CN114970946A - PM2.5 pollution concentration long-term space prediction method based on deep learning model and empirical mode decomposition coupling - Google Patents

PM2.5 pollution concentration long-term space prediction method based on deep learning model and empirical mode decomposition coupling Download PDF

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CN114970946A
CN114970946A CN202210322031.3A CN202210322031A CN114970946A CN 114970946 A CN114970946 A CN 114970946A CN 202210322031 A CN202210322031 A CN 202210322031A CN 114970946 A CN114970946 A CN 114970946A
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杨光飞
张强
关晓微
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Dalian University of Technology
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Abstract

A PM2.5 pollution concentration long-time space prediction method based on deep learning model and empirical mode decomposition coupling collects PM2.5 pollution data and related variable data, and data cleaning and correlation analysis determine the correlation of selected variables; constructing a graph data structure and inputting the graph data structure into a GAT module of the model to obtain spatial information of PM2.5 pollution; inputting the PM2.5 sequence into an EMD module of the model, decomposing the PM2.5 sequence into a plurality of low-frequency time sequences and residual errors, and splicing to obtain PM2.5 polluted time sequence information; and integrating the spatial information and the time sequence information to obtain the spatial-temporal information polluted by PM2.5, inputting the spatial-temporal information into a GRU (generalized regression Unit) module of the model, and obtaining a final prediction result through a full connection layer. According to the method, the time and the spatial information of PM2.5 pollution are combined, and the empirical mode decomposition algorithm and the deep learning algorithm in the signal decomposition field are combined, so that the accuracy of PM2.5 long-step prediction is improved.

Description

PM2.5 pollution concentration long-term space prediction method based on deep learning model and empirical mode decomposition coupling
Technical Field
The invention relates to the field of prediction and prediction of atmospheric pollutants, in particular to a PM2.5 pollution concentration long-time and long-time space prediction method based on deep learning model and empirical mode decomposition coupling, and the model name is GAT-EGRU.
Background
With the rapid development of economy and the continuous progress of industrialization, air pollution has become an important problem affecting daily life and economic development. Among the various air pollutants, the most harmful to the human body in recent years is PM 2.5. Compared with the thicker atmospheric particulate matters, the PM2.5 has small particle size, large area, strong activity, easy attachment of toxic and harmful substances (such as heavy metals, microorganisms and the like), long retention time in the atmosphere and long conveying distance, thereby having larger influence on human health and atmospheric environmental quality. How to accurately predict the concentration of PM2.5 at the future moment is of great significance to control of heavily polluted weather, government decision planning and prevention of diseases in respiratory centers.
In recent years, researchers have conducted extensive studies on how to accurately predict the PM2.5 concentration at a future time. The existing prediction methods mainly include a numerical simulation based method, a measurement statistics based method and a machine learning based method. Numerical simulation models have high dependence on data resources (such as real-time weather data and continuously updated emission lists), long computation time delay, difficulty in capturing nonlinear relations between variables, and therefore low accuracy. The method based on metering statistics predicts based on linear relation of PM2.5 and other pollutants, weather variables. The method needs to artificially select variables, has few influence factors considered in research, is difficult to capture the nonlinear relation between the variables and PM2.5, obtains a prediction result with timeliness, and can only predict in a short-term range.
The methods based on machine learning are mainly classified into conventional shallow models and deep learning models. Compared with the traditional machine learning method, the deep learning method not only can model more variables, but also can capture long-term and short-term characteristics in historical data. The conventional deep learning method, such as the conventional Recurrent Neural Network (RNN), has a problem of loss of timing information in the aspect of PM2.5 long-term prediction, while the Convolutional Neural Network (CNN) usually loses spatial information when applied to PM2.5 prediction, which all result in low accuracy in the aspect of PM2.5 long-term prediction. How to utilize a model and a method to mine space-time characteristics of PM2.5 and various variables and perform long-step prediction is a problem to be solved urgently in the field at present.
Related academic literature 1(Zhang L, Liu P, Zhao L, et al. air quality prediction with a semi-super long bidirectional LSTM neural network [ J ]. Atmospheric polarization Research,2021,12(1):328-339. DOI: 10.1016/J. apr.2020.09.003) combines Empirical Mode Decomposition (EMD) and a two-way long short-term memory (Bi-LSTM) neural network to propose a semi-supervised model for predicting PM2.5 concentration, which uses empirical mode decomposition as an unsupervised feature learning method to decompose data and extract frequency and amplitude features. This approach improves the short-term trend prediction of PM2.5 concentration. However, the method only depends on the time series of PM2.5, neglects the transmission and diffusion in the PM2.5 space, and cannot obtain the spatial correlation of PM2.5 on the data level, so that the prediction error will be greatly improved when the long-term prediction of PM2.5 is performed.
