A PM2.5 fitting method and system based on DEM weighting spatio-temporal full connection residual neural network

Abstract

The application provides a PM2.5 fitting method and system based on a DEM weighted spatio-temporal full connection residual neural network.The application introduces a spatial feature vector into a nonlinear model to eliminate the influence of spatial autocorrelation, realizes the expansion of a spatial filter value model, realizes the influence of spatial heterogeneity by using an attention mechanism, and converts the time without numerical size into a time feature vector by using a novel "ont-hot coding + inlaying" method to eliminate the influence of time, and the loss function is modified, the fitting precision of a high-altitude area is improved without reducing the fitting precision of the whole research area, so that a ground PM2.5 fitting result with higher precision is obtained.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spatial statistical analysis service application, and particularly relates to a PM2.5 fitting method and system based on a DEM weighted spatio-temporal full connection residual neural network. BACKGROUND

[0002] PM2.5 refers to particulate matter with an aerodynamic diameter of ≤2.5 μm, and research shows that it will bring negative effects to human health. Due to its small particle size, large surface area and strong activity, it is easy to adsorb toxic and harmful substances such as heavy metals and microorganisms, and it floats in the atmosphere for a long time, has a long transmission distance, and has a stronger harmful effect than other air pollutants. Although some research shows that PM2.5 may have a positive impact on the climate, compared with the negative effects it brings to humans, PM2.5 is more harmful than beneficial. It is necessary to obtain the accurate spatio-temporal distribution of ground PM2.5 concentration to solve the environmental health problems it brings.

[0003] Although the number of ground PM2.5 monitoring stations nationwide has been increasing year by year since 2013, the number is still very limited and the spatial distribution is very uneven. These monitoring stations are mostly distributed in urban central areas, and the number of stations in suburban and rural areas is very limited, and the area of PM2.5 monitoring is limited. The limited number and uneven distribution of ground monitoring stations result in the fact that some scholars use spatial interpolation methods such as spline function method, inverse distance weighted method and Kriging interpolation method to obtain continuous surface data from discrete point data, and the precision is limited.

[0004] With the development of remote sensing technology, satellite-derived aerosol optical depth (AOD) products have been widely used to expand the monitoring range of PM2.5. AOD refers to the integral of the extinction coefficient of the medium in the vertical direction, indicating the light reduction effect of aerosols, and is a key physical quantity representing the degree of atmospheric turbidity, which has a clear correlation with PM2.5. More and more scholars use AOD products, including those retrieved from the Moderate Resolution Imaging Spectrometer (MOD). Resolution Imaging Spectrometer (MODIS), Multi-Angle Imaging Spectrometer, Visible Infrared Imaging Radiometer Suite and Geostationary Operational Environmental Satellite Aerosol / Smoke Products, etc. In addition, other factors related to PM2.5 are also used with AOD to retrieve PM2.5 concentration. Commonly used data includes normalized difference vegetation index (NDVI), digital elevation model (DEM), and various meteorological factor data (wind speed, wind direction, planetary boundary layer height, surface temperature, humidity, pressure, etc.) and pollution source data, etc.

[0005] In addition, many models have been used to establish the relationship between AOD and PM2.5, such as multiple linear regression model, geographically weighted regression model, spatial filter model, linear mixed effects model, random forest, neural network, etc. These methods can be divided into three categories: linear regression model, chemical transport model and machine learning method.

[0006] According to the first and second laws of geography, the spatial distribution of PM2.5 has spatial autocorrelation and spatial heterogeneity. "All things or phenomena are related in space, but the relationship between things or phenomena close to each other is generally closer than that between things or phenomena far apart", which shows that things and phenomena are interdependent, interdependent, interdependent and interdependent in space, which means that the distribution of things and phenomena has spatial autocorrelation. Spatial heterogeneity refers to the fact that things and phenomena in each spatial unit are significantly different from those in other locations, reflecting the non-stationarity of things and phenomena in space. The observation location may be different, and the observation results may also be different. Spatial heterogeneity mainly comes from two aspects: one is that various things and phenomena in space are not constant, lack of stationary structure, and the other is that the spatial unit itself is not homogeneous, and the shape and area of each spatial unit are different. Therefore, the fitting effect of the general model on PM2.5 is poor, and the influence of space on PM2.5 must be considered. And studies have shown that considering the influence of spatial autocorrelation and spatial heterogeneity at the same time is better than considering the influence of spatial autocorrelation and spatial heterogeneity respectively.

