Spatiotemporal interpolation method of PM2.5 data based on spatiotemporal Kriging neural network

Abstract

The present invention provides a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal kriging neural network, which belongs to the field of data processing technology. The method specifically includes the following steps: collecting spatiotemporal monitoring point data; dividing the spatiotemporal sampling point and unsampled point sets according to PM2.5 concentration; mapping the attributes of the spatiotemporal monitoring points to a high-dimensional space to obtain an attribute representation vector; mapping time and space information to a high-dimensional space to obtain a time and space representation vector; designing a spatiotemporal covariance network based on the attributes, time and space representation vectors to fit the covariance matrix of the sampling points and the unsampled points; designing a spatiotemporal trend element network to fit the non-stationary spatiotemporal trend relationship to obtain a trend feature matrix of the spatiotemporal sampling points and the unsampled points; estimating the PM2.5 concentration of the unsampled points using the spatiotemporal kriging equation based on the covariance matrix and the trend feature matrix; and optimizing the model and implementing data interpolation prediction. The present invention improves interpolation accuracy.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of data processing technology, and in particular to a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal Kriging neural network. Background Art

[0002] Currently, due to the limitations of various objective factors such as construction costs and environmental conditions, the spatiotemporal monitoring data from air quality monitoring stations are sparse and non-uniformly distributed in time and space. Existing mainstream spatiotemporal data interpolation methods expand on the spatial interpolation methods based on the above spatiotemporal properties and can be divided into two categories: deterministic spatiotemporal interpolation and geostatistical spatiotemporal interpolation. Deterministic spatiotemporal interpolation methods use mathematical geometric functions of a predetermined form to fit the internal correlations of the data based on the numerical attributes of the spatiotemporal data, and estimate the attribute values ​​of unsampled points in time and space. These methods include spatiotemporal inverse distance weighting, radial basis function method, trend surface method, etc. For example, the trend surface method uses polynomial regression to fit the spatiotemporal sampling point data to a spatiotemporal trend surface function, thereby estimating the attribute values ​​of any unsampled points in time and space. Geostatistical spatiotemporal interpolation treats data attributes as random variables under a spatiotemporal random process. Based on the assumption of second-order stationarity, it couples temporal and spatial covariance functions to establish a spatiotemporal covariance function to express spatiotemporal dependencies. This allows for optimal linear unbiased estimation of the spatiotemporal attribute values ​​of unsampled points. Typical methods include spatiotemporal ordinary kriging and spatiotemporal simple kriging. Based on this, improved methods such as spatiotemporal cokriging and spatiotemporal universal kriging have been introduced into PM2.5 spatiotemporal interpolation to capture multivariate spatiotemporal dependencies and trends, taking into account the influence of multiple factors and the presence of spatiotemporal trends. However, these methods all rely on certain expert prior knowledge and assumptions, such as predefined functional forms and linear relationship assumptions. These methods struggle to cope with the complex nonlinear and nonstationary spatiotemporal evolution of PM2.5, leading to suboptimal interpolation accuracy.

[0003] It can be seen that there is an urgent need for a spatiotemporal interpolation method for PM2.5 data based on spatiotemporal Kriging neural network with high interpolation accuracy. Summary of the Invention

[0004] In view of this, an embodiment of the present invention provides a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal Kriging neural network, which at least partially solves the problem of poor interpolation accuracy in the prior art.

[0005] The embodiment of the present invention provides a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal Kriging neural network, comprising:

[0006] Step 1: Collect the total air quality monitoring stations in the study area within the preset time range. spatiotemporal monitoring point data, wherein each spatiotemporal monitoring point data includes its corresponding spatial information, time information and attribute characteristics;

[0007] Step 2: According to the PM2.5 concentration monitoring value in the attribute characteristics, The data of each spatiotemporal monitoring point are divided into a spatiotemporal sampling point set and a spatiotemporal unsampled point set;

[0008] Step 3: Design an attribute representation encoder consisting of two network hidden layers to map the attribute features of all spatiotemporal monitoring points into a high-dimensional latent space to obtain an attribute representation vector.

[0009] Step 4: Design a temporal representation encoder and a spatial representation encoder to map temporal information and spatial information into a high-dimensional latent space to obtain a temporal representation vector and a spatial representation vector.

[0010] Step 5: Based on the attribute representation vector, the time representation vector, and the space representation vector, a spatiotemporal covariance network is designed to fit a first spatiotemporal covariance matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal covariance matrix corresponding to the spatiotemporal unsampled point set;

[0011] Step 6: Based on the time characterization vector and the space characterization vector, a spatiotemporal trend element network is designed to fit the non-stationary spatiotemporal trend relationship, thereby obtaining a first spatiotemporal trend feature matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal trend feature matrix corresponding to the spatiotemporal unsampled point set;

[0012] Step 7, based on the first spatiotemporal covariance matrix, the second spatiotemporal covariance matrix, the first spatiotemporal trend characteristic matrix, and the second spatiotemporal trend characteristic matrix, calculate the estimated PM2.5 concentration of the spatiotemporal unsampled points according to the spatiotemporal Kriging equation based on geostatistical theory;

[0013] Step 8: Divide the spatiotemporal sampling point set into a training set and a validation set according to a preset ratio, calculate the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, and update the learnable parameters in the model through a cyclic iteration with the goal of minimizing the error. When the model achieves the minimum interpolation error in the validation set, the target model is obtained to interpolate the data to be processed.