Academic literature 2(Wang S, Li Y, Zhang J, et al. Pm2.5-gnn: A domain knowledge enhanced graph neural network for pm2.5for estimating [ C ]// Proceedings of the 28th International Conference on Advances in Geographic Information systems.2020: 163-166. DOI: 10.1145/3397536.3422208) the study was conducted by constructing a graph data structure, combining PM2.5 concentration data with weather variable data, and integrating the domain knowledge of PM2.5 to embody diffusion and transmission in PM2.5 space, so that the study was able to capture the long-term dependence relationship in PM2.5 prediction. But the relevance among the urban nodes cannot be reflected when the graph data structure is built, the PM2.5 time sequence data is not processed, the prediction is accurate only when the data volume is large, and the prediction precision is low when the data volume is too small.
Academic literature 3 (Liujin culture, Chenlijuan, Wang Queen, Chenhuayou, PM2.5 triangular fuzzy sequence multi-factor combined prediction research based on MEMD and spatial hierarchical clustering [ J/OL ]. control and decision: 1-9[2022-02-17]. DOI:10.13195/j.kzyjc.2021.1163) the research proposes a PM2.5 triangular fuzzy sequence multi-factor combined prediction model based on multivariate empirical mode decomposition and spatial hierarchical clustering. Analyzing the correlation between PM2.5 and the local pollutant concentration and meteorological elements by using a Pearman correlation coefficient, and selecting a local influence factor; secondly, calculating the correlation degree between PM2.5 and the concentration of the space pollutants, clustering K-means space of adjacent cities according to the correlation degree to obtain core influence, general influence and remote influence urban groups, and counting the comprehensive indexes of different pollutants of each urban group, namely space influence factors; and further, decomposing the PM2.5 and the triangular fuzzy sequence of the influence factors simultaneously by using the MEMD, and reconstructing to obtain a high-frequency sequence, a low-frequency sequence and a trend sequence. And finally, performing multi-input single-output prediction on the subsequence by using BP, LSTM and LSSVR respectively, and finally integrating to obtain a calculation result. The research is mainly limited by high requirements on atmospheric pollution data, and calculation is performed through a combined prediction model, so that the algorithm complexity is high, and the calculation efficiency is low.
Related prior art patent 1(CN202011041190.3 a PM2.5 high-precision space-time prediction method (censoring-substantial censoring) based on deep learning) discloses a method for space-time prediction based on deep learning PM2.5 concentration, which can not only improve the precision of long-term space-time prediction, but also be used for predicting PM2.5 concentration at a continuous and large-range future moment in space, and meet the requirements in practical application. The method comprises the steps of 1) selecting multi-source data influencing PM2.5for preprocessing and influencing factor analysis, wherein the multi-source data comprises ground monitoring station PM2.5 data, meteorological data, space related data and physical characteristic data; step 2) performing space-time matching on the multi-source data; step 3) clustering multi-source data based on the spatio-temporal correlation and finding a proper time lag value; step 4) training the PM2.5 of each clustered station by using a recursive LSTM model, and evaluating the precision of the prediction method; and 5) carrying out fine PM2.5 space-time distribution charting on the forecast result.
The prior patent 2(CN202110598978.2 a PM2.5 prediction method and storage medium (censorship-substantial censorship) based on graph self-supervised learning) relates to a PM2.5 prediction method and storage medium based on graph self-supervised learning, and establishes a prediction model by using a graph neural network to have strong learning capability on non-european data. In the invention, the PM2.5 prediction method comprises the following steps: step 1) inputting historical environment space-time data of multiple sites in an area to construct a graph; step 2), constructing a PM2.5 prediction model; step 3) inputting the time-space diagram sequence data, and training the prediction model constructed in the step 2; step 4) calculating the accuracy of model prediction, if the accuracy exceeds a preset threshold, executing step 5, otherwise, returning to step 3; and 5) inputting the multi-site data in the area into the trained prediction model to obtain the PM2.5 predicted concentration value of the multi-site in the area.
The prior patent 3(cn201911359480.x an urban PM2.5 concentration prediction method (censoring-substantial examination) fusing EMD and LSTM) relates to an air quality concentration prediction method, in particular to an urban PM2.5 concentration prediction method for deep learning fusing EMD and LSTM. The method comprises the following steps: 1) acquiring hourly time series data, and performing data cleaning on the acquired data; 2) performing stabilization processing on PM2.5 concentration data by using Empirical Mode Decomposition (EMD) to obtain a plurality of components; 3) determining a sliding time window T, carrying out data sequence segment segmentation processing on each component, and normalizing the unified dimension to obtain a plurality of data sets; 4) dividing a data set into a training set and a testing set, respectively constructing an LSTM network model for training, predicting each component by using the trained model, and carrying out inverse normalization processing on the components to obtain a final urban PM2.5 concentration prediction result; 5) constructing a long-short term memory neural network LSTM model on the basis and training; 6) and predicting by using the trained model, and carrying out inverse normalization processing on the model to obtain a final urban PM2.5 concentration prediction result.