[0007] Linear regression models are used to deal with the linear relationship between PM2.5 and influencing factors from a statistical point of view. However, although some linear regression models take into account the spatial influence, such as spatial filter model, geographically weighted regression model, spatial lag model and the like, the relationship between PM2.5 and influencing factors is very complex and cannot be summarized by a simple linear relationship, so the effect of these models on the fitting precision of PM2.5 concentration is limited. Chemical transport models simulate the transmission mechanism of PM2.5 in the air from the mechanism of PM2.5. However, due to the complex propagation mechanism of PM2.5 in the air, the result precision is limited. Therefore, machine learning algorithms such as neural networks, random forests, support vector machines and gradient machines have been increasingly used to deal with the non-linear relationship between PM2.5 and influencing factors. With the development of deep learning technology, deep learning methods have also been widely used to explore the relationship between PM2.5 and influencing factors. However, general neural networks such as deep neural networks and deep belief networks rarely consider the influence of space and time on the relationship between PM2.5 and influencing factor data. Therefore, many scholars have proposed some spatio-temporal neural networks, which add time and space influencing factors such as longitude and latitude or time to the neural network as input for training. However, they do not comprehensively consider the spatial influence, and do not consider the spatial autocorrelation and spatial heterogeneity together. In addition, most PM2.5 monitoring sites are located in low-altitude areas, which means that the amount of PM2.5 sample data at high altitudes is small when training the network, which may lead to insufficient learning of the relationship between PM2.5 and influencing factors at high altitudes. In order to improve the overall fitting result, there is a large error between the fitted value and the true value of PM2.5 at high altitudes.

[0008] In summary, the existing neural networks either do not consider or one-sidedly and generally consider the influence of space and time on PM2.5, and do not focus on the influence of site sample data elevation on the fitting result, resulting in poor fitting effect of PM2.5 at high altitudes. Therefore, there is an urgent need for a PM2.5 fitting method that can comprehensively consider the influence of space and time and improve the fitting effect at high altitudes to achieve accurate spatio-temporal monitoring of PM2.5 in a large area. SUMMARY

[0009] The purpose of the present application is to provide a PM2.5 fitting method based on DEM weighted spatio-temporal full connection residual neural network, which realizes large-scale high-precision fitting of ground PM2.5.

[0010] The core idea of the application is to comprehensively consider the influence of space on PM2.5 and influencing factors by dividing the influence into spatial autocorrelation and spatial heterogeneity, extract the feature vector containing spatial autocorrelation information by using the spatial filter value method, score the importance of each influencing factor by using the attention mechanism, multiply the original influencing factor, obtain the locally weighted influencing factor, process the influence of time on PM2.5 by using a novel 'one-hot coding + inlaying' method, and weight the loss function by using the site elevation, and a PM2.5 fitting method based on DEM weighted spatio-temporal full connection residual neural network is proposed.

[0011] The technical scheme adopted by the application comprises the following steps:

[0012] Step 1, PM2.5 data and factor data acquisition and preprocessing, the factor data includes remote sensing data, meteorological factors and other factors; the preprocessed factor data is extracted to the ground monitoring station to obtain a PM2.5 data set, each record of the data set containing PM2.5 data, factor data, spatial coordinates and time data at the monitoring station;

[0013] Step 2, extracting a spatial feature vector containing spatial data;

[0014] Step 3, encoding and dimensionality reduction of time data;

[0015] Step 4, obtaining locally important weighted factor data; scoring the importance of the factor data to obtain locally important weighted data of each factor, the selected influencing factors are first passed through an adaptive attention layer to obtain the importance score of each influencing factor, and then the importance score is multiplied by the influencing factor to obtain the locally important weighted factor data;

[0016] Step 5, constructing a DEM weighted spatio-temporal full connection residual neural network, the spatial feature vector in step 2, the time data in step 3 and the factor data in step 4 are spliced as input; the DEM weighted spatio-temporal full connection residual neural network comprises an input layer, a full connection neural network with symmetric neuron numbers before and after, and an output layer; wherein the input layer only comprises a full connection layer and a BN layer, each layer of the full connection neural network comprises a full connection layer, a BN and a ReLU function, the output results of the front several layers are connected to the full connection layer with the same number of neurons, the output layer is directly output after a full connection layer, and finally the output is the estimated value of PM2.5;

[0017] Step 6, after the model is built, set the total number of training rounds and the learning rate, get the estimated value of PM2.5 in the output layer through forward propagation, then calculate the global loss according to the estimated value and the true value using the loss function, then use the Adam algorithm to reduce the gradient for back propagation, and continuously adjust the parameters until the model converges.

[0018] Further, in step 1, the remote sensing data includes AOD and NDVI, the meteorological factors include temperature, pressure, relative humidity, planetary boundary layer height, wind direction and wind speed, and the other factors include vegetation coverage, land use status, population density, elevation, factory and road distribution density.

[0019] Further, the preprocessing includes unifying the time resolution of all factor data to the same time resolution as the PM2.5 data; by resampling or spatial interpolation, the spatial resolution of the remaining factors except AOD data is consistent with AOD data; the obtained factory data and road network data are point data and line data respectively, which are converted into raster images covering the entire study area by calculating the kernel density. Before calculating the kernel density, the PM2.5 monitoring site coordinates are projected and converted from spherical coordinates to plane coordinates, with the same spatial reference system as AOD. Then use the "Extract multi values to points" tool in ArcGIS to extract the processed factor data to the ground monitoring site, and get the PM2.5 data set.