[0014] According to a specific implementation of the embodiment of the present invention, step 2 specifically includes:

[0015] Determine attribute characteristics Whether the PM2.5 concentration monitoring value in is null, if the attribute feature If the PM2.5 concentration monitoring value is not null, the time and space monitoring point Include the spatiotemporal sampling point set SP, otherwise include the spatiotemporal unsampled point set UP, and set the corresponding PM2.5 concentration value to 0, where the number of spatiotemporal sampling points and spatiotemporal unsampled points are and ,and .

[0016] According to a specific implementation of the embodiment of the present invention, step 4 specifically includes:

[0017] Step 4.1, based on spatiotemporal monitoring points Time information , calculate the time representation sub-direction by sine and cosine functions :

[0018] ;

[0019] in, ;

[0020] Step 4.2: Concatenate all time representation sub-vectors , and get the time representation vector :

[0021] ;

[0022] in, Represents the vector concatenation operator;

[0023] Step 4.3, based on spatiotemporal monitoring points Spatial information , by calculating the corresponding spatial representation subvector through different combinations of sine and cosine functions :

[0024] ;

[0025] in, ;

[0026] Step 4.4, concatenate all spatial representation sub-vectors , and obtain the spatial representation vector :

[0027] ;

[0028] in, Represents the vector concatenation operator.

[0029] According to a specific implementation of the embodiment of the present invention, step 5 specifically includes:

[0030] Step 5.1: Characterize the attribute vectors of all spatiotemporal monitoring points , time representation vector and spatial representation vector , projected to the temporal query space and spatial query space respectively, and obtain the corresponding temporal query vector With spatial query vector :

[0031] ;

[0032] ;

[0033] in, are the network learnable parameters, represents the vector concatenation operator, Represents the weight of the time and space representation vector, which is used to control the importance of the time and space dependence in the space-time covariance;

[0034] Step 5.2: The attribute representation vector of the spatiotemporal sampling point set , time representation vector and spatial representation vector , projected into the time key space and space key space respectively, and obtain the corresponding time key vector With spatial key vector :

[0035] ;

[0036] ;

[0037] in, are the network learnable parameters;

[0038] Step 5.3, calculate the time query vector With all time key vectors Similarity in high-dimensional space, expressing the time covariance relationship, and obtaining spatiotemporal monitoring points and the temporal covariance vector between all spatiotemporal sampling points :

[0039] ;

[0040] Step 5.4, calculate the spatial query vector With all spatial key vectors Similarity in high-dimensional space, expressing spatial covariance relationship, and obtaining spatiotemporal monitoring points and the spatial covariance vector between all spatiotemporal sampling points :

[0041] ;

[0042] Step 5.5, based on spatiotemporal monitoring points The time covariance vector of and the spatial covariance vector , adaptive mapping is performed through three network layers to obtain the spatiotemporal covariance weights :

[0043] ;

[0044] in, is the network learnable parameter, spatiotemporal covariance weight Contains three weighted weight values, namely ;

[0045] Step 5.6, combine spatiotemporal covariance weighting , time covariance vector and the spatial covariance vector , get the spatiotemporal monitoring points The spatiotemporal covariance vector of :

[0046] ;

[0047] in, represents the Hadamard product;

[0048] Step 5.7, extract the spatiotemporal covariance vector belonging to the set of spatiotemporal unsampled points, and construct the second spatiotemporal covariance matrix corresponding to the unsampled points , and at the same time extract the spatiotemporal covariance vector belonging to the spatiotemporal sampling point set, and construct the first spatiotemporal covariance matrix corresponding to the spatiotemporal sampling point set , and the first spatiotemporal covariance matrix The diagonal elements of are set to 0.

[0049] According to a specific implementation of the embodiment of the present invention, step 6 specifically includes:

[0050] Step 6.1: transform the spatial representation vector of each spatiotemporal monitoring point into and time representation vector As meta-knowledge, the spatiotemporal trend mapping weights are obtained through the meta-learner :

[0051] ;

[0052] ;

[0053] in, represents the learnable parameters of the meta-learner;

[0054] Step 6.2: Based on the spatiotemporal trend mapping weight, each spatiotemporal monitoring point Time and space position Mapped into spatiotemporal trend feature vector :

[0055] ;

[0056] in, is the spatiotemporal trend mapping weight obtained in step 6.1, Indicates the dimension of the spatiotemporal trend feature vector;

[0057] Step 6.3: Extract the spatiotemporal trend vectors of the spatiotemporal sampling point set and the spatiotemporal unsampled point set respectively to form the first spatiotemporal trend feature matrix corresponding to the spatiotemporal sampling point set. , and the second spatiotemporal trend characteristic matrix corresponding to the spatiotemporal unsampled point set .