The three patents basically focus on the deep learning technology, and relevant variables are selected to predict the concentration of PM2.5, however, the relevant patents have the following problems: too many variables are selected in the patent 1, so that the complexity of the algorithm is easily too high, and the practicability of the model is insufficient; the GCN adopted by the patent 2 is a calculation mode aiming at the whole graph, the node characteristics of the whole graph need to be updated by one-time calculation, and the applicability is insufficient for complex and variable PM2.5 prediction; patent 3 only considers PM2.5 time series, does not utilize spatial information causing PM2.5 pollution, and has limited prediction accuracy in the face of long-step spatio-temporal prediction.
A scientific and reasonable PM2.5 long time-space sequence prediction method is a premise for guaranteeing an air pollution joint defense joint control policy, and the prior art has the following problems:
1. the method is limited in use, and the existing research is mostly aimed at short-time prediction and cannot meet the requirements in the actual application process;
2. the practicability is poor, massive atmospheric pollution data and geographic data are needed, a numerical simulation model needs a large number of parameters, the model is complex to construct, and the number of computing resources is excessive;
3. most of the existing deep learning methods only aim at PM2.5 sequences, or have higher complexity when extracting spatial related information polluted by PM2.5, and have insufficient accuracy for long-term and space prediction.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a PM2.5 concentration long-term space prediction method based on a GAT-EMD-GRU deep learning algorithm, provide a new idea for solving the PM2.5 concentration prediction problem, combine an empirical mode decomposition algorithm in the signal decomposition field with a deep learning algorithm, and improve the PM2.5 long-term space prediction accuracy.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a PM2.5 pollution concentration long-time space prediction method based on deep learning model and empirical mode decomposition coupling comprises the following steps:
step 000, collecting PM2.5 pollution data and related meteorological variable data, performing data cleaning, and performing correlation analysis;
step 010, constructing a graph data structure through the collected data, and inputting the graph data structure into a GAT module of the model to obtain spatial information of PM2.5 pollution;
step 020, decomposing the PM2.5 pollution sequence into a plurality of low-frequency sub-pollution sequences and residual errors according to an empirical mode decomposition algorithm, and splicing the sub-sequences and the residual errors to obtain time information of PM2.5 pollution;
and 030, selecting a gating circulation unit as a basic unit, aggregating the space-time characteristic information obtained in the two steps, inputting the aggregated space-time characteristic information into a GRU (general purpose unit) for calculation, and finally outputting the calculated space-time characteristic information through a full connection layer to obtain a prediction result.
Preferably, the method further comprises the following steps:
and 001, performing correlation analysis through Pearson correlation coefficient (Pearson correlation coefficient) to determine the correlation between the selected meteorological variable and PM2.5 pollution.
Preferably, the step 010 further includes the steps of:
and 011, constructing a graph data structure according to the selected variables and the association rules.
Step 012, inputting the graph data structure into GAT, and obtaining spatial information of PM2.5 pollution based on attention mechanism of GAT;
and 013, in order to make the prediction result more stable and accurate, adopting a multi-head attention mechanism, performing parallel operation on K independent attention mechanisms, and splicing the results to obtain the final spatial feature output result.
Preferably, step 020 specifically includes the following steps:
021, acquiring all maximum values and minimum values of the signal sequence through a Find Peaks algorithm;
022, obtaining two smooth peak/trough fitting curves, namely an upper envelope line and a lower envelope line of the signal through a cubic spline interpolation method according to a maximum value set and a minimum value set of the signal sequence;
023, averaging the two extreme value curves to obtain an average envelope curve;
024, according to the IMF function definition, after the first IMF is obtained, subtracting the IMF1 from the original signal to be used as a new original signal, and obtaining the IMF2 by the screening analysis, and so on, and completing the empirical mode decomposition.
Step 025, obtaining the city nodesi, splicing the IMF subsequence and the residual error at the time t to obtain an EMD matrix of the city node i at the time t
Figure RE-GDA0003772280920000061
Preferably, the step 030 specifically includes the steps of:
and 031, aggregating the spatio-temporal feature information obtained in the two steps, and inputting the aggregated spatio-temporal feature information into the GRU for calculation.
Step 032: and transmitting the output of the GRU to a full connection layer to obtain a prediction result.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the method, other complex variables are not needed, and the accurate prediction effect can be completed only by utilizing PM2.5 pollution data and meteorological variable data.
2. And a complex model is established without the help of simulation and numerical simulation software, and a large amount of computing resources are not needed.
3. For long predictions, such as 24 hours and 48 hours, the present invention is still more effective than other methods.
4. The method integrates the meteorological field knowledge and the geographic knowledge, and has certain interpretability with other deep learning methods.