[0020] Further, the specific implementation of step 2 is as follows:

[0021] Step 2.1, construct the spatial weight matrix W0, for the coordinates of the reprojected ground station, based on the Gaussian kernel function, convert the spatial relationship into weight values, construct the spatial adjacency matrix, the specific formula is as follows:

[0022]

[0023] Where i, j represent position points i and j respectively, W i,j represents the adjacency between position points i and j, located in the i-th row and j-th column of W0, d i,j represents the distance between position points i and j, r represents the maximum distance in the minimum spanning tree of all stations;

[0024] Step 2.2, center the spatial adjacency matrix and calculate the eigenvalue and eigenvector; perform matrix centering operation on the spatial adjacency matrix obtained from step 2.1, the centering formula is as follows:

[0025]

[0026] Where I is an n-dimensional identity matrix, 11T is an n x n matrix, all elements in the matrix are equal to 1, n is the number of monitoring sites in the study area; W0 is the original spatial weight matrix obtained in step 2.1, and then the eigenvalue and eigenvector E = {E1, E2, E3, …, En} of W1 are solved;

[0027] Then the eigenvectors are preliminarily screened; the spatial eigenvectors whose eigenvalues are greater than 0 and meet the following empirical model requirements are preliminarily screened out:

[0028]

[0029] Where λ i represents the eigenvalue to be screened, λ max represents the maximum eigenvalue;

[0030] Step 2.3, further screening of spatial eigenvectors; using the stepwise method, the eigenvectors are added to the regression equation one by one according to the size of the eigenvalue, and the eigenvector that makes the AIC value of the regression equation minimum is selected, until the AIC index does not decrease when the eigenvector is continuously added;

[0031] Step 2.4, constructing a screening layer; the spatial eigenvectors after further screening in step 2.3 are first passed through a full connection layer, which plays a filtering role, filtering out s eigenvectors that are most suitable for the spatial autocorrelation characteristics of the study area from the current n spatial eigenvectors.

[0032] Further, in step 3, the year, month and day of the PM2.5 data obtained by the station are encoded by one-hot, expanded from one dimension to n dimensions, n being the time span of the data used, and then reduced to t dimensions through a full connection layer, t being a hyperparameter set artificially according to the training results.

[0033] Further, in step 4, the factor data obtained in step 1 is passed through a full connection layer and then through a Sigmoid activation function to obtain the importance score of each factor.

[0034] Further, in step 6, the data set obtained in step 1 is used as the training sample data, and the training sample data is divided into multiple batches, and then trained using the global loss, the formula of which is:

[0035]

[0036] Where y i is the estimated value, is the true value, N is the number of training samples, w i is the elevation weight of the sample, and the specific formula is:

[0037]

[0038] where k is a hyper-parameter, DEM i is the elevation at the sample, DEM min is the minimum elevation among all samples, DEM max is the maximum elevation among all samples.

[0039] Further, it also includes step 7, model verification and accuracy evaluation, using 10-fold cross-validation method, respectively, site cross-validation and sample cross-validation; site cross-validation is divided into 10 parts, of which 9 parts of all sample data of the site are used as the training set, and one part of all sample data of the site is used as the validation set; sample cross-validation is divided into 10 parts, of which 9 parts are used as the training set, and 1 part is used as the validation set; then the goodness of fit R 2 , root mean square error RMSE and mean absolute error MAE of the obtained model are calculated, and the average value of ten results is taken as the final result; wherein the calculation formula of R 2 is as follows:

[0040]

[0041] where y i is the observed value of PM2.5 concentration of site i, is the average value of the observation data, is the predicted PM2.5 concentration of site i, and n is the number of monitoring sites;

[0042]

[0043]

[0044] Further, it also includes step 8, result mapping and outlier processing, the specific steps are as follows:

[0045] Step 8.1, result mapping, the trained DEM weighted spatio-temporal full connection residual neural network is obtained in step 6, then the entire study area is converted into points by using the "Raster to Point" tool of ArcGIS, then the "extract values to point" tool is used to extract each factor to the entire study area, and the pandas library of python is used to add time information to the data table, then the data of the entire study area is put into the network model obtained in step 6 to obtain the fitting value of the entire study area, and the "Point to Raster" tool of ArcGIS is used to convert the fitting value into a raster image, i.e. PM2.5 concentration distribution map;

[0046] Step 8.2, outlier processing, for the obtained PM2.5 concentration distribution, negative PM2.5 concentration values are set to 0, and a threshold is set for PM2.5 concentration values, and PM2.5 concentration values exceeding the threshold are all modified to the threshold.