[0058] According to a specific implementation of the embodiment of the present invention, step 7 specifically includes:

[0059] Step 7.1, for each unsampled point in time and space Construct the space-time Kriging equation and solve the space-time interpolation weights corresponding to the unsampled points in the space-time :

[0060] ;

[0061] in, is the Lagrange term coefficient, represents the second spatiotemporal covariance matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding space-time covariance vector; Represents the second spatiotemporal trend characteristic matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding spatiotemporal trend eigenvector;

[0062] Step 7.2, according to the spatiotemporal interpolation weight , a vector consisting of PM2.5 concentration monitoring values ​​at all spatiotemporal sampling points , calculate the unsampled points in time and space Estimated PM2.5 concentration :

[0063] .

[0064] According to a specific implementation of the embodiment of the present invention, step 8 specifically includes:

[0065] Step 8.1, calculate the root mean square error (RMS) as the loss function for model training based on the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, where the expression of the loss function is:

[0066] ;

[0067] in, Indicates the PM2.5 concentration monitoring value, represents the number of spatiotemporal monitoring points in the training set;

[0068] Step 8.2, use the back propagation algorithm to calculate the loss each time All learnable parameters in the model are passed to it, and the Adam optimization strategy is used to iteratively update each learnable parameter based on the gradient of the returned loss until the model reaches the minimum interpolation error in the validation set, and the target model is obtained;

[0069] In step 8.3, the target model is used to interpolate the data to be processed.

[0070] The spatiotemporal interpolation scheme of PM2.5 data based on spatiotemporal Kriging neural network in the embodiment of the present invention includes: step 1, collecting the total PM2.5 data from air quality monitoring stations in the study area within a preset time range. spatiotemporal monitoring point data, wherein each spatiotemporal monitoring point data includes its corresponding spatial information, time information and attribute characteristics; step 2, according to the PM2.5 concentration monitoring value in the attribute characteristics, The data of each spatiotemporal monitoring point are divided into a set of spatiotemporal sampling points and a set of spatiotemporal unsampled points; Step 3, an attribute representation encoder including two network hidden layers is designed to map the attribute features of all spatiotemporal monitoring points to a high-dimensional latent space to obtain an attribute representation vector; Step 4, a time representation encoder and a space representation encoder are designed to map the time information and the spatial information to a high-dimensional latent space to obtain a time representation vector and a space representation vector; Step 5, based on the attribute representation vector, the time representation vector and the space representation vector, a spatiotemporal covariance network is designed to fit the first spatiotemporal covariance matrix corresponding to the spatiotemporal sampling point set and the second spatiotemporal covariance matrix corresponding to the spatiotemporal unsampled point set; Step 6, based on the time representation vector and the space representation vector, a spatiotemporal trend element network is designed to fit the non-stationary spatiotemporal trend relationship. system, obtaining a first spatiotemporal trend characteristic matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal trend characteristic matrix corresponding to the spatiotemporal unsampled point set; step 7, based on the first spatiotemporal covariance matrix, the second spatiotemporal covariance matrix, the first spatiotemporal trend characteristic matrix and the second spatiotemporal trend characteristic matrix, calculating the PM2.5 concentration estimation value of the spatiotemporal unsampled points according to the spatiotemporal Kriging equation based on geostatistical theory; step 8, dividing the spatiotemporal sampling point set into a training set and a validation set according to a preset ratio, calculating the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, and updating the learnable parameters in the model through a cyclic iteration method with the goal of minimizing the error. When the model achieves the minimum interpolation error in the validation set, the target model is obtained to interpolate the data to be processed.

[0071] The beneficial effects of the embodiments of the present invention are as follows: through the scheme of the present invention, a time and space representation encoder and a space-time covariance network are designed, and in a high-dimensional latent space, the space-time covariance of the potential influence of multiple factors and complex space-time dependencies is adaptively mapped to model nonlinear multivariate space-time dependencies; a space-time trend meta-network is designed, and based on the idea of ​​meta-learning, the dynamic process of the spatiotemporal evolution trend of PM2.5 is accurately captured and fitted, and non-stationary space-time trend relationships are modeled; based on the space-time kriging method, the multivariate space-time dependencies and non-stationary space-time trend relationships are comprehensively expressed, and the back-propagation process of deep learning is used to adaptively adjust the network parameters to achieve a high-precision and intelligent space-time interpolation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0073] Figure 1A schematic diagram of a process flow of a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal Kriging neural network provided by an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of a specific implementation process of a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal Kriging neural network provided by an embodiment of the present invention;

[0075] Figure 3 This is a spatial distribution diagram of average errors of different spatiotemporal interpolation methods provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0077] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0078] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present invention, those skilled in the art will appreciate that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0079] It should also be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. The illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0080] Additionally, in the following description, specific details are provided to provide a thorough understanding of the examples. However, one skilled in the art will appreciate that the aspects described can be practiced without these specific details.