Drawings
FIG. 1 is a flow chart of a long-term and long-term spatial prediction method of PM2.5 pollution concentration based on deep learning model and empirical mode decomposition coupling according to the present invention;
FIG. 2 is a Pearson correlation coefficient plot between PM2.5 and a weather variable, with p-values all less than 0.05;
FIG. 3 is a decomposition result diagram of the EMD algorithm;
FIG. 4 is a graph comparing the predicted value and the true value of the GAT-EGRU model on the test set (node is big city, prediction time is 24h, and the value is normalized);
FIG. 5 is a graph showing the performance of the model and a comparison thereof, where (a) is the MSE index result; (b) MAE index results.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Other embodiments, which can be derived by one of ordinary skill in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A PM2.5 pollution concentration long-term space prediction method based on deep learning model and empirical mode decomposition coupling comprises the following steps:
step 1, collecting PM2.5 pollution data and related meteorological variable data, cleaning the data and carrying out correlation analysis;
and performing correlation analysis through a Pearson correlation coefficient to determine the correlation between the selected related meteorological variable data and the PM2.5 pollution data, wherein the Pearson correlation coefficient formula is as follows:
Figure RE-GDA0003772280920000081
this is the overall correlation coefficient, where X, Y refers to two random variables, PM2.5 and a single relevant meteorological variable; the single relevant meteorological variable data and PM2.5 pollution data are overall samples, cov (X, Y) refers to the covariance of the PM2.5 data and the single meteorological variable data, sigma refers to the standard deviation of sample data, E [ ] refers to the expectation of random variable, and mu refers to the mean value of the sample data; for sample data, i.e., PM2.5 data and single meteorological variable data, cov (X, Y) and σ equations are:
cov(X,Y)＝E[XY]-E[X]E[Y]
Figure RE-GDA0003772280920000082
substitutes it into ρ X,Y The pearson correlation coefficient r of the sample is obtained in the formula (1):
Figure RE-GDA0003772280920000083
wherein, X i ，Y i Refers to samples in random variables X, Y, refers to a single piece of PM2.5 pollution data and a single piece of meteorological variable data,
Figure RE-GDA0003772280920000084
the overall mean value of PM2.5 pollution data and single meteorological variable data is referred, and n is the number of data;
step 2, constructing a graph data structure through the relevant meteorological variable data cleaned in the step 1, constructing a GAT module of a model GAT-EGRU based on an attention mechanism and the graph data structure, and inputting PM2.5 pollution data and the relevant meteorological variable data to obtain new spatial characteristic information;
step 2.1, constructing a graph data structure according to the relevant meteorological variable data and the association rule selected in the step 1, wherein the association rule is as follows:
A ij ＝H(d θ -d ij )·H(m θ -m ij )
wherein d is ij ＝||ρ i -ρ j ||，
Figure RE-GDA0003772280920000091
Wherein A is ij Represents whether there is a relationship: a value of 0 indicates no correlation, a value of 1 indicates correlation, and ρ i Representing the position of the city node i, d in the graph data structure ij Represents the distance between two nodes; m is ij Representing the mountain elevation between the city node i and the city node j, solving for m ij In the formula (2), h (·) is a height function, λ is a proportion parameter, and sup { } represents solving an upper bound; II is L of vector 2 Norm, H (·) is a step function, if and only if x>At 0, h (x) is 1; d θ 、m θ Thresholds for distance and altitude;
step 2.2, constructing the GAT module of the model, specifically the formula for constructing GAT, based on the attention mechanism of GAT and the graph data structure of step 2.1 as follows:
Figure RE-GDA0003772280920000095
Figure RE-GDA0003772280920000092
wherein, a: r p′ ×R p′ → R is the self-attention mechanism, W ∈ R p×p′ For the weight matrix, M is the set of neighbor nodes of node i,
Figure RE-GDA0003772280920000093
is a spatial feature matrix of node i, e ij Representing the importance of node j to node i; to e is making e ij Easily compared among different nodes, and all attention coefficients of j are normalized by using a Softmax function to obtain alpha ij Wherein Softmax (·) refers to the Softmax function;
in the experiment, the attention mechanism a is a single-layer feedforward neural network and consists of a weight vector
Figure RE-GDA0003772280920000094
Parameterizing and applying a LeakyReLU nonlinear function; coefficient alpha calculated by attention mechanism after full expansion ij Expressed as:
Figure RE-GDA0003772280920000101
wherein · - T Representing transposition, and | l represents splicing operation;
finally, attention coefficient alpha of the node i and the neighbor node j is calculated ij And weight matrix W, original spatial feature matrix
Figure RE-GDA0003772280920000102
Multiplying to obtain a new node matrix integrated with the neighbor node information
Figure RE-GDA0003772280920000103
Figure RE-GDA0003772280920000104
Wherein ω is a nonlinear operation;
and 2.3, in order to enable the prediction result to be more stable and accurate, performing parallel operation on the K independent attention mechanisms in the step 2.2 by adopting a multi-head attention mechanism, and splicing the results to obtain a final spatial characteristic output result:
Figure RE-GDA0003772280920000105
wherein, the first and the second end of the pipe are connected with each other,
Figure RE-GDA0003772280920000106
the result of the normalization of the attention coefficient representing the kth attention mechanism is the feature matrix finally output
Figure RE-GDA0003772280920000107
The model GAT-GRU has Kp' characteristics, so that the construction of the GAT module of the model GAT-GRU is completed;
step 3, serializing the PM2.5 pollution data according to an empirical mode decomposition algorithm to obtain a PM2.5 pollution data sequence, namely a numerical sequence of PM2.5 changing along with time, decomposing the numerical sequence into a plurality of low-frequency sub-pollution sequences and residual errors, and splicing the sub-pollution sequences and the residual errors to obtain time information of PM2.5 pollution;