[0047] The application also provides a PM2.5 fitting system based on a DEM weighted spatio-temporal full connection residual neural network, comprising the following modules:

[0048] A data acquisition and preprocessing module is used for PM2.5 data and factor data acquisition and preprocessing, and the factor data includes remote sensing data, meteorological factors and other factors; the preprocessed factor data is extracted to a ground monitoring station to obtain a PM2.5 data set, and each record of the data set contains PM2.5 data, factor data, spatial coordinates and time data at the monitoring station;

[0049] A spatial feature vector extraction module is used for extracting a spatial feature vector containing spatial data;

[0050] A time encoding module is used for encoding and dimensionality reduction of time data;

[0051] A factor data weighting module is used for obtaining locally important weighted factor data; the importance of the factor data is scored to obtain locally important weighted data of each factor, and the selected influence factors are first passed through an adaptive attention layer to obtain importance scores of the influence factors, and then the importance scores are multiplied by the influence factors to obtain the locally important weighted factor data;

[0052] A network model construction module is used for constructing a DEM weighted spatio-temporal full connection residual neural network, and the spatial feature vector in the spatial feature vector extraction module, the time data in the time encoding module and the factor data in the factor data weighting module are spliced as inputs; the DEM weighted spatio-temporal full connection residual neural network comprises an input layer, a full connection neural network with symmetric numbers of front and rear neurons and an output layer; wherein the input layer only comprises a full connection layer and a BN layer, each layer of the full connection neural network comprises a full connection layer, a BN and a ReLU function, the output results of the front several layers are jump-connected to a full connection layer with the same number of neurons, the output layer directly outputs results after a full connection layer, and finally outputs an estimated value of PM2.5;

[0053] A model training module, after the model is constructed, the total number of training rounds and the learning rate are set, the estimated value of PM2.5 is obtained at the output layer through forward propagation, then the global loss is calculated according to the estimated value and the true value by using a loss function, then the gradient is reduced by using an Adam algorithm for back propagation, and the parameters are continuously adjusted until the model converges.

[0054] The PM2.5 fitting method based on the DEM weighted spatio-temporal full connection residual neural network provided by the application does not consider the spatial influence in general, but considers the spatial autocorrelation influence and the spatial heterogeneity influence at the same time, introduces the spatial feature vector into the nonlinear model to eliminate the influence of the spatial autocorrelation, realizes the expansion of the spatial filter value model (ESF), realizes the influence of the spatial heterogeneity by using the attention mechanism, and adopts the novel 'one-hot coding + inlay' method to convert the time with no numerical size into a 'time feature vector' to eliminate the influence of the time, and the loss function is modified, the fitting precision of the high-altitude area is improved without reducing the fitting precision of the whole research area, so that the ground PM2.5 fitting result with higher precision is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The flowchart of the embodiment of the application.

[0056] Figure 2 The sub-flowchart of step 4 of the embodiment of the application.

[0057] Figure 3 The DEM weighted spatio-temporal full connection residual neural network structure diagram provided by the application. Specific implementation method

[0058] In order to facilitate those skilled in the art to understand and implement the application, the application will be further described below in combination with the drawings and examples, and it should be understood that the examples described herein are only used to illustrate and explain the application, and are not used to limit the application.

[0059] The problem to be solved by the application is that the insufficient number of ground monitoring points makes it difficult to obtain the continuous PM2.5 concentration distribution in a large range, and the ground PM2.5 concentration is affected by spatial factors, the existing neural network rarely considers the spatial influence by dividing it into spatial autocorrelation and spatial heterogeneity, and rarely considers the problem of low fitting precision in high-altitude areas caused by the fact that most PM2.5 sites are distributed in low-altitude areas. In view of these problems, the application uses the PM2.5 fitting method based on the DEM weighted spatio-temporal full connection residual neural network to construct a fitting model based on remote sensing image data, and then makes a PM2.5 distribution map.

[0060] Reference Figure 1 The PM2.5 fitting method based on the DEM weighted spatio-temporal full connection residual neural network provided by the embodiment of the application comprises the following steps:

[0061] Step 1: PM2.5 and factor data acquisition and processing.

[0062] (1) Data acquisition: PM2.5 data is from the national urban air quality real-time publishing platform (http: / / 106.37.208.233:20035 / ), which publishes real-time PM2.5 concentration data of each monitoring site every hour. Remote sensing data such as AOD and NDVI can be obtained from MISR, MODIS, and VIIRS, etc. Meteorological factors: temperature, pressure, relative humidity, planetary boundary layer height, wind direction, wind speed, etc. can be obtained from the European Weather Forecast Center (ECMWF, https: / / cds.climate.copernicus.eu / #! / home). Other factors: such as vegetation coverage, land use, population density, elevation, factory and road distribution density, etc., all affect PM2.5 concentration to some extent, which can be crawled from statistical yearbook and Gaode map or Baidu map.

[0063] (2) Data processing: From the original hourly PM2.5 concentration, the daily, monthly, quarterly and annual concentration values are calculated in turn, and the corresponding dates (year, month, day) are recorded. All the influencing factors of PM2.5 will be unified to the same time resolution as the PM2.5 data. By resampling or spatial interpolation, the spatial resolution of the remaining factors is consistent with the AOD data. The obtained factory data and road network data are point and line data respectively, which are converted to raster images covering the entire study area by calculating the kernel density. Before calculating the kernel density, the PM2.5 monitoring site coordinates need to be projected from spherical coordinates (latitude and longitude) to planar coordinates, with the same spatial reference system as AOD, and then use the "Extract multi values to points" tool in ArcGIS to extract the processed factor data to the ground monitoring site, get the PM2.5 data set, which contains PM2.5 data, factor data, spatial coordinates and time (date) data at the site.