[0081] Due to objective factors such as construction costs and environmental conditions, spatiotemporal data from air quality monitoring stations exhibit sparse and uneven distribution in both time and space. Therefore, designing an accurate spatiotemporal interpolation method for PM2.5 data—modeling the inherent temporal and spatial evolution of PM2.5 based on known spatiotemporal sampling point data, and thereby inferring PM2.5 concentrations at unsampled points—is crucial for achieving sustainable urban development and improving residents' well-being.

[0082] The spatiotemporal distribution of PM2.5 exhibits certain systematic characteristics during its dynamic evolution, known as spatiotemporal trends. Accurately capturing and fitting these dynamically changing spatiotemporal trends is the underlying goal of spatiotemporal interpolation models. Furthermore, because the spatiotemporal evolution of PM2.5 is influenced by confounding factors such as other atmospheric particulate matter and wind speed, it exhibits corresponding random fluctuations based on the spatiotemporal trends. Furthermore, the spatiotemporal distribution of PM2.5 exhibits spatiotemporal dependence, meaning that PM2.5 concentrations in close proximity are closer. Therefore, fitting and coupling complex multivariate spatiotemporal dependencies with spatiotemporal trends is key to guiding the design of high-precision spatiotemporal interpolation models for PM2.5 data.

[0083] Based on the above-mentioned spatiotemporal properties, existing mainstream spatiotemporal data interpolation methods extend spatial interpolation methods and can be divided into two categories: deterministic spatiotemporal interpolation and geostatistical spatiotemporal interpolation. Deterministic spatiotemporal interpolation methods use predetermined mathematical geometric functions to fit internal data correlations based on the numerical attributes of spatiotemporal data, estimating attribute values ​​at unsampled points in space and time. These methods include spatiotemporal inverse distance weighting, radial basis functions, and trend surface methods. For example, the trend surface method uses polynomial regression to fit a spatiotemporal trend surface function to the spatiotemporal sampled data points, thereby estimating the attribute values ​​of any unsampled points in space and time. Geostatistical spatiotemporal interpolation, on the other hand, treats data attributes as random variables in a spatiotemporal random process. Based on the assumption of second-order stationarity, it couples the temporal and spatial covariance functions to establish a spatiotemporal covariance function to express spatiotemporal dependencies. This allows the inference of attribute values ​​at unsampled points in space and time using the best linear unbiased estimation method. Typical methods include spatiotemporal ordinary kriging and spatiotemporal simple kriging. Based on this, improved methods such as space-time cokriging and space-time universal kriging have been introduced into PM2.5 spatiotemporal interpolation to capture the multivariate spatiotemporal dependencies and trends, taking into account the influence of multiple factors and the existence of spatiotemporal trends. However, these methods are based on certain expert prior knowledge and assumptions, such as predefined functional forms and linear relationship assumptions. These methods are difficult to handle the complex nonlinear and nonstationary spatiotemporal evolution of PM2.5, resulting in unsatisfactory interpolation accuracy.

[0084] With the rapid development of deep learning technology and its mature application across various industries in recent years, various deep learning models have been applied to address the challenge of accurate spatiotemporal interpolation of PM2.5, such as recurrent neural networks, graph neural networks, attention networks, and meta-learning networks. However, these methods often only address single challenges, such as the nonlinearity of multivariate spatiotemporal dependencies or the nonstationary nature of spatiotemporal trends. They fail to comprehensively consider both within a unified framework, resulting in insufficient information utilization and limited interpolation accuracy.

[0085] An embodiment of the present invention provides a spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal Kriging neural network, which can be applied to the air pollution prevention and control process in environmental protection scenarios.

[0086] See also Figure 1 , is a flow chart of a method for spatiotemporal interpolation of PM2.5 data based on spatiotemporal Kriging neural network provided by an embodiment of the present invention. Figure 1 and Figure 2 As shown, the method mainly includes the following steps:

[0087] Step 1: Collect the total air quality monitoring stations in the study area within the preset time range. spatiotemporal monitoring point data, wherein each spatiotemporal monitoring point data includes its corresponding spatial information, time information and attribute characteristics;

[0088] The PM2.5 data used in this implementation comes from hourly monitoring data collected from 19 air quality monitoring stations in City A from March 1 to March 7, 2021, as provided by the National Urban Air Quality Real-Time Release Platform. This data includes PM2.5 concentration values ​​as interpolation targets, as well as other relevant monitoring covariates (PM10, SO2, NO2, O3, and CO). After data cleaning, valid data from a total of 3,108 spatiotemporal monitoring points is included, which will be used to illustrate the implementation process of this invention.

[0089] When implementing, collect the research area Air quality monitoring stations within a certain time range Total spatiotemporal monitoring point data, a single spatiotemporal monitoring point Contains site spatial location information , time information , and attribute characteristics Among them, attribute features Contains multiple monitoring attributes related to PM2.5, Indicates the PM2.5 concentration monitoring value, express covariates.