step 3.1, acquiring a signal sequence, namely all maximum values and minimum values of the PM2.5 pollution sequence, by a Find Peaks algorithm;
step 3.2, obtaining two smooth wave crest/wave trough fitting curves, namely an upper envelope line and a lower envelope line of the signal, by carrying out cubic spline interpolation on the signal sequence;
step 3.3, averaging the two extreme value curves to obtain an average envelope curve;
step 3.4, after the first IMF is obtained according to the IMF function definition, subtracting the IMF1 from the original signal to be used as a new original signal, wherein the signal is an intermediate signal, obtaining an IMF2 through the screening analysis, and so on, and completing empirical mode decomposition; the calculation formula is as follows:
Figure RE-GDA0003772280920000111
where s represents the number of IMF functions after decomposition is complete, x i (t) is PM2.5 contamination sequence, u i (t) is the decomposed subsequence, r n (t) residual error that cannot be finally decomposed;
the two conditions for judging whether the intermediate signal obtained in the step 3.4 meets the IMF specifically mean that (1) in the whole data segment, the number of extreme points and the number of zero-crossing points must be equal or the difference cannot exceed one at most; (2) at any time, the average value of an upper envelope formed by the local maximum value points and a lower envelope formed by the local minimum value points is zero, namely the upper envelope and the lower envelope are locally symmetrical relative to a time axis;
step 3.5, splicing the obtained IMF sub-sequence and residual error of the city node i at the time t to obtain an EMD matrix of the city node i at the time t
Figure RE-GDA0003772280920000112
Figure RE-GDA0003772280920000113
Step 4, selecting a gating cycle unit as a basic unit, constructing a GRU module of the GAT-EGRU model, aggregating the space-time characteristic information obtained in the two steps, inputting the aggregated space-time characteristic information into the GRU for calculation, and finally outputting the aggregated space-time characteristic information through a full connection layer to obtain a prediction result;
step 4.1, firstly, a gating cycle unit is selected as a basic unit to construct the GRU, and specifically, the specific formula of the GRU is as follows:
Figure RE-GDA0003772280920000114
Figure RE-GDA0003772280920000115
Figure RE-GDA0003772280920000116
Figure RE-GDA0003772280920000117
Figure RE-GDA0003772280920000121
wherein
Figure RE-GDA0003772280920000122
The output of the GAT module and the EMD module respectively,
Figure RE-GDA0003772280920000123
represents information after the aggregation of the two, W z ，W r W is a weight matrix which can be learned in the training process,
Figure RE-GDA0003772280920000124
in order to be an input, the user can select,
Figure RE-GDA0003772280920000125
is the space-time information of the last moment,
Figure RE-GDA0003772280920000126
in order to update the door,
Figure RE-GDA0003772280920000127
in order to reset the gate, the gate is reset,
Figure RE-GDA0003772280920000128
representing the space-time information at the current time, and keeping the needed space-time information and abandoning the unneeded space-time information by updating the gate to obtain the final space-time information
Figure RE-GDA0003772280920000129
So far, a GRU module of a model GAT-EGRU is successfully constructed;
step 4.2: and transmitting the output of the GRU to a full connection layer to obtain a prediction result, wherein the full connection layer has the following formula:
Figure RE-GDA00037722809200001210
wherein Ω represents a fully connected layer.
As shown in fig. 1 to 5, the present invention provides a PM2.5 pollution concentration long-term space prediction method based on deep learning model and empirical mode decomposition coupling, which specifically includes the following steps:
the method comprises the steps of firstly, collecting PM2.5 pollution data and meteorological variable data, and constructing a large pollution prediction data set. 184 cities with serious pollution in the area of the long triangle and Jingjin Ji were selected, the time span was 2015 to 2018, and data was recorded every 3 hours. Wherein, the PM2.5 data is obtained from a national control site, and the meteorological data is a large data set of climate reanalysis data ERA5 from a European weather forecasting center (ECMWF), and the large data set is inverted by satellite data and is subjected to multi-source data reanalysis correction. The selected meteorological variable data are shown in table 1.
Table 1 is a meteorological variable selected by the invention;
Figure RE-GDA00037722809200001211
Figure RE-GDA0003772280920000131
next, correlation analysis is performed by Pearson correlation coefficient (Pearson correlation coefficient) to determine the correlation between the selected meteorological variables and PM2.5 pollution.
The pearson correlation coefficient calculation formula is as follows:
the pearson correlation coefficient between two variables is defined as the quotient of the covariance and the standard deviation between the two variables:
Figure RE-GDA0003772280920000132
the above formula defines the overall correlation coefficient, often using the greek lowercase ρ as the representative symbol. Estimating the covariance and standard deviation of the sample to obtain a Pearson correlation coefficient, which is usually represented by a lower case letter r in English:
Figure RE-GDA0003772280920000133
and secondly, determining a pollution association rule according to the obtained pollution prediction data set, constructing a graph data structure, transmitting the graph data structure to a GAT module of the model, and learning to obtain the influence of the adjacent association nodes on each node. And (3) obtaining a graph data structure according to the pollution prediction data set and the association rule, wherein the urban PM2.5 pollution value and the weather variable are used as node attributes of the graph structure data, and edges in the graph structure data are determined according to a formula (3).