[0064] Step 2: Extract spatial feature vectors containing spatial autocorrelation information. The specific steps are as follows:

[0065] Step 2.1: Construct spatial weight matrix W0. In step 1, the coordinates of the reprojected ground monitoring sites are obtained, and based on the Gaussian kernel function, the spatial relationship is converted to weight value to construct the spatial adjacency matrix. The specific formula is as follows:

[0066]

[0067] Where i, j represent position points i and j respectively. W i,j indicates the adjacency (weight) between position points i and j, located in the i-th row and j-th column of W0. d i,jThe distance between position points i and j is represented. r represents the maximum distance in the minimum spanning tree of all stations. From the formula, W i,j j,i i.e. the adjacency between two points is the same, and if the number of monitoring stations is n, the spatial weight matrix has a latitude of n x n, and the diagonal elements are 0 (the distance from the monitoring station to itself is 0) of the symmetric matrix.

[0068] Step 2.2: Center the spatial adjacency matrix and calculate the eigenvalues and eigenvectors. The spatial adjacency matrix obtained in step 2.1 is subjected to matrix centering operation, and the centering formula is as follows:

[0069]

[0070] where I is an n-dimensional unit matrix, and 11 T is an n x n matrix, all elements in the matrix are equal to 1, and n is the number of monitoring stations in the study area. W0 is the original spatial weight matrix obtained in step 2.1. Then solve the eigenvalues and eigenvectors E = {E1, E2, E3, …, En} of W1, which can be calculated using the eigenvalue function provided in software such as Matlab, R, etc.

[0071] Then the eigenvectors are preliminarily screened. The spatial eigenvectors whose eigenvalues are greater than 0 and meet the following empirical model requirements are preliminarily screened out:

[0072]

[0073] where λ i represents the eigenvalue to be screened, and λ max represents the maximum eigenvalue.

[0074] Step 2.3: Further screening of spatial eigenvectors. Using stepwise regression method, the eigenvectors are added to the regression equation one by one according to the size of the eigenvalue, and the eigenvector that makes the AIC value of the regression equation minimum is selected, until the AIC index does not decrease by continuing to add the eigenvectors.

[0075] Step 2.4: Construct a screening layer. The spatial eigenvectors obtained in step 2.3 are subjected to a fully connected layer before being used as input for subsequent networks. This layer acts as a filter, filtering out s eigenvectors that are most suitable for the spatial autocorrelation characteristics of the study area from the current n spatial eigenvectors.

[0076] Step 3: Encode and reduce the dimension of the time information. The specific steps are as follows:

[0077] ​Step 3.1: Time information encoding. In step 1, the PM2.5 site value is obtained, and the acquisition time is recorded as year, month, and day. Through one-hot encoding, the time information is expanded. For example, the day data "1st", through one-hot encoding, is expanded to "[1, 0, 0, 0, …, 0]" with 31 dimensions, and the position of 1 indicates which day of the month it is. The month is the same, and is expanded to 12 dimensions, but the year needs to be expanded to y dimensions according to the year span of the data used.

[0078] Step 3.2: Dimensionality reduction of time information. In step 3.1, the time information is one-hot encoded and expanded to high dimensions, but this will make the time information sparse and reduce the efficiency of model training. Therefore, before being input into the subsequent network, it needs to pass through a fully connected layer (embedding layer) to reduce the high-dimensional time vector to t (hyperparameter) dimensions, where t = d + m + y (d, m, y are the hyperparameters corresponding to day, month, and year, respectively).

[0079] Step 4: Local importance weighting factor data acquisition. Referring to Figure 2 , the specific steps are as follows:

[0080] Step 4.1: Factor importance scoring. The x factor data obtained in step 1 is passed through a fully connected layer and then through a Sigmoid activation function to obtain the importance score of each factor. This scoring mechanism is learned by the network adaptively, rather than being set by humans.

[0081] Step 4.2: Factor data weighting. In step 4.1, the importance score of each factor for each sample is obtained, which is the weight of the factor data. Multiplying the score by the factor data gives the weighted factor data, which is then input into the subsequent network.

[0082] Step 5: Constructing a DEM-weighted spatio-temporal fully connected residual neural network. The network structure is shown in Figure 3The spatial feature vector best reflecting the distribution mode of PM2.5 in the research area is obtained from step 2, and then the local importance weighted factor data obtained in step 4 and the time information data obtained in step 3 are combined as the input of the DEM weighted spatio-temporal full connection residual neural network, and the dimension is s+x+t. The DEM weighted spatio-temporal full connection residual neural network includes an input layer, a full connection neural network with symmetric number of neurons before and after, and an output layer; wherein the input layer only includes a full connection layer and a BN layer, each layer of the full connection neural network includes a full connection layer, a BN (Batch normalization) and a ReLU function, the output results of the front several layers are connected to the full connection layer with the same number of neurons behind, the output layer is directly output after a full connection layer, and finally the output is the estimated value of PM2.5. Figure 3 The numbers below the full connection layer represent the number of neurons.