[0090] Step 2: According to the PM2.5 concentration monitoring value in the attribute characteristics, The data of each spatiotemporal monitoring point are divided into a spatiotemporal sampling point set and a spatiotemporal unsampled point set;

[0091] When implementing it, you can determine whether the attribute feature is a null value. If the PM2.5 concentration monitoring value is not null, the time and space monitoring point Include the spatiotemporal sampling point set SP; otherwise, include it in the spatiotemporal non-sampling point set NP, and set the corresponding PM2.5 concentration value to 0. The number of spatiotemporal sampling points and spatiotemporal non-sampling points are and ,and .

[0092] Step 3: Design an attribute representation encoder consisting of two network hidden layers to map the attribute features of all spatiotemporal monitoring points into a high-dimensional latent space to obtain an attribute representation vector.

[0093] In the specific implementation, the attribute representation encoder with two network hidden layers is designed to Mapped to high-dimensional latent space, the attribute representation vector is obtained :

[0094] ;

[0095] in, are the network learnable parameters, is a nonlinear activation function, Indicates the dimension of the high-dimensional latent space.

[0096] Step 4: Design a temporal representation encoder and a spatial representation encoder to map temporal information and spatial information into a high-dimensional latent space to obtain a temporal representation vector and a spatial representation vector.

[0097] In specific implementation, for each spatiotemporal monitoring point Time information and spatial information , respectively design the time representation encoder and the space representation encoder, map the low-dimensional time and space information to the high-dimensional latent space, and obtain the time representation vector and spatial representation vector The main steps include:

[0098] Time information based on spatiotemporal monitoring points , the corresponding time representation subvector is calculated by sine and cosine functions :

[0099] ;

[0100] in, .

[0101] Then, concatenate all the time representation sub-vectors , and get the corresponding time representation vector :

[0102] ;

[0103] in, Represents the vector concatenation operator.

[0104] Spatial location information based on spatiotemporal monitoring points , by calculating the corresponding spatial representation subvector through different combinations of sine and cosine functions :

[0105] ;

[0106] in, .

[0107] Then, concatenate all the spatial representation sub-vectors , and get the corresponding space representation vector :

[0108] ;

[0109] in, Represents a vector concatenation operator. Based on the properties of the sine and cosine functions, the dot product of two time-representing vectors gradually decays with increasing temporal distance, thereby expressing temporal dependence. Similarly, the dot product of two spatial-representing vectors gradually decays with increasing spatial distance, thereby expressing spatial dependence.

[0110] Step 5: Based on the attribute representation vector, the time representation vector, and the space representation vector, a spatiotemporal covariance network is designed to fit a first spatiotemporal covariance matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal covariance matrix corresponding to the spatiotemporal unsampled point set;

[0111] In specific implementation, based on the attribute representation vector and the time representation vector and spatial representation vector , design the spatiotemporal covariance network, fit the spatiotemporal covariance matrix between the spatiotemporal monitoring points and the spatiotemporal sampling points: specifically including the spatiotemporal covariance matrix of the spatiotemporal sampling points , and the spatiotemporal covariance matrix of the unsampled points in space and time , including the following steps.

[0112] Extract attribute representation vectors of all spatiotemporal monitoring points , time representation vector and spatial representation vector , projected to the temporal query space and spatial query space respectively, and obtain the corresponding temporal query vector With spatial query vector , the formula is as follows:

[0113] ;

[0114] ;

[0115] in, are the network learnable parameters, represents the vector concatenation operator, Represents the weight of the time and space representation vector, which is used to control the importance of the spatiotemporal dependency in the spatiotemporal covariance.

[0116] Extract attribute representation vectors belonging to a set of spatiotemporal sampling points , time representation vector and spatial representation vector , projected into the time key space and space key space respectively, and obtain the corresponding time key vector With spatial key vector , the formula is as follows:

[0117] ;

[0118] ;

[0119] in, are the network learnable parameters.

[0120] Compute time query vector With all time key vectors Similarity in high-dimensional space, expressing the time covariance relationship, and obtaining spatiotemporal monitoring points and the temporal covariance vector between all spatiotemporal sampling points , the specific formula is as follows:

[0121] ;

[0122] Calculate spatial query vector With all spatial key vectors Similarity in high-dimensional space, expressing spatial covariance relationship, and obtaining spatiotemporal monitoring points and the spatial covariance vector between all spatiotemporal sampling points , the specific formula is as follows:

[0123] ;

[0124] Based on spatiotemporal monitoring points The time covariance vector of and the spatial covariance vector , adaptive mapping is performed through three network layers to obtain the spatiotemporal covariance weights , the specific formula is as follows:

[0125] ;

[0126] in, is the network learnable parameter, spatiotemporal covariance weight Contains three weighted weight values, namely .

[0127] Combined with spatiotemporal covariance weighting and the spatial and temporal covariance vector , get the spatiotemporal monitoring points The spatiotemporal covariance vector of :

[0128] ;

[0129] in, Represents the Hadamard product.