A ij ＝H(d θ -d ij )·H(m θ -m ij ) Wherein d is ij ＝||ρ i -ρ j ||，
Wherein
Figure RE-GDA0003772280920000134
Where ρ is i Representing the location (latitude and longitude), s, of node i ij Representing the distance between two nodes, H (-) is a step function, if and only if x>At 0 time，H(x)＝1。d θ ，m θ The threshold values for distance and altitude are here 300km,1200m, respectively.
With the constraints described above, PM2.5 can only be transported and spread when the distance between two urban nodes is less than 300km and the mountain range between them is less than 1200 m.
Then, the current characteristics of the node at the time t are represented
Figure RE-GDA0003772280920000141
And the last time PM 2.5 Splicing the predicted values of the concentrations to obtain node representation
Figure RE-GDA0003772280920000142
Representing nodes
Figure RE-GDA0003772280920000143
And graph data structures are input to the graph attention network GAT. And obtaining the attention coefficient of the surrounding associated nodes of each city node to the city node and the spatial feature information after the surrounding associated node information is fused. Specifically, the formula for the GAT module is expressed as follows:
Figure RE-GDA0003772280920000144
Figure RE-GDA0003772280920000145
Figure RE-GDA0003772280920000146
Figure RE-GDA0003772280920000147
wherein, a: r p′ ×R p′ → R is the self-attention mechanism, Q ∈ R p×p′ For the weight matrix, M is the node iSet of neighbor nodes, · T Indicating transposition and | | indicating a splicing operation.
In order to make the prediction result more accurate and stable, a multi-head attention mechanism is adopted, K independent attention mechanisms are subjected to parallel operation, then the results are spliced, and the final spatial characteristic output result is obtained
Figure RE-GDA0003772280920000148
Wherein the content of the first and second substances,
Figure RE-GDA0003772280920000149
representing the result of normalization of the attention coefficient of the kth attention mechanism, the feature matrix P 'that is finally output' t Has Kp' characteristics.
Thirdly, decomposing the PM2.5 pollution sequence into a plurality of low-frequency sub-pollution sequences according to an empirical mode decomposition algorithm, wherein the empirical mode decomposition algorithm comprises the following steps:
1. solving the extreme point and obtaining all the maximum values and the minimum values of the signal sequence through a Find Peaks algorithm;
2. fitting an envelope curve through a maximum value and a minimum value group of a signal sequence, and obtaining two smooth peak/trough fitting curves, namely an upper envelope curve and a lower envelope curve of a signal through a cubic spline interpolation method;
3. the mean envelope curve averages the two extreme value curves to obtain a mean envelope curve;
4. subtracting the mean envelope of the original signal of the intermediate signal to obtain an intermediate signal;
5. the eigenmode function (IMF) IMF needs to be judged to meet two conditions:
1) the number of extreme points and the number of zero crossings must be equal or differ by at most not more than one within the whole data segment.
2) At any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper and lower envelopes are locally symmetrical with respect to the time axis.
After the first IMF is obtained by the method, the IMF1 is subtracted from the original signal to be used as a new original signal, and then the IMF2 can be obtained by the screening analysis, and so on, and the empirical mode decomposition is completed. The decomposition formula is as follows:
Figure RE-GDA0003772280920000151
then, the EMD matrix is obtained by using the formula (10) to carry out polymerization
Figure RE-GDA0003772280920000152
Figure RE-GDA0003772280920000153
And fourthly, considering that a gating cycle unit (GRU) can solve the problems of long-term dependence and gradient disappearance in the RNN, the invention selects the gating cycle unit as a basic unit, aggregates the spatio-temporal characteristic information obtained in the two steps, inputs the spatio-temporal characteristic information into the GRU for calculation, and finally obtains a prediction result through full-connection layer output. The GRU formula is as follows:
Figure RE-GDA0003772280920000154
Figure RE-GDA0003772280920000155
Figure RE-GDA0003772280920000156
Figure RE-GDA0003772280920000157
Figure RE-GDA0003772280920000161
wherein W z ，W r W is a weight matrix which can be learned in the training process,
Figure RE-GDA0003772280920000162
in order to be an input, the user can select,
Figure RE-GDA0003772280920000163
in order to update the door or doors,
Figure RE-GDA0003772280920000164
in order to reset the gate, the gate is reset,
Figure RE-GDA0003772280920000165
representing the space-time information at the current time, and keeping the needed space-time information and abandoning the unneeded space-time information by updating the gate to obtain the final space-time information
Figure RE-GDA0003772280920000166
Finally, through the full link layer, the final predicted value is obtained:
Figure RE-GDA0003772280920000167
where Ω represents the fully connected layer.