[0083] Step 6: model training. After the model is built, the total number of training rounds epoch and the learning rate lr are set. The data set obtained in 1.2 is used as the sample data for training, and in order to obtain the global optimal solution, the training sample data is divided into multiple batches batch to speed up the convergence speed, then the estimated value of PM2.5 is obtained through forward propagation in the output layer, and then the global loss is calculated according to the estimated value and the true value by using the loss function. The formula of the loss function is:

[0084]

[0085] Where y i is the estimated value, is the true value, N is the number of training samples, w i is the elevation weight of the sample, and the specific formula is:

[0086]

[0087] Where k is a hyperparameter, DEM i is the elevation of the sample, DEM min is the minimum elevation of all samples, and DEM max is the maximum elevation of all samples. By weighting the loss, the loss of the station at higher altitude is amplified, and in order to reduce the loss, the network will be trained in the direction of reducing the loss of the station at high altitude, and will not make the fitting effect of the station at high altitude worse in order to improve the overall fitting accuracy.

[0088] Then the Adam algorithm is used to reduce the gradient for back propagation, and the parameters are continuously adjusted until the model converges.

[0089] Step 7: Model validation and accuracy evaluation. 10-fold cross-validation method was used for site cross-validation and sample cross-validation. In site cross-validation, all sample data of 9 sites were used as training set and all sample data of 1 site were used as validation set. In sample cross-validation, all sample data were divided into 10 parts, 9 parts were used as training set and 1 part was used as validation set. Then the goodness of fit (R 2 ), root mean square error (RMSE) and mean absolute error (MAE) of the obtained model were calculated, and the average of ten results was taken as the final result. Site cross-validation was used to verify the fitting accuracy of the model in the non-site area, and sample cross-validation was used to verify the overall fitting accuracy of the model. 2 The higher the R

[0090]

[0091] where y i is the observed PM2.5 concentration of site i, is the average of the observed data, is the predicted PM2.5 concentration of site i by the model, and n is the number of monitoring sites.

[0092]

[0093]

[0094] where the parameters have the same meaning as above. The smaller the RMSE and MAE, the higher the model accuracy.

[0095] Step 8: Mapping and outlier processing. The specific steps are as follows:

[0096] Step 8.1: Result mapping. The DEM weighted spatio-temporal full connection residual neural network was obtained in step 6. Then the entire study area was converted to points using the "Raster to Point" tool of ArcGIS, and then the "extract values to point" tool was used to extract each factor to the entire study area. Then the pandas library of python was used to add time information to the data table, and then the data of the entire study area was put into the network model obtained in step 6 to obtain the fitting value of the entire study area. The fitting value was converted to a raster image, i.e. PM2.5 concentration distribution map, using the "Point to Raster" tool of ArcGIS.

[0097] Step 8.2: Abnormal value processing. In the PM2.5 concentration distribution map obtained in step 8.1, a small part of the PM2.5 concentration values are negative due to errors, and there are also a small number of abnormal high PM2.5 concentration values, which need to be processed. The negative PM2.5 concentration value represents that the PM2.5 concentration at this point is low, so the PM2.5 concentration value is set to 0, and a threshold value is set for the PM2.5 concentration value. The PM2.5 concentration value exceeding the threshold value is modified to the threshold value.

[0098] In specific implementation, the method proposed in the technical scheme of the present application can be automatically run by a computer software technology, and the system device of the method, such as a computer readable storage medium storing the corresponding computer program of the technical scheme of the present application and a computer device including the running of the corresponding computer program, should also be within the protection scope of the present application.

[0099] The embodiment of the present application also provides a PM2.5 fitting system based on a DEM weighted spatio-temporal full connection residual neural network, comprising the following modules:

[0100] A data acquisition and preprocessing module is used for PM2.5 data and factor data acquisition and preprocessing, and the factor data includes remote sensing data, meteorological factors and other factors. The preprocessed factor data is extracted to a ground monitoring station to obtain a PM2.5 data set, and each record of the data set contains PM2.5 data, factor data, spatial coordinates and time data at the monitoring station.

[0101] A spatial feature vector extraction module is used for extracting a spatial feature vector containing spatial data.

[0102] A time coding module is used for coding and dimensionality reduction of time data.

[0103] A factor data weighting module is used for obtaining locally important weighted factor data. The importance of the factor data is scored to obtain locally important weighted data of each factor. The selected influence factors are first passed through an adaptive attention layer to obtain the importance score of each influence factor, and then the importance score is multiplied by the influence factor to obtain the locally important weighted factor data.

[0104] The network model construction module is configured to construct a DEM-weighted spatio-temporal full-connection residual neural network, and the DEM-weighted spatio-temporal full-connection residual neural network is used as input by splicing the spatial feature vector in the spatial feature vector extraction module, the time data in the time encoding module and the factor data in the factor data weighting module; the DEM-weighted spatio-temporal full-connection residual neural network comprises an input layer, a full-connection neural network with symmetric neuron numbers in front and back, and an output layer; wherein the input layer only comprises a full-connection layer and a BN layer, each layer of the full-connection neural network comprises a full-connection layer, a BN and a ReLU function, the output results of the front several layers are jump-connected to the full-connection layer with the same neuron number in back, the output layer directly outputs the results after a full-connection layer, and finally the output is an estimated value of PM2.5.