[0130] Extract the spatiotemporal covariance vector belonging to the set of spatiotemporal unsampled points and construct the spatiotemporal covariance matrix of the unsampled points At the same time, the spatiotemporal covariance vector belonging to the spatiotemporal sampling point set is extracted to construct the spatiotemporal covariance matrix of the sampling points Among them, in order to avoid the influence of its own information, the matrix The diagonal elements of are set to 0.

[0131] Step 6: Based on the time characterization vector and the space characterization vector, a spatiotemporal trend element network is designed to fit the non-stationary spatiotemporal trend relationship, thereby obtaining a first spatiotemporal trend feature matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal trend feature matrix corresponding to the spatiotemporal unsampled point set;

[0132] In specific implementation, based on the spatial representation vector and time representation vector , design the spatiotemporal trend element network and fit the non-stationary spatiotemporal trend relationship. The specific steps are as follows:

[0133] The spatial representation vector of each spatiotemporal monitoring point and time representation vector As meta-knowledge, the spatiotemporal trend mapping weights are obtained through the meta-learner , the specific formula is as follows:

[0134] ;

[0135] ;

[0136] in, represents the learnable parameters of the meta-learner.

[0137] Based on the spatiotemporal trend mapping weight, each spatiotemporal monitoring point Time and space position Mapped into spatiotemporal trend feature vector , the calculation formula is as follows:

[0138] ;

[0139] in, is the spatiotemporal trend mapping weight obtained in step 6.1, Indicates the dimension of the spatiotemporal trend feature vector.

[0140] Extract the spatiotemporal trend vectors of the spatiotemporal sampling points and the unsampled points respectively to form the spatiotemporal trend feature matrix of the unsampled points , and the spatiotemporal trend characteristic matrix of the sampling points .

[0141] Step 7, based on the first spatiotemporal covariance matrix, the second spatiotemporal covariance matrix, the first spatiotemporal trend characteristic matrix, and the second spatiotemporal trend characteristic matrix, calculate the estimated PM2.5 concentration of the spatiotemporal unsampled points according to the spatiotemporal Kriging equation based on geostatistical theory;

[0142] In specific implementation, based on the spatiotemporal covariance matrix and spatiotemporal trend characteristic matrix According to the space-time Kriging equation based on geostatistical theory, the above two types of space-time relationships are combined to calculate the estimated PM2.5 concentration at the unsampled points in space and time. , including the following steps.

[0143] For each unsampled point in space and time Construct the space-time Kriging equation and solve the space-time interpolation weights corresponding to the unsampled points in the space-time , the specific formula is:

[0144] ;

[0145] in, is the Lagrange term coefficient, represents the spatiotemporal covariance matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding space-time covariance vector; Representing the spatiotemporal trend characteristic matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding spatiotemporal trend feature vector.

[0146] According to the spatiotemporal interpolation weight , a vector consisting of PM2.5 concentration values ​​at all spatiotemporal sampling points , calculate the unsampled points in time and space Estimated PM2.5 concentration :

[0147] .

[0148] Step 8: Divide the spatiotemporal sampling point set into a training set and a validation set according to a preset ratio, calculate the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, and update the learnable parameters in the model through a cyclic iteration with the goal of minimizing the error. When the model achieves the minimum interpolation error in the validation set, the target model is obtained to interpolate the data to be processed.

[0149] In the specific implementation, 80% of the spatiotemporal sampling points are used as the training set, and the remaining 20% ​​are used as the validation set. The true value of PM2.5 concentration in the training set is calculated. and model estimates The error between them is minimized, and the goal is to minimize the error. This is done by continuously updating the learnable parameters in the model through iterative cycles, ultimately achieving the minimum interpolation error in the validation set. This involves the following steps:

[0150] The root mean square error is used as the model training loss function. The specific formula is:

[0151] ;

[0152] in, and Represent the model estimated value and true value of PM2.5 concentration in the training set, Represents the number of spatiotemporal monitoring points in the training set.

[0153] Use the back propagation algorithm to calculate the loss each time All learnable parameters in the model are passed to it, and the Adam optimization strategy is used to iteratively update each learnable parameter based on the gradient of the returned loss until the model reaches the lowest interpolation error in the validation set.

[0154] Finally, the trained target model can be used for actual high-precision spatiotemporal interpolation applications.

[0155] The effectiveness of the proposed method was tested by comparing it with several existing spatiotemporal interpolation methods. The selected comparison methods included: space-time inverse distance weighting (STIDW), space-time ordinary kriging (STOK), and geographic-temporal neural network weighted regression (GTNNWR).