The invention is proved to be feasible by comparing experiments with the existing prediction model method.
The invention has the beneficial effects that:
1. according to the method, other complex variables are not needed, and the accurate prediction effect can be completed only by utilizing PM2.5 pollution data and meteorological variable data.
2. And a complex model is established without the help of simulation and numerical simulation software, and a large amount of computing resources are not needed.
3. For long-term predictions, such as 24 hours and 48 hours, the method is still more effective compared with other methods.
4. The method integrates the meteorological field knowledge and the geographic knowledge, and has certain interpretability with other deep learning methods.
In light of the foregoing description of the preferred embodiments of the present invention, those skilled in the art can now make various alterations and modifications without departing from the scope of the invention. The technical scope of the present invention is not limited to the contents of the specification, and must be determined according to the scope of the claims.

Claims (1)

1. A PM2.5 pollution concentration long-term space prediction method based on deep learning model and empirical mode decomposition coupling is characterized by comprising the following steps:
step 1, collecting PM2.5 pollution data and related meteorological variable data, cleaning the data and carrying out correlation analysis;
and performing correlation analysis through a Pearson correlation coefficient to determine the correlation between the selected related meteorological variable data and the PM2.5 pollution data, wherein the Pearson correlation coefficient formula is as follows:
Figure FDA0003572119320000011
this is the overall correlation coefficient, where X, Y refers to two random variables, PM2.5 and a single relevant meteorological variable; the single relevant meteorological variable data and PM2.5 pollution data are overall samples, cov (X, Y) refers to the covariance of the PM2.5 data and the single meteorological variable data, sigma refers to the standard deviation of sample data, E [ ] refers to the expectation of random variable, and mu refers to the mean value of the sample data; for sample data, i.e., PM2.5 data and single meteorological variable data, cov (X, Y) and σ equations are:
cov(X，Y)＝E[XY]-E[X]E[Y]
Figure FDA0003572119320000012
substitutes it into ρ X，Y The pearson correlation coefficient r of the sample is obtained in the formula (1):
Figure FDA0003572119320000013
wherein, X i ，Y i Refers to samples in random variables X, Y, refers to a single piece of PM2.5 pollution data and a single piece of meteorological variable data,
Figure FDA0003572119320000014
the overall mean value of PM2.5 pollution data and single meteorological variable data is referred, and n is the number of data;
step 2, constructing a graph data structure through the relevant meteorological variable data cleaned in the step 1, constructing a GAT module of a model GAT-EGRU based on an attention mechanism and the graph data structure, and inputting PM2.5 pollution data and the relevant meteorological variable data to obtain new spatial characteristic information;
step 2.1, constructing a graph data structure according to the relevant meteorological variable data and the association rule selected in the step 1, wherein the association rule is as follows:
A ij ＝H(d θ -d ij )·H(m θ -m ij )
wherein d is ij ＝||ρ i -ρ j ||，
Figure FDA0003572119320000021
Wherein, A ij Represents whether there is a relationship: a value of 0 indicates no correlation, a value of 1 indicates correlation, and ρ i Representing the position of the city node i, d in the graph data structure ij Represents the distance between two nodes; m is ij Representing the mountain elevation between the city node i and the city node j, solving for m ij In the formula (2), h (·) is a height function, λ is a proportion parameter, and sup { } represents solving an upper bound;l of vector | | · | | 2 Norm, H (·) is a step function, H (x) is 1 if and only if x > 0; d θ 、m θ Thresholds for distance and altitude;
step 2.2, constructing the GAT module of the model, specifically the formula for constructing GAT, based on the attention mechanism of GAT and the graph data structure of step 2.1 as follows:
Figure FDA0003572119320000022
Figure FDA0003572119320000023
wherein, a: r is p′ ×R p′ → R is the self-attention mechanism, W ∈ R p×p′ For the weight matrix, M is the set of neighbor nodes of node i,
Figure FDA0003572119320000024
is a spatial feature matrix of node i, e ij Representing the importance of node j to node i; to e to make e ij Easily compared among different nodes, and all attention coefficients of j are normalized by using a Softmax function to obtain alpha ij Wherein Softmax (·) refers to the Softmax function;
in the experiment, the attention mechanism a is a single-layer feedforward neural network and consists of a weight vector
Figure FDA0003572119320000025
Parameterizing and applying a LeakyReLU nonlinear function; coefficient alpha calculated by attention mechanism after full expansion ij Expressed as:
Figure FDA0003572119320000031
wherein, T represents transposition, and | represents splicing operation;
finally, attention coefficient alpha of the node i and the neighbor node j is calculated ij And weight matrix W, original spatial feature matrix
Figure FDA0003572119320000032
Multiplying to obtain a new node matrix integrated with the neighbor node information
Figure FDA0003572119320000033
Figure FDA0003572119320000034
Wherein σ is a nonlinear operation;
and 2.3, in order to enable the prediction result to be more stable and accurate, performing parallel operation on the K independent attention mechanisms in the step 2.2 by adopting a multi-head attention mechanism, and splicing the results to obtain a final spatial characteristic output result:
