz, The adaptive determination process is as follows:
[0072] VMD decomposition was performed on IMF1, resulting in two VMFs. The center frequency was extracted as follows: Hz, calculate the maximum difference between adjacent center frequencies. Hz. Due to Hz Hz, proceed to step 45. Because ,make Return to step 42.
[0073] VMD decomposition was performed on IMF1, resulting in 3 VMFs. The center frequency was extracted as follows. Hz, calculated Hz ,make .
[0074] And so on, until... , Hz ,make .
[0075] VMD decomposition was performed on IMF1, resulting in 10 VMFs. The center frequency was extracted as follows: Hz, calculated Hz, still greater than Proceed to step 45. Stop the loop and determine the optimal number of modes. and use directly The obtained VMD decomposition results (10 VMFs) are used as the output.
[0076] Step 5: Since Step 4 has been performed, the 10 VMFs obtained from VMD decomposition are directly concatenated with the IMF2 to IMF9 and residual R obtained from CEEMDAN decomposition along the feature dimension according to the same time point index, resulting in 19 components (a multi-scale time feature matrix), which are used as inputs for the subsequent ozone concentration prediction model.
[0077] Example 2: Demonstration of the first-order backoff mechanism (the first-order backoff mechanism has been defined in the second case of step 44: when redundant modes with overlapping center frequencies are detected, the optimal number of modes is determined). That is, back off one order from the current mode number).
[0078] Example 2 uses the same monitoring station as Example 1, but selects a period with richer high-frequency noise and more complex data fluctuations, and sets... All other parameters remain unchanged. The VMD decomposition process is as follows:
[0079] ,right Performing VMD decomposition yields two VMFs, and the center frequency is extracted as follows: Hz, calculated Hz Execute step 45, and let Return to step 4, step 42.
[0080] ,right Performing VMD decomposition yields 3 VMFs, and the center frequency is extracted as follows: Hz, calculated Hz ,make .
[0081] ,right Performing VMD decomposition yields 4 VMFs, and the center frequency is extracted as follows: Hz, calculated Hz ,and Redundant modes are identified. The optimal number of modes is determined. and directly use the previous The decomposition results (3 VMFs) obtained at that time are used as output.
[0082] Steps 1-3 of Example 2 are the same as steps 1-3 of Example 1 (Step 1: Obtain data; Step 2: Perform CEEMDAN decomposition to obtain...). to and residuals Step 3: Calculate NMI and select As the high-frequency component to be decomposed in the second step); the VMD decomposition process in step 4 of Example 2 is as described above (i.e., the above-mentioned...). (Iterative process).
[0083] Step 5: Concatenate the three VMFs with IMF2 to IMF9 and the residual R to form a multi-scale time feature matrix as input for the subsequent ozone concentration prediction model.
[0084] Example 3: Demonstration =2 and the bandwidth is too narrow;
[0085] This embodiment selects a period of ozone concentration with extremely smooth fluctuations and highly concentrated spectral energy, where the IMF1 component is approximately a single-frequency signal. Let... The remaining parameters remain unchanged. The VMD decomposition process is as follows:
[0086] VMD decomposition was performed on IMF1, resulting in two VMFs. The center frequency was extracted as follows: Hz, calculated Hz. This value is less than the second preset threshold. Hz, and This triggers the first scenario in step 44. It is determined that the high-frequency component has too narrow a bandwidth, so VMD decomposition is unnecessary; the IMF1 component is directly output as the processing result of step 4.
[0087] Step 5: The original IMF1 component is concatenated with IMF2 to IMF9 obtained from the CEEMDAN decomposition in Step 2 and the residual R to form a multi-scale time feature matrix as the input for the subsequent ozone concentration prediction model.
[0088] Comparative experiment: Using the adaptive scheme of this invention, ozone concentration single-step prediction results with RMSE (root mean square error) of 5.84, 7.53 and 8.95 were obtained on the datasets of three cities, which are all better than the fixed parameter scheme.
[0089] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The embodiments of the present invention can be implemented using various computer languages.
[0090] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.
[0091] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0092] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0093] The above description is merely an embodiment of the present invention and does not limit the scope of the invention. Any equivalent structural or procedural transformations made based on the description and drawings of this invention, or direct or indirect applications in other related system fields, are similarly included within the protection scope of this invention. Contents not described in detail in this specification are prior art known to those skilled in the art.
Claims
1. An adaptive quadratic decomposition feature extraction method for ozone concentration time series, characterized in that, include: Step 1: Obtain historical ozone concentration time series data for monitoring stations within the study area. ,in, For sequence length, Historical ozone concentration time series The specific values of ozone concentration at the corresponding discrete time points; Step 2: Use CEEMDAN to analyze the historical ozone concentration time series obtained in Step 1. Decompose to obtain One IMF and one residual term ; Step 3: Calculate the relationship between each IMF component and the historical ozone concentration time series. The normalized mutual information; if there is a normalized mutual information value lower than the first preset threshold. The IMF components, from the normalized mutual information being lower than a first preset threshold Among the IMF components, only the IMF component with the smallest normalized mutual information value is selected as the high-frequency component to be decomposed in the second step; otherwise, skip to step 5. Step 4: For the high-frequency components to be decomposed in Step 3, perform adaptive VMD decomposition based on the center frequency observation method. Step 5: If step 4 was executed, then combine all the outputs obtained in step 4 with the output obtained in step 2. All other IMFs that were not selected as high-frequency components for secondary decomposition in step 3, as well as the residual terms. Following the same time point index, the features are directly concatenated along the feature dimension to form a multi-scale time feature matrix; if step 4 is skipped, then all the features obtained in step 2 are directly used. IMF and residuals The matrix is spliced into a multi-scale time feature matrix, which serves as the input for subsequent ozone concentration prediction models.
2. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 1, characterized in that, In step 2, the termination condition for CEEMDAN is: when the residual term... The decomposition stops when the function is monotonic or has fewer than 2 extreme points, yielding an adaptive quantity. One IMF component.
3. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 1, characterized in that, In step 3, the components of normalized mutual information The calculation formula is: ； in, For mutual information, For information entropy, For the first One eigenmode function This is a time series of historical ozone concentrations.
4. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 3, characterized in that, In step 3, the mutual information is: ； Information entropy is: ； in, for The marginal probability mass function; for The marginal probability mass function; for The binned values are indexed in the range of 1, 2, ... ; for The binned values are indexed in the range of 1, 2, ... , This represents the total number of boxes. for The value falls on the Each box and The value falls on the The joint probability mass function of each bin; The equal-width binning method was used in the calculation. and The range of values is evenly divided into The compartments are divided into sections, with the left-closed and right-open sections used during containerization. The compartments are divided, with the last compartment using a closed section. , These are the left and right endpoints of the interval used in the last binning; mutual information is calculated after calculating the joint probability and marginal probability. and information entropy .
5. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 4, characterized in that, In step 3, the total number of boxes Based on sequence length Adaptive determination: when hour, ;when hour, ;when hour, ;in, When the value is 10000 or 30000, they are respectively assigned to [the appropriate category]. and The range.
6. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 1, characterized in that, In step 3, the first preset threshold The value range is from 0.1 to 0.
3.
7. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 5, characterized in that, Step 4, the adaptive VMD decomposition based on the center frequency observation method includes: Step 41, Initialize parameters: Initialize the number of candidate modes Preset the maximum number of VMD modes The sampling frequency of the high-frequency components to be decomposed is: For sampling at equal time intervals, ,in, The sampling time interval; The parameters for VMD decomposition are set as follows: Penalty factor Noise tolerance Convergence Criterion The initial center frequencies of each mode in the VMD decomposition are initialized using a uniform initialization method. Step 42, Perform VMD and extract the center frequency: Perform VMD decomposition on the high-frequency components to be decomposed in the secondary decomposition, and obtain... For each VMF, perform a Fast Fourier Transform on the time-domain signal of each VMF, and take the frequency value corresponding to the global maximum value of the amplitude-frequency response as the center frequency of that VMF. Step 43: Calculate the maximum difference between adjacent center frequencies. : ； in, This is the index of the VMF, with values ranging from 2, 3, ... , For the total number of VMFs, For the first The center frequency of each VMF, For the first The center frequency of each VMF; Step 44, will A second preset threshold associated with the sampling frequency In comparison, among which, , Preset coefficients: like : First scenario: If If the high-frequency component to be decomposed is determined to have too narrow a bandwidth, VMD decomposition is not required, and the high-frequency component to be decomposed is directly used as the processing result of step 4, thus terminating step 4. Second scenario: If Determine the number of candidate modes Given redundant modes with overlapping center frequencies, determine the optimal number of modes. And will be the result of performing VMD decomposition in the previous iteration. The VMF is output, and step 4 is terminated. like Then proceed to step 45; Step 45, The maximum number of modes is preset; if ,make And return to step 42; if Stop the loop and determine the optimal number of modes. Used in candidate mode number equal The result of performing VMD decomposition at that time One VMF is used as the output.
8. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 7, characterized in that, In step 41, the uniform initialization method is as follows: the frequency range of the signal to be decomposed is... Divided into equal parts There are several intervals, and the frequency value at the midpoint of each interval is used as the initial center frequency of the corresponding mode.
9. The adaptive quadratic decomposition feature extraction method for ozone concentration time series according to claim 7, characterized in that, In step 4, preset coefficients are used. The value range is from 0.015 to 0.025, with a preset maximum number of modes. The value ranges from 8 to 12, and the penalty factor is... The value range is from 500 to 3000.
10. An adaptive quadratic decomposition feature extraction system for ozone concentration time series, characterized in that, include: The data acquisition module obtains the historical ozone concentration time series of monitoring stations within the study area. ,in, For sequence length, Historical ozone concentration time series The specific values of ozone concentration at the corresponding discrete time points; The CEEMDAN decomposition module uses CEEMDAN to analyze the historical ozone concentration time series obtained by the data acquisition module. Decompose to obtain One IMF and one residual term ; The high-frequency component selection module calculates the relationship between each IMF component and historical ozone concentration time series. The normalized mutual information; if there is a normalized mutual information value lower than the first preset threshold. The IMF components, from the normalized mutual information being lower than a first preset threshold Among the IMF components, only the IMF component with the smallest normalized mutual information value is selected as the high-frequency component to be decomposed in the second step; otherwise, the process jumps to the operation of the feature merging module. The VMD secondary decomposition module performs adaptive VMD decomposition based on the center frequency observation method for the high-frequency components to be decomposed in the high-frequency component selection module. If the feature merging module has executed the VMD secondary decomposition module's operations, then it will merge all the outputs obtained from the VMD secondary decomposition module with the outputs obtained from the CEEMDAN decomposition module. All other IMFs in the IMFs that were not selected by the high-frequency component selection module as high-frequency components to be decomposed in the secondary decomposition, as well as the residual terms. Following the same time point index, the features are directly concatenated along the feature dimension to form a multi-scale time feature matrix; if the VMD secondary decomposition module is skipped, all the features obtained from the CEEMDAN decomposition module are directly used. IMF and residuals The matrix is spliced into a multi-scale time feature matrix, which serves as the input for subsequent ozone concentration prediction models.