[0156] 60% of all spatiotemporal monitoring points in the dataset were randomly selected as the spatiotemporal unsampled point set, and the rest were included in the spatiotemporal sampled point set. Model construction and training were performed based on the spatiotemporal sampled point set to estimate the PM2.5 concentration values ​​of the spatiotemporal unsampled points. Multiple accuracy evaluation indicators were used to quantitatively evaluate the spatiotemporal interpolation results, including ① mean absolute error (MAE); ② root mean square error (RMSE); and ③ mean absolute percentage error (MAPE). The calculation formula is as follows:

[0157] ;

[0158] ;

[0159] ;

[0160] in, and Respectively represent The actual value of PM2.5 concentration at the unsampled points in time and space and the model estimated value, Indicates the number of unsampled points in space and time. For the above three evaluation indicators, the smaller the value of the indicator, the higher the accuracy of the space-time interpolation method.

[0161] Table 1 shows the accuracy comparison results of the proposed method and the comparative method on the PM2.5 dataset. It can be found that the proposed method outperforms the comparative method in all three evaluation indicators, indicating that the proposed method achieves the best accuracy performance overall.

[0162] Table 1

[0163] ;

[0164] Based on the interpolation results of the method of the present invention and the comparative method, the absolute values ​​of the PM2.5 spatiotemporal interpolation errors are averaged according to the spatial positions of the unsampled points in time and space, and spatial visualization is performed, such as Figure 3 As shown in the figure, (a) represents the method of the present invention, and (b), (c), and (d) are existing comparison methods. It can be seen that the average spatial error of the method of the present invention is relatively smaller and more evenly distributed than that of the comparison methods, indicating that the method of the present invention can effectively improve the stability of spatiotemporal interpolation.

[0165] The spatiotemporal interpolation method for PM2.5 data based on a spatiotemporal kriging neural network provided in this embodiment adaptively maps the spatiotemporal covariance of the potential impacts of coupled multiple factors and complex spatiotemporal dependencies in a high-dimensional latent space by designing a time and space representation encoder and a spatiotemporal covariance network, thereby modeling nonlinear multivariate spatiotemporal dependencies. A spatiotemporal trend meta-network is designed to accurately capture and fit the dynamic process of the spatiotemporal evolution trend of PM2.5 based on the idea of ​​meta-learning, thereby modeling non-stationary spatiotemporal trend relationships. Based on the spatiotemporal kriging method, the multivariate spatiotemporal dependencies and non-stationary spatiotemporal trend relationships are comprehensively expressed, and the network parameters are adaptively adjusted using the back-propagation process of deep learning to achieve a high-precision and intelligent spatiotemporal interpolation process.

[0166] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware or a combination thereof.

[0167] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A spatiotemporal interpolation method for PM2.5 data based on spatiotemporal Kriging neural network, characterized in that: include: Step 1: Collect the total air quality monitoring stations in the study area within the preset time range. spatiotemporal monitoring point data, wherein each spatiotemporal monitoring point data includes its corresponding spatial information, time information and attribute characteristics; Step 2: According to the PM2.5 concentration monitoring value in the attribute characteristics, The data of each spatiotemporal monitoring point are divided into a spatiotemporal sampling point set and a spatiotemporal unsampled point set; Step 3: Design an attribute representation encoder consisting of two network hidden layers to map the attribute features of all spatiotemporal monitoring points into a high-dimensional latent space to obtain an attribute representation vector. Step 4: Design a temporal representation encoder and a spatial representation encoder to map temporal information and spatial information into a high-dimensional latent space to obtain a temporal representation vector and a spatial representation vector. Step 5: Based on the attribute representation vector, the time representation vector, and the space representation vector, a spatiotemporal covariance network is designed to fit a first spatiotemporal covariance matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal covariance matrix corresponding to the spatiotemporal unsampled point set; Step 6: Based on the time characterization vector and the space characterization vector, a spatiotemporal trend element network is designed to fit the non-stationary spatiotemporal trend relationship, thereby obtaining a first spatiotemporal trend feature matrix corresponding to the spatiotemporal sampling point set and a second spatiotemporal trend feature matrix corresponding to the spatiotemporal unsampled point set; Step 7, based on the first spatiotemporal covariance matrix, the second spatiotemporal covariance matrix, the first spatiotemporal trend characteristic matrix, and the second spatiotemporal trend characteristic matrix, calculate the estimated PM2.5 concentration of the spatiotemporal unsampled points according to the spatiotemporal Kriging equation based on geostatistical theory; Step 8: Divide the spatiotemporal sampling point set into a training set and a validation set according to a preset ratio, calculate the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, and update the learnable parameters in the model through a cyclic iteration with the goal of minimizing the error. When the model achieves the minimum interpolation error in the validation set, the target model is obtained to interpolate the data to be processed.

2. The method according to claim 1, characterized in that The step 2 specifically includes: Determine attribute characteristics Whether the PM2.5 concentration monitoring value in is null, if the attribute feature If the PM2.5 concentration monitoring value is not null, the time and space monitoring point Include the spatiotemporal sampling point set SP, otherwise include the spatiotemporal unsampled point set UP, and set the corresponding PM2.5 concentration value to 0, where the number of spatiotemporal sampling points and spatiotemporal unsampled points are and ,and .