Figure FDA0003572119320000035
wherein the content of the first and second substances,
Figure FDA0003572119320000036
expressing the result of normalization of attention coefficient of kth attention mechanism, and finally outputting feature matrix
Figure FDA0003572119320000037
The model GAT-GRU has Kp' characteristics, so that the construction of the GAT module of the model GAT-GRU is completed;
step 3, serializing the PM2.5 pollution data according to an empirical mode decomposition algorithm to obtain a PM2.5 pollution data sequence, namely a numerical sequence of PM2.5 changing along with time, decomposing the numerical sequence into a plurality of low-frequency sub-pollution sequences and residual errors, and splicing the sub-pollution sequences and the residual errors to obtain time information of PM2.5 pollution;
step 3.1, acquiring a signal sequence, namely all maximum values and minimum values of the PM2.5 pollution sequence, by a Find Peaks algorithm;
step 3.2, the signal sequence is subjected to a cubic spline interpolation method to obtain two smooth wave crest/wave trough fitting curves, namely an upper envelope curve and a lower envelope curve of the signal;
step 3.3, averaging the two extreme value curves to obtain an average envelope curve;
step 3.4, after the first IMF is obtained according to the IMF function definition, subtracting the IMF1 from the original signal to be used as a new original signal, wherein the signal is an intermediate signal, obtaining an IMF2 through the screening analysis, and so on, and completing empirical mode decomposition; the calculation formula is as follows:
Figure FDA0003572119320000041
where s represents the number of IMF functions after decomposition is complete, x i (t) is PM2.5 contamination sequence, u i (t) is the decomposed subsequence, r n (t) residual error that cannot be finally decomposed;
the two conditions for judging whether the intermediate signal obtained in the step 3.4 meets the IMF specifically mean that (1) in the whole data segment, the number of extreme points and the number of zero-crossing points must be equal or the difference cannot exceed one at most; (2) at any time, the average value of an upper envelope formed by the local maximum value points and a lower envelope formed by the local minimum value points is zero, namely the upper envelope and the lower envelope are locally symmetrical relative to a time axis;
step 3.5, splicing the obtained IMF sub-sequence and residual error of the city node i at the time t to obtain an EMD matrix of the city node i at the time t
Figure FDA0003572119320000042
Figure FDA0003572119320000043
Step 4, selecting a gating cycle unit as a basic unit, constructing a GRU module of the GAT-EGRU model, aggregating the space-time characteristic information obtained in the two steps, inputting the aggregated space-time characteristic information into the GRU for calculation, and finally outputting the aggregated space-time characteristic information through a full connection layer to obtain a prediction result;
step 4.1, firstly, a gating cycle unit is selected as a basic unit to construct the GRU, and specifically, the specific formula of the GRU is as follows:
Figure FDA0003572119320000044
Figure FDA0003572119320000045
Figure FDA0003572119320000046
Figure FDA0003572119320000047
Figure FDA0003572119320000048
wherein
Figure FDA0003572119320000049
The output of the GAT module and the EMD module respectively,
Figure FDA00035721193200000410
represents information after the aggregation of the two, W z ，W r W is a weight matrix which can be learned in the training process,
Figure FDA0003572119320000051
in order to be an input, the user can select,
Figure FDA0003572119320000052
is the space-time information of the last moment,
Figure FDA0003572119320000053
in order to update the door,
Figure FDA0003572119320000054
in order to reset the gate, the gate is reset,
Figure FDA0003572119320000055
representing the space-time information at the current time, and keeping the needed space-time information and abandoning the unneeded space-time information by updating the gate to obtain the final space-time information
Figure FDA0003572119320000056
So far, a GRU module of a model GAT-EGRU is successfully constructed;
step 4.2: and transmitting the output of the GRU to a full connection layer to obtain a prediction result, wherein the full connection layer has the following formula:
Figure FDA0003572119320000057
wherein Ω represents a fully connected layer.
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* Cited by examiner, † Cited by third party
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CN116050583A (en) * 2022-12-15 2023-05-02 生态环境部华南环境科学研究所(生态环境部生态环境应急研究所) Water environment quality deep learning prediction method coupled with space-time context information
CN117434153A (en) * 2023-12-20 2024-01-23 吉林蛟河抽水蓄能有限公司 Road nondestructive testing method and system based on ultrasonic technology

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116050583A (en) * 2022-12-15 2023-05-02 生态环境部华南环境科学研究所(生态环境部生态环境应急研究所) Water environment quality deep learning prediction method coupled with space-time context information
CN116050583B (en) * 2022-12-15 2024-05-28 生态环境部华南环境科学研究所(生态环境部生态环境应急研究所) Water environment quality deep learning prediction method coupled with space-time context information
CN117434153A (en) * 2023-12-20 2024-01-23 吉林蛟河抽水蓄能有限公司 Road nondestructive testing method and system based on ultrasonic technology
CN117434153B (en) * 2023-12-20 2024-03-05 吉林蛟河抽水蓄能有限公司 Road nondestructive testing method and system based on ultrasonic technology

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