[0105] The model training module is configured to set the total number of training rounds and the learning rate after the model is constructed, obtain the estimated value of PM2.5 in the output layer through forward propagation, calculate the global loss according to the estimated value and the real value by using a loss function, reduce the gradient by using an Adam algorithm for back propagation, and continuously adjust the parameters until the model converges.

[0106] The specific implementation modes of the modules correspond to the steps, and the application will not be described.

[0107] It should be understood that the above description of the preferred embodiments of the application is more detailed, but it should not be considered as a limitation on the scope of patent protection of the application. Those skilled in the art can make substitutions or modifications within the scope of protection of the claims of the application under the inspiration of the application, and all fall within the scope of protection of the application. The scope of protection of the application is subject to the appended claims.

Claims

1. A PM2.5 fitting method based on DEM weighted spatio-temporal full connection residual neural network, characterized in that, Comprising the following steps: Step 1, PM2.5 data and factor data acquisition and preprocessing, factor data including remote sensing data, meteorological factors and other factors; The preprocessed factor data is extracted to the ground monitoring station to obtain a PM2.5 data set, each record of which contains PM2.5 data, factor data, spatial coordinates and time data at the monitoring station; Step 2, extract spatial feature vectors containing spatial data; The specific implementation of step 2 is as follows: Step 2.1, Constructing the spatial weight matrix For the coordinates of the ground stations after the re-projection, the spatial relationship is converted into weight values based on the Gaussian kernel function, and a spatial adjacency matrix is constructed. The specific formula is as follows: where i, j represent position point i and position point j respectively, indicates the adjacency between position points i and j, located the i-th row and the j-th column of the matrix, indicates the distance between position points i and j, r represents the maximum distance in the minimum spanning tree of all stations; Step 2.2, center the spatial adjacency matrix and calculate the eigenvalue and eigenvector; the spatial adjacency matrix obtained from step 2.1 is subjected to matrix centering operation, and the centering formula is as follows: Where I is an n-dimensional identity matrix. It is an n×n matrix, where all elements are equal to 1, and n is the number of monitoring stations in the study area; The original spatial weight matrix obtained in step 2.1 is then solved. eigenvalues ​​and eigenvectors ; Then the eigenvectors are preliminarily screened; the spatial eigenvectors whose eigenvalues are greater than 0 and meet the following empirical model requirements are preliminarily screened out: wherein denotes the characteristic value to be screened, denotes the largest characteristic value; Step 2.3, further screening of spatial eigenvectors; using stepwise method, the eigenvectors are added to the regression equation one by one according to the size of the eigenvalue, and the eigenvector that makes the AIC value of the regression equation minimum is selected until the AIC index does not decrease by continuing to add the eigenvectors; Step 2.4, construct a screening layer; the spatial eigenvectors obtained in step 2.3 are first subjected to a full connection layer, which plays a filtering role, and from the current n spatial eigenvectors, s eigenvectors that are most suitable for the spatial autocorrelation characteristics of the study area are filtered out; Step 3, encode and reduce the dimension of the time data; Step 4, obtain local importance weighted factor data; score the importance of the factor data to obtain local importance weighted data of each factor, and the selected influence factors are first subjected to an adaptive attention layer to obtain the importance score of each influence factor, and then the importance score is multiplied by the influence factor to obtain the factor data after local importance weighting; Step 5, construct a DEM weighted spatio-temporal full connection residual neural network, and splice the spatial eigenvectors in step 2, the time data in step 3 and the factor data in step 4 as input; the DEM weighted spatio-temporal full connection residual neural network comprises an input layer, a full connection neural network with symmetric number of neurons in front and back, and an output layer; wherein the input layer only includes a full connection layer and a BN layer, each layer of the full connection neural network includes a full connection layer, a BN and a ReLU function, the output results of the front several layers are connected to the full connection layer with the same number of neurons in the back, the output layer directly outputs the results after a full connection layer, and finally outputs the estimated value of PM2.5; Step 6, after the model is constructed, set the total number of training rounds and the learning rate, obtain the estimated value of PM2.5 in the output layer through forward propagation, then calculate the global loss according to the estimated value and the true value by using the loss function, then reduce the gradient by using the Adam algorithm for back propagation, and continuously adjust the parameters until the model converges.

2. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 1, wherein: In step 1, the remote sensing data includes AOD and NDVI, the meteorological factors include air temperature, air pressure, relative humidity, planetary boundary layer height, wind direction and wind speed, and the other factors include vegetation coverage, land use status, population density, elevation, factory and road distribution density.

3. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 2, characterized in that: The preprocessing includes unifying the time resolution of all factor data to the same time resolution as the PM2.5 data; making the spatial resolution of the remaining factors except AOD data consistent with AOD data through resampling or spatial interpolation; obtaining factory data and road network data as point data and line data respectively, converting them into raster images covering the entire study area by calculating kernel density, and projecting the PM2.5 monitoring site coordinates from spherical coordinates to plane coordinates before calculating the kernel density, with the spatial reference system consistent with AOD, then using the "Extract multivalues to points" tool in ArcGIS to extract the processed factor data to the ground monitoring site to obtain the PM2.5 data set.

4. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 1, characterized in that: In step 3, the year, month and day of the PM2.5 data obtained by the site are encoded using one-hot encoding, expanding from one dimension to n dimensions, where n is the time span of the data used, and then reduced to t dimensions through a fully connected layer, where t is a hyperparameter set manually according to the training results.

5. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 1, characterized in that: In step 4, the factor data obtained in step 1 is passed through a fully connected layer and then through a Sigmoid activation function to obtain the importance score of each factor.

6. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 1, characterized in that: In step 6, the data set obtained in step 1 is used as training sample data, and the training sample data is divided into multiple batches, then trained using global loss, and the formula for global loss is: wherein is an estimated value, is a true value, and N is the number of training samples, is an elevation weight of the sample, and the specific formula is: where k is a hyperparameter, is the elevation at the sample, is the minimum elevation among all samples, is the maximum elevation among all samples.

7. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 1, characterized in that: Also included is step 7, model verification and accuracy evaluation, using 10-fold cross-validation method, respectively, site cross-validation and sample cross-validation; site cross-validation is divided into 10 sites, of which 9 sites are all sample data as training set, a site of all sample data as validation set; sample cross-validation is divided into 10 samples, of which 9 are training set, 1 is validation set; then calculate the fitting goodness R 2 , root mean square error RMSE and mean absolute error MAE of the resulting model training set and validation set, taking the average of ten results as the final result; wherein the calculation formula of R 2 is as follows: wherein is the PM2.5 concentration observation value of site i, is the average value of observation data, is the PM2.5 concentration of site i predicted by the model, and n is the number of monitoring sites. 。 8. The PM2.5 fitting method based on DEM weighted spatio-temporal fully connected residual neural network according to claim 1, characterized in that: Step 8, result mapping and outlier processing, the specific steps are as follows: Step 8.1, result mapping, the trained DEM weighted spatio-temporal fully connected residual neural network is obtained in step 6, then the entire study area is converted to points using the "Raster to Point" tool in ArcGIS, then the "extract values to point" tool is used to extract each factor to the entire study area, and the pandas library in python is used to add time information to the data table, then the data of the entire study area is input into the network model obtained in step 6 to obtain the fitting value of the entire study area, and the "Point to Raster" tool in ArcGIS is used to convert the fitting value to a raster image, i.e. the PM2.5 concentration distribution map; Step 8.2, outlier processing, for the obtained PM2.5 concentration distribution map, set the negative PM2.5 concentration value to 0, and set a threshold for the PM2.5 concentration value, and modify the PM2.5 concentration value exceeding the threshold to the threshold.

9. A DEM-weighted spatio-temporal fully connected residual neural network-based PM2.5 fitting system for implementing the DEM-weighted spatio-temporal fully connected residual neural network-based PM2.5 fitting method according to any one of claims 1-8, characterized in that, The following modules are included: A data acquisition and preprocessing module for PM2.5 data and factor data acquisition and preprocessing, factor data including remote sensing data, meteorological factors and other factors; the factor data after preprocessing is extracted to the ground monitoring site to obtain the PM2.5 data set, which contains PM2.5 data, factor data, spatial coordinates and time data at the monitoring site; A spatial feature vector extraction module for extracting spatial feature vectors containing spatial data; A time coding module is configured to code and reduce dimensions of time data; The factor data weighting module is configured to obtain locally important weighted factor data by scoring importance of factor data; the selected influence factors are first passed through an adaptive attention layer to obtain importance scores of the influence factors, and then the importance scores are multiplied by the influence factors to obtain the locally important weighted factor data; The network model construction module is configured to construct a DEM weighted spatio-temporal fully connected residual neural network, and concatenate the spatial feature vectors in the spatial feature vector extraction module, the time data in the time coding module and the factor data in the factor data weighting module as inputs; the DEM weighted spatio-temporal fully connected residual neural network comprises an input layer, a fully connected neural network with symmetric numbers of front and rear neurons, and an output layer; wherein the input layer only comprises a fully connected layer and a BN layer, each layer of the fully connected neural network comprises a fully connected layer, a BN and a ReLU function, the output results of the front several layers are connected to the fully connected layer with the same number of neurons, the output layer directly outputs the results after passing through a fully connected layer, and finally outputs the estimated value of PM2.5; The model training module is configured to set the total number of training rounds and the learning rate after the model is constructed, obtain the estimated value of PM2.5 at the output layer through forward propagation, calculate the global loss according to the estimated value and the true value by using a loss function, reduce the gradient by using an Adam algorithm for back propagation, and continuously adjust the parameters until the model converges.

Images