3. The method according to claim 2, characterized in that The step 4 specifically includes: Step 4.1, based on spatiotemporal monitoring points Time information , calculate the time representation subvector by sine and cosine functions : in, ; Step 4.2: Concatenate all time representation sub-vectors , and get the time representation vector : in, Represents the vector concatenation operator; Step 4.3, based on spatiotemporal monitoring points Spatial information , by calculating the corresponding spatial representation subvector through different combinations of sine and cosine functions : in, ; Step 4.4, concatenate all spatial representation sub-vectors , and obtain the spatial representation vector : in, Represents the vector concatenation operator.

4. The method according to claim 3, characterized in that The step 5 specifically includes: Step 5.1: Characterize the attribute vectors of all spatiotemporal monitoring points , time representation vector and spatial representation vector , projected to the temporal query space and spatial query space respectively, and obtain the corresponding temporal query vector With spatial query vector : in, are the network learnable parameters, represents the vector concatenation operator, Represents the weight of the time and space representation vector, which is used to control the importance of the time and space dependence in the space-time covariance; Step 5.2: The attribute representation vector of the spatiotemporal sampling point set , time representation vector and spatial representation vector , projected into the time key space and space key space respectively, and obtain the corresponding time key vector With spatial key vector : in, are the network learnable parameters; Step 5.3, calculate the time query vector With all time key vectors Similarity in high-dimensional space, expressing the time covariance relationship, and obtaining spatiotemporal monitoring points and the temporal covariance vector between all spatiotemporal sampling points : ； Step 5.4, calculate the spatial query vector With all spatial key vectors Similarity in high-dimensional space, expressing spatial covariance relationship, and obtaining spatiotemporal monitoring points and the spatial covariance vector between all spatiotemporal sampling points : ； Step 5.5, based on spatiotemporal monitoring points The time covariance vector of and the spatial covariance vector , adaptive mapping is performed through three network layers to obtain the spatiotemporal covariance weights : in, is the network learnable parameter, spatiotemporal covariance weight Contains three weighted weight values, namely ; Step 5.6, combine spatiotemporal covariance weighting , time covariance vector and the spatial covariance vector , get the spatiotemporal monitoring points The spatiotemporal covariance vector of : in, represents the Hadamard product; Step 5.7, extract the spatiotemporal covariance vector belonging to the set of spatiotemporal unsampled points, and construct the second spatiotemporal covariance matrix corresponding to the unsampled points , and at the same time extract the spatiotemporal covariance vector belonging to the spatiotemporal sampling point set, and construct the first spatiotemporal covariance matrix corresponding to the spatiotemporal sampling point set , and the first spatiotemporal covariance matrix The diagonal elements of are set to 0.

5. The method according to claim 4, characterized in that The step 6 specifically includes: Step 6.1: transform the spatial representation vector of each spatiotemporal monitoring point into and time representation vector As meta-knowledge, the spatiotemporal trend mapping weights are obtained through the meta-learner : in, represents the learnable parameters of the meta-learner; Step 6.2: Based on the spatiotemporal trend mapping weight, each spatiotemporal monitoring point Time and space position Mapped into spatiotemporal trend feature vector : in, is the spatiotemporal trend mapping weight obtained in step 6.1, Indicates the dimension of the spatiotemporal trend feature vector; Step 6.3: Extract the spatiotemporal trend vectors of the spatiotemporal sampling point set and the spatiotemporal unsampled point set respectively to form the first spatiotemporal trend feature matrix corresponding to the spatiotemporal sampling point set. , and the second spatiotemporal trend characteristic matrix corresponding to the spatiotemporal unsampled point set .

6. The method according to claim 5, characterized in that The step 7 specifically includes: Step 7.1, for each unsampled point in time and space Construct the space-time Kriging equation and solve the space-time interpolation weights corresponding to the unsampled points in the space-time : in, is the Lagrange term coefficient, represents the second spatiotemporal covariance matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding space-time covariance vector; Represents the second spatiotemporal trend characteristic matrix Middle A vector of row elements, i.e., unsampled points in time and space The corresponding spatiotemporal trend eigenvector; Step 7.2, according to the spatiotemporal interpolation weight , a vector consisting of PM2.5 concentration monitoring values ​​at all spatiotemporal sampling points , calculate the unsampled points in time and space Estimated PM2.5 concentration : 。 7. The method according to claim 6, characterized in that The step 8 specifically includes: Step 8.1, calculate the root mean square error (RMS) as the loss function for model training based on the error between the PM2.5 concentration monitoring value and the PM2.5 concentration estimation value in the training set, where the expression of the loss function is: in, Indicates the PM2.5 concentration monitoring value, represents the number of spatiotemporal monitoring points in the training set; Step 8.2, use the back propagation algorithm to calculate the loss each time All learnable parameters in the model are passed to it, and the Adam optimization strategy is used to iteratively update each learnable parameter based on the gradient of the returned loss until the model reaches the minimum interpolation error in the validation set, and the target model is obtained; In step 8.3, the target model is used to interpolate the data to be processed.

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